%% MSC2000 msce.ye

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|00-XX  General 
8=|00-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|00-02  Research exposition (monographs, survey articles)

2=|00Axx  General and miscellaneous specific topics
3=|00A05  General mathematics
3=|00A06  Mathematics for nonmathematicians (engineering, 
..........social sciences, etc.)
3=|00A07  Problem books
3>|00A08  Recreational mathematics  [See also 97A20] /:> [See also 97A20]
3=|00A15  Bibliographies
3+|00A17  External book reviews 
3=|00A20  Dictionaries and other general reference works
3=|00A22  Formularies
3=|00A30  Philosophy of mathematics [See also 03A05]
3>|00A35  Methodology of mathematics, didactics [See also 97Cxx, 97Dxx] /:> [See also 97Cxx, 97Dxx]
3=|00A69  General applied mathematics {For physics, see 00A79
..........and Sections 70 through 86}
3=|00A71  Theory of mathematical modeling
3=|00A72  General methods of simulation
3=|00A73  Dimensional analysis
3=|00A79  Physics (use more specific entries from Sections 70
..........through 86 when possible)
3=|00A99  Miscellaneous topics

2=|00Bxx  Conference proceedings and collections of papers
3=|00B05  Collections of abstracts of lectures
3=|00B10  Collections of articles of general interest
3=|00B15  Collections of articles of miscellaneous specific content
3=|00B20  Proceedings of conferences of general interest
3=|00B25  Proceedings of conferences of miscellaneous specific interest
3=|00B30  Festschriften
3=|00B50  Volumes of selected translations
3=|00B55  Miscellaneous volumes of translations
3=|00B60  Collections of reprinted articles [See also 01A75]

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|01-XX  History and biography 
..........[See also the classification number -03 in the other sections] 
8=|01-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|01-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|01-02  Research exposition (monographs, survey articles)
8=|01-06  Proceedings, conferences, collections, etc.
8=|01-08  Computational methods

2=|01Axx  History of mathematics and mathematicians
3=|01A05  General histories, source books
3=|01A07  Ethnomathematics, general
3=|01A10  Paleolithic, Neolithic
3=|01A12  Indigenous cultures of the Americas
3=|01A13  Other indigenous cultures (non-European)
3=|01A15  Indigenous European cultures (pre-Greek, etc.)
3=|01A16  Egyptian
3=|01A17  Babylonian
3=|01A20  Greek, Roman
3=|01A25  China
3=|01A27  Japan
3=|01A29  Southeast Asia
3=|01A30  Islam (Medieval)
3=|01A32  India
3=|01A35  Medieval
3=|01A40  15th and 16th centuries, Renaissance
3=|01A45  17th century
3=|01A50  18th century
3=|01A55  19th century
3=|01A60  20th century
3+|01A61  Twenty-first century 
3=|01A65  Contemporary
3=|01A67  Future prospectives 
3=|01A70  Biographies, obituaries, personalia, bibliographies
3=|01A72  Schools of mathematics
3=|01A73  Universities
3=|01A74  Other institutions and academies
3=|01A75  Collected or selected works; reprintings or
..........translations of classics [See also 00B60]
3=|01A80  Sociology (and profession) of mathematics
3+|01A85  Historiography 
3+|01A90  Bibliographic studies 
3=|01A99  Miscellaneous topics

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|03-XX  Mathematical logic and foundations 
8=|03-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|03-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|03-02  Research exposition (monographs, survey articles)
8=|03-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|03-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|03-06  Proceedings, conferences, collections, etc.

4=|03A05  Philosophical and critical {For philosophy of
..........mathematics, see also 00A30}

2=|03Bxx  General logic
3=|03B05  Classical propositional logic
3=|03B10  Classical first-order logic
3=|03B15  Higher-order logic and type theory 
3=|03B20  Subsystems of classical logic (including
..........intuitionistic logic)
3=|03B22  Abstract deductive systems
3=|03B25  Decidability of theories and sets of sentences [See
..........also 11U05, 12L05, 20F10]
3~|03B30  Foundations of classical theories (including reverse mathematics) 
..........[See also 03F35] 
........../~ Foundation and axiomatics of classical theories 
3=|03B35  Mechanization of proofs and logical operations [See
..........also 68T15]
3>|03B40  Combinatory logic and lambda-calculus [See also 68N18] 
........../:> [See also 68N18]
3+|03B42  Logic of knowledge and belief 
3+|03B44  Temporal logic 
3~|03B45  Modal logic {For knowledge and belief see 03B42; for temporal 
..........logic see 03B44; for provability logic see also 03F45} 
........../~ modal and tense logic {for provability logic see also 03F40}
3-|03B46  relevance and entailment 
3+|03B47  Substructural logics (including relevance, entailment, linear 
..........logic, Lambek calculus, BCK and BCI logics) 
..........{For proof-theoretic aspects see 03F52} 
3=|03B48  Probability and inductive logic [See also 60A05]
3=|03B50  Many-valued logic
3>|03B52  Fuzzy logic; logic of vagueness [See also 68T27, 68T37, 94D05] 
........../:> ; logic of vagueness /:> 68T27, 68T37, 
3~|03B53  Logics admitting inconsistency (paraconsistent logics, 
..........discussive logics, etc.) /~ paraconsistent logic 
3=|03B55  Intermediate logics
3=|03B60  Other nonclassical logic
3~|03B65  Logic of natural languages 
..........[See also 68T50, 91F20] // 68T50, 91F20 ~ 68S05, 92K20
3~|03B70  Logic in computer science [See also 68-XX] 
........../~ logic of programming [See also 68Q55, 68Q60]
3=|03B80  Other applications of logic
3=|03B99  None of the above, but in this section

2=|03Cxx  Model theory
3>|03C05  Equational classes, universal algebra [See also 08Axx, 18C05] 
........../:> , 18C05
3=|03C07  Basic properties of first-order languages and
..........structures
3>|03C10  Quantifier elimination, model completeness and related topics 
........../:> , model completeness 
3>|03C13  Finite structures [See also 68Q15, 68Q19] 
........../:> [See also 68Q15, 68Q19]
3=|03C15  Denumerable structures
3=|03C20  Ultraproducts and related constructions
3=|03C25  Model-theoretic forcing
3=|03C30  Other model constructions
3=|03C35  Categoricity and completeness of theories
3=|03C40  Interpolation, preservation, definability
3>|03C45  Classification theory, stability and related concepts 
........../:> Classification theory
3=|03C50  Models with special properties (saturated, rigid, etc.)
3=|03C52  Properties of classes of models
3=|03C55  Set-theoretic model theory
3>|03C57  Effective and recursion-theoretic model theory [See also 03D45] 
........../:> Effective and
3=|03C60  Model-theoretic algebra [See also 08C10, 12Lxx, 13L05]
3=|03C62  Models of arithmetic and set theory [See also 03Hxx]
3+|03C64  Model theory of ordered structures; o-minimality 
3=|03C65  Models of other mathematical theories
3=|03C68  Other classical first-order model theory
3=|03C70  Logic on admissible sets
3=|03C75  Other infinitary logic
3>|03C80  Logic with extra quantifiers and operators 
..........[See also 03B42, 03B44, 03B45, 03B48] /:> 03B42, 03B44, 03B48, 
3=|03C85  Second- and higher-order model theory
3=|03C90  Nonclassical models (Boolean-valued, sheaf, etc.)
3=|03C95  Abstract model theory
3+|03C98  Applications of model theory [See also 03C60] 
3=|03C99  None of the above, but in this section

2>|03Dxx  Computability and recursion theory /:> Computability and 
3=|03D03  Thue and Post systems, etc.
3~|03D05  Automata and formal grammars in connection with logical questions 
..........[See also 68Q45, 68Q70, 68R15] // 68Q45, 68Q70, 68R15 ~ 68Qxx
3=|03D10  Turing machines and related notions [See also 68Q05]
3>|03D15  Complexity of computation [See also 68Q15, 68Q17] 
........../:> 68Q17
3=|03D20  Recursive functions and relations, subrecursive hierarchies
3>|03D25  Recursively (computably) enumerable sets and degrees 
........../:> (computably) 
3+|03D28  Other Turing degree structures 
3=|03D30  Other degrees and reducibilities
3=|03D35  Undecidability and degrees of sets of sentences
3=|03D40  Word problems, etc. [See also 06B25, 08A50, 20F10]
3>|03D45  Theory of numerations, effectively presented structures 
..........[See also 03C57; for intuitionistic and similar approaches see 03F55]
........../:> ; for intuitionistic and similar approaches see 03F55]
3=|03D50  Recursive equivalence types of sets and structures, isols
3=|03D55  Hierarchies
3>|03D60  Computability and recursion theory on ordinals, 
..........admissible sets, etc. /:> Computability and 
3=|03D65  Higher-type and set recursion theory
3=|03D70  Inductive definability
3>|03D75  Abstract and axiomatic computability and recursion theory 
........../:> computability and 
3=|03D80  Applications of computability and recursion theory
3=|03D99  None of the above, but in this section

2=|03Exx  Set theory /:< [See also 04-XX]
3+|03E02  Partition relations 
3+|03E04  Ordered sets and their cofinalities; pcf theory 
3~|03E05  Other combinatorial set theory /:< [See also 04A20] /:> Other
3<|03E10  Ordinal and cardinal numbers /:< [See also 04A10]
3<|03E15  Descriptive set theory [See also 28A05, 54H05] /:< 04A10
3+|03E17  Cardinal characteristics of the continuum 
3>|03E20  Other classical set theory (including functions, relations, and 
..........set algebra) /:> (including functions, relations, and set algebra) 
3<|03E25  Axiom of choice and related propositions /:< [See also 04A25]
3=|03E30  Axiomatics of classical set theory and its fragments
3=|03E35  Consistency and independence results
3=|03E40  Other aspects of forcing and Boolean-valued models
3~|03E45  Inner models, including constructibility, ordinal definability, 
..........and core models 
........../:> Inner models, including // core models ~ related notions 
3=|03E47  Other notions of set-theoretic definability
3<|03E50  Continuum hypothesis and Martin's axiom /:< [See also 04A30, 54A25]
3=|03E55  Large cardinals
3~|03E60  Determinacy principles /~ determinacy and related principles 
..........which contradict the axiom of choice
3=|03E65  Other hypotheses and axioms
3=|03E70  Nonclassical and second-order set theories
3~|03E72  Fuzzy set theory /~ fuzzy sets [see mainly 04A72] 
3>|03E75  Applications of set theory /:> of set theory
3=|03E99  None of the above, but in this section

2=|03Fxx  Proof theory and constructive mathematics
3=|03F03  Proof theory, general
3=|03F05  Cut-elimination and normal-form theorems
3=|03F07  Structure of proofs
3=|03F10  Functionals in proof theory
3=|03F15  Recursive ordinals and ordinal notations
3=|03F20  Complexity of proofs
3=|03F25  Relative consistency and interpretations
3=|03F30  First-order arithmetic and fragments
3~|03F35  Second- and higher-order arithmetic and fragments 
..........[See also 03B30] // 03B30 ~ 03E30, 03E70
3=|03F40  G\"odel numberings in proof theory
3+|03F45  Provability logics and related algebras (e.g., 
..........diagonalizable algebras) [See also 03B45, 03G25, 06E25] 
3=|03F50  Metamathematics of constructive systems
3+|03F52  Linear logic and other substructural logics [See also 03B47] 
3=|03F55  Intuitionistic mathematics
3>|03F60  Constructive and recursive analysis 
..........[See also 03B30, 03D45, 26E40, 46S30, 47S30] /:> 03B30, 03D45, 
3~|03F65  Other constructive mathematics 
..........[See also 03D45] // 03D45 ~ 26E40, 46S30, 47S30
3=|03F99  None of the above, but in this section

2=|03Gxx  Algebraic logic
3=|03G05  Boolean algebras [See also 06Exx]
3=|03G10  Lattices and related structures [See also 06Bxx]
3>|03G12  Quantum logic [See also 06C15, 81P10] /:> 06C15, 
3=|03G15  Cylindric and polyadic algebras; relation algebras
3=|03G20  Lukasiewicz and Post algebras [See also 06D25, 06D30]
3>|03G25  Other algebras related to logic 
..........[See also 03F45,  06D20, 06E25, 06F35] /:> 03F45, 06D20, 06E25,
3>|03G30  Categorical logic, topoi 
..........[See also 18B25, 18C05, 18C10] /:> 18C05, 18C10,
3=|03G99  None of the above, but in this section

2=|03Hxx  Nonstandard models [See also 03C62] 
3=|03H05  Nonstandard models in mathematics [See also 26E35,
..........28E05, 30G06, 46S20, 47S20, 54J05]
3=|03H10  Other applications of nonstandard models (economics,
..........physics, etc.)
3=|03H15  Nonstandard models of arithmetic [See also 11U10,
..........12L15, 13L05]
3=|03H99  None of the above, but in this section

%%-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1-|04-XX  Set theory [See also 03Exx] 
..........%% This section has been deleted {For set theory see 03Exx} 
8-|04-00  general reference works (handbooks, dictionaries, 
..........bibliographies, etc.) 
8-|04-01  instructional exposition (textbooks, tutorial papers, etc.) 
8-|04-02  research exposition (monographs, survey articles) 
8-|04-03  historical (must also be assigned at least one classification number 
..........from Section 01) 
8-|04-04  explicit machine computation and programs (not the theory of 
..........computation or programming) 
8-|04-06  proceedings, conferences, collections, etc. 

5-|04A03  set algebra 
5-|04A05  relations, functions [See also 08A02] 
5-|04A10  ordinal and cardinal numbers; generalizations [See also 03E10] 
5-|04A15  descriptive set theory; Borel classifications, Suslin schemes, 
..........etc. [See also 03E15, 26A21, 28A05, 54H05] 
5-|04A20  combinatorial set theory [See also 03E05, 05A05]; filters 
5-|04A25  axiom of choice and equivalent propositions (Zorn's lemma, etc.) 
..........[See also 03E25] 
5-|04A30  continuum hypothesis, generalized continuum hypothesis 
..........[See also 03E50, 54A25] 
5-|04A72  fuzzy sets, fuzzy relations [See also 03E72, 94D05], 
..........{For fuzzy versions, See specific sections} 
5-|04A99  miscellaneous topics 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|05-XX  Combinatorics {For finite fields, see 11Txx} 
8=|05-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|05-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|05-02  Research exposition (monographs, survey articles)
8=|05-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|05-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|05-06  Proceedings, conferences, collections, etc.

2=|05Axx  Classical combinatorial problems
3=|05A05  Combinatorial choice problems (subsets,
..........representatives, permutations)
3=|05A10  Factorials, binomial coefficients, combinatorial
..........functions [See also 11B65, 33Cxx]
3=|05A15  Exact enumeration problems, generating functions [See
..........also 33Cxx, 33Dxx]
3=|05A16  Asymptotic enumeration
3=|05A17  Partitions of integers [See also 11P81, 11P82, 11P83]
3=|05A18  Partitions of sets
3=|05A19  Combinatorial identities
3=|05A20  Combinatorial inequalities
3=|05A30  $q$-calculus and related topics [See also 03Dxx]
3=|05A40  Umbral calculus
3=|05A99  None of the above, but in this section

2=|05Bxx  Designs and configurations {For applications of design
..........theory, see 94C30}
3=|05B05  Block designs [See also 51E05, 62K10]
3=|05B07  Triple systems
3=|05B10  Difference sets (number-theoretic, group-theoretic,
..........etc.) [See also 11B13]
3=|05B15  Orthogonal arrays, Latin squares, Room squares
3=|05B20  Matrices (incidence, Hadamard, etc.)
3=|05B25  Finite geometries [See also 51D20, 51Exx]
3=|05B30  Other designs, configurations [See also 51E30]
3=|05B35  Matroids, geometric lattices [See also 52B40, 90C27]
3=|05B40  Packing and covering [See also 11H31, 52C15, 52C17]
3=|05B45  Tessellation and tiling problems [See also 52C20,
..........52C22]
3=|05B50  Polyominoes
3=|05B99  None of the above, but in this section

2<|05Cxx  Graph theory {For applications of graphs, see 
..........68R10, 90C35, 94C15} /:< 68Q90,
3=|05C05  Trees
3+|05C07  Degree sequences 
3=|05C10  Topological graph theory, imbedding [See also 57M15,
..........57M25]
3=|05C12  Distance in graphs
3=|05C15  Chromatic theory of graphs and maps
3+|05C17  Perfect graphs 
3=|05C20  Directed graphs (digraphs), tournaments
3+|05C22  Signed, gain and biased graphs
3=|05C25  Graphs and groups [See also 20F32]
3=|05C30  Enumeration of graphs and maps
3=|05C35  Extremal problems [See also 90C35]
3=|05C38  Paths and cycles [See also 90B10]
3=|05C40  Connectivity
3=|05C45  Eulerian and Hamiltonian graphs
3=|05C50  Graphs and matrices
3=|05C55  Generalized Ramsey theory
3~|05C60  Isomorphism problems (reconstruction conjecture, etc.)
........../~ Isomorphism problems (reconstruction conjecture, perfect graphs, etc.) 
3+|05C62  Graph representations (geometric and intersection representations, 
..........etc.) 
3=|05C65  Hypergraphs
3+|05C69  Dominating sets, independent sets, cliques 
3=|05C70  Factorization, matching, covering and packing
3=|05C75  Structural characterization of types of graphs
3=|05C78  Graph labelling (graceful graphs, bandwidth, etc.)
3=|05C80  Random graphs
3+|05C83  Graph minors 
3~|05C85  Graph algorithms [See also 68W05, 68R10] // 68W05 ~ 68Q20
3=|05C90  Applications
3=|05C99  None of the above, but in this section

2=|05Dxx  Extremal combinatorics
3=|05D05  Extremal set theory
3=|05D10  Ramsey theory
3=|05D15  Transversal (matching) theory
3+|05D40  Probabilistic methods 
3=|05D99  None of the above, but in this section

2=|05Exx  Algebraic combinatorics
3=|05E05  Symmetric functions
3=|05E10  Tableaux, representations of the symmetric group [See
..........also 20C30]
3=|05E15  Combinatorial problems concerning the classical groups
..........[See also 22E45, 33C80]
3=|05E20  Group actions on designs, geometries and codes
3~|05E25  Group actions on posets and homology groups of posets
..........[See also 06A11] // 06A11 ~ 06A09
3=|05E30  Association schemes, strongly regular graphs
3=|05E35  Orthogonal polynomials [See also 33C45, 33C50, 33D45]
3=|05E99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|06-XX  Order, lattices, ordered algebraic structures 
..........[See also 18B35] 
8=|06-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|06-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|06-02  Research exposition (monographs, survey articles)
8=|06-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|06-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|06-06  Proceedings, conferences, collections, etc.

2=|06Axx  Ordered sets 
3=|06A05  Total order
3=|06A06  Partial order, general
3=|06A07  Combinatorics of partially ordered sets
3-|06A08  shellable posets, Cohen-Macaulay posets [See also 52B20] 
3-|06A09  cohomology of posets [See also 52B20] 
3+|06A11  Algebraic aspects of posets [See also 05E25] 
3>|06A12  Semilattices [See also 20M10; for topological semilattices see 22A26]
........../:> for topological semilattices see 22A26] 
3=|06A15  Galois correspondences, closure operators
3-|06A23  complete lattices, completions 
3=|06A99  None of the above, but in this section

2=|06Bxx  Lattices [See also 03G10]
3=|06B05  Structure theory
3=|06B10  Ideals, congruence relations
3=|06B15  Representation theory
3=|06B20  Varieties of lattices
3+|06B23  Complete lattices, completions 
3=|06B25  Free lattices, projective lattices, word problems [See
..........also 03D40, 08A50, 20F10]
3=|06B30  Topological lattices, order topologies [See also
..........06F30, 22A26, 54F05, 54H12]
3~|06B35  Continuous lattices and posets, applications [See also
..........06B30, 06D10, 06F30, 18B35, 22A26, 68Q10] // 68Q10 ~ 68Q55
3=|06B99  None of the above, but in this section

2=|06Cxx  Modular lattices, complemented lattices
3=|06C05  Modular lattices, Desarguesian lattices
3=|06C10  Semimodular lattices, geometric lattices
3>|06C15  Complemented lattices, orthocomplemented lattices and posets 
..........[See also 03G12, 81P10] /:> and posets [See also 03G12, 81P10] 
3=|06C20  Complemented modular lattices, continuous geometries
3=|06C99  None of the above, but in this section

2=|06Dxx  Distributive lattices
3=|06D05  Structure and representation theory
3=|06D10  Complete distributivity
3=|06D15  Pseudocomplemented lattices
3~|06D20  Heyting algebras [See also 03G25] // 03G25 ~ 03Gxx
3+|06D22  Frames, locales {For topological questions see 54-XX} 
3=|06D25  Post algebras [See also 03G20]
3=|06D30  De Morgan algebras, Lukasiewicz algebras [See also 03G20]
3+|06D35  MV-algebras 
3+|06D50  Lattices and duality 
3+|06D72  Fuzzy lattices (soft algebras) and related topics 
3=|06D99  None of the above, but in this section

2=|06Exx  Boolean algebras (Boolean rings) [See also 03G05]
3=|06E05  Structure theory
3=|06E10  Chain conditions, complete algebras
3=|06E15  Stone space and related constructions
3=|06E20  Ring-theoretic properties [See also 16E50, 16G30]
3>|06E25  Boolean algebras with additional operations (diagonalizable 
..........algebras, etc.) [See also 03G25, 03F45] /:> [See also 03G25, 03F45]
3=|06E30  Boolean functions [See also 94C10]
3=|06E99  None of the above, but in this section

2=|06Fxx  Ordered structures
3>|06F05  Ordered semigroups and monoids [See also 20Mxx] /:> and monoids 
3+|06F07  Quantales 
3=|06F10  Noether lattices
3=|06F15  Ordered groups [See also 20F60]
3=|06F20  Ordered abelian groups, Riesz groups, ordered linear
..........spaces [See also 46A40]
3=|06F25  Ordered rings, algebras, modules {For ordered fields,
..........see 12J15; see also 13J25, 16W80}
3=|06F30  Topological lattices, order topologies [See also
..........06B30, 22A26, 54F05, 54H12]
3=|06F35  BCK-algebras, BCI-algebras [See also 03G25]
3=|06F99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|08-XX  General algebraic systems 
8=|08-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|08-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|08-02  Research exposition (monographs, survey articles)
8=|08-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|08-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|08-06  Proceedings, conferences, collections, etc.

2=|08Axx  Algebraic structures [See also 03C05]
3=|08A02  Relational systems, laws of composition
3=|08A05  Structure theory
3=|08A30  Subalgebras, congruence relations
3=|08A35  Automorphisms, endomorphisms
3=|08A40  Operations, polynomials, primal algebras
3=|08A45  Equational compactness
3=|08A50  Word problems [See also 03D40, 06B25, 20F10, 68R15]
3=|08A55  Partial algebras
3=|08A60  Unary algebras
3=|08A62  Finitary algebras
3=|08A65  Infinitary algebras
3+|08A68  Heterogeneous algebras 
3=|08A70  Applications of universal algebra in computer science
3+|08A72  Fuzzy algebraic structures 
3=|08A99  None of the above, but in this section

2=|08Bxx  Varieties
3=|08B05  Equational logic, Malcev (Maltsev) conditions
3=|08B10  Congruence modularity, congruence distributivity
3=|08B15  Lattices of varieties
3=|08B20  Free algebras
3=|08B25  Products, amalgamated products, and other kinds of
..........limits and colimits [See also 18A30]
3=|08B26  Subdirect products and subdirect irreducibility
3=|08B30  Injectives, projectives
3=|08B99  None of the above, but in this section

2=|08Cxx  Other classes of algebras
3=|08C05  Categories of algebras [See also 18C05]
3=|08C10  Axiomatic model classes [See also 03Cxx, in particular 03C60]
3=|08C15  Quasivarieties
3=|08C99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|11-XX  Number theory 
8=|11-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|11-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|11-02  Research exposition (monographs, survey articles)
8=|11-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|11-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|11-06  Proceedings, conferences, collections, etc.

2=|11Axx  Elementary number theory {For analogues in number
..........fields, see 11R04}
3=|11A05  Multiplicative structure; Euclidean algorithm;
..........greatest common divisors
3=|11A07  Congruences; primitive roots; residue systems
3=|11A15  Power residues, reciprocity
3=|11A25  Arithmetic functions; related numbers; inversion
..........formulas
3=|11A41  Primes
3=|11A51  Factorization; primality
3=|11A55  Continued fractions {For approximation results, see
..........11J70} [See also 11K50, 30B70, 40A15}
3=|11A63  Radix representation; digital problems {For metric
..........results, see 11K16}
3=|11A67  Other representations
3=|11A99  None of the above, but in this section

2=|11Bxx  Sequences and sets
3=|11B05  Density, gaps, topology
3=|11B13  Additive bases [See also 05B10]
3=|11B25  Arithmetic progressions [See also 11N13]
3=|11B34  Representation functions
3=|11B37  Recurrences {For applications to special functions,
..........see 33-XX}
3=|11B39  Fibonacci and Lucas numbers and polynomials and
..........generalizations
3=|11B50  Sequences (mod m)
3=|11B57  Farey sequences; the sequences ${1^k, 2^k, ... }$
3=|11B65  Binomial coefficients; factorials; $q$-identities [See
..........also 05A10, 05A30]
3=|11B68  Bernoulli and Euler numbers and polynomials
3=|11B73  Bell and Stirling numbers
3=|11B75  Other combinatorial number theory
3=|11B83  Special sequences and polynomials
3=|11B85  Automata sequences
3=|11B99  None of the above, but in this section

2=|11Cxx  Polynomials and matrices
3=|11C08  Polynomials [See also 13F20]
3=|11C20  Matrices, determinants [See also 15A36]
3=|11C99  None of the above, but in this section

2=|11Dxx  Diophantine equations [See also 11Gxx, 14Gxx]
3=|11D04  Linear equations
3=|11D09  Quadratic and bilinear equations
3=|11D25  Cubic and quartic equations
3=|11D41  Higher degree equations; Fermat's equation
3+|11D45  Counting solutions of Diophantine equations 
3=|11D57  Multiplicative and norm form equations
3+|11D59  Thue-Mahler equations 
3=|11D61  Exponential equations
3=|11D68  Rational numbers as sums of fractions
3=|11D72  Equations in many variables [See also 11P55]
3=|11D75  Diophantine inequalities [See also 11J25]
3=|11D79  Congruences in many variables
3=|11D85  Representation problems [See also 11P55]
3=|11D88  $p$-adic and power series fields
3=|11D99  None of the above, but in this section

2=|11Exx  Forms and linear algebraic groups [See also 19Gxx]
..........{For quadratic forms in linear algebra, see 15A63}
3=|11E04  Quadratic forms over general fields
3=|11E08  Quadratic forms over local rings and fields
3=|11E10  Forms over real fields
3=|11E12  Quadratic forms over global rings and fields
3=|11E16  General binary quadratic forms
3=|11E20  General ternary and quaternary quadratic forms; forms
..........of more than two variables
3=|11E25  Sums of squares and representations by other
..........particular quadratic forms
3=|11E39  Bilinear and Hermitian forms
3=|11E41  Class numbers of quadratic and Hermitian forms
3=|11E45  Analytic theory (Epstein zeta functions; relations
..........with automorphic forms and functions)
3=|11E57  Classical groups [See also 14Lxx, 20Gxx]
3=|11E70  $K$-theory of quadratic and Hermitian forms
3=|11E72  Galois cohomology of linear algebraic groups [See also
..........20G10]
3=|11E76  Forms of degree higher than two
3=|11E81  Algebraic theory of quadratic forms; Witt groups and
..........rings [See also 19G12, 19G24]
3=|11E88  Quadratic spaces; Clifford algebras [See also 15A63,
..........15A66]
3=|11E95  $p$-adic theory
3=|11E99  None of the above, but in this section

2=|11Fxx  Discontinuous groups and automorphic forms [See also 11R39, 
..........11S37, 14-XX, 22Exx, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx] 
..........{For relations with quadratic forms, see 11E45}
3=|11F03  Modular and automorphic functions
3=|11F06  Structure of modular groups and generalizations;
..........arithmetic groups [See also 20H05, 20H10, 22E40]
3=|11F11  Modular forms, one variable
3=|11F12  Automorphic forms, one variable
3=|11F20  Dedekind eta function, Dedekind sums
3=|11F22  Relationship to Lie algebras and finite simple groups
3+|11F23  Relations with algebraic geometry and topology 
3=|11F25  Hecke-Petersson operators, differential operators (one variable)
3=|11F27  Theta series; Weil representation
3=|11F30  Fourier coefficients of automorphic forms
3=|11F32  Modular correspondences, etc.
3=|11F33  Congruences for modular and $p$-adic modular forms
..........[See also 14G20, 22E50]
3=|11F37  Forms of half-integer weight; nonholomorphic modular forms
3=|11F41  Hilbert and Hilbert-Siegel modular groups and their
..........modular and automorphic forms; Hilbert modular surfaces 
..........[See also 14J20]
3=|11F46  Siegel modular groups and their modular and automorphic forms
3+|11F50  Jacobi forms 
3+|11F52  Modular forms associated to Drinfel'd modules 
3=|11F55  Other groups and their modular and automorphic forms
..........(several variables)
3=|11F60  Hecke-Petersson operators, differential operators
..........(several variables)
3=|11F66  Dirichlet series and functional equations in
..........connection with modular forms
3=|11F67  Special values of automorphic $L$-series, periods of modular forms, 
..........cohomology, modular symbols
3=|11F70  Representation-theoretic methods; automorphic
..........representations over local and global fields
3=|11F72  Spectral theory; Selberg trace formula
3=|11F75  Cohomology of arithmetic groups
3~|11F80  Galois representations // representations ~ properties
3=|11F85  $p$-adic theory, local fields [See also 14G20, 22E50]
3=|11F99  None of the above, but in this section

2=|11Gxx  Arithmetic algebraic geometry (Diophantine geometry)
..........[See also 11Dxx, 14-XX, 14Gxx, 14Kxx]
3=|11G05  Elliptic curves over global fields [See also 14H52]
3=|11G07  Elliptic curves over local fields [See also 14G20, 14H52]
3=|11G09  Drinfeld modules; higher-dimensional motives, etc.
..........[See also 14L05]
3=|11G10  Abelian varieties of dimension $\gtr 1$ [See also 14Kxx]
3=|11G15  Complex multiplication and moduli of abelian varieties
..........[See also 14K22]
3=|11G16  Elliptic and modular units [See also 11R27]
3=|11G18  Arithmetic aspects of modular and Shimura varieties
..........[See also 14G35]
3=|11G20  Curves over finite and local fields [See also 14H25]
3=|11G25  Varieties over finite and local fields [See also
..........14G15, 14G20]
3=|11G30  Curves of arbitrary genus or genus $\ne 1$ over global
..........fields [See also 14H25]
3=|11G35  Varieties over global fields [See also 14G25]
3=|11G40  $L$-functions of varieties over global fields;
..........Birch-Swinnerton-Dyer conjecture [See also 14G10]
3=|11G45  Geometric class field theory [See also 11R37, 14C35, 19F05]
3+|11G50  Heights 
3+|11G55  Polylogarithms and relations with $K$-theory 
3=|11G99  None of the above, but in this section

2=|11Hxx  Geometry of numbers {For applications in coding theory, see 94B75}
3=|11H06  Lattices and convex bodies [See also 11P21, 52C05, 52C07] 
3=|11H16  Nonconvex bodies
3=|11H31  Lattice packing and covering [See also 05B40, 52C15, 52C17]
3=|11H46  Products of linear forms
3=|11H50  Minima of forms
3=|11H55  Quadratic forms (reduction theory, extreme forms, etc.)
3=|11H56  Automorphism groups of lattices
3=|11H60  Mean value and transfer theorems
3+|11H71  Relations with coding theory 
3=|11H99  None of the above, but in this section

2=|11Jxx  Diophantine approximation, transcendental number
..........theory [See also 11K60]
3=|11J04  Homogeneous approximation to one number
3=|11J06  Markov and Lagrange spectra and generalizations
3=|11J13  Simultaneous homogeneous approximation, linear forms
3=|11J17  Approximation by numbers from a fixed field
3=|11J20  Inhomogeneous linear forms
3=|11J25  Diophantine inequalities [See also 11D75]
3=|11J54  Small fractional parts of polynomials and generalizations
3=|11J61  Approximation in non-Archimedean valuations
3=|11J68  Approximation to algebraic numbers
3=|11J70  Continued fractions and generalizations [See also 11A55, 11K50]
3=|11J71  Distribution modulo one [See also 11K06]
3=|11J72  Irrationality; linear independence over a field
3=|11J81  Transcendence (general theory)
3=|11J82  Measures of irrationality and of transcendence
3=|11J83  Metric theory
3=|11J85  Algebraic independence; Gelfond's method
3=|11J86  Linear forms in logarithms; Baker's method
3=|11J89  Transcendence theory of elliptic and abelian functions
3=|11J91  Transcendence theory of other special functions
3+|11J93  Transcendence theory of Drinfel'd and $t$-modules 
3+|11J95  Results involving abelian varieties 
3+|11J97  Analogues of methods in Nevanlinna theory (work of Vojta et al.) 
3=|11J99  None of the above, but in this section

2=|11Kxx  Probabilistic theory: distribution modulo $1$; metric theory 
..........of algorithms
3=|11K06  General theory of distribution modulo $1$ [See also 11J71]
3=|11K16  Normal numbers, radix expansions, etc. [See also 11A63]
3=|11K31  Special sequences
3=|11K36  Well-distributed sequences and other variations
3=|11K38  Irregularities of distribution, discrepancy [See also 11Nxx]
3=|11K41  Continuous, $p$-adic and abstract analogues
3=|11K45  Pseudo-random numbers; Monte Carlo methods
3=|11K50  Metric theory of continued fractions [See also 11A55, 11J70]
3=|11K55  Metric theory of other algorithms and expansions;
..........measure and Hausdorff dimension [See also 11N99, 28Dxx]
3=|11K60  Diophantine approximation [See also 11Jxx]
3=|11K65  Arithmetic functions [See also 11Nxx]
3=|11K70  Harmonic analysis and almost periodicity
3=|11K99  None of the above, but in this section

2=|11Lxx  Exponential sums and character sums {For finite fields, see 11Txx}
3=|11L03  Trigonometric and exponential sums, general
3=|11L05  Gauss and Kloosterman sums; generalizations
3=|11L07  Estimates on exponential sums
3=|11L10  Jacobsthal and Brewer sums; other complete character sums
3=|11L15  Weyl sums
3=|11L20  Sums over primes
3=|11L26  Sums over arbitrary intervals
3=|11L40  Estimates on character sums
3=|11L99  None of the above, but in this section

2=|11Mxx  Zeta and $L$-functions: analytic theory
3=|11M06  $\zeta(s)$ and $L(s,\chi)$
3=|11M20  Real zeros of $L(s,\chi)$; results on $L(1,\chi)$
3=|11M26  Nonreal zeros of $\zeta(s)$ and $L(s,\chi)$; Riemann
..........and other hypotheses
3=|11M35  Hurwitz and Lerch zeta functions
3+|11M36  Selberg zeta functions and regularized determinants 
3+|11M38  Zeta and $L$-functions in characteristic $p$ 
3=|11M41  Other Dirichlet series and zeta functions {For local and global 
..........ground fields, see 11R42, 11R52, 11S40, 11S45. 
..........For algebro-geometric methods, see 14G10} 
..........[See also 11E45, 11F66, 11F70, 11F72}
3=|11M45  Tauberian theorems [See also 40E05] 
3=|11M99  None of the above, but in this section

2=|11Nxx  Multiplicative number theory
3=|11N05  Distribution of primes
3=|11N13  Primes in progressions [See also 11B25]
3=|11N25  Distribution of integers with specified multiplicative constraints
3=|11N30  Turan theory [See also 30Bxx]
3=|11N32  Primes represented by polynomials; other multiplicative 
..........structure of polynomial values
3=|11N35  Sieves
3=|11N36  Applications of sieve methods
3=|11N37  Asymptotic results on arithmetic functions
3=|11N45  Asymptotic results on counting functions for algebraic
..........and topological structures
3=|11N56  Rate of growth of arithmetic functions
3=|11N60  Distribution functions associated with additive and
..........positive multiplicative functions
3=|11N64  Other results on the distribution of values or the
..........characterization of arithmetic functions
3=|11N69  Distribution of integers in special residue classes
3=|11N75  Applications of automorphic functions and forms to
..........multiplicative problems [See also 11Fxx]
3=|11N80  Generalized primes and integers
3=|11N99  None of the above, but in this section

2=|11Pxx  Additive number theory; partitions
3=|11P05  Waring's problem and variants
3=|11P21  Lattice points in specified regions
3=|11P32  Goldbach-type theorems; other additive questions
..........involving primes
3=|11P55  Applications of the Hardy-Littlewood method [See also 11D85]
3+|11P70  Inverse problems of additive number theory 
3=|11P81  Elementary theory of partitions [See also 05A17]
3=|11P82  Analytic theory of partitions
3=|11P83  Partitions; congruences and congruential restrictions
3=|11P99  None of the above, but in this section

2=|11Rxx  Algebraic number theory: global fields {For complex multiplication, 
..........see 11G15}
3=|11R04  Algebraic numbers; rings of algebraic integers
3=|11R06  PV-numbers and generalizations; other special algebraic numbers
3=|11R09  Polynomials (irreducibility, etc.)
3=|11R11  Quadratic extensions
3=|11R16  Cubic and quartic extensions
3=|11R18  Cyclotomic extensions
3=|11R20  Other abelian and metabelian extensions
3=|11R21  Other number fields
3=|11R23  Iwasawa theory
3=|11R27  Units and factorization
3=|11R29  Class numbers, class groups, discriminants
3=|11R32  Galois theory
3=|11R33  Integral representations related to algebraic numbers; Galois module 
..........structure of rings of integers [See also 20C10]
3=|11R34  Galois cohomology [See also 12Gxx, 16H05, 19A31]
3=|11R37  Class field theory
3=|11R39  Langlands-Weil conjectures, nonabelian class field theory 
..........[See also 11Fxx, 22E55]
3=|11R42  Zeta functions and $L$-functions of number fields 
..........[See also 11M41, 19F27]
3=|11R44  Distribution of prime ideals [See also 11N05]
3=|11R45  Density theorems
3=|11R47  Other analytic theory [See also 11Nxx]
3=|11R52  Quaternion and other division algebras: arithmetic, zeta functions
3=|11R54  Other algebras and orders, and their zeta and $L$-functions 
..........[See also 11S45, 16H05, 16Kxx]
3=|11R56  Adele rings and groups
3=|11R58  Arithmetic theory of algebraic function fields [See also 14-XX]
3+|11R60  Cyclotomic function fields (class groups, Bernoulli objects, etc.) 
3=|11R65  Class groups and Picard groups of orders
3=|11R70  $K$-theory of global fields [See also 19Fxx]
3=|11R80  Totally real and totally positive fields [See also 12J15]
3=|11R99  None of the above, but in this section

2=|11Sxx  Algebraic number theory: local and $p$-adic fields
3=|11S05  Polynomials
3=|11S15  Ramification and extension theory
3=|11S20  Galois theory
3=|11S23  Integral representations
3=|11S25  Galois cohomology [See also 12Gxx, 16H05]
3=|11S31  Class field theory; $p$-adic formal groups [See also 14L05]
3=|11S37  Langlands-Weil conjectures, nonabelian class field theory 
..........[See also 11Fxx, 22E50]
3=|11S40  Zeta functions and $L$-functions [See also 11M41, 19F27]
3=|11S45  Algebras and orders, and their zeta functions 
..........[See also 11R52, 11R54, 16H05, 16Kxx]
3=|11S70  $K$-theory of local fields [See also 19Fxx]
3=|11S80  Other analytic theory (analogues of beta and gamma functions, 
..........$p$-adic integration, etc.)
3=|11S85  Other nonanalytic theory
3+|11S90  Prehomogeneous vector spaces 
3=|11S99  None of the above, but in this section

2=|11Txx  Finite fields and commutative rings (number-theoretic aspects)
3=|11T06  Polynomials
3=|11T22  Cyclotomy
3=|11T23  Exponential sums
3=|11T24  Other character sums and Gauss sums
3=|11T30  Structure theory
3=|11T55  Arithmetic theory of polynomial rings over finite fields
3+|11T60  Finite upper-half planes 
3=|11T71  Algebraic coding theory; cryptography
3=|11T99  None of the above, but in this section

2=|11Uxx  Connections with logic
3=|11U05  Decidability [See also 03B25]
3=|11U07  Ultraproducts [See also 03C20]
3=|11U09  Model theory [See also 03Cxx]
3=|11U10  Nonstandard arithmetic [See also 03H15]
3=|11U99  None of the above, but in this section

2=|11Yxx  Computational number theory [See also 11-04]
3=|11Y05  Factorization
3=|11Y11  Primality
3=|11Y16  Algorithms; complexity [See also 68Q25]
3=|11Y35  Analytic computations
3=|11Y40  Algebraic number theory computations
3=|11Y50  Computer solution of Diophantine equations
3=|11Y55  Calculation of integer sequences
3=|11Y60  Evaluation of constants
3=|11Y65  Continued fraction calculations
3=|11Y70  Values of arithmetic functions; tables
3=|11Y99  None of the above, but in this section

4=|11Z05  Miscellaneous applications of number theory 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|12-XX  Field theory and polynomials 
8=|12-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|12-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|12-02  Research exposition (monographs, survey articles)
8=|12-03  Historical (must also be assigned at least one classification 
..........number from Section 01)
8=|12-04  Explicit machine computation and programs (not the theory 
..........of computation or programming)
8=|12-06  Proceedings, conferences, collections, etc.

2=|12Dxx  Real and complex fields
3=|12D05  Polynomials: factorization
3=|12D10  Polynomials: location of zeros (algebraic theorems)
..........{For the analytic theory, see 26C10, 30C15}
3=|12D15  Fields related with sums of squares (formally real fields, 
..........Pythagorean fields, etc.) [See also 11Exx]
3=|12D99  None of the above, but in this section

2=|12Exx  General field theory
3=|12E05  Polynomials (irreducibility, etc.)
3=|12E10  Special polynomials
3=|12E12  Equations
3=|12E15  Skew fields, division rings [See also 11R52, 11R54, 11S45, 16Kxx]
3=|12E20  Finite fields (field-theoretic aspects)
3=|12E25  Hilbertian fields; Hilbert's irreducibility theorem
3+|12E30  Field arithmetic 
3=|12E99  None of the above, but in this section

2=|12Fxx  Field extensions
3=|12F05  Algebraic extensions
3=|12F10  Separable extensions, Galois theory
3=|12F12  Inverse Galois theory
3=|12F15  Inseparable extensions
3=|12F20  Transcendental extensions
3=|12F99  None of the above, but in this section

2=|12Gxx  Homological methods (field theory)
3~|12G05  Galois cohomology [See also 14F22, 16H05, 16K50] // 14F22 ~ 13A20 /:> 16K50
3=|12G10  Cohomological dimension
3=|12G99  None of the above, but in this section

2=|12Hxx  Differential and difference algebra
3=|12H05  Differential algebra [See also 13Nxx]
3=|12H10  Difference algebra [See also 39Axx]
3~|12H20  Abstract differential equations [See also 34Mxx] // 34Mxx ~ 34Gxx
3=|12H25  $p$-adic differential equations [See also 11S80, 14G20, 34Gxx]
3=|12H99  None of the above, but in this section

2=|12Jxx  Topological fields
3=|12J05  Normed fields
3=|12J10  Valued fields
3=|12J12  Formally $p$-adic fields
3=|12J15  Ordered fields
3=|12J17  Topological semifields
3>|12J20  General valuation theory [See also 13A18] /:> [See also 13A18]
3=|12J25  Non-Archimedean valued fields [See also 30G06, 32P05, 46S10, 47S10]
3=|12J27  Krasner-Tate algebras [See mainly 32P05] [See also 46S10, 47S10]
3=|12J99  None of the above, but in this section

2=|12Kxx  Generalizations of fields
3=|12K05  Near-fields [See also 16Y30]
3=|12K10  Semifields [See also 16Y60]
3=|12K99  None of the above, but in this section

2=|12Lxx  Connections with logic
3=|12L05  Decidability [See also 03B25]
3=|12L10  Ultraproducts [See also 03C20]
3=|12L12  Model theory [See also 03C60]
3=|12L15  Nonstandard arithmetic [See also 03H15]
3=|12L99  None of the above, but in this section

4=|12Y05  Computational aspects of field theory and polynomials

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|13-XX  Commutative rings and algebras 
8=|13-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|13-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|13-02  Research exposition (monographs, survey articles)
8=|13-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|13-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|13-06  Proceedings, conferences, collections, etc.

2=|13Axx  General commutative ring theory
3=|13A02  Graded rings [See also 16W50]
3=|13A05  Divisibility
3=|13A10  Radical theory
3=|13A15  Ideals; multiplicative ideal theory
3>|13A18  Valuations and their generalizations [See also 12J20] /:> [See also 12J20]
3-|13A20  Brauer groups [See also 12Gxx, 16H05] 
3>|13A30  Associated graded rings of ideals (Rees ring, form ring), 
..........analytic spread and related topics /:> , analytic spread 
3~|13A35  Characteristic $p$ methods (Frobenius endomorphism) and 
..........reduction to characteristic $p$; tight closure 
..........[See also 13B22] /:> ; tight closure // 13B22 ~ 13Mxx
3~|13A50  Actions of groups on commutative rings; invariant theory 
..........[See also 14L25] /~ Invariant theory [See also 14D25] 
3=|13A99  None of the above, but in this section

2=|13Bxx  Ring extensions and related topics
3=|13B02  Extension theory
3=|13B05  Galois theory (commutative rings)
3<|13B10  Morphisms /:< and derivations 
3-|13B15  ramification theory 
3=|13B21  Integral dependence
3>|13B22  Integral closure of rings and ideals; integrally closed rings, 
..........related rings (Japanese, etc.) /:> of rings and ideals 
3=|13B24  Going up; going down; going between
3>|13B25  Polynomials over commutative rings [See also 11C08, 13F20, 13M10] /:> [See also 11C08, ..........13F20, 13M10]
3=|13B30  Quotients and localization
3=|13B35  Completion [See also 13J10]
3~|13B40  \'Etale and flat extensions; Henselization; Artin approximation 
..........[See also 13J15, 14B12, 14B25] 
........../~ \'Etale extensions and Henselization; Artin approximation 
..........[See also 13J15, 14B12] 
3=|13B99  None of the above, but in this section

2=|13Cxx  Theory of modules and ideals
3=|13C05  Structure, classification theorems
3<|13C10  Projective and free modules and ideals [See also 19A13] 
........../:< , 18G05
3<|13C11  Injective and flat modules and ideals /:< [See also 18G05] 
3=|13C12  Torsion modules and ideals
3=|13C13  Other special types
3=|13C14  Cohen-Macaulay modules [See also 13H10]
3=|13C15  Dimension theory, depth, related rings (catenary, etc.)
3>|13C20  Class groups [See also 11R29] /:> [See also 11R29]
3=|13C40  Linkage, complete intersections and determinantal
..........ideals [See also 14M12]
3=|13C99  None of the above, but in this section

2~|13Dxx  Homological methods {For noncommutative rings, see 16Exx; 
..........for general categories, see 18Gxx} /~ (co)homological methods
3<|13D02  Syzygies and resolutions /:> and resolutions 
3>|13D03  (Co)homology of commutative rings and algebras 
..........(e.g., Hochschild, Andr\'e-Quillen, cyclic, dihedral, etc.) 
........../:> (e.g., Hochschild, Andr\'e-Quillen, cyclic, dihedral, etc.) 
3~|13D05  Homological dimension /~ (co)homological dimension [See also 18G05] 
3+|13D07  Homological functors on modules (Tor, Ext, etc.) 
3~|13D10  Deformations and infinitesimal methods [See also 14B10, 14B12, 14D15, 
.......... 32Gxx] /:< 16S80, /:> 14B10,
3~|13D15  Grothendieck groups, $K$-theory [See also 14C35, 18F30, 19Axx, 19D50] 
..........// 19Axx, 19D50 ~ 19-XX
3+|13D22  Homological conjectures (intersection theorems) 
3=|13D25  Complexes
3=|13D30  Torsion theory [See also 13C12, 18E40]
3>|13D40  Hilbert-Samuel and Hilbert-Kunz functions; Poincar\'e series
........../:> and Hilbert-Kunz 
3=|13D45  Local cohomology [See also 14B15]
3=|13D99  None of the above, but in this section

2=|13Exx  Chain conditions, finiteness conditions
3=|13E05  Noetherian rings and modules
3=|13E10  Artinian rings and modules, finite-dimensional algebras
3>|13E15  Rings and modules of finite generation or presentation; 
..........number of generators /:> ; number of generators
3=|13E99  None of the above, but in this section

2<|13Fxx  Arithmetic rings and other special rings /:< [See also 12-XX]
3~|13F05  Dedekind, Pr\"ufer and Krull rings and their 
..........generalizations /~ Dedekind and Pr\"ufer rings and their 
..........generalizations 
3=|13F07  Euclidean rings and generalizations
3=|13F10  Principal ideal rings
3=|13F15  Factorial rings, unique factorization domains [See also 14M05]
3>|13F20  Polynomial rings and ideals; rings of integer-valued polynomials 
..........[See also 11C08, 13B25] /:> ; rings of integer-valued polynomials /:> , 13B25 
3=|13F25  Formal power series rings [See also 13J05]
3>|13F30  Valuation rings [See also 13A18] /:> [See also 13A18]
3=|13F40  Excellent rings
3=|13F45  Seminormal rings
3=|13F50  Rings with straightening laws, Hodge algebras
3+|13F55  Face and Stanley-Reisner rings; simplicial complexes [See also 55U10]
3=|13F99  None of the above, but in this section

4=|13G05  Integral domains

2=|13Hxx  Local rings and semilocal rings
3=|13H05  Regular local rings
3=|13H10  Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) 
..........[See also 14M05]
3>|13H15  Multiplicity theory and related topics [See also 14C17] 
........../:> [See also 14C17]
3=|13H99  None of the above, but in this section

2=|13Jxx  Topological rings and modules [See also 16W60, 16W80]
3=|13J05  Power series rings [See also 13F25]
3=|13J07  Analytical algebras and rings [See also 32B05]
3=|13J10  Complete rings, completion [See also 13B35]
3=|13J15  Henselian rings [See also 13B40]
3=|13J20  Global topological rings
3=|13J25  Ordered rings [See also 06F25]
3+|13J30  Real algebra [See also 12D12, 14Pxx] 
3=|13J99  None of the above, but in this section

4=|13K05  Witt vectors and related rings

4=|13L05  Applications of logic to commutative algebra [See also 03Cxx, 03Hxx]

2=|13Mxx  Finite commutative rings {For number-theoretic aspects, see 11Txx}
3=|13M05  Structure
3<|13M10  Polynomials /:< (commutative rings)
3=|13M99  None of the above, but in this section

2=|13Nxx  Differential algebra [See also 12H05, 14F10]
3=|13N05  Modules of differentials [See also 16S32]
3>|13N10  Rings of differential operators and their modules 
..........[See also 16S32, 32C38] /:> and their modules 
3+|13N15  Derivations 
3=|13N99  None of the above, but in this section

2~|13Pxx  Computational aspects of commutative algebra [See also 68W30] // 68W30 ~ 68Q40
3=|13P05  Polynomials, factorization [See also 12Y05]
3>|13P10  Polynomial ideals, Gr\"obner bases [See also 13F20] /:> [See also 13F20]
3=|13P99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|14-XX  Algebraic geometry 
8=|14-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|14-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|14-02  Research exposition (monographs, survey articles)
8=|14-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|14-04  Explicit machine computation and programs (not the theory 
..........of computation or programming)
8=|14-06  Proceedings, conferences, collections, etc.

2=|14Axx  Foundations
3=|14A05  Relevant commutative algebra [See also 13-XX]
3>|14A10  Varieties and morphisms /:> and morphisms
3>|14A15  Schemes and morphisms /:> and morphisms
3~|14A20  Generalizations (algebraic spaces, stacks) 
........../~ Generalizations (algebraic spaces, motifs) 
3<|14A22  Noncommutative algebraic geometry /:< algebraic supervarieties 
..........[See also 14M30, 32C11, 58A50]
3=|14A25  Elementary questions
3=|14A99  None of the above, but in this section

2<|14Bxx  Local theory /:< [See also 32Sxx] 
3~|14B05  Singularities [See also 14E15, 14H20, 32Sxx, 58Kxx] // 58Kxx ~ 58C27
3~|14B07  Deformations of singularities [See also 14D15, 32S30] 
..........// 32S30 ~ 32Sxx
3=|14B10  Infinitesimal methods [See also 13D10]
3=|14B12  Local deformation theory, Artin approximation, etc.
..........[See also 13B40, 13D10]
3=|14B15  Local cohomology [See also 13D45, 32C36]
3=|14B20  Formal neighborhoods
3+|14B25  Local structure of morphisms: \'etale, flat, etc. 
..........[See also 13B40] 
3=|14B99  None of the above, but in this section

2=|14Cxx  Cycles and subschemes
3=|14C05  Parametrization (Chow and Hilbert schemes)
3-|14C10  equivalence relations 
3~|14C15  Chow groups and rings /~ Rational equivalence rings
3>|14C17  Intersection theory, characteristic classes, intersection 
..........multiplicities [See also 13H15] 
........../:> , characteristic classes, intersection multiplicities 
3=|14C20  Divisors, linear systems, invertible sheaves
3=|14C21  Pencils, nets, webs [See also 53A60]
3=|14C22  Picard groups
3=|14C25  Algebraic cycles
3=|14C30  Transcendental methods, Hodge theory [See also 14D07, 32G20, 
..........32J25, 32S35], Hodge conjecture
3=|14C34  Torelli problem [See also 32G20] 
3<|14C35  Applications of methods of algebraic $K$-theory [See also 19Exx] 
........../:< 14F05,
3=|14C40  Riemann-Roch theorems [See also 19E20, 19L10] 
3=|14C99  None of the above, but in this section

2=|14Dxx  Families, fibrations
3~|14D05  Structure of families (Picard-Lefschetz, monodromy, etc.) 
..........// monodromy, ~ Picard-Fuchs theory, 
3+|14D06  Fibrations, degenerations 
3>|14D07  Variation of Hodge structures [See also 32G20] /:> [See also 32G20]
3=|14D10  Arithmetic ground fields (finite, local, global)
3<|14D15  Formal methods; deformations [See also 13D10, 14B07, 32Gxx] 
........../:< 16S80,
3=|14D20  Algebraic moduli problems, moduli of vector bundles
..........{For analytic moduli problems, see 32G13}
3+|14D21  Applications of vector bundles and moduli spaces in mathematical 
..........physics (twistor theory, instantons, quantum field theory) 
3=|14D22  Fine and coarse moduli spaces
3-|14D25  geometric invariants [See also 14L30] 
3=|14D99  None of the above, but in this section

2~|14Exx  Birational geometry /~ mappings and correspondences
3~|14E05  Rational and birational maps /~ rational maps, birational 
..........correspondences
3<|14E07  Birational automorphisms, Cremona group and generalizations 
........../:< [See also 32G20]
3+|14E08  Rationality questions 
3-|14E09  automorphisms [See also 14J50, 14L27] 
3~|14E15  Global theory and resolution of singularities [See also 14B05, 
..........32S20, 32S45] 
..........// and resolution of singularities ~ of singularities, resolution 
3~|14E20  Coverings [See also 14H30]
........../~ Coverings, fundamental group (mappings) 
3=|14E22  Ramification problems [See also 11S15] 
3=|14E25  Embeddings
3~|14E30  Minimal model program (Mori theory, extremal rays) /~ minimal models 
3-|14E35  results in dimensions $\geq 3$ 
3-|14E40  local structure of maps: etale, flat, etc. 
..........[See also 13-XX, 14F20] 
3=|14E99  None of the above, but in this section

2=|14Fxx  (Co)homology theory [See also 13Dxx]
3>|14F05  Vector bundles, sheaves, related construction [See also 14H60, 
..........14J60, 18F20, 32Lxx, 46M20] /:> 14H60, 14J60, 
3>|14F10  Differentials and other special sheaves [See also 13Nxx, 32C38] 
........../:> 13Nxx
3=|14F17  Vanishing theorems [See also 32L20]
3=|14F20  \'Etale and other Grothendieck topologies and cohomologies 
3+|14F22  Brauer groups of schemes [See also 12G05, 16K50] 
3=|14F25  Classical real and complex cohomology
3=|14F30  $p$-adic cohomology, crystalline cohomology
3-|14F32  intersection (co)homology [$ 32S60] 
3<|14F35  Homotopy theory; fundamental groups [See also 14H30] 
........../:< 14E20, 
3=|14F40  de Rham cohomology [See also 14C30, 32C35, 32L10]
3+|14F42  Motivic cohomology 
3+|14F43  Other algebro-geometric (co)homologies (e.g., intersection, 
..........equivariant, Lawson, Deligne (co)homologies) 
3=|14F45  Topological properties
3=|14F99  None of the above, but in this section

2=|14Gxx  Arithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx]
3~|14G05  Rational points /~ Rationality questions, rational points 
3=|14G10  Zeta-functions and related questions [See also 11G40]
..........(Birch-Swinnerton-Dyer conjecture)
3=|14G15  Finite ground fields
3~|14G20  Local ground fields /~ p-adic ground fields
3+|14G22  Rigid analytic geometry 
3=|14G25  Global ground fields
3>|14G27  Other nonalgebraically closed ground fields /:> Other 
3+|14G32  Universal profinite groups (relationship to moduli 
..........spaces, projective and moduli towers) 
3=|14G35  Modular and Shimura varieties [See also 11F41, 11F46, 11G18]
3>|14G40  Arithmetic varieties and schemes; Arakelov theory; heights 
........../:> ; heights
3+|14G50  Applications to coding theory and cryptography [See also 94B27, 
..........94B40] 
3=|14G99  None of the above, but in this section

2=|14Hxx  Curves
3=|14H05  Algebraic functions; function fields [See also 11R58]
3=|14H10  Families, moduli (algebraic)
3=|14H15  Families, moduli (analytic) [See also 30F10, 32Gxx]
3>|14H20  Singularities, local rings [See also 13Hxx, 14B05] /:> , 14B05
3=|14H25  Arithmetic ground fields [See also 11Dxx, 11G05, 14Gxx]
3=|14H30  Coverings, fundamental group [See also 14E20, 14F35]
3-|14H35  correspondences [See also 14Exx] 
3+|14H37  Automorphisms 
3>|14H40  Jacobians, Prym varieties [See also 32G20] /:> , Prym varieties 
3=|14H42  Theta functions; Schottky problem [See also 14K25, 32G20]
3=|14H45  Special curves and curves of low genus
3>|14H50  Plane and space curves /:> Plane and 
3+|14H51  Special divisors (gonality, Brill-Noether theory) 
3=|14H52  Elliptic curves [See also 11G05, 11G07, 14Kxx]
3=|14H55  Riemann surfaces; Weierstrass points; gap sequences [See also 30Fxx]
3>|14H60  Vector bundles on curves and their moduli [See also 14D20, 14F05] 
........../:> and their moduli /:> 14D20,
3+|14H70  Relationship to integrable systems 
3+|14H81  Relationship to physics 
3=|14H99  None of the above, but in this section

2=|14Jxx  Surfaces and higher-dimensional varieties {For analytic theory, 
..........see 32Jxx}
3-|14J05  Picard group [See also 14C22, 19A49, 32L05] 
3=|14J10  Families, moduli, classification: algebraic theory
3~|14J15  Moduli, classification: analytic theory; relations with modular forms 
..........[See also 32G13] /:> ; relations with modular forms /:< , 32J15 
3~|14J17  Singularities /:< of surfaces /:> [See also 14B05, 14E15]
3=|14J20  Arithmetic ground fields [See also 11Dxx, 11G25, 11G35, 14Gxx]
3=|14J25  Special surfaces {For Hilbert modular surfaces, see 14G35}
3=|14J26  Rational and ruled surfaces
3=|14J27  Elliptic surfaces
3=|14J28  $K3$ surfaces and Enriques surfaces
3=|14J29  Surfaces of general type
3~|14J30  $3$-folds /~ Special $3$-folds[See also 14E05] 
3+|14J32  Calabi-Yau manifolds, mirror symmetry 
3~|14J35  $4$-folds /~ Special $4$-folds [See also 14E05]
3=|14J40  $n$-folds ($n>4$)
3=|14J45  Fano varieties
3<|14J50  Automorphisms of surfaces and higher-dimensional varieties 
........../:< [See also 14E09]
3>|14J60  Vector bundles on surfaces and higher-dimensional varieties, 
..........and their moduli [See also 14D20, 14F05, 32Lxx] 
........../:> , and their moduli /:> 14D20,
3=|14J70  Hypersurfaces
3+|14J80  Topology of surfaces (Donaldson polynomials, Seiberg-Witten 
..........invariants) 
3+|14J81  Relationship to physics 
3=|14J99  None of the above, but in this section

2=|14Kxx  Abelian varieties and schemes
3=|14K02  Isogeny
3=|14K05  Algebraic theory
3>|14K10  Algebraic moduli, classification [See also 11G15] /:> [See also 11G15]
3+|14K12  Subvarieties 
3=|14K15  Arithmetic ground fields [See also 11Dxx, 11Fxx, 11Gxx, 14Gxx]
3=|14K20  Analytic theory; abelian integrals and differentials
3=|14K22  Complex multiplication [See also 11G15]
3>|14K25  Theta functions [See also 14H42] /:> [See also 14H42]
3=|14K30  Picard schemes, higher Jacobians [See also 14H40, 32G20]
3=|14K99  None of the above, but in this section

2~|14Lxx  Algebraic groups {For linear algebraic groups, see 20Gxx; 
..........for Lie algebras, see 17B45} // Algebraic groups ~ group schemes 
3=|14L05  Formal groups, $p$-divisible groups [See also 55N22] 
3=|14L10  Group varieties
3=|14L15  Group schemes
3=|14L17  Affine algebraic groups, hyperalgebra constructions
..........[See also 17B45, 18D35]
3+|14L25  Geometric invariant theory [See also 13A50] 
3-|14L27  automorphism groups [See also14E09] 
3~|14L30  Group actions on varieties or schemes (quotients) [See also 13A50, 
..........14L25] // 13A50, 14L25 ~ 14D25
3=|14L35  Classical groups (geometric aspects) [See also 20Gxx, 51N30]
3=|14L40  Other algebraic groups (geometric aspects)
3=|14L99  None of the above, but in this section

2=|14Mxx  Special varieties
3=|14M05  Varieties defined by ring conditions (factorial,
..........Cohen-Macaulay, seminormal) [See also 13C14, 13F45, 13H10]
3=|14M06  Linkage [See also 13C40]
3>|14M07  Low codimension problems /:< [See also 14Cxx]
3=|14M10  Complete intersections [See also 13C40]
3=|14M12  Determinantal varieties [See also 13C40]
3=|14M15  Grassmannians, Schubert varieties, flag manifolds 
..........[See also 32M10, 51M35]
3=|14M17  Homogeneous spaces and generalizations 
..........[See also 32M10, 53C30, 57T15]
3>|14M20  Rational and unirational varieties /:> and unirational 
3>|14M25  Toric varieties, Newton polyhedra [See also 52B20] /:> [See also 52B20]
3<|14M30  Supervarieties [See also 32C11, 58A50] /:< 14A22, 
3=|14M99  None of the above, but in this section

2~|14Nxx  Projective and enumerative geometry [See also 51-XX]
........../~ classical methods and problems [See also 51-XX] 
3=|14N05  Projective techniques [See also 51N35]
3=|14N10  Enumerative problems (combinatorial problems)
3+|14N15  Classical problems, Schubert calculus 
3+|14N20  Configurations of linear subspaces 
3+|14N25  Varieties of low degree 
3+|14N30  Adjunction problems 
3+|14N35  Gromov-Witten invariants, quantum cohomology [See also 53D45]
3=|14N99  None of the above, but in this section

2=|14Pxx  Real algebraic and real analytic geometry
3=|14P05  Real algebraic sets [See also 12Dxx]
3=|14P10  Semialgebraic sets and related spaces
3=|14P15  Real analytic and semianalytic sets [See also 32B20, 32C05]
3=|14P20  Nash functions and manifolds [See also 32C07, 58A07]
3=|14P25  Topology of real algebraic varieties
3=|14P99  None of the above, but in this section

2~|14Qxx  Computational aspects in algebraic geometry [See also 12Y05, 
..........13Pxx, 68W30] // 12Y05, 13Pxx, 68W30 ~ 12-04, 68Q40 
3=|14Q05  Curves
3=|14Q10  Surfaces, hypersurfaces
3=|14Q15  Higher-dimensional varieties
3=|14Q20  Effectivity
3=|14Q99  None of the above, but in this section

2+|14Rxx  Affine geometry 
3+|14R05  Classification of affine varieties
3+|14R10  Affine spaces (automorphisms, embeddings, exotic
..........structures, cancellation problem)
3+|14R15  Jacobian problem
3+|14R20  Group actions on affine varieties [See also 13A50, 14L30]
3+|14R25  Affine fibrations [See also 14D06]
3+|14R99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1<|15-XX  Linear and multilinear algebra; matrix theory 
........../:< (finite and infinite)
8=|15-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|15-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|15-02  Research exposition (monographs, survey articles)
8=|15-03  Historical (must also be assigned at least one classification 
..........number from Section 01)
8=|15-04  Explicit machine computation and programs (not the theory 
..........of computation or programming)
8=|15-06  Proceedings, conferences, collections, etc.

5=|15A03  Vector spaces, linear dependence, rank
5=|15A04  Linear transformations, semilinear transformations
5=|15A06  Linear equations
5=|15A09  Matrix inversion, generalized inverses
5=|15A12  Conditioning of matrices [See also 65F35]
5=|15A15  Determinants, permanents, other special matrix
..........functions [See also 19B10, 19B14]
5=|15A18  Eigenvalues, singular values, and eigenvectors
5=|15A21  Canonical forms, reductions, classification
5=|15A22  Matrix pencils [See also 47A56]
5=|15A23  Factorization of matrices
5=|15A24  Matrix equations and identities
5=|15A27  Commutativity
5+|15A29  Inverse problems 
5=|15A30  Algebraic systems of matrices [See also 16S50, 20Gxx, 20Hxx]
5=|15A33  Matrices over special rings (quaternions, finite fields, etc.)
5=|15A36  Matrices of integers [See also 11C20]
5=|15A39  Linear inequalities
5=|15A42  Inequalities involving eigenvalues and eigenvectors
5=|15A45  Miscellaneous inequalities involving matrices
5=|15A48  Positive matrices and their generalizations; cones of matrices
5=|15A51  Stochastic matrices
5=|15A52  Random matrices
5=|15A54  Matrices over function rings in one or more variables
5=|15A57  Other types of matrices (Hermitian, skew-Hermitian, etc.)
5=|15A60  Norms of matrices, numerical range, applications of functional 
..........analysis to matrix theory [See also 65F35, 65J05]
5=|15A63  Quadratic and bilinear forms, inner products [See mainly 11Exx]
5=|15A66  Clifford algebras, spinors
5=|15A69  Multilinear algebra, tensor products
5~|15A72  Vector and tensor algebra, theory of invariants [See also 13A50, 
..........14L25] // 14L25 ~ 14D25 
5=|15A75  Exterior algebra, Grassmann algebras
5=|15A78  Other algebras built from modules
5=|15A90  Applications of matrix theory to physics
5=|15A99  Miscellaneous topics 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|16-XX  Associative rings and algebras 
..........{For the commutative case, see 13-XX} 
8=|16-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|16-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|16-02  Research exposition (monographs, survey articles)
8=|16-03  Historical (must also be assigned at least one classification 
..........number from Section 01)
8=|16-04  Explicit machine computation and programs (not the theory 
..........of computation or programming)
8=|16-06  Proceedings, conferences, collections, etc.

2=|16Bxx  General and miscellaneous
3=|16B50  Category-theoretic methods and results (except as in 16D90, 16E10) 
..........[See also 18-XX]
3=|16B70  Applications of logic [See also 03Cxx]
3=|16B99  None of the above, but in this section

2=|16Dxx  Modules, bimodules and ideals
3=|16D10  General module theory
3-|16D15  1-sided ideals 
3=|16D20  Bimodules
3~|16D25  Ideals /~ 2-sided ideals 
3~|16D30  Infinite-dimensional simple rings (except as in 16Kxx) 
........../~ maximal and prime 2-sided ideals [See also 16N60, 16D60]
..........(except as in 16Kxx) 
3<|16D40  Free, projective, and flat modules and ideals [See also 19A13] 
........../:< 18G05, 
3<|16D50  Injective modules, self-injective rings [See also 16L60] 
........../:< , 18G05
3=|16D60  Simple and semisimple modules, primitive rings and ideals
3=|16D70  Structure and classification (except as in 16Gxx),
..........direct sum decomposition, cancellation
3=|16D80  Other classes of modules and ideals [See also 16G60]
3~|16D90  Module categories [See also 16Gxx, 16S90];
..........module theory in a category-theoretic context; Morita
..........equivalence and duality /~ Module categories [See also 16Exx, 16Gxx, 16S90];
..........module theory in a category-theoretic context; Morita
..........equivalence and duality
3=|16D99  None of the above, but in this section

2~|16Exx  Homological methods {For commutative rings, see 13Dxx; 
..........for general categories, see 18Gxx} 
........../~ Homological methods and results [See also 18Gxx] 
3+|16E05  Syzygies, resolutions, complexes 
3=|16E10  Homological dimension
3~|16E20  Grothendieck groups, $K$-theory, etc. [See also 18F30,
..........19Axx, 19D50] // 19Axx, 19D50 ~ 19-XX
3>|16E30  Homological functors on modules (Tor, Ext, etc.) /:> (Tor, Ext, etc.)
3~|16E40  (Co)homology of rings and algebras (e.g. Hochschild, cyclic, 
..........dihedral, etc.) 
........../~ Hochschild and other homology and cohomology theories for rings
3+|16E45  Differential graded algebras and applications 
3=|16E50  von Neumann regular rings and generalizations
3=|16E60  Semihereditary and hereditary rings, free ideal rings,
..........Sylvester rings, etc.
3+|16E65  Homological conditions on rings (generalizations of regular, 
..........Gorenstein, Cohen-Macaulay rings, etc.) 
3-|16E70  other rings of low global or flat dimension 
3=|16E99  None of the above, but in this section

2=|16Gxx  Representation theory of rings and algebras
3=|16G10  Representations of Artinian rings
3=|16G20  Representations of quivers and partially ordered sets
3=|16G30  Representations of orders, lattices, algebras over
..........commutative rings [See also 16H05]
3=|16G50  Cohen-Macaulay modules
3=|16G60  Representation type (finite, tame, wild, etc.)
3=|16G70  Auslander-Reiten sequences (almost split sequences)
..........and Auslander-Reiten quivers
3=|16G99  None of the above, but in this section

4<|16H05  Orders and arithmetic, separable algebras, Azumaya
..........algebras [See also 11R52, 11R54, 11S45] /:< 13A20, 

2=|16Kxx  Division rings and semisimple Artin rings 
..........[See also 12E15, 15A30]
3~|16K20  Finite-dimensional {For crossed products, see 16S35}
........../~ Finite-dimensional {for Brower group theory, see 12Gxx, 13A20; 
..........For crossed products, see 16S35}
3=|16K40  Infinite-dimensional and general
3+|16K50  Brauer groups [See also 12G05, 14F22] 
3=|16K99  None of the above, but in this section

2=|16Lxx  Local rings and generalizations
3=|16L30  Noncommutative local and semilocal rings, perfect rings
3=|16L60  Quasi-Frobenius rings [See also 16D50]
3=|16L99  None of the above, but in this section

2=|16Nxx  Radicals and radical properties of rings
3=|16N20  Jacobson radical, quasimultiplication
3=|16N40  Nil and nilpotent radicals, sets, ideals, rings
3<|16N60  Prime and semiprime rings [See also 16D60, 16U10] /:< 16D30, 
3=|16N80  General radicals and rings {For radicals in module
..........categories, see 16S90}
3=|16N99  None of the above, but in this section

2=|16Pxx  Chain conditions, growth conditions, and other forms
..........of finiteness
3=|16P10  Finite rings and finite-dimensional algebras {For
..........semisimple, see 16K20; for commutative, see 11Txx,
..........13Mxx}
3=|16P20  Artinian rings and modules
3=|16P40  Noetherian rings and modules
3=|16P50  Localization and Noetherian rings [See also 16U20]
3=|16P60  Chain conditions on annihilators and summands: Goldie
..........type conditions [See also 16U20], Krull dimension
3=|16P70  Chain conditions on other classes of submodules,
..........ideals, subrings, etc.; coherence
3=|16P90  Growth rate, Gelfand-Kirillov dimension
3=|16P99  None of the above, but in this section

2=|16Rxx  Rings with polynomial identity
3=|16R10  $T$-ideals, identities, varieties of rings and
..........algebras
3=|16R20  Semiprime p.i. rings, rings embeddable in matrices
..........over commutative rings
3=|16R30  Trace rings and invariant theory
3=|16R40  Identities other than those of matrices over
..........commutative rings
3=|16R50  Other kinds of identities (generalized polynomial,
..........rational, involution)
3=|16R99  None of the above, but in this section

2=|16Sxx  Rings and algebras arising under various constructions
3=|16S10  Rings determined by universal properties (free
..........algebras, coproducts, adjunction of inverses, etc.)
3=|16S15  Finite generation, finite presentability, normal forms
..........(diamond lemma, term-rewriting)
3=|16S20  Centralizing and normalizing extensions
3=|16S30  Universal enveloping algebras of Lie algebras [See mainly 17B35]
3=|16S32  Rings of differential operators [See also 13N10, 32C38]
3=|16S34  Group rings [See also 20C05, 20C07], Laurent polynomial rings
3=|16S35  Twisted and skew group rings, crossed products
3=|16S36  Ordinary and skew polynomial rings and semigroup rings
..........[See also 20M25]
3+|16S37  Quadratic and Koszul algebras 
3+|16S38  Rings arising from non-commutative algebraic geometry 
3=|16S40  Smash products of general Hopf actions [See also 16W30]
3=|16S50  Endomorphism rings; matrix rings [See also 15-XX]
3=|16S60  Rings of functions, subdirect products, sheaves of rings
3=|16S70  Extensions of rings by ideals
3>|16S80  Deformations of rings [See also 13D10, 14D15] /:> 13D10
3=|16S90  Maximal ring of quotients, torsion theories, radicals
..........on module categories [See also 13D30, 18E40] 
..........{For radicals of rings, see 16Nxx}
3=|16S99  None of the above, but in this section

2<|16Uxx  Conditions on elements /:< (including elements of matrix rings, etc.)
3=|16U10  Integral domains
3=|16U20  \Ore rings, multiplicative sets, \Ore localization
3=|16U30  Divisibility, noncommutative UFDs
3-|16U50  algebraicity and local finiteness [See also 16N40] 
3<|16U60  Units, groups of units /:< , general linear groups
3=|16U70  Center, normalizer (invariant elements)
3=|16U80  Generalizations of commutativity
3=|16U99  None of the above, but in this section

2=|16Wxx  Rings and algebras with additional structure
3=|16W10  Rings with involution: Lie, Jordan and other
..........nonassociative structures [See also 17B60, 17C50, 46Kxx]
3<|16W20  Automorphisms and endomorphisms 
........../:< actions of groups and semigroups and their fixed rings
3+|16W22  Actions of groups and semigroups; invariant theory 
3=|16W25  Derivations, actions of Lie algebras
3~|16W30  Coalgebras, bialgebras, Hopf algebras [See also 57T05,
..........16S30, 16S40]; rings, modules, etc. on which these act // 
..........16S30, 16S40 ~16S30, 16S32, 16S34, 16S35, 16S36, 16S40
3+|16W35  Ring-theoretic aspects of quantum groups [See also 17B37, 
..........20G42, 81R50] 
3=|16W50  Graded rings and modules
3~|16W55  ``Super'' (or ``skew'') structure [See also 17A70, 17C70] 
..........{For exterior algebras, see 15A75; for Clifford algebras, 
..........see 11E88, 15A66} // 17A70, 17C70 ~ 17A70, 17B70, 17C70
3~|16W60  Valuations, completions, formal power series and 
..........related constructions [See also 13Jxx]
........../~ Filtrations and valuations, genalizations of Euclidean algorithm, 
..........completions, formal power series and related constructions 
..........[See also 13Jxx]
3+|16W70  Filtered rings; filtrational and graded techniques 
3=|16W80  Topological and ordered rings and modules [See also 13Jxx]
3=|16W99  None of the above, but in this section

2=|16Yxx  Generalizations {For nonassociative rings, see 17-XX}
3=|16Y30  Near-rings [See also 12K05]
3=|16Y60  Semirings [See also 12K10]
3=|16Y99  None of the above, but in this section

4+|16Z05  Computational aspects of associative rings [See also 68W30] 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|17-XX  Nonassociative rings and algebras 
8=|17-00  General reference works (handbooks, dictionaries, 
..........bibliographies, etc.)
8=|17-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|17-02  Research exposition (monographs, survey articles)
8=|17-03  Historical (must also be assigned at least one classification 
..........number from Section 01)
8=|17-04  Explicit machine computation and programs (not the theory 
..........of computation or programming)
8=|17-06  Proceedings, conferences, collections, etc.
8=|17-08  Computational methods

2=|17Axx  General nonassociative rings
3=|17A01  General theory
3>|17A05  Power-associative rings /:> rings
3-|17A10  commutative power-associative 
3=|17A15  Noncommutative Jordan algebras
3=|17A20  Flexible algebras
3-|17A25  nodal algebras 
3=|17A30  Algebras satisfying other identities
3+|17A32  Leibniz algebras 
3=|17A35  Division algebras
3=|17A36  Automorphisms, derivations, other operators
3=|17A40  Ternary compositions
3>|17A42  Other $n$-ary compositions $(n \ge 3)$ /:> $(n \ge 3)$
3=|17A45  Quadratic algebras (but not quadratic Jordan algebras)
3=|17A50  Free algebras
3=|17A60  Structure theory
3=|17A65  Radical theory
3=|17A70  Superalgebras 
3=|17A75  Composition algebras
3=|17A80  Valued algebras
3=|17A99  None of the above, but in this section

2>|17Bxx  Lie algebras and Lie superalgebras {For Lie groups, see 22Exx} 
........../:> and Lie superalgebras
3>|17B01  Identities, free Lie (super)algebras /:> (super) 
3=|17B05  Structure theory
3=|17B10  Representations, algebraic theory (weights)
3=|17B15  Representations, analytic theory
3>|17B20  Simple, semisimple, reductive (super)algebras (roots) /:> (super)
3=|17B25  Exceptional (super)algebras /:> {super) 
3>|17B30  Solvable, nilpotent (super)algebras /:> (super) 
3=|17B35  Universal enveloping algebras [See also 16S30]
3~|17B37  Quantum groups (quantized enveloping algebras) and related 
..........deformations [See also 16W35, 20G42, 81R50, 82B23] 
........../~ Quantum groups and related deformations 
..........[See also 16W30, 81R50, 82B23] 
3=|17B40  Automorphisms, derivations, other operators
3=|17B45  Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx]
3>|17B50  Modular Lie (super)algebras /:> (super)
3>|17B55  Homological methods in Lie (super)algebras /:> (super)
3>|17B56  Cohomology of Lie (super)algebras /:> {super}
3~|17B60  Lie (super)algebras associated with other structures (associative, 
..........Jordan, etc.) [See also 16W10, 17C40, 17C50] 
..........// (super)algebras ~ rings /:< 15A30
3+|17B62  Lie bialgebras 
3+|17B63  Poisson algebras 
3>|17B65  Infinite-dimensional Lie (super)algebras [See also 22E65] /:> (super)
3=|17B66  Lie algebras of vector fields and related algebras
3=|17B67  Kac-Moody algebras (structure and representation theory)
3=|17B68  Virasoro and related algebras
3+|17B69  Vertex operators, vertex operator algebras and related structures 
3>|17B70  Graded Lie (super)algebras /:> (super) 
3+|17B75  Color Lie (super)algebras 
3+|17B80  Applications to integrable systems 
3=|17B81  Applications to physics
3=|17B99  None of the above, but in this section

2=|17Cxx  Jordan algebras (algebras, triples and pairs)
3=|17C05  Identities and free Jordan structures
3=|17C10  Structure theory
3=|17C17  Radicals
3=|17C20  Simple, semisimple algebras
3=|17C27  Idempotents, Peirce decompositions
3=|17C30  Associated groups, automorphisms
3=|17C36  Associated manifolds
3=|17C37  Associated geometries
3=|17C40  Exceptional Jordan structures
3=|17C50  Jordan structures associated with other structures
..........[See also 16W10]
3=|17C55  Finite-dimensional structures
3=|17C60  Division algebras
3=|17C65  Jordan structures on Banach spaces and algebras 
..........[See also 46H70, 46L70]
3=|17C70  Super structures
3=|17C90  Applications to physics
3=|17C99  None of the above, but in this section

2=|17Dxx  Other nonassociative rings and algebras
3=|17D05  Alternative rings
3=|17D10  Malcev (Maltsev) rings and algebras
3=|17D15  Right alternative rings
3=|17D20  $(\gamma,\delta)$-rings, including $(1,-1)$-rings
3=|17D25  Lie-admissible algebras
3=|17D92  Genetic algebras
3=|17D99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1~|18-XX  Category theory; abstract homological algebra 
..........{See 13Dxx for commutative rings, 16Exx for associative rings, 
..........20Jxx for groups, 57Txx for topological groups and related 
..........structures; see also 55Nxx and 55Uxx for algebraic topology}
........../~ Category theory, homological algebra

8=|18-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|18-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|18-02  Research exposition (monographs, survey articles)
8=|18-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|18-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|18-06  Proceedings, conferences, collections, etc.

2=|18Axx  General theory of categories and functors
3=|18A05  Definitions, generalizations
3~|18A10  Graphs, diagram schemes, precategories [See especially 20L05] 
........../~ graphs, diagram schemes, precategories, neocategories [see also 20Lxx]
3~|18A15  Foundations, relations to logic and deductive systems
..........[See especially 03-XX] // especially ~ also 
3<|18A20  Epimorphisms, monomorphisms, special classes of
..........morphisms, null morphisms /:< factorization (bicategories)
3=|18A22  Special properties of functors (faithful, full, etc.)
3=|18A23  Natural morphisms, dinatural morphisms
3=|18A25  Functor categories, comma categories
3=|18A30  Limits and colimits (products, sums, directed limits, pushouts, 
..........fiber products, equalizers, kernels, ends and coends, etc.)
3~|18A32  Factorization of morphisms, substructures, quotient 
..........structures, congruences, amalgams /~
..........Factorization of morphisms (via images, coimages, dominions, 
..........codominions), substructures, quotient structures,  
..........congruences, amalgams
3~|18A35  Categories admitting limits (complete categories),
..........functors preserving limits, completions 
........../~ Categories admitting limits (complete categories),
..........functors commuting with limits, continuous functors, completions
3=|18A40  Adjoint functors (representable functors, universal
..........constructions, reflective subcategories, reflections, etc.), 
..........constructions of adjoints (Kan extensions, etc.)
3=|18A99  None of the above, but in this section

2=|18Bxx  Special categories
3=|18B05  Category of sets, characterizations [See also 03-XX]
3=|18B10  Category of relations, additive relations
3=|18B15  Embedding theorems, universal categories [See also 18E20]
3=|18B20  Categories of machines, automata, operative categories
..........[See also 03D05, 68Qxx]
3=|18B25  Topoi [See also 03G30]
3=|18B30  Categories of topological spaces and continuous
..........mappings [See also 54-XX]
3=|18B35  Preorders, orders and lattices (viewed as categories)
..........[See also 06-XX]
3=|18B40  Groupoids, semigroupoids, semigroups, groups (viewed
..........as categories) [See also 20Axx, 20L05, 20Mxx]
3=|18B99  None of the above, but in this section

2~|18Cxx  Categories and theories /~ Categories and algebraic theories
3=|18C05  Equational categories [See also 03C05, 08C05]
3=|18C10  Theories (e.g. algebraic theories), structure, and
..........semantics [See also 03G30]
3=|18C15  Triples (=standard construction, monad or triad),
..........algebras for a triple, homology and derived functors
..........for triples [See also 18Gxx]
3=|18C20  Algebras and Kleisli categories associated with monads
3+|18C30  Sketches and generalizations 
3+|18C35  Accessible and locally presentable categories 
3+|18C50  Categorical semantics of formal languages [See also 68Q55, 68Q65] 
3=|18C99  None of the above, but in this section

2=|18Dxx  Categories with structure
3~|18D05  Double categories, $2$-categories, bicategories and generalizations 
..........// and generalizations ~ hypercategories 
3>|18D10  Monoidal categories (=multiplicative categories),
..........symmetric monoidal categories, braided categories [See also 19D23]
........../:> symmetric monoidal categories, braided categories
3=|18D15  Closed categories (closed monoidal and Cartesian
..........closed categories, etc.)
3=|18D20  Enriched categories (over closed or monoidal categories)
3=|18D25  Strong functors, strong adjunctions
3=|18D30  Fibered categories
3=|18D35  Structured objects in a category (group objects, etc.)
3+|18D50  Operads [See also 55P48] 
3=|18D99  None of the above, but in this section

2=|18Exx  Abelian categories
3=|18E05  Preadditive, additive categories
3=|18E10  Exact categories, abelian categories
3=|18E15  Grothendieck categories
3=|18E20  Embedding theorems [See also 18B15] 
3=|18E25  Derived functors and satellites
3=|18E30  Derived categories, triangulated categories
3=|18E35  Localization of categories
3=|18E40  Torsion theories, radicals [See also 13D30, 16S90]
3=|18E99  None of the above, but in this section

2=|18Fxx  Categories and geometry
3=|18F05  Local categories and functors
3=|18F10  Grothendieck topologies [See also 14F20]
3=|18F15  Abstract manifolds and fiber bundles [See also 55Rxx, 57Pxx]
3=|18F20  Presheaves and sheaves [See also 14F05, 32C35, 32L10, 54B40, 55N30]
3=|18F25  Algebraic $K$-theory and $L$-theory [See also 11Exx, 11R70, 
..........11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67]
3=|18F30  Grothendieck groups [See also 13D15, 16E20, 19Axx]
3=|18F99  None of the above, but in this section

2>|18Gxx  Abstract homological algebra [See also 13Dxx, 16Exx, 
..........20Jxx, 55Nxx, 55Uxx, 57Txx] /:> Abstract /:> 20Jxx, 55Nxx, 57Txx,
3=|18G05  Projectives and injectives [See also 13C10, 13C11, 16D40, 16D50]
3>|18G10  Resolutions; derived functors 
..........[See also 13D02, 16E05, 18E25] /:> 13D02, 16E05
3=|18G15  Ext and Tor, generalizations, K\"unneth formula [See also 55U25]
3=|18G20  Homological dimension [See also 13D05, 16E10]
3=|18G25  Relative homological algebra, projective classes
3=|18G30  Simplicial sets, simplicial objects (in a category)
..........[See also 55U10]
3=|18G35  Chain complexes [See also 18E30, 55U15]
3=|18G40  Spectral sequences, hypercohomology [See also 55Txx]
3=|18G50  Nonabelian homological algebra
3=|18G55  Nonabelian homotopical algebra
3~|18G60  Other (co)homology theories 
..........[See also 19D55, 46L80, 58J20, 58J22] 
........../~ Other (co)homology theories (cyclic, dihedral, etc.) 
..........[See also 19D55, 46L80, 58B30, 58G12]
3=|18G99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|19-XX  K-theory [See also 16E20, 18F25] 
8=|19-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|19-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|19-02  Research exposition (monographs, survey articles)
8=|19-03  Historical (must also be assigned at least one classification 
..........number from Section 01)
8=|19-04  Explicit machine computation and programs (not the theory 
..........of computation or programming)
8=|19-06  Proceedings, conferences, collections, etc.

2=|19Axx  Grothendieck groups and $K_0$ [See also 13D15, 18F30]
3=|19A13  Stability for projective modules [See also 13C10]
3=|19A15  Efficient generation
3=|19A22  Frobenius induction, Burnside and representation rings
3=|19A31  $K_0$ of group rings and orders
3=|19A49  $K_0$ of other rings
3=|19A99  None of the above, but in this section

2=|19Bxx  Whitehead groups and $K_1$
3=|19B10  Stable range conditions
3=|19B14  Stability for linear groups
3=|19B28  $K_1$ of group rings and orders [See also 57Q10]
3=|19B37  Congruence subgroup problems [See also 20H05]
3=|19B99  None of the above, but in this section

2=|19Cxx  Steinberg groups and $K_2$
3=|19C09  Central extensions and Schur multipliers
3=|19C20  Symbols, presentations and stability of $K_2$ 
3=|19C30  $K_2$ and the Brauer group
3=|19C40  Excision for $K_2$
3=|19C99  None of the above, but in this section

2=|19Dxx  Higher algebraic $K$-theory
3=|19D06  $Q$- and plus-constructions
3=|19D10  Algebraic $K$-theory of spaces
3=|19D23  Symmetric monoidal categories [See also 18D10]
3=|19D25  Karoubi-Villamayor-Gersten $K$-theory
3=|19D35  Negative $K$-theory, NK and Nil
3=|19D45  Higher symbols, Milnor $K$-theory
3=|19D50  Computations of higher $K$-theory of rings [See also 13D15, 16E20]
3=|19D55  $K$-theory and homology; cyclic homology and cohomology 
..........[See also 18G60]
3=|19D99  None of the above, but in this section

2=|19Exx  $K$-theory in geometry
3=|19E08  $K$-theory of schemes [See also 14C35]
3>|19E15  Algebraic cycles and motivic cohomology [See also 14C25, 14C35] 
........../:> and mothivic cohomology
3=|19E20  Relations with cohomology theories [See also 14Fxx]
3=|19E99  None of the above, but in this section

2=|19Fxx  $K$-theory in number theory [See also 11R70, 11S70]
3=|19F05  Generalized class field theory [See also 11G45]
3=|19F15  Symbols and arithmetic [See also 11R37]
3=|19F27  Etale cohomology, higher regulators, zeta and $L$-functions 
..........[See also 11G40, 11R42, 11S40, 14F20, 14G10]
3=|19F99  None of the above, but in this section

2=|19Gxx  $K$-theory of forms [See also 11Exx]
3=|19G05  Stability for quadratic modules
3=|19G12  Witt groups of rings [See also 11E81]
3=|19G24  $L$-theory of group rings [See also 11E81]
3=|19G38  Hermitian $K$-theory, relations with $K$-theory of rings
3=|19G99  None of the above, but in this section

2=|19Jxx  Obstructions from topology
3=|19J05  Finiteness and other obstructions in $K_0$
3=|19J10  Whitehead (and related) torsion
3=|19J25  Surgery obstructions [See also 57R67]
3=|19J35  Obstructions to group actions
3=|19J99  None of the above, but in this section

2=|19Kxx  $K$-theory and operator algebras [See mainly 46L80, and also 46M20]
3=|19K14  $K_0$ as an ordered group, traces
3=|19K33  EXT and $K$-homology [See also 55N22]
3~|19K35  Kasparov theory ($KK$-theory) [See also 58J22] 
..........// 58J22 ~ 58G12
3~|19K56  Index theory 
..........[See also 58J20, 58J22] // 58J20, 58J22 ~ 58G12
3=|19K99  None of the above, but in this section

2=|19Lxx  Topological $K$-theory [See also 55N15, 55R50, 55S25]
3=|19L10  Riemann-Roch theorems, Chern characters
3=|19L20  $J$-homomorphism, Adams operations [See also 55Q50]
3=|19L41  Connective $K$-theory, cobordism [See also 55N22]
3=|19L47  Equivariant $K$-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91]
3=|19L64  Computations, geometric applications
3=|19L99  None of the above, but in this section

4=|19M05  Miscellaneous applications of $K$-theory 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|20-XX  Group theory and generalizations 
8=|20-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|20-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|20-02  Research exposition (monographs, survey articles)
8=|20-03  Historical (must also be assigned at least one classification 
..........number from Section 01)
8=|20-04  Explicit machine computation and programs (not the theory 
..........of computation or programming)
8=|20-06  Proceedings, conferences, collections, etc.

2=|20Axx  Foundations
3=|20A05  Axiomatics and elementary properties
3=|20A10  Metamathematical considerations {For word problems, see 20F10}
3=|20A15  Applications of logic to group theory
3=|20A99  None of the above, but in this section

2=|20Bxx  Permutation groups
3=|20B05  General theory for finite groups
3=|20B07  General theory for infinite groups
3=|20B10  Characterization theorems
3=|20B15  Primitive groups
3=|20B20  Multiply transitive finite groups
3=|20B22  Multiply transitive infinite groups
3=|20B25  Finite automorphism groups of algebraic, geometric, or combinatorial 
..........structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX]
3=|20B27  Infinite automorphism groups [See also 12F10]
3=|20B30  Symmetric groups
3=|20B35  Subgroups of symmetric groups
3=|20B40  Computational methods
3=|20B99  None of the above, but in this section

2=|20Cxx  Representation theory of groups [See also 19A22 (for
..........representation rings and Burnside rings)]
3=|20C05  Group rings of finite groups and their modules [See also 16S34]
3=|20C07  Group rings of infinite groups and their modules [See also 16S34]
3+|20C08  Hecke algebras and their representations 
3=|20C10  Integral representations of finite groups
3=|20C11  $p$-adic representations of finite groups
3=|20C12  Integral representations of infinite groups
3=|20C15  Ordinary representations and characters
3=|20C20  Modular representations and characters
3=|20C25  Projective representations and multipliers
3=|20C30  Representations of finite symmetric groups
3=|20C32  Representations of infinite symmetric groups
3=|20C33  Representations of finite groups of Lie type
3=|20C34  Representations of sporadic groups
3=|20C35  Applications of group representations to physics
3=|20C40  Computational methods
3=|20C99  None of the above, but in this section

2=|20Dxx  Abstract finite groups
3=|20D05  Classification of simple and nonsolvable groups
3=|20D06  Simple groups: alternating groups and groups of Lie type 
..........[See also 20Gxx, 22Exx]
3=|20D08  Simple groups: sporadic groups
3=|20D10  Solvable groups, theory of formations, Schunck classes, 
..........Fitting classes, $\pi$-length, ranks [See also 20F17] 
3=|20D15  Nilpotent groups, $p$-groups
3=|20D20  Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure
3=|20D25  Special subgroups (Frattini, Fitting, etc.)
3=|20D30  Series and lattices of subgroups
3=|20D35  Subnormal subgroups
3=|20D40  Products of subgroups
3=|20D45  Automorphisms
3-|20D50  covering of subgroups 
3=|20D60  Arithmetic and combinatorial problems
3=|20D99  None of the above, but in this section

2=|20Exx  Structure and classification of infinite or finite groups
3=|20E05  Free nonabelian groups
3=|20E06  Free products, free products with amalgamation,
..........Higman-Neumann-Neumann extensions, and generalizations
3>|20E07  Subgroup theorems; subgroup growth /:> subgroup growth
3>|20E08  Groups acting on trees [See also 20F65] /:> [See also 20F65]
3=|20E10  Quasivarieties and varieties of groups
3=|20E15  Chains and lattices of subgroups, subnormal subgroups
..........[See also 20F22]
3=|20E18  Limits, profinite groups
3=|20E22  Extensions, wreath products, and other compositions [See also 20J05]
3=|20E25  Local properties
3=|20E26  Residual properties and generalizations
3=|20E28  Maximal subgroups
3=|20E32  Simple groups [See also 20D05]
3=|20E34  General structure theorems
3=|20E36  General theorems concerning automorphisms of groups
3=|20E42  Groups with a $BN$-pair; buildings [See also 51E24]
3+|20E45  Conjugacy classes 
3=|20E99  None of the above, but in this section

2=|20Fxx  Special aspects of infinite or finite groups
3=|20F05  Generators, relations, and presentations
3=|20F06  Cancellation theory; application of van Kampen diagrams 
..........[See also 57M05]
3~|20F10  Word problems, other decision problems, connections
..........with logic and automata [See also 03B25, 03D05,
..........03D40, 06B25, 08A50, 68Q70] // 68Q70 ~ 68Qxx 
3=|20F12  Commutator calculus
3=|20F14  Derived series, central series, and generalizations
3>|20F16  Solvable groups, supersolvable groups [See also 20D10] 
........../:> [See also 20D10]
3=|20F17  Formations of groups, Fitting classes [See also 20D10]
3>|20F18  Nilpotent groups [See also 20D10] /:> [See also 20D10]
3=|20F19  Generalizations of solvable and nilpotent groups
3=|20F22  Other classes of groups defined by subgroup chains
3=|20F24  FC-groups and their generalizations
3=|20F28  Automorphism groups of groups [See also 20E36]
3=|20F29  Representations of groups as automorphism groups of algebraic systems
3-|20F32  geometric group theory [See also 05C25, 20Exx, 20Gxx] 
3<|20F34  Fundamental groups and their automorphisms [See also 57M05, 57Sxx,] 
........../:< , 22E40
3=|20F36  Braid groups; Artin groups
3=|20F38  Other groups related to topology or analysis
3=|20F40  Associated Lie structures
3=|20F45  Engel conditions
3=|20F50  Periodic groups; locally finite groups
3>|20F55  Reflection and Coxeter groups [See also 22E40, 51F15] 
........../:> Reflection and /:> , 51F15 
3=|20F60  Ordered groups [See mainly 06F15]
3+|20F65  Geometric group theory [See also 05C25, 20E08, 57Mxx] 
3+|20F67  Hyperbolic groups and nonpositively curved groups 
3+|20F69  Asymptotic properties of groups 
3=|20F99  None of the above, but in this section

2~|20Gxx  Linear algebraic groups (classical groups) {For
..........arithmetic theory, see 11E57, 11H56; for geometric theory, see
..........14Lxx, 22Exx; for other methods in representation theory,
..........see 15A30, 22E45, 22E46, 22E47, 22E50, 22E55}
..........// 11H56 ~ 11H06
3=|20G05  Representation theory
3=|20G10  Cohomology theory
3=|20G15  Linear algebraic groups over arbitrary fields
3=|20G20  Linear algebraic groups over the reals, the complexes, 
..........the quaternions
3=|20G25  Linear algebraic groups over local fields and their integers
3=|20G30  Linear algebraic groups over global fields and their integers
3=|20G35  Linear algebraic groups over ad\`eles and other rings and schemes
3=|20G40  Linear algebraic groups over finite fields
3+|20G42  Quantum groups (quantized function algebras) and their
..........representations [See also 16W35, 17B37, 16W35] 
3<|20G45  Applications to physics /:< ; explicit representations 
3=|20G99  None of the above, but in this section

2=|20Hxx  Other groups of matrices [See also 15A30]
3=|20H05  Unimodular groups, congruence subgroups 
..........[See also 11F06, 19B37, 22E40, 51F20]
3=|20H10  Fuchsian groups and their generalizations 
..........[See also 11F06, 22E40, 30F35, 32Nxx]
3=|20H15  Other geometric groups, including crystallographic
..........groups [See also 51-XX, especially 51F15, and 82D25] 
3=|20H20  Other matrix groups over fields
3=|20H25  Other matrix groups over rings
3=|20H30  Other matrix groups over finite fields
3=|20H99  None of the above, but in this section

2=|20Jxx  Connections with homological algebra and category theory
3=|20J05  Homological methods in group theory
3=|20J06  Cohomology of groups
3-|20J10  groups arising as cohomology groups 
3=|20J15  Category of groups
3=|20J99  None of the above, but in this section

2=|20Kxx  Abelian groups
3=|20K01  Finite abelian groups
3-|20K05  finitely generated groups 
3=|20K10  Torsion groups, primary groups and generalized primary groups
3-|20K12  Ulm sequences 
3=|20K15  Torsion free groups, finite rank
3=|20K20  Torsion free groups, infinite rank
3=|20K21  Mixed groups
3=|20K25  Direct sums, direct products, etc.
3-|20K26  indecomposable groups 
3=|20K27  Subgroups
3=|20K30  Automorphisms, homomorphisms, endomorphisms, etc.
3=|20K35  Extensions
3=|20K40  Homological and categorical methods
3=|20K45  Topological methods [See also 22A05, 22B05]
3=|20K99  None of the above, but in this section

2-|20Lxx  groupoids (i.e. small categories in which all morphisms are
..........isomorphisms) {for sets with a single binary operation, see 20N02;
..........for topological groupoids, See 22A22, 58H05} 
4*|20L05  Groupoids (i.e. small categories in which all morphisms are 
..........isomorphisms) {For sets with a single binary operation, see 20N02; 
..........for topological groupoids, see 22A22, 58H05} 
........../~ general theory 
3-|20L10  connections with group theory 
3-|20L13  mappings of groupoids 
3-|20L15  connections with topology 
3-|20L17  connections with category theory 
3-|20L99  none of the above, but in this section 

2=|20Mxx  Semigroups
3=|20M05  Free semigroups, generators and relations, word problems 
3=|20M07  Varieties of semigroups
3=|20M10  General structure theory
3=|20M11  Radical theory
3=|20M12  Ideal theory
3=|20M14  Commutative semigroups
3=|20M15  Mappings of semigroups
3=|20M17  Regular semigroups
3=|20M18  Inverse semigroups
3=|20M19  Orthodox semigroups
3=|20M20  Semigroups of transformations, etc. [See also 47D03, 47H20, 54H15]
3=|20M25  Semigroup rings, multiplicative semigroups of rings
..........[See also 16S36, 16Y60]
3>|20M30  Representation of semigroups; actions of semigroups on sets 
........../:> ; actions of semigroups on sets 
3~|20M35  Semigroups in automata theory, linguistics, etc. [See
..........also 03D05, 68Q70, 68T50] // 68Q70, 68T50, ~ 68Qxx, 68S05,
3=|20M50  Connections of semigroups with homological algebra and
..........category theory
3=|20M99  None of the above, but in this section

2=|20Nxx  Other generalizations of groups
3=|20N02  Sets with a single binary operation (groupoids)
3=|20N05  Loops, quasigroups [See also 05Bxx]
3-|20N07  mappings of loops 
3=|20N10  Ternary systems (heaps, semiheaps, heapoids, etc.)
3=|20N15  $n$-ary systems
3=|20N20  Hypergroups
3~|20N25  Fuzzy groups [See also 03E72] // 03E72 ~ 04A72
3=|20N99  None of the above, but in this section

4>|20P05  Probabilistic methods in group theory [See also 60Bxx] 
........../:> [See also 60Bxx]

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|22-XX  Topological groups, Lie groups 
..........{For transformation groups see 54H15, 57Sxx, 58-XX. For
..........abstract harmonic analysis see 43-XX} 
8=|22-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|22-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|22-02  Research exposition (monographs, survey articles)
8=|22-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|22-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|22-06  Proceedings, conferences, collections, etc.

2<|22Axx  Topological and differentiable algebraic systems 
..........{For topological rings and fields see 12Jxx, 13Jxx, 16W80} 
........../:< ; for dual spaces of operator algebras and topological 
..........groups, see 47D35
3=|22A05  Structure of general topological groups
3=|22A10  Analysis on general topological groups
3=|22A15  Structure of topological semigroups
3=|22A20  Analysis on topological semigroups
3<|22A22  Topological groupoids (including differentiable and Lie groupoids) 
..........[See also 58H05] /:> [See also 58H05]
3=|22A25  Representations of general topological groups and semigroups
3=|22A26  Topological semilattices, lattices and applications
..........[See also 06B30, 06B35, 06F30]
3=|22A30  Other topological algebraic systems and their representations
3=|22A99  None of the above, but in this section

2=|22Bxx  Locally compact abelian groups (LCA groups)
3=|22B05  General properties and structure of LCA groups
3=|22B10  Structure of group algebras of LCA groups
3=|22B99  None of the above, but in this section

4=|22C05  Compact groups

2=|22Dxx  Locally compact groups and their algebras
3=|22D05  General properties and structure of locally compact groups
3=|22D10  Unitary representations of locally compact groups
3=|22D12  Other representations of locally compact groups
3=|22D15  Group algebras of locally compact groups
3=|22D20  Representations of group algebras
3=|22D25  $C^*$-algebras and $W$*-algebras in relation to group
..........representations [See also 46Lxx]
3=|22D30  Induced representations
3=|22D35  Duality theorems
3<|22D40  Ergodic theory on groups [See also 28Dxx] /:< , 43A60
3=|22D45  Automorphism groups of locally compact groups
3=|22D99  None of the above, but in this section

2=|22Exx  Lie groups {For the topology of Lie groups and homogeneous 
..........spaces see 57Sxx, 57Txx; for analysis theorem 
..........see  43A80, 43A85, 43A90}  
3=|22E05  Local Lie groups [See also 34-XX, 35-XX, 58H05] 
3=|22E10  General properties and structure of complex Lie groups 
..........[See also 32M05]
3=|22E15  General properties and structure of real Lie groups
3=|22E20  General properties and structure of other Lie groups
3=|22E25  Nilpotent and solvable Lie groups
3=|22E27  Representations of nilpotent and solvable Lie groups
..........(special orbital integrals, non-type I representations, etc.)
3=|22E30  Analysis on real and complex Lie groups [See also 33C80, 43-XX]
3<|22E35  Analysis on $p$-adic Lie groups /:< [See also 11R56]
3=|22E40  Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
3=|22E41  Continuous cohomology [See also 57R32, 57Txx, 58H10]
3=|22E43  Structure and representation of the Lorentz group
3=|22E45  Representations of Lie and linear algebraic groups
..........over real fields: analytic methods {For the purely
..........algebraic theory, see 20G05}
3=|22E46  Semisimple Lie groups and their representations
3~|22E47  Representations of Lie and real algebraic groups:
..........algebraic methods (Verma modules, etc.) [See also 17B10] 
..........// 17B10 ~ 17B35
3>|22E50  Representations of Lie and linear algebraic groups
..........over local fields [See also 20G05] /:> [See also 20G05]
3=|22E55  Representations of Lie and linear algebraic groups
..........over global fields and ad\`ele rings [See also 20G05]
3=|22E60  Lie algebras of Lie groups {For the algebraic theory
..........of Lie algebras, see 17Bxx}
3=|22E65  Infinite-dimensional Lie groups and their Lie algebras
..........[See also 17B65, 58B25, 58H05]
3=|22E67  Loop groups and related constructions, group-theoretic
..........treatment [See also 58D05]
3=|22E70  Applications of Lie groups to physics; explicit
..........representations [See also 81R05, 81R10]
3=|22E99  None of the above, but in this section

2+|22Fxx  Noncompact transformation groups 
3+|22F05  General theory of group and pseudogroup actions {For
..........topological properties of spaces with an action, see 57S20}
3+|22F10  Measurable group actions [see also 28Dxx and 22D40]
3+|22F30  Homogeneous spaces {For general actions on manifolds
..........or preserving geometrical structures see 57M60, 57Sxx; for
..........discrete subgroups of Lie groups see especially 22E40}
3+|22F50  Groups as automorphisms of other structures

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|26-XX  Real functions [See also 54C30] 
8=|26-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|26-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|26-02  Research exposition (monographs, survey articles)
8=|26-03  Historical (must also be assigned at least one classification 
..........number from Section 01)
8=|26-04  Explicit machine computation and programs (not the theory 
..........of computation or programming)
8=|26-06  Proceedings, conferences, collections, etc.

2=|26Axx  Functions of one variable
3=|26A03  Foundations: limits and generalizations, elementary
..........topology of the line
3=|26A06  One-variable calculus
3=|26A09  Elementary functions
3=|26A12  Rate of growth of functions, orders of infinity,
..........slowly varying functions [See also 26A48]
3=|26A15  Continuity and related questions (modulus of
..........continuity, semicontinuity, discontinuities, etc.) {For
..........properties determined by Fourier coefficients, see
..........42A16; for those determined by approximation
..........properties, see 41A25, 41A27}
3=|26A16  Lipschitz (H\"older) classes
3~|26A18  Iteration [See also 37Bxx, 37Cxx, 37Exx,, 39B12, 47H10, 54H25] 
..........// 37Bxx, 37Cxx, 37Exx ~ 58F08, 58F13, 
3~|26A21  Classification of real functions; Baire classification of sets 
..........and functions [See also 03E15, 28A05, 54C50] // 03A15 ~ 04A15
3=|26A24  Differentiation (functions of one variable): general
..........theory, generalized derivatives, mean-value
..........theorems [See also 28A15]
3=|26A27  Nondifferentiability (nondifferentiable functions,
..........points of nondifferentiability), discontinuous
..........derivatives
3=|26A30  Singular functions, Cantor functions, functions with
..........other special properties
3=|26A33  Fractional derivatives and integrals
3=|26A36  Antidifferentiation
3=|26A39  Denjoy and Perron integrals, other special integrals
3=|26A42  Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX]
3=|26A45  Functions of bounded variation, generalizations
3=|26A46  Absolutely continuous functions
3=|26A48  Monotonic functions, generalizations
3=|26A51  Convexity, generalizations
3=|26A99  None of the above, but in this section

2=|26Bxx  Functions of several variables
3=|26B05  Continuity and differentiation questions
3=|26B10  Implicit function theorems, Jacobians, transformations
..........with several variables
3=|26B12  Calculus of vector functions
3=|26B15  Integration: length, area, volume [See also 28A75, 51M25]
3=|26B20  Integral formulas (Stokes, Gauss, Green, etc.)
3=|26B25  Convexity, generalizations
3=|26B30  Absolutely continuous functions, functions of bounded variation
3=|26B35  Special properties of functions of several variables,
..........H\"older conditions, etc.
3=|26B40  Representation and superposition of functions
3=|26B99  None of the above, but in this section

2=|26Cxx  Polynomials, rational functions
3=|26C05  Polynomials: analytic properties, etc. [See also 12Dxx, 12Exx]
3=|26C10  Polynomials: location of zeros [See also 12D10, 30C15, 65H05]
3=|26C15  Rational functions [See also 14Pxx]
3=|26C99  None of the above, but in this section

2=|26Dxx  Inequalities {For maximal function inequalities, see 42B25; 
..........for functional inequalities, see 39B72; for probabilistic 
..........inequalities, see 60E15}
3=|26D05  Inequalities for trigonometric functions and polynomials
3=|26D07  Inequalities involving other types of functions
3=|26D10  Inequalities involving derivatives and differential
..........and integral operators
3=|26D15  Inequalities for sums, series and integrals
3=|26D20  Other analytical inequalities
3=|26D99  None of the above, but in this section

2=|26Exx  Miscellaneous topics [See also 58Cxx]
3=|26E05  Real-analytic functions [See also 32B05, 32C05]
3=|26E10  $C^\infty$-functions, quasi-analytic functions [See also 58C25]
3=|26E15  Calculus of functions on infinite-dimensional spaces
..........[See also 46G05, 58Cxx]
3=|26E20  Calculus of functions taking values in infinite-dimensional 
..........spaces [See also 46E40, 46G10, 58Cxx] 
3=|26E25  Set-valued functions [See also 28B20, 54C60] {For nonsmooth 
..........analysis, see 49J52, 58Cxx, 90Cxx}
3=|26E30  Non-Archimedean analysis [See also 12J25]
3=|26E35  Nonstandard analysis [See also 03H05, 28E05, 54J05]
3<|26E40  Constructive real analysis [See also 03F60] /:< , 03F65
3~|26E50  Fuzzy real analysis [See also 03E72, 28E10] // 03E72 ~ 04A72 
3+|26E60  Means [See also 47A64] 
3=|26E99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|28-XX  Measure and integration 
..........{For analysis on manifolds, see 58-XX} 
8=|28-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|28-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|28-02  Research exposition (monographs, survey articles)
8=|28-03  Historical (must also be assigned at least one classification 
..........number from Section 01)
8=|28-04  Explicit machine computation and programs (not the theory 
..........of computation or programming)
8=|28-06  Proceedings, conferences, collections, etc.

2=|28Axx  Classical measure theory
3<|28A05  Classes of sets (Borel fields, $sigma$-rings, etc.), measurable sets, 
..........Suslin sets, analytic sets [See also 03E15, 26A21, 54H05] 
........../:< 04A15, 
3=|28A10  Real- or complex-valued set functions
3=|28A12  Contents, measures, outer measures, capacities
3=|28A15  Abstract differentiation theory, differentiation of set functions 
..........[See also 26A24]
3=|28A20  Measurable and nonmeasurable functions, sequences of
..........measurable functions, modes of convergence
3=|28A25  Integration with respect to measures and other set functions
3=|28A33  Spaces of measures, convergence of measures [See also 46E27, 60Bxx]
3=|28A35  Measures and integrals in product spaces
3=|28A50  Integration and disintegration of measures
3=|28A51  Lifting theory [See also 46G15]
3=|28A60  Measures on Boolean rings, measure algebras [See also 54H10] 
3=|28A75  Length, area, volume, other geometric measure theory
..........[See also 26B15, 49Q15]
3>|28A78  Hausdorff and packing measures /:> and packing 
3~|28A80  Fractals [See also 37Fxx] // 37Fxx ~ 58Fxx
3=|28A99  None of the above, but in this section

2=|28Bxx  Set functions, measures and integrals with values in
..........abstract spaces
3=|28B05  Vector-valued set functions, measures and integrals
..........[See also 46G10]
3=|28B10  Group- or semigroup-valued set functions, measures and integrals
3=|28B15  Set functions, measures and integrals with values in ordered spaces
3~|28B20  Set-valued set functions and measures; integration of
..........set-valued functions; measurable selections [See
..........also 26E25, 54C60, 54C65, 91B14] // 91B14 ~ 90A14
3=|28B99  None of the above, but in this section

2=|28Cxx  Set functions and measures on spaces with additional
..........structure [See also 46G12, 58C35, 58D20]
3=|28C05  Integration theory via linear functionals (Radon
..........measures, Daniell integrals, etc.), representing set
..........functions and measures
3=|28C10  Set functions and measures on topological groups, Haar
..........measures, invariant measures [See also 22Axx, 43A05]
3=|28C15  Set functions and measures on topological spaces
..........(regularity of measures, etc.)
3=|28C20  Set functions and measures and integrals in
..........infinite-dimensional spaces (Wiener measure, Gaussian
..........measure, etc.) [See also 46G12, 58C35, 58D20, 60B11]
3=|28C99  None of the above, but in this section

2~|28Dxx  Measure-theoretic ergodic theory [See also 11K50,
..........11K55, 22D40, 47A35, 54H20, 37Axx, 60Fxx, 60G10] // 37Axx ~ 58Fxx 
3=|28D05  Measure-preserving transformations
3=|28D10  One-parameter continuous families of measure-preserving 
..........transformations
3=|28D15  General groups of measure-preserving transformations
3=|28D20  Entropy and other invariants
3=|28D99  None of the above, but in this section

2=|28Exx  Miscellaneous topics in measure theory
3=|28E05  Nonstandard measure theory [See also 03H05, 26E35]
3~|28E10  Fuzzy measure theory [See also 03E72, 26E50, 94D05] 
..........// 03E72 ~ 04A72
3=|28E15  Other connections with logic and set theory
3=|28E99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|30-XX  Functions of a complex variable 
..........{For analysis on manifolds, see 58-XX}
8=|30-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|30-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|30-02  Research exposition (monographs, survey articles)
8=|30-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|30-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|30-06  Proceedings, conferences, collections, etc.

2=|30Axx  General properties
3=|30A05  Monogenic properties of complex functions (including
..........polygenic and areolar monogenic functions)
3=|30A10  Inequalities in the complex domain
3=|30A99  None of the above, but in this section

2=|30Bxx  Series expansions
3=|30B10  Power series (including lacunary series)
3=|30B20  Random power series
3=|30B30  Boundary behavior of power series, over-convergence
3=|30B40  Analytic continuation
3=|30B50  Dirichlet series and other series expansions, exponential series 
..........[See also 11M41, 42-XX]
3=|30B60  Completeness problems, closure of a system of functions
3=|30B70  Continued fractions [See also 11A55, 40A15]
3=|30B99  None of the above, but in this section

2=|30Cxx  Geometric function theory
3=|30C10  Polynomials
3=|30C15  Zeros of polynomials, rational functions, and other
..........analytic functions (e.g. zeros of functions with
..........bounded Dirichlet integral) {For algebraic theory,
..........see 12D10; for real methods, see 26C10}
3=|30C20  Conformal mappings of special domains
3=|30C25  Covering theorems in conformal mapping theory
3=|30C30  Numerical methods in conformal mapping theory [See also 65E05]
3=|30C35  General theory of conformal mappings
3=|30C40  Kernel functions and applications
3=|30C45  Special classes of univalent and multivalent functions
..........(starlike, convex, bounded rotation, etc.)
3=|30C50  Coefficient problems for univalent and multivalent functions
3=|30C55  General theory of univalent and multivalent functions
3=|30C62  Quasiconformal mappings in the plane
3=|30C65  Quasiconformal mappings in $R^n$, other generalizations
3=|30C70  Extremal problems for conformal and quasiconformal mappings, 
..........variational methods
3=|30C75  Extremal problems for conformal and quasiconformal mappings, 
..........other methods
3=|30C80  Maximum principle; Schwarz's lemma, Lindelof principle, 
..........analogues and generalizations; subordination
3=|30C85  Capacity and harmonic measure in the complex plane
..........[See also 31A15]
3=|30C99  None of the above, but in this section

2=|30Dxx  Entire and meromorphic functions, and related topics
3~|30D05  Functional equations in the complex domain, iteration and 
..........composition of analytic functions [See also 34Mxx, 39-XX, 37Fxx] 
..........// 34mxx, 39-XX, 37Fxx ~ 34A20, 39-XX, 58F05, 58F23
3=|30D10  Representations of entire functions by series and integrals
3=|30D15  Special classes of entire functions and growth estimates
3=|30D20  Entire functions, general theory
3=|30D30  Meromorphic functions, general theory
3=|30D35  Distribution of values, Nevanlinna theory
3=|30D40  Cluster sets, prime ends, boundary behavior
3=|30D45  Bloch functions, normal functions, normal families
3=|30D50  Blaschke products, bounded mean oscillation, bounded characteristic, 
..........bounded functions, functions with positive real part
3=|30D55  ${H}^p$-classes
3=|30D60  Quasi-analytic and other classes of functions
3=|30D99  None of the above, but in this section

2=|30Exx  Miscellaneous topics of analysis in the complex domain
3=|30E05  Moment problems, interpolation problems
3=|30E10  Approximation in the complex domain
3=|30E15  Asymptotic representations in the complex domain
3=|30E20  Integration, integrals of Cauchy type, integral representations 
..........of analytic functions [See also 45Exx]
3=|30E25  Boundary value problems [See also 45Exx]
3=|30E99  None of the above, but in this section

2=|30Fxx  Riemann surfaces
3=|30F10  Compact Riemann surfaces and uniformization [See also 14H15, 32G15]
3=|30F15  Harmonic functions on Riemann surfaces
3=|30F20  Classification theory of Riemann surfaces
3=|30F25  Ideal boundary theory
3=|30F30  Differentials on Riemann surfaces
3=|30F35  Fuchsian groups and automorphic functions 
..........[See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]
3=|30F40  Kleinian groups [See also 20H10]
3=|30F45  Conformal metrics (hyperbolic, Poincar\'e, distance functions)
3=|30F50  Klein surfaces
3=|30F60  Teichm\"uller theory [See also 32G15]
3=|30F99  None of the above, but in this section

2=|30Gxx  Generalized function theory
3=|30G06  Non-Archimedean function theory [See also 12J25];
..........nonstandard function theory [See also 03H05]
3=|30G12  Finely holomorphic functions and topological function theory
3-|30G15  topological function theory 
3=|30G20  Generalizations of Bers or Vekua type (pseudoanalytic,
..........$p$-analytic, etc.)
3=|30G25  Discrete analytic functions
3=|30G30  Other generalizations of analytic functions (including
..........abstract-valued functions)
3=|30G35  Functions of hypercomplex variables and generalized variables
3=|30G99  None of the above, but in this section

4~|30H05  Spaces and algebras of analytic functions [See also 32A38, 
..........46Exx, 46J15] // 32A38 ~ 32E25

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|31-XX  Potential theory 
..........{For probabilistic potential theory, see 60J45} 
8=|31-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|31-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|31-02  Research exposition (monographs, survey articles)
8=|31-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|31-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|31-06  Proceedings, conferences, collections, etc.

2=|31Axx  Two-dimensional theory
3=|31A05  Harmonic, subharmonic, superharmonic functions
3=|31A10  Integral representations, integral operators, integral
..........equations methods
3=|31A15  Potentials and capacity, harmonic measure, extremal
..........length [See also 30C85]
3=|31A20  Boundary behavior (theorems of Fatou type, etc.)
3=|31A25  Boundary value and inverse problems
3=|31A30  Biharmonic, polyharmonic functions and equations,
..........Poisson's equation
3=|31A35  Connections with differential equations
3=|31A99  None of the above, but in this section

2=|31Bxx  Higher-dimensional theory
3=|31B05  Harmonic, subharmonic, superharmonic functions
3=|31B10  Integral representations, integral operators, integral
..........equations methods
3=|31B15  Potentials and capacities, extremal length
3=|31B20  Boundary value and inverse problems
3=|31B25  Boundary behavior
3=|31B30  Biharmonic and polyharmonic equations and functions
3=|31B35  Connections with differential equations
3=|31B99  None of the above, but in this section

2=|31Cxx  Other generalizations
3=|31C05  Harmonic, subharmonic, superharmonic functions
3~|31C10  Pluriharmonic and plurisubharmonic functions [See also 32U05] 
..........// 32U05 ~ 32F05
3=|31C12  Potential theory on Riemannian manifolds 
..........[See also 53C20; for Hodge theory, see 58A14]
3=|31C15  Potentials and capacities
3=|31C20  Discrete potential theory and numerical methods
3=|31C25  Dirichlet spaces
3=|31C35  Martin boundary theory [See also 60J50]
3=|31C40  Fine potential theory
3=|31C45  Other generalizations (nonlinear potential theory, etc.)
3=|31C99  None of the above, but in this section

4=|31D05  Axiomatic potential theory 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|32-XX  Several complex variables and analytic spaces 
..........{For infinite-dimensional holomorphy, see also 46G20, 58B12}
8=|32-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|32-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|32-02  Research exposition (monographs, survey articles)
8=|32-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|32-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|32-06  Proceedings, conferences, collections, etc.

2=|32Axx  Holomorphic functions of several complex variables
3=|32A05  Power series, series of functions
3~|32A07  Special domains (Reinhardt, Hartogs, circular, tube) 
..........// circular, tube ~ tube domains, etc.
3=|32A10  Holomorphic functions
3+|32A12  Multifunctions 
3=|32A15  Entire functions
3<|32A17  Special families of functions /:< (e.g. normal families)
3+|32A18  Bloch functions, normal functions 
3+|32A19  Normal families of functions, mappings 
3=|32A20  Meromorphic functions
3=|32A22  Nevanlinna theory (local); growth estimates; other
..........inequalities {For geometric theory, see 32H25, 32H30}
3>|32A25  Integral representations; canonical kernels (Szeg\"o, Bergman, etc.) 
........../:> canonical kernels (Szeg\"o, Bergman, etc.) 
3+|32A26  Integral representations, constructed kernels 
..........(e.g. Cauchy, Fantappi\`e-type kernels) 
3=|32A27  Local theory of residues [See also 32C30]
3=|32A30  Other generalizations of function theory of one
..........complex variable (should also be assigned at least one
..........classification number from Section 30) 
..........{For functions of several hypercomplex variables, see 30G35}
3=|32A35  ${H}^p$-spaces, Nevanlinna spaces [See also 32M15, 42B30, 
..........43A85, 46J15]
3+|32A36  Bergman spaces 
3<|32A37  Other spaces of holomorphic functions (e.g. bounded 
..........mean oscillation (BMOA), vanishing mean oscillation (VMOA) 
..........[See also 46Exx] // vanishing mean oscillation (VMOA) ~ 
..........vanishing mean oscillation (VMOA) in $n$ dimensions
3+|32A38  Algebras of holomorphic functions [See also 30H05, 46J10, 46J15] 
3>|32A40  Boundary behavior of holomorphic functions 
........../:> of olomorphic functions 
3=|32A45  Hyperfunctions [See also 46F15]
3+|32A50  Harmonic analysis of several complex variables [See mainly 43-XX] 
3+|32A55  Singular integrals 
3+|32A60  Zero sets of holomorphic functions 
3+|32A65  Banach algebra techniques [See mainly 46Jxx] 
3+|32A70  Functional analysis techniques [See mainly 46Exx] 
3=|32A99  None of the above, but in this section

2=|32Bxx  Local analytic geometry [See also 13-XX and 14-XX]
3=|32B05  Analytic algebras and generalizations, preparation theorems
3>|32B10  Germs of analytic sets, local parametrization 
........../:> , local parametrization
3=|32B15  Analytic subsets of affine space
3=|32B20  Semi-analytic sets and subanalytic sets [See also 14P15]
3=|32B25  Triangulation and related questions
3=|32B99  None of the above, but in this section

2~|32Cxx  Analytic spaces /~ General theory of analytic spasec
3=|32C05  Real-analytic manifolds, real-analytic spaces [See also 14Pxx, 58A07]
3=|32C07  Real-analytic sets, complex Nash functions [See also 14P15, 14P20]
3+|32C09  Embedding of real analytic manifolds 
3-|32C10  complex manifolds {For almost complex manifolds, See 53C15} 
3=|32C11  Complex supergeometry [See also 14A22, 14M30, 58A50]
3=|32C15  Complex spaces
3-|32C16  CR-manifolds 
3-|32C17  K\"ahler geometry {For differential-geometric methods, See 53C55} 
3=|32C18  Topology of analytic spaces
3=|32C20  Normal analytic spaces
3+|32C22  Embedding of analytic spaces 
3=|32C25  Analytic subsets and submanifolds
3=|32C30  Integration on analytic sets and spaces, currents {For local theory, 
..........see 32A25 or 32A27}
3=|32C35  Analytic sheaves and cohomology groups [See also
..........14Fxx, 18F20, 55N30]
3=|32C36  Local cohomology of analytic spaces
3=|32C37  Duality theorems
3~|32C38  Sheaves of differential operators and their modules, D-modules 
..........[See also 14F10, 16S32, 35A27, 58J15] // 58J15 ~ 58G07 /:> D-modules
3+|32C55  The Levi problem in complex spaces; generalizations 
3=|32C81  Applications to physics
3=|32C99  None of the above, but in this section

2=|32Dxx  Analytic continuation
3=|32D05  Domains of holomorphy
3=|32D10  Envelopes of holomorphy
3=|32D15  Continuation of analytic objects
3=|32D20  Removable singularities
3+|32D25  Riemann domains 
3=|32D99  None of the above, but in this section

2=|32Exx  Holomorphic convexity
3=|32E05  Holomorphically convex complex spaces, reduction theory
3=|32E10  Stein spaces, Stein manifolds
3=|32E20  Polynomial convexity
3-|32E25  algebras of holomorphic functions [See also 30H05, 46J10, 46J15] 
3=|32E30  Holomorphic and polynomial approximation, Runge pairs, interpolation
3=|32E35  Global boundary behavior of holomorphic functions
3+|32E40  The Levi problem 
3=|32E99  None of the above, but in this section

2<|32Fxx  Geometric convexity /:< partial differential operators
3-|32F05  plurisubharmonic functions and generalizations [See also 31C10] 
3-|32F07  complex Monge-Ampere operator 
3=|32F10  $q$-convexity, $q$-concavity
3-|32F15  pseudoconvex domains 
3+|32F17  Other notions of convexity 
3+|32F18  Finite-type conditions 
3-|32F20  $\overline\partial$-Neumann and $\overline\partial_b$-Neumann 
..........problems [See also 35N15] 
3-|32F25  real submanifolds in complex manifolds 
3+|32F27  Topological consequences of geometric convexity 
3-|32F30  pseudoconvex manifolds 
3+|32F32  Analytical consequences of geometric convexity (vanishing theorems, 
..........etc.) 
3-|32F40  CR structures (tangential) CR operators and generalizations 
3+|32F45  Invariant metrics and pseudodistances 
3=|32F99  None of the above, but in this section

2=|32Gxx  Deformations of analytic structures
3=|32G05  Deformations of complex structures 
..........[See also 13D10, 16S80, 58H10, 58H15]
3=|32G07  Deformations of special (e.g. CR) structures
3=|32G08  Deformations of fiber bundles
3=|32G10  Deformations of submanifolds and subspaces
3=|32G13  Analytic moduli problems {For algebraic moduli problems, 
..........see 14D20, 14D22, 14H10, 14J10} [See also 14H15, 14J15]
3=|32G15  Moduli of Riemann surfaces, Teichm\"uller theory 
..........[See also 14H15, 30Fxx]
3=|32G20  Period matrices, variation of Hodge structure; degenerations 
..........[See also 14D05, 14D07, 14K30]
3~|32G34  Moduli and deformations for ordinary differential equations 
..........(e.g. Khnizhnik-Zamolodchikov equation)[See also 34Mxx] 
..........// 34Mxx ~ 34A20 /:> (e.g. Khnizhnik-Zamolodchikov equation) 
3=|32G81  Applications to physics
3=|32G99  None of the above, but in this section

2=|32Hxx  Holomorphic mappings and correspondences
3=|32H02  Holomorphic mappings, (holomorphic) embeddings and related questions
3=|32H04  Meromorphic mappings
3-|32H10  Bergman kernel function, representative domains 
3+|32H12  Boundary uniqueness of mappings 
3-|32H15  invariant metrics and pseudodistances 
3-|32H20  hyperbolic complex manifolds 
3=|32H25  Picard-type theorems and generalizations 
..........{For function-theoretic properties, see 32A22}
3=|32H30  Value distribution theory in higher dimensions 
..........{For function-theoretic properties, see 32A22}
3=|32H35  Proper mappings, finiteness theorems
3~|32H40  Boundary regularity of mappings // mappings ~ holomorphic maps
3-|32H50  iterations problems 
3=|32H99  None of the above, but in this section

2=|32Jxx  Compact analytic spaces {For Riemann surfaces, see 14Hxx, 30Fxx; 
..........for algebraic theory, see 14Jxx}
3=|32J05  Compactification of analytic spaces
3=|32J10  Algebraic dependence theorems
3=|32J15  Compact surfaces
3=|32J17  Compact $3$-folds
3<|32J18  Compact $n$-folds /:< $(n\geq 4)$
3-|32J20  algebraicity criteria 
3=|32J25  Transcendental methods of algebraic geometry [See also 14C30]
3=|32J27  Compact K\"ahler manifolds: generalizations, classification
3=|32J81  Applications to physics
3=|32J99  None of the above, but in this section

2~|32Kxx  Generalizations of analytic spaces {(should also be assigned 
..........at least one other classification number from section 32 describing the type of problem}
..........// from section 32 describing the type of problem ~ in this section
3=|32K05  Banach analytic spaces [See also 58Bxx]
3=|32K07  Formal and graded complex spaces [See also 58C50]
3=|32K15  Differentiable functions on analytic spaces, differentiable 
..........spaces [See also 58C25]
3=|32K99  None of the above, but in this section

2=|32Lxx  Holomorphic fiber spaces [See also 55Rxx]
3~|32L05  Holomorphic bundles and generalizations 
........../~ Holomorphic fiber bundles and generalizations 
3-|32L07  Hermite-Einstein bundles; Kahler-Einstein bundles [See also 53C07] 
3=|32L10  Sheaves and cohomology of sections of holomorphic
..........vector bundles, general results [See also 14F05, 18F20, 55N30]
3=|32L15  Bundle convexity [See also 32F10]
3=|32L20  Vanishing theorems
3>|32L25  Twistor theory, double fibrations [See also 53C28] /:> [See also 53C28]
3-|32L30  holomorphic foliations [See also 58F18] 
3=|32L81  Applications to physics
3=|32L99  None of the above, but in this section

2=|32Mxx  Complex spaces with a group of automorphisms
3~|32M05  Complex Lie groups, automorphism groups acting on complex spaces 
..........[See also 22E10] // acting on ~ of 
3=|32M10  Homogeneous complex manifolds [See also 14M17, 57T15]
3=|32M12  Almost homogeneous manifolds and spaces [See also 14M17]
3>|32M15  Hermitian symmetric spaces, bounded symmetric domains
..........Jordan algebras [See also 22E10, 22E40, 53C35, 57T15] 
........../:> Jordan algebras
3+|32M17  Automorphism groups of ${\bf C}^n$ and affine manifolds 
3+|32M25  Complex vector fields 
3=|32M99  None of the above, but in this section

2=|32Nxx  Automorphic functions [See also 11Fxx, 20H10, 22E40, 30F35]
3=|32N05  General theory of automorphic functions of several complex variables
3=|32N10  Automorphic forms
3=|32N15  Automorphic functions in symmetric domains
3=|32N99  None of the above, but in this section

4=|32P05  Non-Archimedean complex analysis (should also be
..........assigned at least one other classification number from Section 32
..........describing the type of problem)

2+|32Qxx  Complex manifolds 
3+|32Q05  Negative curvature manifolds
3+|32Q10  Positive curvature manifolds
3+|32Q15  K\"ahler manifolds
3+|32Q20  K\"ahler-Einstein manifolds [See also 53Cxx]
3+|32Q25  Calabi-Yau theory
3+|32Q28  Stein manifolds
3+|32Q30  Uniformization
3+|32Q35  Complex manifolds as subdomains of Euclidean space
3+|32Q40  Embedding theorems
3+|32Q45  Hyperbolic and Kobayashi hyperbolic manifolds
3+|32Q55  Topological aspects of complex manifolds
3+|32Q57  Classification theorems
3+|32Q60  Almost complex manifolds
3+|32Q65  Pseudoholomorphic curves
3+|32Q99  None of the above, but in this section

2=|32Sxx  Singularities
3~|32S05  Local singularities [See also 14J17] // 14J17 ~ 14B05 
3=|32S10  Invariants of analytic local rings
3=|32S15  Equisingularity (topological and analytic) [See also 14E15]
3=|32S20  Global theory of singularities; cohomological properties 
..........[See also 14E15]
3+|32S22  Relations with arrangements of hyperplanes [See also 52C30] 
3~|32S25  Surface and hypersurface singularities [See also 14J17]
..........// Surface and hypersurface singularities  ~ (Hyper-) surface singularities 
3=|32S30  Deformations of singularities; vanishing cycles [See also 14B07]
3=|32S35  Mixed Hodge theory of singular varieties [See also 14C30, 14D07]
3=|32S40  Monodromy; relations with differential equations and $D$-modules
3=|32S45  Modifications; resolution of singularities [See also 14E15]
3=|32S50  Topological aspects: Lefschetz theorems, topological classification, 
..........invariants
3=|32S55  Milnor fibration; relations with knot theory [See also 57M25, 57Q45]
3=|32S60  Stratifications; constructible sheaves; intersection cohomology 
..........[See also 58Kxx] // 58Kxx ~ 58C27
3=|32S65  Singularities of holomorphic vector fields and foliations 
3=|32S70  Other operations on singularities
3=|32S99  None of the above, but in this section

2+|32Txx  Pseudoconvex domains 
3+|32T05  Domains of holomorphy
3+|32T15  Strongly pseudoconvex domains
3+|32T20  Worm domains
3+|32T25  Finite type domains
3+|32T27  Geometric and analytic invariants on weakly pseudoconvex boundaries
3+|32T35  Exhaustion functions
3+|32T40  Peak functions
3+|32T99  None of the above, but in this section

2+|32Uxx  Pluripotential theory 
3+|32U05  Plurisubharmonic functions and generalizations [See also 31C10] 
3+|32U10  Plurisubharmonic exhaustion functions
3+|32U15  Pluripotential theory
3+|32U20  Capacity theory and generalizations
3+|32U25  Lelong numbers
3+|32U30  Removable sets
3+|32U35  Pluricomplex Green functions
3+|32U40  Currents
3+|32U99  None of the above, but in this section

2+|32Vxx  $CR$ Manifolds 
3+|32V05  $CR$ structures, $CR$ operators, and generalizations
3+|32V10  $CR$ functions
3+|32V15  $CR$ manifolds as boundaries of domains
3+|32V20  Analysis on $CR$ manifolds
3+|32V25  Extension of functions and other analytic objects from $CR$ manifolds
3+|32V30  Embeddings of $CR$ manifolds
3+|32V35  Finite type conditions on $CR$ manifolds
3+|32V40  Real submanifolds in complex manifolds
3+|32V99  None of the above, but in this section

2+|32Wxx  Differential operators in several variables 
3+|32W05  $\overline\partial$ and $\overline\partial$-Neumann operators
3+|32W10  $\overline\partial_b$ and $\overline\partial_b$-Neumann operators
3+|32W20  Complex Monge-Amp\`ere operators
3+|32W25  Pseudodifferential operators in several complex variables
3+|32W30  Heat kernels in several complex variables
3+|32W50  Other partial differential equations of complex analysis
3+|32W99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|33-XX  Special functions {33-XX deals with the properties of functions 
..........as functions. For orthogonal functions see also 42Cxx; for aspects 
..........of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; 
..........for representation theory see 22Exx} 
8=|33-00  General reference works (handbooks, dictionaries, 
..........bibliographies, etc.)
8=|33-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|33-02  Research exposition (monographs, survey articles)
8=|33-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|33-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|33-06  Proceedings, conferences, collections, etc.

2=|33Bxx  Elementary classical functions
3=|33B10  Exponential and trigonometric functions
3=|33B15  Gamma, beta and polygamma functions
3=|33B20  Incomplete beta and gamma functions (error functions, 
..........probability integral, Fresnel integrals)
3+|33E30  Higher logarithm functions 
3=|33B99  None of the above, but in this section

2=|33Cxx  Hypergeometric functions
3=|33C05  Classical hypergeometric functions, $_2F_1$
3=|33C10  Bessel and Airy functions, cylinder functions, $_0F_1$
3=|33C15  Confluent hypergeometric functions, Whittaker functions, $_1F_1$
3=|33C20  Generalized hypergeometric series, $_pF_q$
3~|33C45  Orthogonal polynomials and functions of hypergeometric type 
..........(Jacobi, Laguerre, Hermite, Askey scheme, etc.; 
..........see 42C05 for general orthogonal polynomials and functions) 
..........// (Jacobi, Laguerre, Hermite, Askey scheme, etc.; 
..........see 42C05 for general orthogonal polynomials and functions) 
..........~ (Chebyshev, Legendre, Gegenbauer, Jacobi, Laguerre, Hermite, 
..........Hahn, etc.) /:> of hypergeometric type
3+|33C47  Other special orthogonal polynomials and functions 
3>|33C50  Orthogonal polynomials and functions in several variables 
..........expressible in terms of special functions in one varaible
........../:> expressible in terms of special functions in one varaible
3+|33C52  Orthogonal polynomials and functions associated with root systems 
3~|33C55  Spherical harmonics /~ Spherical functions, spherical harmonics, 
..........ultraspherical polynomials
3=|33C60  Hypergeometric integrals and functions defined by them
..........($E$, $G$ and ${H}$ functions)
3=|33C65  Appell, Horn and Lauricella functions
3+|33C67  Hypergeometric functions associated with root systems 
3=|33C70  Other hypergeometric functions and integrals in several variables
3=|33C75  Elliptic integrals as hypergeometric functions
3~|33C80  Connections with groups, algebras, and related topics 
........../~ Connections with groups, algebras, root systems and related topics 
3=|33C90  Applications
3=|33C99  None of the above, but in this section

2=|33Dxx  Basic hypergeometric functions
3=|33D05  $q$-gamma functions, $q$-beta functions and integrals
3-|33D10  basic theta functions 
3>|33D15  Basic hypergeometric functions in one variable, ${}_r\phi_s$ 
........../:> , ${}_r\phi_s$ 
3-|33D20  generalized basic hypergeometric series 
3~|33D45  Basic orthogonal polynomials and functions 
..........(Askey-Wilson polynomials, etc.) 
..........// (Askey-Wilson polynomials, etc.) ~ in one and several variables
3+|33D50  Orthogonal polynomials and functions in several variables expressible 
..........in terms of basic hypergeometric functions in one variable 
3+|33D52  Basic orthogonal polynomials and functions associated 
..........with root systems (Macdonald polynomials, etc.) 
3-|33D55  basic spherical functions, spherical harmonics 
..........(continuous and discrete) 
3=|33D60  Basic hypergeometric integrals and functions defined by them
3=|33D65  Bibasic functions and multiple bases
3+|33D67  Basic hypergeometric functions associated with root systems 
3=|33D70  Other basic hypergeometric functions and integrals in several 
..........variables
3~|33D80  Connections with quantum groups, Chevalley groups, 
..........$p$-adic groups, Hecke algebras, and related topics
........../~ Connections with groups, algebras and related topics
3=|33D90  Applications
3=|33D99  None of the above, but in this section

2=|33Exx  Other special functions
3=|33E05  Elliptic functions and integrals
3=|33E10  Lam\'e, Mathieu, and spheroidal wave functions
3+|33E12  Mittag-leffler functions and generalizations 
3=|33E15  Other wave functions
3+|33E17  Painlev\'e-type functions 
3=|33E20  Other functions defined by series and integrals
3=|33E30  Other functions coming from differential, difference and 
..........integral equations
3+|33E50  Special functions in characteristic $p$ (gamma functions etc.) 
3=|33E99  None of the above, but in this section

2+|33Fxx  Computational aspects 
3+|33F05  Numerical approximation [See also 65D20]
3+|33F10  Symbolic computation (Gosper and Zeilberger algorithms, etc.) 
..........[See also 68Q40]
3+|33F99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|34-XX  Ordinary differential equations 
8=|34-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|34-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|34-02  Research exposition (monographs, survey articles)
8=|34-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|34-04  Explicit machine computation and programs 
..........(not the theory of computation or programming)
8=|34-06  Proceedings, conferences, collections, etc.

2=|34Axx  General theory
3=|34A05  Explicit solutions and reductions
3>|34A09  Implicit equations, differential-algebraic equations 
..........[See also 65L80] /:> , differential-algebraic equations 
3=|34A12  Initial value problems, existence, uniqueness,
..........continuous dependence and continuation of solutions
3-|34A20  differential equations in the complex domain 
..........[See also 30D05, 32G34] 
3<|34A25  Analytical theory: series, transformations, transforms, 
..........operational calculus, etc. [See also 44-XX] 
........../:< , 47E05
3=|34A26  Geometric methods in differential equations
3=|34A30  Linear equations and systems
3=|34A34  Nonlinear equations and systems, general
3=|34A35  Differential equations of infinite order
3+|34A36  Discontinuous equations 
3=|34A37  Differential equations with impulses
3>|34A40  Differential inequalities [See also 26D20] /:> [See also 26D20]
3>|34A45  Theoretical approximation of solutions {For numerical
..........analysis, see 65Lxx} /:> {For numerical analysis, see 65Lxx} 
3-|34A46  theoretical solution methods other than approximations 
3-|34A47  bifurcation 
3-|34A50  numerical approximation of solutions 
..........{For numerical analysis, See 65Lxx} 
3=|34A55  Inverse problems
3~|34A60  Differential inclusions [See also 49J24, 49K24] // Differential inclusions~ Equations with ..........multivalued right-hand sides
3-|34A65  stiff equations 
3=|34A99  None of the above, but in this section

2=|34Bxx  Boundary value problems {For ordinary differential
..........operators, see 34Lxx}
3~|34B05  Linear boundary value problems /~ linear equations
3=|34B10  Multipoint boundary value problems
3=|34B15  Nonlinear boundary value problems
3+|34B16  Singular nonlinear boundary value problems 
3+|34B18  Positive solutions of nonlinear boundary value problems 
3=|34B20  Weyl theory and its generalizations
3=|34B24  Sturm-Liouville theory [See also 34Lxx]
3=|34B27  Green functions
3=|34B30  Special equations (Mathieu, Hill, Bessel, etc.)
3+|34B37  Boundary value problems with impulses 
3+|34B40  Boundary values on infinite intervals 
3+|34B45  Boundary value problems on graphs and networks 
3+|34B60  Applications 
3=|34B99  None of the above, but in this section

2~|34Cxx  Qualitative theory [See also 37-XX] // 37-XX ~ 58Fxx 
3=|34C05  Location of integral curves, singular points, limit cycles
3+|34C07  Theory of limit cycles of polynomial and analytic vector fields 
..........(existence, uniqueness, bounds, Hilbert's 16th problem and ramifications)
3+|34C08  Connections with real algebraic geometry (fewnomials, desingularization, 
..........zeros of Abelian integrals, etc.)
3=|34C10  Oscillation theory, zeros, disconjugacy and comparison theory
3=|34C11  Growth, boundedness, comparison of solutions
3+|34C12  Monotone systems 
3+|34C14  Symmetries, invariants 
3>|34C15  Nonlinear oscillations, coupled oscillators /:> , coupled oscillators
3=|34C20  Transformation and reduction of equations and systems,
..........normal forms
3~|34C23  Bifurcation [See mainly 37Gxx] // 37Gxx ~ 58F14
3=|34C25  Periodic solutions
3+|34C26  Relaxation oscillations 
3=|34C27  Almost periodic solutions
3~|34C28  Complex behavior, chaotic systems [See mainly 37Dxx] 
........../~ Other types of "recurrent" solutions
3=|34C29  Averaging method
3=|34C30  Manifolds of solutions
3-|34C35  dynamical systems [See also 54H20, 58Fxx, 70-XX] 
3<|34C37  Homoclinic and heteroclinic solutions /:< [See also 58F15]
3<|34C40  Equations and systems on manifolds /:< [See mainly 58Fxx, 58Gxx]
3+|34C41  Equivalence, asymptotic equivalence 
3=|34C45  Method of integral manifolds
3-|34C50  method of accelerated convergence 
3+|34C55  Hysteresis 
3+|34C60  Applications 
3=|34C99  None of the above, but in this section

2~|34Dxx  Stability theory [See also 37C75, 93Dxx] // 37C75 ~ 58F10
3=|34D05  Asymptotic properties
3>|34D08  Characteristic and Lyapunov exponents /:> Characteristic and
3+|34D09  Dichotomy, trichotomy 
3=|34D10  Perturbations
3=|34D15  Singular perturbations
3=|34D20  Lyapunov stability
3+|34D23  Global stability 
3-|34D25  Popov-type stability 
3~|34D30  Structural stability and analogous concepts [See also 37C20] 
..........// 37C20 ~ 58F10, 58F12
3=|34D35  Stability of manifolds of solutions
3=|34D40  Ultimate boundedness
3>|34D45  Attractors [See also 37C70, 37D50] /:> [See also 37C70, 37D50] 
3=|34D99  None of the above, but in this section

2=|34Exx  Asymptotic theory
3=|34E05  Asymptotic expansions
3=|34E10  Perturbations, asymptotics
3+|34E13  Multiple scale methods 
3=|34E15  Singular perturbations, general theory
3+|34E18  Methods of nonstandard analysis 
3=|34E20  Singular perturbations, turning point theory, WKB methods
3=|34E99  None of the above, but in this section

4=|34F05  Equations and systems with randomness [See also 34K50, 60H10, 93E03]

2>|34Gxx  Differential equations in abstract spaces 
..........[See also 37Kxx, 34Lxx, 47Dxx, 47Hxx, 47Jxx, 58D25] 
........../:> 37Kxx, 34Lxx, 47Dxx, 47Hxx, 47Jxx,
3<|34G10  Linear equations [See also 47D06, 47D09] /:< 47Axx, 47Bxx,
3>|34G20  Nonlinear equations [See also 47Hxx, 47Jxx] /:> , 47Jxx
3+|34G25  Evolution inclusions 
3=|34G99  None of the above, but in this section

4=|34H05  Control problems [See also 49J25, 49K25, 93C15]

2~|34Kxx  Functional-differential and differential-difference equations [See also 37-XX]
........../:< , with or without deviating arguments /:> [See also 37-XX]
3=|34K05  General theory
3+|34K06  Linear functional-differential equations 
3+|34K07  Theoretical approximation of solutions 
3=|34K10  Boundary value problems
3+|34K11  Oscillation theory 
3=|34K12  Growth, boundedness, comparison of solutions 
3+|34K13  Periodic solutions 
3+|34K14  Almost-periodic solutions 
3-|34K15  qualitative theory 
3+|34K17  Transformation and reduction of equations and systems, normal forms 
3+|34K18  Bifurcation theory 
3+|34K19  Invariant manifolds 
3=|34K20  Stability theory
3+|34K23  Complex (chaotic) behavior of solutions 
3=|34K25  Asymptotic theory
3+|34K26  Singular perturbations 
3+|34K28  Numerical approximation of solutions 
3+|34K29  Inverse problems 
3>|34K30  Equations in abstract spaces [See also 34Gxx, 47Dxx, 47Hxx] /:> 47Dxx, 47Hxx
3=|34K35  Control problems [See also 49J25, 49K25, 93C15]
3=|34K40  Neutral equations
3=|34K50  Stochastic delay equations [See also 34F05, 60Hxx]
3+|34K60  Applications 
3=|34K99  None of the above, but in this section

2=|34Lxx  Ordinary differential operators [See also 47E05]
3=|34L05  General spectral theory
3=|34L10  Eigenfunction expansions, completeness of eigenfunctions
3=|34L15  Estimation of eigenvalues, upper and lower bounds
3+|34L16  Numerical approximation of eigenvalues and of other parts 
..........of the spectrum 
3=|34L20  Asymptotic distribution of eigenvalues, asymptotic
..........theory of eigenfunctions
3=|34L25  Scattering theory
3=|34L30  Nonlinear ordinary differential operators
3=|34L40  Particular operators (Dirac, one-dimensional
..........Schr\"odinger, etc.)
3=|34L99  None of the above, but in this section

2+|34Mxx  Differential equations in the complex domain [See also 30Dxx, 32G34] 
3+|34M05  Entire and meromorphic solutions
3+|34M10  Oscillation, growth of solutions
3+|34M15  Algebraic aspects (differential-algebraic, hypertranscendence, 
..........group-theoretical)
3+|34M20  Nonanalytic aspects
3+|34M25  Formal solutions, transform techniques
3+|34M30  Asymptotics, summation methods
3+|34M35  Singularities, monodromy, local behavior of solutions,
..........normal forms
3+|34M40  Stokes phenomena and connection problems (linear and nonlinear)
3+|34M45  Differential equations on complex manifolds
3+|34M50  Inverse problems (Riemann-Hilbert, inverse differential 
..........Galois, etc.)
3+|34M55  Painlev\'e and other special equations; classification, 
..........hierarchies; isomonodromic deformations
3+|34M60  Singular perturbation problems in the complex domain
..........(complex WKB, turning points, steepest descent)
..........[See also 34E20]
3+|34M99  None of the above, but in the same section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|35-XX  Partial differential equations 
8=|35-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|35-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|35-02  Research exposition (monographs, survey articles)
8=|35-03  Historical (must also be assigned at least one classification 
..........number from Section 01)
8=|35-04  Explicit machine computation and programs (not the theory 
..........of computation or programming)
8=|35-06  Proceedings, conferences, collections, etc.

2=|35Axx  General theory
3=|35A05  General existence and uniqueness theorems
3=|35A07  Local existence and uniqueness theorems [See also 35H05, 35Sxx]
3=|35A08  Fundamental solutions
3=|35A10  Cauchy-Kovalevskaya theorems
3=|35A15  Variational methods
3+|35A17  Parametrices 
3+|35A18  Wave front sets 
3=|35A20  Analytic methods, singularities
3+|35A21  Propagation of singularities 
3=|35A22  Transform methods (e.g. integral transforms)
3=|35A25  Other special methods
3~|35A27  Microlocal methods; methods of sheaf theory and
..........homological algebra in PDE [See also 32C38,58J15]
..........// 58J15 ~ 58G07 
3~|35A30  Geometric theory, characteristics, transformations 
..........[See also 58J70, 58J72] // 58J70, 58J72 ~ 58G35, 58G37
3>|35A35  Theoretical approximation to solutions {For numerical
..........analysis, see 65Mxx, 65Nxx} /:> {For numerical analysis, 
..........see 65Mxx, 65Nxx}
3=|35A99  None of the above, but in this section

2=|35Bxx  Qualitative properties of solutions
3=|35B05  General behavior of solutions of PDE (comparison theorems; 
..........oscillation, zeros and growth of solutions; mean value theorems)
3=|35B10  Periodic solutions
3=|35B15  Almost periodic solutions
3=|35B20  Perturbations
3=|35B25  Singular perturbations
3~|35B27  Homogenization; partial differential equations in
..........media with periodic structure [See also 74Qxx, 76M50] // 74Qxx, 76M50 ~ 73B27, 76D30
3~|35B30  Dependence of solutions of PDE on initial and boundary data, 
..........parameters [See also 37Cxx] 
..........// 37Cxx ~ 58F14
3~|35B32  Bifurcation [See also 37Gxx, 37K50]
..........// 37Gxx, 37K50 ~ 58F14
3+|35B33  Critical exponents 
3+|35B34  Resonances 
3=|35B35  Stability, boundedness
3=|35B37  PDE in connection with control problems [See also 49J20, 
..........49K20, 93C20]
3+|35B38  Critical points 
3=|35B40  Asymptotic behavior of solutions
3+|35B41  Attractors 
3+|35B42  Inertial manifolds 
3=|35B45  A priori estimates
3=|35B50  Maximum principles
3=|35B60  Continuation and prolongation of solutions of PDE 
..........[See also 58A15, 58A17, 58Hxx]
3~|35B65  Smoothness and regularity of solutions of PDE
..........// Smoothness and regularity ~ Smoothness/regularity
3=|35B99  None of the above, but in this section

2=|35Cxx  Representations of solutions
3=|35C05  Solutions in closed form
3=|35C10  Series solutions, expansion theorems
3=|35C15  Integral representations of solutions of PDE
3=|35C20  Asymptotic expansions
3=|35C99  None of the above, but in this section

2=|35Dxx  Generalized solutions of partial differential equations
3=|35D05  Existence of generalized solutions
3=|35D10  Regularity of generalized solutions
3=|35D99  None of the above, but in this section

2=|35Exx  Equations and systems with constant coefficients [See also 35N05]
3=|35E05  Fundamental solutions
3=|35E10  Convexity properties
3=|35E15  Initial value problems
3=|35E20  General theory
3=|35E99  None of the above, but in this section

2=|35Fxx  General first-order equations and systems
3=|35F05  General theory of linear first-order PDE
3=|35F10  Initial value problems for linear first-order PDE,
..........linear evolution equations
3=|35F15  Boundary value problems for linear first-order PDE
3=|35F20  General theory of nonlinear first-order PDE
3=|35F25  Initial value problems for nonlinear first-order PDE,
..........nonlinear evolution equations
3=|35F30  Boundary value problems for nonlinear first-order PDE
3=|35F99  None of the above, but in this section

2=|35Gxx  General higher-order equations and systems
3=|35G05  General theory of linear higher-order PDE
3=|35G10  Initial value problems for linear higher-order PDE,
..........linear evolution equations
3=|35G15  Boundary value problems for linear higher-order PDE
3=|35G20  General theory of nonlinear higher-order PDE
3=|35G25  Initial value problems for nonlinear higher-order PDE,
..........nonlinear evolution equations
3=|35G30  Boundary value problems for nonlinear higher-order PDE
3=|35G99  None of the above, but in this section

2+|35Hxx  Close-to-elliptic equations 
4-|35H05  hypoelliptic equations and systems [See also 58Gxx] 
3+|35H10  Hypoelliptic equations 
3+|35H20  Subelliptic equations 
3+|35H30  Quasi-elliptic equations 
3+|35H99  None of the above, but in this section 

2~|35Jxx  Partial differential equations of elliptic type 
..........[See also 58Jxx, 58J10, 58J20] 
..........// 58Jxx, 58J10, 58J20 ~ 58G05, 58G10
3=|35J05  Laplace equation, reduced wave equation (Helmholtz),
..........Poisson equation [See also 31Axx, 31Bxx]
3=|35J10  Schr\"odinger operator [See also 35Pxx]
3=|35J15  General theory of second-order, elliptic equations
3=|35J20  Variational methods for second-order, elliptic equations
3=|35J25  Boundary value problems for second-order, elliptic equations
3=|35J30  General theory of higher-order, elliptic equations
..........[See also 31A30, 31B30]
3=|35J35  Variational methods for higher-order, elliptic equations
3=|35J40  Boundary value problems for higher-order, elliptic equations
3=|35J45  General theory of elliptic systems of PDE
3=|35J50  Variational methods for elliptic systems
3=|35J55  Boundary value problems for elliptic systems
3=|35J60  Nonlinear PDE of elliptic type
3=|35J65  Nonlinear boundary value problems for linear elliptic PDE; 
..........boundary value problems for nonlinear elliptic PDE
3=|35J67  Boundary values of solutions to elliptic PDE
3=|35J70  Elliptic partial differential equations of degenerate type
3=|35J85  Unilateral problems and variational inequalities for elliptic 
..........PDE [See also 35R35, 49J40]
3=|35J99  None of the above, but in this section

2~|35Kxx  Parabolic equations and systems 
..........[See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35]
..........// 58J35 ~ 58G11 
3=|35K05  Heat equation
3=|35K10  General theory of second-order, parabolic equations
3=|35K15  Initial value problems for second-order, parabolic equations
3=|35K20  Boundary value problems for second-order, parabolic equations
3-|35K22  evolution equations (any order in the spatial derivatives)
..........[See also 58D25] 
3=|35K25  General theory of higher-order, parabolic equations
3=|35K30  Initial value problems for higher-order, parabolic equations
3=|35K35  Boundary value problems for higher-order, parabolic equations
3=|35K40  General theory of parabolic systems of PDE
3=|35K45  Initial value problems for parabolic systems
3=|35K50  Boundary value problems for parabolic systems
3=|35K55  Nonlinear PDE of parabolic type
3=|35K57  Reaction-diffusion equations
3=|35K60  Nonlinear boundary value problems for linear parabolic PDE; 
..........boundary value problems for nonlinear parabolic PDE
3=|35K65  Parabolic partial differential equations of degenerate type
3=|35K70  Ultraparabolic, pseudoparabolic PDE, etc.
3=|35K85  Unilateral problems and variational inequalities for parabolic PDE 
..........[See also 35R35, 49J40]
3+|35K90  Abstract parabolic evolution equations 
3=|35K99  None of the above, but in this section

2~|35Lxx  Partial differential equations of hyperbolic type [See also 58J45] 
..........// 58J45 ~ 58G16
3=|35L05  Wave equation
3=|35L10  General theory of second-order, hyperbolic equations
3=|35L15  Initial value problems for second-order, hyperbolic equations 
3=|35L20  Boundary value problems for second-order, hyperbolic equations 
3=|35L25  General theory of higher-order, hyperbolic equations
3=|35L30  Initial value problems for higher-order, hyperbolic equations 
3=|35L35  Boundary value problems for higher-order, hyperbolic equations 
3=|35L40  General theory of hyperbolic systems of first-order PDE
3=|35L45  Initial value problems for hyperbolic systems of
..........first-order PDE
3=|35L50  Boundary value problems for hyperbolic systems of
..........first-order PDE
3=|35L55  Hyperbolic systems of higher-order PDE
3=|35L60  Nonlinear first-order PDE of hyperbolic type
3=|35L65  Conservation laws
3~|35L67  Shocks and singularities [See also 58Kxx, 76L05] // 58Kxx ~ 58C27
3=|35L70  Nonlinear second-order PDE of hyperbolic type
3=|35L75  Nonlinear hyperabolic PDE of higher ($\gtr 2$) order 
3=|35L80  Hyperbolic PDE of degenerate type
3+|35L82  Pseudohyperbolic equations 
3=|35L85  Unilateral problems; variational inequalities forhyperbolic PDE 
..........[See also 35R35, 49J40]
3+|35L90  Abstract hyperbolic evolution equations 
3=|35L99  None of the above, but in this section

2=|35Mxx  Partial differential equations of special type (mixed, composite, 
..........etc.) {For degenerate types, see 35J70, 35K65, 35L80}
3=|35M10  PDE of mixed type
3=|35M20  PDE of composite type
3=|35M99  None of the above, but in this section

2~|35Nxx  Overdetermined systems [See also 58Jxx, 58J10, 58J15, 58Hxx] 
..........// 58Jxx, 58J10, 58J15 ~ 58G05, 58G07
3=|35N05  Overdetermined systems with constant coefficients
3=|35N10  Overdetermined systems with variable coefficients (general)
3~|35N15  $\overline\partial$-Neumann problem and generalizations; 
..........formal complexes [See also 32W05, 32W10, 58J10] 
..........// 32W05, 32W10, 58J10 ~  32F20 and 58G05
3=|35N99  None of the above, but in this section

2=|35Pxx  Spectral theory and eigenvalue problems for partial
..........differential operators [See also 47Axx, 47Bxx, 47F05]
3=|35P05  General spectral theory of PDE
3=|35P10  Completeness of eigenfunctions, eigenfunction expansions for PDO
3=|35P15  Estimation of eigenvalues, upper and lower bounds
3=|35P20  Asymptotic distribution of eigenvalues and eigenfunctions for PDO
3=|35P25  Scattering theory for PDE [See also 47A40]
3=|35P30  Nonlinear eigenvalue problems, nonlinear spectral theory for PDO
3=|35P99  None of the above, but in this section

2=|35Qxx  Equations of mathematical physics and other areas of
..........application [See also 35J05, 35J10, 35K05, 35L05]
3=|35Q05  Euler-Poisson-Darboux equation and generalizations
3=|35Q15  Riemann-Hilbert problems [See also 30E25, 31A25, 31B20]
3=|35Q30  Stokes and Navier-Stokes equations [See also 76D05, 76D07, 76N10]
3=|35Q35  Other equations arising in fluid mechanics
3=|35Q40  Equations from quantum mechanics
3~|35Q51  Solitons [See also 37K40] // 37K40 ~ 58F07
3~|35Q53  KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, 
..........sinh-Gordon, etc.) [See also 37K10] // 37K10~ 58F07
3~|35Q55  NLS-like (nonlinear Schr\"odinger) equations [See also 37K10] 
..........// 37K10 ~ 58F07
3~|35Q58  Other completely integrable equations [See also 37J35, 37K10] 
..........// 37J35, 37K10 ~ 58F07
3=|35Q60  Equations of electromagnetic theory and optics
3=|35Q72  Other equations from mechanics
3=|35Q75  PDE in relativity
3=|35Q80  Applications of PDE in areas other than physics
3=|35Q99  None of the above, but in this section

2~|35Rxx  Miscellaneous topics involving partial differential equations 
..........{For equations on manifolds, see 58Jxx; for manifolds of 
..........solutions, see 58Bxx; for stochastic PDEs, see also 60H15} 
..........// 58Jxx ~ 58Gxx
3=|35R05  PDE with discontinuous coefficients or data
3=|35R10  Partial functional-differential or differential-difference 
..........equations, with or without deviating arguments
3+|35R12  Impulsive partial differential equations 
3=|35R15  Partial differential equations on infinite-dimensional
..........(e.g. function) spaces (=PDE in infinitely many variables) 
..........[See also 46Gxx, 58D25]
3~|35R20  Partial operator-differential equations (i.e. PDE on
..........finite-dimensional spaces for abstract space valued functions) 
..........[See also 34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx] // 47Jxx ~ 47H15
3=|35R25  Improperly posed problems for PDE
3=|35R30  Inverse problems (undetermined coefficients, etc.) for PDE
3=|35R35  Free boundary problems for PDE
3=|35R45  Partial differential inequalities
3=|35R50  Partial differential equations of infinite order
3=|35R60  Partial differential equations with randomness [See also 60H15]
3=|35R70  PDE with multivalued right-hand sides
3=|35R99  None of the above, but in this section

2~|35Sxx  Pseudodifferential operators and other generalizations
..........of partial differential operators [See also 47G30, 58J40] 
..........// 58J40 ~ 58G15
3=|35S05  General theory of $\Psi$DO
3=|35S10  Initial value problems for $\Psi$DO
3=|35S15  Boundary value problems for $\Psi$DO
3=|35S30  Fourier integral operators
3~|35S35  Topological aspects: intersection cohomology, stratified sets, etc. 
..........[See also 32C38, 32S40, 32S60, 58J15] 
..........// 58J15 ~ 58G07
3=|35S50  Paradifferential operators
3=|35S99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1+|37-XX  Dynamical systems and ergodic theory 
..........[See also 26A18, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] 
8+|37-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.) 
8+|37-01  Instructional exposition (textbooks, tutorial papers, etc.) 
8+|37-02  Research exposition (monographs, survey articles) 
8+|37-03  Historical (must also be assigned at least one
..........classification number from Section 01) 
8+|37-04  Explicit machine computation and programs (not the
..........theory of computation or programming) 
8+|37-06  Proceedings, conferences, collections, etc. 

2+|37Axx  Ergodic theory 
3+|37A05  Measure-preserving transformations 
3+|37A10  One-parameter continuous families of measure-preserving 
..........transformations 
3+|37A15  General groups of measure-preserving transformation
..........[See mainly 22Fxx] 
3+37A17  Homogeneous flows [See also 22Fxx]
3+|37A20  Orbit equivalence, cocycles, ergodic equivalence relations 
3+|37A25  Ergodicity, mixing, rates of mixing 
3+|37A30  Ergodic theorems, spectral theory, Markov operators {For operator
..........ergodic theory, see mainly 47A35} 
3+|37A35  Entropy and other invariants, isomorphism,
..........classification 
3+|37A40  Nonsingular (and infinite-measure preserving) transformations 
3+|37A45  Relations with number theory and harmonic analysis
..........[See also 11Kxx] 
3+|37A50  Relations with probability theory and stochastic processes 
3+|37A55  Relations with the theory of C*-algebras [See mainly 46L55] 
3+|37A60  Dynamical systems in statistical mechanics [See also 82Cxx] 
3+|37A99  None of the above, but in this section 

2+|37Bxx  Topological dynamics [See also 54H20] 
3+|37B05  Transformations and group actions with special
..........properties (minimality, distality, proximality, etc.) 
3+|37B10  Symbolic dynamics [See also 37Cxx, 37Dxx] 
3+|37B15  Cellular automata 
3+|37B20  Notions of recurrence 
3+|37B25  Lyapunov functions and stability; attractors, repellers 
3+|37B30  Index theory, Morse-Conley indices
3+|37B35  Gradient-like and recurrent behavior; isolated (locally-maximal) invariant sets
3+|37B40  Topological entropy
3+|37B45  Continua theory in dynamics
3+|37B50  Multi-dimensional shifts of finite type, tiling dynamics
3+|37B55  Nonautonomous dynamical systems
3+|37B99  None of the above, but in this section 

2+|37Cxx  Smooth dynamical systems: general theory [See also 34Cxx, 34Dxx]
3+|37C05  Smooth mappings and diffeomorphisms 
3+|37C10  Vector fields, flows, ordinary differential equations
3+|37C15  Topological and differentiable equivalence, conjugacy,
..........invariants, moduli, classification 
3+|37C20  Generic properties, structural stability 
3+|37C25  Fixed points, periodic points, fixed-point index theory 
3+|37C30  Zeta functions, (Ruelle-Frobenius) transfer operators,
..........and other functional analytic techniques in dynamical systems 
3+|37C35  Orbit growth 
3+|37C40  Smooth ergodic theory, invariant measures [See also 37Dxx] 
3+|37C45  Dimension theory of dynamical systems 
3+|37C50  Approximate trajectories (pseudotrajectories, shadowing, etc.) 
3+|37C55  Periodic and quasiperiodic flows and diffeomorphisms 
3+|37C60  Nonautonomous smooth dynamical systems [See also 37B50] 
3+|37C65  Monotone flows 
3+|37C70  Attractors and repellers, topological structure 
3+|37C75  Stability theory 
3+|37C80  Symmetries, equivariant dynamical systems 
3+|37C85  Dynamics of group actions other than Z and R, and foliations 
..........[See mainly 22Fxx] 
3+|37C99  None of the above, but in this section 

2+|37Dxx  Dynamical systems with hyperbolic behavior 
3+|37D05  Hyperbolic orbits and sets 
3+|37D10  Invariant manifold theory 
3+|37D15  Morse-Smale systems 
3+|37D20  Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) 
3+|37D25  Nonuniformly hyperbolic systems (Lyapunov exponents,
..........Pesin theory, etc.) 
3+|37D30  Partially hyperbolic systems and dominated splittings 
3+|37D35  Thermodynamic formalism, variational principles, equilibrium states 
3+|37D40  Dynamical systems of geometric origin and hyperbolicity(geodesic and horocycle 
..........flows, etc.) 
3+|37D45  Strange attractors, chaotic dynamics 
3+|37D50  Hyperbolic systems with singularities (billiards, etc.) 
3+|37D99  None of the above, but in this section 

2+|37Exx  Low-dimensional dynamical systems 
3+|37E05  Maps of the interval (piecewise continuous, continuous, smooth) 
3+|37E10  Maps of the circle 
3+|37E15  Combinatorial dynamics (types of periodic orbits) 
3+|37E20  Universality, renormalization [See also 37F25] 
3+|37E25  Maps of trees and graphs 
3+|37E30  Homeomorphism and diffeomorphisms of plane and surfaces 
3+|37E35  Flows on surfaces 
3+|37E40  Twist maps 
3+|37E45  Rotation numbers and vectors 
3+|37E99  None of the above, but in this section 

2+|37Fxx  Complex dynamical systems [See also 30D05, 32Hxx] 
3+|37F05  Relations and correspondences 
3+|37F10  Polynomials; rational maps; entire and meromorphic functions 
3+|37F15  Expanding maps; hyperbolicity; structural stability 
3+|37F20  Combinatorics and topology 
3+|37F25  Renormalization 
3+|37F30  Quasiconformal methods and Teichm\"uller theory;
..........Fuchsian and Kleinian groups as dynamical systems 
3+|37F35  Conformal densities and Hausdorff dimension 
3+|37F40  Geometric limits 
3+|37F45  Holomorphic families of dynamical systems; the Mandelbrot set; 
..........bifurcations 
3+|37F50  Small divisors, rotation domains and linearization;
..........Fatou and Julia sets 
3+|37F75  Holomorphic foliations and vector fields 
3+|37F99  None of the above, but in this section 

2+|37Gxx  Local and global bifurcation theory 
3+|37G05  Normal forms 
3+|37G10  Bifurcations of singular points 
3+|37G15  Bifurcations of limit cycles and periodic orbits 
3+|37G20  Hyperbolic singular points with homoclinic trajectories 
3+|37G25  Bifurcations connected with nontransversal intersection 
3+|37G30  Infinite nonwandering sets 
3+|37G35  Attractors and their bifurcations arising in bifurcations
3+|37G40  Symmetries, equivariant bifurcation theory 
3+|37G99  None of the above, but in this section 

2+|37Hxx  Random dynamical systems 
3+|37H05  Foundations, general theory of cocycles, algebraic ergodic theory 
..........[See also 37Axx] 
3+|37H10  Generation, random and stochastic difference and differential 
..........equations [See also 34K50, 37F05, 60Hxx]
3+|37H15  Multiplicative ergodic theory, Lyapunov exponents 
..........[See also 34D08, 37Axx, 37Cxx, 37Dxx] 
3+|37H20  Bifurcation theory [See also 37Gxx] 
3+|37H99  None of the above, but in this section 

2+|37Jxx  Finite-dimensional Hamiltonian, Lagrangian, contact, and 
..........nonholonomic systems [See also 53Dxx, 70Hxx]
3+|37J05  General theory, relations with symplectic geometry and topology 
3+|37J10  Symplectic mappings, fixed points 
3+|37J15  Symmetries, invariants, invariant manifolds, momentum maps, 
..........reduction [See also 53D20] 
3+|37J20  Bifurcation problems 
3+|37J25  Stability problems 
3+|37J30  Obstructions to integrability (nonintegrability criteria) 
3+|37J35  Completely integrable systems, topological structure
..........of phase space, integration methods 
3+|37J40  Perturbations, normal forms, small divisors, KAM theory, 
..........Arnold diffusion 
3+|37J45  Periodic, homoclinic and heteroclinic orbits; variational
..........methods, degree-theoretic methods 
3+|37J50  Action-minimizing orbits and measures for Lagrangian systems 
3+|37J55  Contact systems [See also 53D10] 
3+|37J60  Nonholonomic dynamical systems [See also 70F25] 
3+|37J99  None of the above, but in this section 

2+|37Kxx  Infinite-dimensional Hamiltonian systems  [See also 35Axx, 35Qxx]
3+|37K05  Hamiltonian structures, symmetries, variational principles, 
..........conservation laws 
3+|37K10  Completely integrable systems, integrability tests,
..........bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.) 
3+|37K15  Integration of completely integrable systems by
..........inverse spectral and scattering methods 
3+|37K20  Relations with algebraic geometry, complex analysis,
..........special functions [See also 14H70] 
3+|37K25  Relations with differential geometry 
3+|37K30  Relations with infinite-dimensional Lie algebras and
..........other algebraic structures 
3+|37K35  Lie-B\"acklund and other transformations 
3+|37K40  Soliton theory, asymptotic behavior of solutions 
3+|37K45  Stability problems 
3+|37K50  Bifurcation problems 
3+|37K55  Perturbations, KAM for infinite-dimensional systems 
3+|37K60  Lattice dynamics [See also 37L60] 
3+|37K65  Hamiltonian systems on groups of diffeomorphisms and
..........on manifolds of mappings and metrics 
3+|37K99  None of the above, but in this section 

2+|37Lxx  Infinite-dimensional dissipative dynamical systems [See also 35Bxx, 35Qxx]
3+|37L05  General theory, nonlinear semigroups, evolution equations 
3+|37L10  Normal forms, center manifold theory, bifurcation theory 
3+|37L15  Stability problems 
3+|37L20  Symmetries 
3+|37L25  Inertial manifolds and other invariant attracting sets 
3+|37L30  Attractors and their dimensions, Lyapunov exponents 
3+|37L40  Invariant measures 
3+|37L45  Hyperbolicity; Lyapunov functions 
3+|37L50  Noncompact semigroups; dispersive equations; perturbations 
..........of Hamiltonian systems 
3+|37L55  Infinite-dimensional random dynamical systems; stochastic equations 
3+|37L60  Lattice dynamics [See also 37K60] 
3+|37L60  Approximation methods (nonlinear Galerkin, etc.) 
3+|37L99  None of the above, but in this section 

2+|37Mxx  Approximation methods and numerical treatment of dynamical systems 
..........[See also 65Pxx] 
3+|37M05  Simulation 
3+|37M10  Time series analysis 
3+|37M15  Symplectic integrators 
3+|37M20  Computation of homoclinic cycles 
3+|37M25  Computational methods for bifurcation problems 
3+|37M30  Computational methods for ergodic theory (approximation of 
..........invariant measures, computation of Lyapunov exponents, entropy) 
3+|37M99  None of the above, but in this section 

2+|37Nxx  Applications 
3+|37N05  Dynamical systems in classical and celestial mechanics
..........[See mainly 70Fxx, 70Hxx, 70Kxx] 
3+|37N10  Dynamical systems in fluid mechanics and meteorology
..........[See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10] 
3+|37N15  Dynamical systems in solid mechanics [See mainly 74Hxx] 
3+|37N20  Dynamical systems in other branches of physics
..........(quantum mechanics, general relativity, laser physics) 
3+|37N25  Dynamical systems in biology [See mainly 92-XX, but also 91-XX] 
3+|37N30  Dynamical systems in numerical analysis 
3+|37N35  Dynamical systems in control 
3+|37N40  Dynamical systems in optimization and economics 
3+|37N99  None of the above, but in this section 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1~|39-XX  Difference and functional equations 
..........// Difference ~ Finite differences 
8=|39-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|39-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|39-02  Research exposition (monographs, survey articles)
8=|39-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|39-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|39-06  Proceedings, conferences, collections, etc.

2~|39Axx  Difference equations {For dynamical systems, see 37-XX} 
..........// 37-XX ~ 58Fxx
3=|39A05  General
3~|39A10  Difference equations, additive /:< [See also 33Dxx] /:> , additive 
3>|39A11  Stability and asymptotics of difference equations, 
..........oscillatory and periodic solutions, etc. /:> and asymptotics 
........../:> , oscillatory and periodic solutions, etc.
3=|39A12  Discrete version of topics in analysis
3+|39A13  Difference equations, scaling ($q$-differences) [See also 33Dxx] 
3+|39A20  Multiplicative and other generalized difference equations, 
..........e.g. of Lyness type 
3=|39A70  Difference operators [See also 47B39]
3=|39A99  None of the above, but in this section

2>|39Bxx  Functional equations and inequalities [See also 30D05] 
........../:> and inequalities 
3=|39B05  General
3~|39B12  Iteration theory, iterative and composite equations
..........[See also 26A18, 30D05, 37-XX] // 37-XX ~ 58F08
3>|39B22  Equations for real functions [See also 26A51, 26B25] 
........../:> [See also 26A51, 26B25] 
3=|39B32  Equations for complex functions [See also 30D05]
3=|39B42  Matrix and operator equations
3=|39B52  Equations for functions with more general domains
..........and/or ranges
3+|39B55  Orthogonal additivity and other conditional equations 
3~|39B62  Functional inequalities, including subadditivity, convexity, etc. 
..........[See also 26A51, 26B25, 26Dxx] /~ Systems of functional equations 
3~|39B72  Systems of functional equations and inequalitites 
........../~ Inequalities involving unknown functions [See also 26A51, 26Dxx]
3+|39B82  Stability, separation, extension, and realted topics 
..........[See also 46A22] 
3=|39B99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|40-XX  Sequences, series, summability 
8=|40-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|40-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|40-02  Research exposition (monographs, survey articles)
8=|40-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|40-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|40-06  Proceedings, conferences, collections, etc.

2=|40Axx  Convergence and divergence of infinite limiting processes
3=|40A05  Convergence and divergence of series and sequences
3=|40A10  Convergence and divergence of integrals 
3=|40A15  Convergence and divergence of continued fractions [See also 30B70]
3=|40A20  Convergence and divergence of infinite products
3=|40A25  Approximation to limiting values (summation of series,
..........etc.) {For the Euler-Maclaurin summation formula, see 65B15}
3=|40A30  Convergence and divergence of series and sequences of functions
3=|40A99  None of the above, but in this section

4=|40B05  Multiple sequences and series {(should also be assigned at 
..........least one other classification number in this section)}

2=|40Cxx  General summability methods
3=|40C05  Matrix methods
3=|40C10  Integral methods
3=|40C15  Function-theoretic methods (including power series
..........methods and semicontinuous methods)
3=|40C99  None of the above, but in this section

2=|40Dxx  Direct theorems on summability
3=|40D05  General theorems
3=|40D09  Structure of summability fields
3=|40D10  Tauberian constants and oscillation limits
3=|40D15  Convergence factors and summability factors
3=|40D20  Summability and bounded fields of methods
3=|40D25  Inclusion and equivalence theorems
3=|40D99  None of the above, but in this section

2=|40Exx  Inversion theorems
3=|40E05  Tauberian theorems, general
3=|40E10  Growth estimates
3=|40E15  Lacunary inversion theorems
3=|40E20  Tauberian constants
3=|40E99  None of the above, but in this section

4=|40F05  Absolute and strong summability

2=|40Gxx  Special methods of summability
3=|40G05  Ces\`aro, Euler, N\"orlund and Hausdorff methods 
3=|40G10  Abel, Borel and power series methods
3=|40G99  None of the above, but in this section

4=|40H05  Functional analytic methods in summability

4=|40J05  Summability in abstract structures [See also 43A55, 46A35, 46B15]

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1>|41-XX  Approximations and expansions 
..........{For all approximation theory in the complex domain, see
..........30Exx, 30E05 and 30E10; for all trigonometric approximation 
..........and interpolation, see 42Axx, 42A10 and 42A15; for 
..........numerical approximation, see 65Dxx} /:> 30Exx /:> 42Axx
8=|41-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|41-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|41-02  Research exposition (monographs, survey articles)
8=|41-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|41-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|41-06  Proceedings, conferences, collections, etc.

5=|41A05  Interpolation [See also 42A15 and 65D05]
5=|41A10  Approximation by polynomials {For approximation by 
..........trigonometric polynomials, see 42A10}
5=|41A15  Spline approximation
5=|41A17  Inequalities in approximation (Bernstein, Jackson,
..........Nikol\cprime ski\u\i-type inequalities) 
5=|41A20  Approximation by rational functions
5=|41A21  Pad\'e approximation 
5=|41A25  Rate of convergence, degree of approximation
5=|41A27  Inverse theorems
5=|41A28  Simultaneous approximation
5=|41A29  Approximation with constraints
5=|41A30  Approximation by other special function classes
5=|41A35  Approximation by operators (in particular, by integral operators)
5=|41A36  Approximation by positive operators
5=|41A40  Saturation
5=|41A44  Best constants
5=|41A45  Approximation by arbitrary linear expressions
5=|41A46  Approximation by arbitrary nonlinear expressions; widths and entropy
5=|41A50  Best approximation, Chebyshev systems
5=|41A52  Uniqueness of best approximation
5=|41A55  Approximate quadratures
5=|41A58  Series expansions (e.g. Taylor, Lidstone series, but
..........not Fourier series)
5=|41A60  Asymptotic approximations, asymptotic expansions
..........(steepest descent, etc.) [See also 30E15]
5=|41A63  Multidimensional problems (should also be assigned at
..........least one other classification number in this section)
5=|41A65  Abstract approximation theory (approximation in normed
..........linear spaces and other abstract spaces)
5=|41A80  Remainders in approximation formulas
5=|41A99  Miscellaneous topics 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|42-XX  Fourier analysis 
8=|42-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|42-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|42-02  Research exposition (monographs, survey articles)
8=|42-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|42-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|42-06  Proceedings, conferences, collections, etc.

2=|42Axx  Fourier analysis in one variable
3=|42A05  Trigonometric polynomials, inequalities, extremal problems
3=|42A10  Trigonometric approximation
3=|42A15  Trigonometric interpolation
3=|42A16  Fourier coefficients, Fourier series of functions with
..........special properties, special Fourier series 
..........{For automorphic theory, see mainly 11F30}
3>|42A20  Convergence and absolute convergence of Fourier and 
..........trigonometric series /:> and absolute convergence 
3>|42A24  Summability and absolute summability of Fourier and 
..........trigonometric series /:> and absolute summability 
3-|42A28  absolute convergence, absolute summability 
3=|42A32  Trigonometric series of special types (positive
..........coefficients, monotonic coefficients, etc.)
3=|42A38  Fourier and Fourier-Stieltjes transforms and other
..........transforms of Fourier type
3=|42A45  Multipliers
3=|42A50  Conjugate functions, conjugate series, singular integrals
3=|42A55  Lacunary series of trigonometric and other functions;
..........Riesz products
3=|42A61  Probabilistic methods
3=|42A63  Uniqueness of trigonometric expansions, uniqueness of
..........Fourier expansions, Riemann theory, localization
3=|42A65  Completeness of sets of functions
3=|42A70  Trigonometric moment problems
3=|42A75  Classical almost periodic functions, mean periodic functions 
..........[See also 43A60]
3=|42A82  Positive definite functions
3=|42A85  Convolution, factorization
3=|42A99  None of the above, but in this section

2=|42Bxx  Fourier analysis in several variables {For automorphic theory, 
..........see mainly 11F30}
3=|42B05  Fourier series and coefficients
3=|42B08  Summability
3=|42B10  Fourier and Fourier-Stieltjes transforms and other
..........transforms of Fourier type
3=|42B15  Multipliers
3=|42B20  Singular integrals (Calder¢n-Zygmund, etc.)
3=|42B25  Maximal functions, Littlewood-Paley theory
3=|42B30  $H^p$-spaces
3+|42B35  Function spaces arising in harmonic analysis 
3=|42B99  None of the above, but in this section

2=|42Cxx  Nontrigonometric Fourier analysis
3<|42C05  Orthogonal functions and polynomials, general theory
..........[See also 33C45, 33C50, 33D45] /:< 33A65,
3=|42C10  Fourier series in special orthogonal functions
..........(Legendre polynomials, Walsh functions, etc.)
3=|42C15  Series of general orthogonal functions, generalized
..........Fourier expansions, nonorthogonal expansions
3=|42C20  Rearrangements and other transformations of Fourier
..........and other orthogonal series
3=|42C25  Uniqueness and localization for orthogonal series
3=|42C30  Completeness of sets of functions
3+|42C40  Wavelets 
3=|42C99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|43-XX  Abstract harmonic analysis 
..........{For other analysis on topological and Lie groups, see 22Exx} 
8=|43-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|43-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|43-02  Research exposition (monographs, survey articles)
8=|43-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|43-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|43-06  Proceedings, conferences, collections, etc.

5=|43A05  Measures on groups and semigroups, etc.
5=|43A07  Means on groups, semigroups, etc.; amenable groups
5=|43A10  Measure algebras on groups, semigroups, etc.
5=|43A15  $L^p$-spaces and other function spaces on groups, semigroups, etc.
5=|43A17  Analysis on ordered groups, ${H}^p$-theory
5=|43A20  $L^1$-algebras on groups, semigroups, etc.
5=|43A22  Homomorphisms and multipliers of function spaces on
..........groups, semigroups, etc.
5=|43A25  Fourier and Fourier-Stieltjes transforms on locally
..........compact abelian groups
5=|43A30  Fourier and Fourier-Stieltjes transforms on nonabelian
..........groups and on semigroups, etc.
5=|43A32  Other transforms and operators of Fourier type
5=|43A35  Positive definite functions on groups, semigroups, etc.
5=|43A40  Character groups and dual objects
5=|43A45  Spectral synthesis on groups, semigroups, etc.
5=|43A46  Special sets (thin sets, Kronecker sets, Helson sets,
..........Ditkin sets, Sidon sets, etc.)
5=|43A50  Convergence of Fourier series and of inverse transforms
5=|43A55  Summability methods on groups, semigroups, etc. [See also 40J05]
5=|43A60  Almost periodic functions on groups and semigroups and
..........their generalizations (recurrent functions, distal
..........functions, etc.); almost automorphic functions
5=|43A62  Hypergroups
5=|43A65  Representations of groups, semigroups, etc. [See also
..........22A10, 22A20, 22Dxx, 22E45]
5=|43A70  Analysis on specific locally compact abelian groups
..........[See also 11R56, 22B05]
5=|43A75  Analysis on specific compact groups
5=|43A77  Analysis on general compact groups
5=|43A80  Analysis on other specific Lie groups [See also 22Exx]
5=|43A85  Analysis on homogeneous spaces
5<|43A90  Spherical functions [See also 22E45, 22E46, 33C65] /:< , 33D55
5=|43A95  Categorical methods [See also 46Mxx]
5=|43A99  Miscellaneous topics 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|44-XX  Integral transforms, operational calculus 
..........{For fractional derivatives and integrals, see 26A33. For Fourier 
..........transforms, see 42A38, 42B10. For integral transforms in distribution 
..........spaces, see 46F12. For numerical methods, see 65R10} 
8=|44-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|44-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|44-02  Research exposition (monographs, survey articles)
8=|44-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|44-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|44-06  Proceedings, conferences, collections, etc.

5=|44A05  General transforms [See also 42A38]
5=|44A10  Laplace transform
5=|44A12  Radon transform [See also 92C55]
5=|44A15  Special transforms (Legendre, Hilbert, etc.)
5=|44A20  Transforms of special functions
5=|44A30  Multiple transforms
5=|44A35  Convolution
5=|44A40  Calculus of Mikusinski and other operational calculi
5=|44A45  Classical operational calculus
5=|44A55  Discrete operational calculus
5=|44A60  Moment problems
5=|44A99  Miscellaneous topics 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|45-XX  Integral equations 
8=|45-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|45-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|45-02  Research exposition (monographs, survey articles)
8=|45-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|45-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|45-06  Proceedings, conferences, collections, etc.

4=|45A05  Linear integral equations

4=|45B05  Fredholm integral equations

4=|45C05  Eigenvalue problems [See also 34Lxx, 35Pxx, 45P05, 47A75]

4=|45D05  Volterra integral equations [See also 34A12]

2>|45Exx  Singular integral equations [See also 30Exx, 44-XX, 
..........30E20, 30E25, 44A15, 44A35] /:> 30Exx, 44-XX,
3=|45E05  Integral equations with kernels of Cauchy type [See also 35J15]
3=|45E10  Integral equations of the convolution type (Abel, Picard, 
..........Toeplitz and Wiener-Hopf type) [See also 47B35]
3=|45E99  None of the above, but in this section

2=|45Fxx  Systems of linear integral equations
3=|45F05  Systems of nonsingular linear integral equations
3=|45F10  Dual, triple, etc., integral and series equations
3=|45F15  Systems of singular linear integral equations
3=|45F99  None of the above, but in this section

2~|45Gxx  Nonlinear integral equations [See also 47H30, 47Jxx] // 47H30, 47Jxx ~ 47H15
3=|45G05  Singular nonlinear integral equations
3=|45G10  Other nonlinear integral equations
3=|45G15  Systems of nonlinear integral equations

4=|45H05  Miscellaneous special kernels [See also 44A15]

4>|45J05  Integro-ordinary differential equations [See also 34K05, 34K30, 47G20] /:> [See also 34K05, ..........34K30, 47G20]

4>|45K05  Integro-partial differential equations [See also 34K30, 35R10, 47G20] /:> [See also 34K30, ..........35R10, 47G20]

2-|45Lxx  approximation of solutions 
4:|45L05  Theoretical approximation of solutions {For numerical
..........analysis, see 65Rxx} /:> {For numerical analysis, see 65Rxx}
3-|45L10  numerical approximation of solutions {For numerical analysis, 
..........see 65R20} 
3-|45L99  none of the above but in this section 

2=|45Mxx  Qualitative behavior
3=|45M05  Asymptotics
3=|45M10  Stability theory
3=|45M15  Periodic solutions
3=|45M20  Positive solutions
3=|45M99  None of the above, but in this section

4=|45N05  Abstract integral equations, integral equations in abstract spaces

4=|45P05  Integral operators [See also 47B38, 47G10]

4+|45Q05  Inverse problems 

4+|45R05  Random integral equations [See also 60H20]

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|46-XX  Functional analysis {For manifolds modeled on topological linear 
..........spaces, see 57N20, 58Bxx}
8=|46-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|46-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|46-02  Research exposition (monographs, survey articles)
8=|46-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|46-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|46-06  Proceedings, conferences, collections, etc.

2=|46Axx  Topological linear spaces and related structures 
..........{For function spaces, see 46Exx}
3=|46A03  General theory of locally convex spaces
3=|46A04  Locally convex Frechet spaces and (DF)-spaces
3=|46A08  Barrelled spaces, bornological spaces
3=|46A11  Spaces determined by compactness or summability properties 
..........(nuclear spaces, Schwartz spaces, Montel spaces, etc.)
3=|46A13  Spaces defined by inductive or projective limits (LB, LF, etc.) 
..........[See also 46M40]
3=|46A16  Not locally convex spaces (metrizable topological
..........linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
3=|46A17  Bornologies and related structures; Mackey convergence, etc.
3=|46A19  Other ``topological'' linear spaces (convergence spaces, 
..........ranked spaces, spaces with a metric taking values in an 
..........ordered structure more general than ${\bf R}$, etc.) 
3=|46A20  Duality theory
3=|46A22  Theorems of Hahn-Banach type; extension and lifting of
..........functionals and operators [See also 46M10]
3=|46A25  Reflexivity and semi-reflexivity [See also 46B10]
3=|46A30  Open mapping and closed graph theorems; completeness
..........(including $B$-, $B_r$-completeness)
3~|46A32  Spaces of linear operators; topological tensor products; 
..........approximation properties [See also 46B28, 46M05, 47L05, 47L20] // 47L05, 47L20 ~ 47D15, ..........47D50
3=|46A35  Summability and bases [See also 46B15]
3=|46A40  Ordered topological linear spaces, vector lattices
..........[See also 06F20, 46B40, 46B42]
3=|46A45  Sequence spaces (including K\"othe sequence spaces)
..........[See also 46B45]
3=|46A50  Compactness in topological linear spaces; angelic spaces, etc.
3=|46A55  Convex sets in topological linear spaces; Choquet theory 
..........[See also 52A07]
3+|46A61  Graded Frechet spaces and tame operators 
3+|46A63  Topological invariants ((DN), ($\Omega$), etc.) 
3=|46A70  Saks spaces and their duals (strict topologies, mixed
..........topologies, two-norm spaces, co-Saks spaces, etc.)
3=|46A80  Modular spaces
3=|46A99  None of the above, but in this section

2=|46Bxx  Normed linear spaces and Banach spaces; Banach lattices 
..........{For function spaces, see 46Exx}
3=|46B03  Isomorphic theory (including renorming) of Banach spaces
3=|46B04  Isometric theory of Banach spaces
3=|46B07  Local theory of Banach spaces
3=|46B08  Ultraproduct techniques in Banach space theory [See also 46M07]
3=|46B09  Probabilistic methods in Banach space theory [See also 60Bxx]
3=|46B10  Duality and reflexivity [See also 46A25]
3=|46B15  Summability and bases [See also 46A35]
3=|46B20  Geometry and structure of normed linear spaces
3=|46B22  Radon-Nikodym, Kreuin-Milman and related properties
..........[See also 46G10]
3=|46B25  Classical Banach spaces in the general theory
3=|46B26  Nonseparable Banach spaces
3~|46B28  Spaces of operators; tensor products; approximation
..........properties [See also 46A32, 46M05, 47L05, 47L20] // 47L05, 47L20 ~ 47D15, 47D50
3=|46B40  Ordered normed spaces [See also 46A40, 46B42]
3=|46B42  Banach lattices [See also 46A40, 46B40]
3=|46B45  Banach sequence spaces [See also 46A45]
3+|46B50  Compactness in Banach (or normed) spaces 
3=|46B70  Interpolation between normed linear spaces [See also 46M35]
3=|46B99  None of the above, but in this section

2=|46Cxx  Inner product spaces and their generalizations,
..........Hilbert spaces {For function spaces, see 46Exx}
3=|46C05  Hilbert and pre-Hilbert spaces: geometry and topology
..........(including spaces with semidefinite inner product)
3+|46C07  Hilbert subspaces; complementation (Aronszajn, de Branges, ...) 
..........[See 46B70, 46M35] 
3=|46C15  Characterizations of Hilbert spaces
3>|46C20  Spaces with indefinite inner product (Krein spaces,
..........Pontryagin spaces, ...) /:> (Krein spaces, Pontryagin spaces, ...) 
3=|46C50  Generalizations of inner products (semi-inner
..........products, partial inner products, etc.)
3=|46C99  None of the above, but in this section

2~|46Exx  Linear function spaces and their duals [See also
..........30H05, 32A38, 46F05; for function algebras, see 46J10] // 32A38 ~ 32E25
3=|46E05  Lattices of continuous, differentiable or analytic functions
3=|46E10  Topological linear spaces of continuous,
..........differentiable or analytic functions
3=|46E15  Banach spaces of continuous, differentiable or analytic functions
3=|46E20  Hilbert spaces of continuous, differentiable or analytic functions
3=|46E22  Hilbert spaces with reproducing kernels (=[proper]
..........functional Hilbert spaces)
3=|46E25  Rings and algebras of continuous, differentiable or analytic 
..........functions {For Banach function algebras, see 46J10, 46J15}
3=|46E27  Spaces of measures [See also 28A33, 46Gxx]
3=|46E30  Spaces of measurable functions ($L^p$-spaces, Orlicz
..........spaces, K\"othe function spaces, Lorentz spaces, rearrangement 
..........invariant spaces, ideal spaces, etc.)
3=|46E35  Sobolev spaces and other spaces of ``smooth''
..........functions, embedding theorems, trace theorems
3=|46E39  Sobolev (and similar kinds of) spaces of functions of
..........discrete variables
3=|46E40  Spaces of vector- and operator-valued functions
3>|46E50  Spaces of differentiable or holomorphic functions on 
..........infinite-dimensional spaces [See also 46G20, 46G25, 47H60] 
........../:> , 46G25, 47H60
3=|46E99  None of the above, but in this section

2~|46Fxx  Distributions, generalized functions, distribution spaces 
..........[See also 46T30] // [See also 46T30] ~ 
..........{For distribution theory on monolinear spaces, see 58Cxx}
3=|46F05  Topological linear spaces of test functions,
..........distributions and ultradistributions [See also 46E10, 46E35]
3=|46F10  Operations with distributions
3=|46F12  Integral transforms in distribution spaces [See also 42-XX, 44-XX]
3~|46F15  Hyperfunctions, analytic functionals 
..........[See also 32A25, 32A45, 32C35, 58J15] // 58J15~ 58G07 
3=|46F20  Distributions and ultradistributions as boundary
..........values of analytic functions [See also 30D40, 30E25, 32A40]
3=|46F25  Distributions on infinite-dimensional spaces [See also 58C35]
3+|46F30  Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
3=|46F99  None of the above, but in this section

2~|46Gxx  Measures, integration, derivative, holomorphy (all involving 
..........infinite-dimensional spaces) [See also 28-XX, 46Txx]
........../:< {For nonlinear functional anlysis, see 47Hxx, 58-XX, 
..........especially 58Cxx} /:> 46Txx
3>|46G05  Derivatives [See also 46T20, 58C20, 58C25] /:> 46T20,
3=|46G10  Vector-valued measures and integration [See also 28Bxx, 46B22]
3>|46G12  Measures and integration on abstract linear spaces
..........[See also 28C20, 46T12] /:> , 46T12
3=|46G15  Functional analytic lifting theory [See also 28A51]
3>|46G20  Infinite-dimensional holomorphy [See also 32-XX,
..........46E50, 46T25 58B12, 58C10] /:> 46T25
3+|46G25  (Spaces of) multilinear mappings, polynomials 
..........[See also 46E50, 46G20, 47H60] 
3=|46G99  None of the above, but in this section

2=|46Hxx  Topological algebras, normed rings and algebras, Banach algebras 
..........{For group algebras, convolution algebras and measure algebras, 
..........see 43A10, 43A20}
3=|46H05  General theory of topological algebras
3=|46H10  Ideals and subalgebras
3=|46H15  Representations of topological algebras
3=|46H20  Structure, classification of topological algebras
3=|46H25  Normed modules and Banach modules, topological modules
..........(if not placed in 13-XX or 16-XX)
3=|46H30  Functional calculus in topological algebras [See also 47A60]
3~|46H35  Topological algebras of operators [See mainly 47Lxx]
.......... // [See mainly 47Lxx] ~ [See mainly 47D30,
..........and also 47D25, 47D50]
3=|46H40  Automatic continuity
3=|46H70  Nonassociative topological algebras [See also 46K70, 46L70]
3=|46H99  None of the above, but in this section

2=|46Jxx  Commutative Banach algebras and commutative
..........topological algebras [See also 46E25]
3=|46J05  General theory of commutative topological algebras
3=|46J10  Banach algebras of continuous functions, function
..........algebras [See also 46E25]
3~|46J15  Banach algebras of differentiable or analytic functions, 
..........${H}^p$-spaces [See also 30D55, 30H05, 32A35,
..........32A37, 32A38, 42B30] // 32A38 ~ 32E25
3=|46J20  Ideals, maximal ideals, boundaries
3=|46J25  Representations of commutative topological algebras
3=|46J30  Subalgebras
3=|46J40  Structure, classification of commutative topological algebras
3=|46J45  Radical Banach algebras
3=|46J99  None of the above, but in this section

2=|46Kxx  Topological (rings and) algebras with an involution [See also 16W10]
3=|46K05  General theory of topological algebras with involution
3=|46K10  Representations of topological algebras with involution
3=|46K15  Hilbert algebras
3=|46K50  Nonselfadjoint (sub)algebras in algebras with involution
3=|46K70  Nonassociative topological algebras with an involution
..........[See also 46H70, 46L70]
3=|46K99  None of the above, but in this section

2=|46Lxx  Selfadjoint operator algebras ($C^*$-algebras, von Neuman ($W$*-) 
..........algebras, etc.) [See also 22D25]
3=|46L05  General theory of $C^*$-algebras
3+|46L06  Tensor products of $C^*$-algebras; free products of $C*$-algebras 
3+|46L07  Operator spaces and completely bounded map [See also 47L25] 
3+|46L08  $C^*$-modules 
3=|46L10  General theory of von Neumann algebras
3=|46L30  States
3=|46L35  Classifications of $C^*$-algebras, factors
3=|46L37  Subfactors and their classification
3=|46L40  Automorphisms
3=|46L45  Decomposition theory for $C^*$-algebras 
3-|46L50  noncommutative measure, integration and probability 
3+|46L51  Noncommutative measure and integration 
3+|46L52  Noncommutative function spaces 
3+|46L53  Noncommutative probability and statistics 
3+|46L54  Free probability and free operator algebras 
3~|46L55  Noncommutative dynamical systems [See also 28Dxx, 54H20, 
..........37Kxx, 37Lxx] // 37Kxx, 37Lxx ~ 58Fxx
3=|46L57  Derivations, dissipations and positive semigroups in $C^*$-algebras
3~|46L60  Applications of selfadjoint operator algebras to physics 
..........[See also 46N50, 46N55, 47L90, 81T05, 82B10, 82C10] // 47L90 ~ 47D45
3+|46L65  Quantizations, deformations 
3=|46L70  Nonassociative selfadjoint operator algebras [See also
..........46H70, 46K70]
3~|46L80  $K$-theory and operator algebras (including cyclic
..........theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22] // 58J22 ~ 58G12
3~|46L85  Noncommutative topology [See also 58B32, 58B34, 58J22] 
..........// 58B32, 58B34, 58J22 ~ 58B30, 58G12
3~|46L87  Noncommutative differential geometry [See also 58B32, 58B34, 58J22] 
..........// 58B32, 58B34, 58J22 ~ 58B30, 58G12
3~|46L89  Other ``noncommutative'' mathematics based on
..........$C^*$-algebra theory [See also 58B32, 58B34, 58J22] 
..........// 58B32, 58B34, 58J22 ~ 58B30, 58G12
3=|46L99  None of the above, but in this section

2=|46Mxx  Methods of category theory in functional analysis [See also 18-XX]
3=|46M05  Tensor products [See also 46A32, 46B28, 47A80]
3=|46M07  Ultraproducts [See also 46B08, 46S20]
3=|46M10  Projective and injective objects [See also 46A22]
3>|46M15  Categories, functors {For $K$-theory, EXT, etc., see 19K33, 
..........46L80, 46M18, 46M20} /:> Categories, /:> 46M18,
3+|46M18  Homological methods (exact sequences, right inverses, 
..........lifting, etc.,) 
3>|46M20  Methods of algebraic topology (cohomology, sheaf and
..........bundle theory, etc.) [See also 14F05, 18Fxx, 19Kxx, 32Cxx,
..........32Lxx, 46L80, 46M15, 46M18, 55Rxx] /:> 46M15, 46M18, 
3=|46M35  Abstract interpolation of topological vector spaces
..........[See also 46B70]
3=|46M40  Inductive and projective limits [See also 46A13]
3=|46M99  None of the above, but in this section

2=|46Nxx  Miscellaneous applications of functional analysis [See also 47Nxx]
3=|46N10  Applications in optimization, convex analysis,
..........mathematical programming, economics
3=|46N20  Applications to differential and integral equations
3=|46N30  Applications in probability theory and statistics
3=|46N40  Applications in numerical analysis [See also 65Jxx]
3=|46N50  Applications in quantum physics
3=|46N55  Applications in statistical physics
3=|46N60  Applications in biology and other sciences
3=|46N99  None of the above, but in this section

2=|46Sxx  Other (nonclassical) types of functional analysis [See also 47Sxx]
3=|46S10  Functional analysis over fields other than R or
..........C or the quaternions; non-Archimedean
..........functional analysis [See also 12J25, 32P05]
3=|46S20  Nonstandard functional analysis [See also 03H05]
3~|46S30  Constructive functional analysis [See also 03F60] // 03F60 ~ 03F65
3~|46S40  Fuzzy functional analysis [See also 03E72] // 03E72 ~ 04A72
3=|46S50  Functional analysis in probabilistic metric linear spaces
3+|46S60  Functional analysis on superspaces (supermanifolds) or graded spaces 
..........[See also 58A50 and 58C50] 
3=|46S99  None of the above, but in this section

2+|46Txx  Nonlinear functional analysis [See also 47Hxx, 47Jxx, 58Cxx, 58Dxx]
3+|46T05  Infinite-dimensional manifolds [See also 53Axx, 58Bxx, 58Dxx, 57N20]
3+|46T10  Manifolds of mappings
3+|46T12  Measure (Gaussian, cylindrical, etc.) and integrals
..........(Feynman, path, Fresnel, etc.) on manifolds 
..........[See also 28Cxx, 46G12, 60-XX]
3+|46T20  Continuous and differentiable maps [See also 46G05]
3+|46T25  Holomorphic maps [See also 46G20]
3+|46T30  Distribution and generalized functions on nonlinear
..........spaces [See also 46Fxx]
3+|46T99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|47-XX  Operator theory 
8=|47-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|47-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|47-02  Research exposition (monographs, survey articles)
8=|47-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|47-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|47-06  Proceedings, conferences, collections, etc.

2=|47Axx  General theory of linear operators
3=|47A05  General (adjoints, conjugates, products, inverses,
..........domains, ranges, etc.)
3+|47A06  Linear relations (multivalued linear operators) 
3+|47A07  Forms (blilinear, sesquilinear, multilinear) 
3=|47A10  Spectrum, resolvent
3=|47A11  Local spectral properties
3>|47A12  Numerical range, numerical radius /:> , numerical radius
3~|47A13  Several-variable operator theory (spectral, Fredholm, etc.) 
..........// operator ~ spectral /:> (spectral, Fredholm, etc.)
3=|47A15  Invariant subspaces
3+|47A16  Cyclic and hypercyclic vectors 
3=|47A20  Dilations, extensions, compressions
3=|47A25  Spectral sets
3=|47A30  Norms (inequalities, more than one norm, etc.)
3~|47A35  Ergodic theory [See also 37Axx] // 37Axx ~ 28Dxx
3=|47A40  Scattering theory [See also 34L25, 35P25, 81Uxx]
3=|47A45  Canonical models for contractions and nonselfadjoint operators
3+|47A46  Chains (nests) of projections or of invariant subspaces, 
..........integrals along chains, etc. 
3~|47A48  Operator colligations (=nodes), vessels, linear systems, 
..........characteristic functions, realizations, etc.
........../~ Operator colligations (=nodes)
3=|47A50  Equations and inequalities involving linear operators,
..........with vector unknowns
3~|47A53  (Semi-) Fredholm operators; index theories 
..........[See also 58B10, 58J20] // 58J20 ~ 58G12
3=|47A55  Perturbation theory
3~|47A56  Functions whose values are linear operators (operator and matrix 
..........valued functions, etc., including analytic and meromorphic ones) 
..........// (operator and matrix valued functions, etc., including
..........analytic and meromorphic ones) ~ (operator and matrix pencils, etc.)
3>|47A57  Operator methods in interpolation, moment and extension problems 
..........[See also 30E05, 42A70, 42A82, 44A60] /:> , 44A60
3=|47A58  Operator approximation theory
3=|47A60  Functional calculus
3=|47A62  Equations involving linear operators, with operator unknowns
3<|47A63  Operator inequalities /:< , operator means, shorted operators, etc.
3+|47A64  Operator means, shorted operators, etc. 
3=|47A65  Structure theory
3~|47A66  Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operators
.......... /~ (Non)quasitriangular, (non)quasidiagonal operators
3=|47A67  Representation theory
3=|47A68  Factorization theory (including Wiener-Hopf and
..........spectral factorizations)
3=|47A70  (Generalized) eigenfunction expansions; rigged Hilbert spaces
3~|47A75  Eigenvalue problems [See also 49R50] // 49R50 ~ 49Rxx
3=|47A80  Tensor products of operators [See also 46M05]
3=|47A99  None of the above, but in this section

2=|47Bxx  Special classes of linear operators
3=|47B06  Riesz operators; eigenvalue distributions;
..........approximation numbers, $s$-numbers, Kolmogorov numbers,
..........entropy numbers, etc. of operators
3=|47B07  Operators defined by compactness properties
3~|47B10  Operators belonging to operator ideals (nuclear, $p$-summing, 
..........in the Schatten-von Neumann classes, etc.) [See also 47L20] // 47L20 ~ 47D50
3=|47B15  Hermitian and normal operators (spectral measures,
..........functional calculus, etc.)
3=|47B20  Subnormal operators, hyponormal operators, etc.
3=|47B25  Symmetric and selfadjoint operators (unbounded)
3+|47B32  Operators in reproducing-kernel Hilbert spaces 
3+|47B33  Composition operators 
3+|47B34  Kernel operators 
3~|47B35  Toeplitz operators, Hankel operators, Wiener-Hopf
..........operators [See also 45P05, 47G10 for other integral
..........operators; see also 32A25, 32M15] // 32A25 ~ 32H10
3+|47B36  Jacobi (tridiagonal) operators (matrices) and generalizations 
3=|47B37  Operators on special spaces (weighted shifts,
..........operators on sequence spaces, etc.)
3~|47B38  Operators on function spaces (general) 
..........// (general) ~ (including composition operators, kernel operators)
3=|47B39  Difference operators [See also 39A70]
3=|47B40  Spectral operators, decomposable operators,
..........well-bounded operators, etc.
3=|47B44  Accretive operators, dissipative operators, etc.
3=|47B47  Commutators, derivations, elementary operators, etc.
3=|47B48  Operators on Banach algebras
3=|47B49  Transformers (=operators on spaces of operators)
3>|47B50  Operators on spaces with an indefinite metric [See also 46C50] 
........../:> [See also 46C50]
3=|47B60  Operators on ordered spaces
3=|47B65  Positive operators and order-bounded operators
3=|47B80  Random operators [See also 60H25]
3=|47B99  None of the above, but in this section

2=|47Cxx  Individual linear operators as elements of algebraic systems
3=|47C05  Operators in algebras
3=|47C10  Operators in *-algebras
3=|47C15  Operators in $C^*$- or von Neumann algebras
3=|47C99  None of the above, but in this section

2~|47Dxx  Groups and semigroups of linear operators, their generalizations and 
..........applications
........../~ algebraic systems of linear operators [See also 46Lxx]
3~|47D03  Groups and semigroups of linear operators {For nonlinear
..........operators, see 47H20; see also 20M20} // Groups and semigroups ~ (Semi)groups
3>|47D06  One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]
.......... /:> [See also 34G10, 34K30]
3=|47D07  Markov semigroups and applications to diffusion
..........processes {For Markov processes, see 60Jxx}
3+|47D08  Schr\"odinger and Feynman-Kac semigroups 
3>|47D09  Operator sine and cosine functions and higher-order Cauchy problems [See also 34G10]
.......... /:> [See also 34G10]
3-|47D15  linear spaces of operators, [See also 46A32, 46B28] 
3-|47D20  convex sets and cones of operators [See also 90C25, 90C31] 
3-|47D25  operator algebras on Hilbert space 
3-|47D27  dual operator algebras 
3-|47D30  operator algebras on Banach spaces and other linear 
..........topological spaces 
3-|47D35  dual spaces of operator algebras and topological groups 
3-|47D40  algebras of unbounded operators 
3-|47D45  applications of operator algebras to physics 
..........[See also 46L60, 46N50, 46N55, 47N50, 47N55] 
3-|47D50  operator ideals 
3+|47D60  C-semigroups 
3+|47D62  Integrated semigroups 
3=|47D99  None of the above, but in this section

4<|47E05  Ordinary differential operators [See also 34Bxx, 34Lxx] 
........../:< ,58F19

4~|47F05  Partial differential operators [See also 35Pxx, 58Jxx] 
..........// 58Jxx ~ 58C05

2>|47Gxx  Integral, integro-differential, and pseudodifferential
..........operators [See also 58Jxx] /:> [See also 58Jxx]
3=|47G10  Integral operators [See also 45P05]
3>|47G20  Integro-differential operators [See also 34K30, 35R10, 45J05, 45K05] /:> 34K30, 35R10,
3~|47G30  Pseudodifferential operators 
..........[See also 35Sxx, 58Jxx] // 58Jxx ~ 58G15
3=|47G99  None of the above, but in this section

2>|47Hxx  Nonlinear operators and their properties {For global and 
..........geometric aspects, see 58-XX, 
..........especially 58Cxx} /:> and their properties 
3=|47H04  Set-valued operators [See also 28B20, 54C60, 58C06]
3=|47H05  Monotone operators (with respect to duality)
3=|47H06  Accretive operators, dissipative operators, etc.
3=|47H07  Monotone and positive operators on ordered Banach
..........spaces or other ordered topological vector spaces
3>|47H09  Nonexpansive mappings, and their generalizations (ultimately 
..........compact mappings, measures of noncompactness and condensing 
..........mappings, $A$-proper mappings, $K$-set contractions, etc.) 
........../:> and condensing mappings 
3=|47H10  Fixed-point theorems [Sse also 54H25, 55M20, 58C30]
3=|47H11  Degree theory [See also 55M25, 58C30]
3=|47H12  Spectral theory of nonlinear operators [See also 58C40]
3+|47H14  Perturbations of nonlinear operators 
3-|47H15  Equations involving nonlinear operators, 
..........[See also 58E07 for abstract bifurcation theory] 
3-|47H17  Methods for solving equations involving nonlinear operators
..........[See also 58C15] {For numerical analysis, see 65J15} 
3-|47H19  Inequalities involving nonlinear operators, 
..........[See also 49J27, 49J40, 49K27] 
3<|47H20  Semigroups of nonlinear operators 
........../:< and nonlinear evolution equations [See also 58D07]
3~|47H30  Particular nonlinear operators (superposition, Hammerstein, 
..........Nemytski\u i, Uryson, etc.) [See also 45P05] 
..........// Uryson, etc. ~ Uryson, hysteresis operators, etc.
3=|47H40  Random operators [See also 60H25]
3+|47H50  Potential operators 
3+|47H60  Multilinear and polynomial operators [See also 46G25] 
3=|47H99  None of the above, but in this section

2+|47Jxx  Equations and inequalities involving linear operators 
3+|47J05  Equations involving nonlinear operators (general)
3+|47J07  Abstract inverse mapping and implicit function theorems 
..........[See also 46T20 and 58C15]
3+|47J10  Nonlinear eigenvalue problems
3+|47J15  Abstract bifurcation theory [See also 58E07, 58E09]
3+|47J20  Variational and other type of inequalities involving
..........nonlinear operators (general)
3+|47J25  Methods for solving nonlinear operator equations (general)
3+|47J30  Infinite-dimensional critical point theory and
..........variational methods [See also 58Exx]
3+|47J35  Nonlinear evolution equations [See also 34G20, 35K90,
..........35L90, 35Qxx, 35R20, 47H20, 58D25]
3+|47J40  Equations with hysteresis
3+|47J99  None of the above, but in this section

2+|47Lxx  Linear spaces and algebras of operators [See also 46Lxx] 
3+|47L05  Linear spaces of operators [See also 46A32 and 46B28]
3+|47L07  Convex sets and cones of operators [See also 46A55,
..........90C25, and 90C31]
3+|47L10  Algebras of operators on Banach spaces and other
..........topological linear spaces
3+|47L15  Operator algebras with symbol structure
3+|47L20  Operator ideals
3+|47L25  Operator spaces (=matricially normed spaces) [See also 46L07]
3+|47L30  Abstract operator algebras on Hilbert spaces
3+|47L35  Nest algebras, CSL algebras
3+|47L40  Limit algebras, subalgebras of $C^*$-algebras
3+|47L45  Dual algebras; weakly closed singly generated operator algebras
3+|47L50  Dual spaces of operator algebras
3+|47L55  Representations of (nonselfadjoint) operator algebras
3+|47L60  Algebras of unbounded operators; partial algebras of operators
3+|47L65  Crossed product algebras (analytic crossed products)
3+|47L70  Nonassociative nonselfadjoint operator algebras
3+|47L75  Other nonselfadjoint operator algebras
3+|47L80  Algebras of specific types of operators (Toeplitz,
..........integral, pseudodifferential, etc.)
3+|47L90  Applications of operator algebras to physics
3+|47L99  None of the above, but in this section

2=|47Nxx  Miscellaneous applications of operator theory [See also 46Nxx]
3=|47N10  Applications in optimization, convex analysis,
..........mathematical programming, economics
3=|47N20  Applications to differential and integral equations
3=|47N30  Applications in probability theory and statistics
3=|47N40  Applications in numerical analysis [See also 65Jxx]
3=|47N50  Applications in quantum physics
3=|47N55  Applications in statistical physics
3=|47N60  Applications in biology and other sciences
3=|47N70  Applications in systems theory, circuits, etc.
3=|47N99  None of the above, but in this section

2=|47Sxx  Other (nonclassical) types of operator theory [See also 46Sxx]
3=|47S10  Operator theory over fields other than R,
..........C or the quaternions; non-Archimedean operator theory
3=|47S20  Nonstandard operator theory [See also 03H05]
3=|47S30  Constructive operator theory [See also 03F65]
3~|47S40  Fuzzy operator theory [See also 03E72] // 03E72 ~ 04A72
3=|47S50  Operator theory in probabilistic metric linear spaces
3=|47S99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1>|49-XX  Calculus of variations and optimal control; optimization 
..........[See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] /:> 34K35
8=|49-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|49-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|49-02  Research exposition (monographs, survey articles)
8=|49-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|49-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|49-06  Proceedings, conferences, collections, etc.

2=|49Jxx  Existence theories
3=|49J05  Free problems in one independent variable
3=|49J10  Free problems in two or more independent variables
3=|49J15  Optimal control problems involving ordinary differential equations
3=|49J20  Optimal control problems involving partial differential equations
3=|49J22  Optimal control problems involving integral equations
3>|49J24  Optimal control problems involving differential
..........inclusions [See also 34A60] /:> [See also 34A60]
3=|49J25  Optimal control problems involving equations with
..........retarded arguments [See also 34K35]
3>|49J27  Problems in abstract spaces [See 90C48, 93C25] /:> , 93C25
3=|49J30  Optimal solutions belonging to restricted classes
..........(Lipschitz controls, bang-bang controls, etc.)
3=|49J35  Minimax problems
3>|49J40  Variational methods including variational inequalities  [See also 47H19]
.......... /:>  [See also 47H19]
3~|49J45  Methods involving semicontinuity and convergence;
..........relaxation // Methods ~ Problems /:> ; relaxation
3=|49J50  Fr\'echet and Gateaux differentiability [See also 46G05, 58C20]
3~|49J52  Nonsmooth analysis [See also 46G05, 58C50] 
........../~ Nonsmooth analysis (other weak concepts of optimality) 
..........[See also 58C20, 90C48] 
3+|49J53  Set-valued and variational analysis 
..........[See also 28B20, 47H04, 54C60, 58C05] 
3=|49J55  Problems involving randomness [See also 93E20]
3=|49J99  None of the above, but in this section

2=|49Kxx  Necessary conditions and sufficient conditions for optimality
3=|49K05  Free problems in one independent variable
3=|49K10  Free problems in two or more independent variables
3=|49K15  Problems involving ordinary differential equations
3=|49K20  Problems involving partial differential equations
3=|49K22  Problems involving integral equations
3>|49K24  Problems involving differential inclusions [See also 34A60] 
........../:> [See also 34A60]
3=|49K25  Problems involving equations with retarded arguments
..........[See also 34K35]
3=|49K27  Problems in abstract spaces [See 90C48, 93C25]
3=|49K30  Optimal solutions belonging to restricted classes
3=|49K35  Minimax problems
3~|49K40  Sensitivity, stability, well-posedness [See also 90C31] 
........../~ Sensitivity of optimal solutions in the presence of perturbations 
3=|49K45  Problems involving randomness [See also 93E20]
3=|49K99  None of the above, but in this section

2~|49Lxx  Hamilton-Jacobi theories, including dynamic programming 
........../~ Carath\'eodory, Hamilton-Jacobi theories, including dynamic 
..........programming 
3-|49L05  free problems and problems involving ordinary differential 
..........equations 
3-|49L10  free problems and problems involving partial differential 
..........equations 
3-|49L15  problems in abstract spaces or problems involving functional 
..........relations other than differential equations 
3=|49L20  Dynamic programming method
3=|49L25  Viscosity solutions
3=|49L99  None of the above, but in this section

2~|49Mxx  Methods of successive approximations [See also 90Cxx, 65Kxx] 
..........// [See also 90Cxx, 65Kxx] ~ {For discrete problems, see 90Cxx; see 
..........also 65Kxx}
3=|49M05  Methods based on necessary conditions
3-|49M07  gradient methods 
3-|49M10  methods of steepest descent type 
3=|49M15  Methods of Newton-Raphson, Galerkin and Ritz types
3=|49M20  Methods of relaxation type
3=|49M25  Discrete approximations
3=|49M27  Decomposition methods
3=|49M29  Methods involving duality
3=|49M30  Other methods, not based on necessary conditions 
..........(penalty function, etc.)
3-|49M35  methods of linear programming type, [See also 90C05] 
3=|49M37  Methods of nonlinear programming type [See also 90C30, 65Kxx]
3-|49M39  semi-infinite programming [See also 90C34] 
3-|49M40  methods of quadratic programming type [See also 90C20] 
3-|49M45  methods of convex programming type [See also 90C25] 
3-|49M49  geometric programming [See also 90C28] 
3=|49M99  None of the above, but in this section

2=|49Nxx  Miscellaneous topics
3=|49N05  Linear optimal control problems [See also 93C05]
3=|49N10  Linear-quadratic problems
3=|49N15  Duality theory
3=|49N20  Periodic optimization
3<|49N25  Impulsive optimal control problems /:< [see also 93C57]
3=|49N30  Problems with incomplete information [See also 93C41]
3~|49N35  Optimal feedback synthesis [See also 93B52] /~ Closed-loop controls
3-|49N40  open-loop controls 
3<|49N45  Inverse problems /:< in calculus of variations
3-|49N50  inverse problems in optimal control theory 
3-|49N55  noneconomic applications of optimal control theory and 
..........differential games [See also 90D25] 
3<|49N60  Regularity of solutions /:< in the calculus of variations
3-|49N65  applications of measurable selections to control theory 
..........[See also 28B20, 26E25] 
3+|49N70  Differential games 
3+|49N75  Pursuit and evasion games 
3+|49N90  Applications of optimal control and differential games 
..........[See also 90C90, 93C95] 
3=|49N99  None of the above, but in this section

2~|49Qxx  Manifolds [See also 58Exx] // 58Exx ~ 58Fxx
3=|49Q05  Minimal surfaces [See also 53A10, 58E12]
3<|49Q10  Optimization of shapes other than minimal surfaces [See also 90C90] 
........../:< 73K40,
3=|49Q12  Sensitivity analysis
3=|49Q15  Geometric measure and integration theory, integral and
..........normal currents [See also 28A75, 32C30, 58A25, 58C35]
3=|49Q20  Variational problems in a geometric measure-theoretic setting
3-|49Q25  surface area 
3=|49Q99  None of the above, but in this section

2-|49Rxx  variational methods {For eigenvalues of operators, See 47A75} 
3-|49R05  variational approach to eigenvalues 
3-|49R10  Rayleigh-Ritz methods 
3-|49R15  Weinstein and Aronszajn methods, intermediate problems 
3-|49R20  linear operators in Hilbert spaces 
46|49R50  Variational methods for eigenvalues of operators [See also 47A75] 
3-|49R99  none of the above but in this section 

4=|49S05  Variational principles of physics 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|51-XX  Geometry {For algebraic geometry, see 14-XX} 
8=|51-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|51-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|51-02  Research exposition (monographs, survey articles)
8=|51-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|51-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|51-06  Proceedings, conferences, collections, etc.

2=|51Axx  Linear incidence geometry
3=|51A05  General theory and projective geometries
3=|51A10  Homomorphism, automorphism and dualities
3=|51A15  Structures with parallelism
3=|51A20  Configuration theorems
3=|51A25  Algebraization [See also 12Kxx, 20N05]
3=|51A30  Desarguesian and Pappian geometries
3=|51A35  Non-Desarguesian affine and projective planes
3=|51A40  Translation planes and spreads
3=|51A45  Incidence structures imbeddable into projective
..........geometries
3=|51A50  Polar geometry, symplectic spaces, orthogonal spaces
3=|51A99  None of the above, but in this section

2=|51Bxx  Nonlinear incidence geometry
3=|51B05  General theory
3=|51B10  M\"obius geometries
3=|51B15  Laguerre geometries
3=|51B20  Minkowski geometries
3=|51B25  Lie geometries
3=|51B99  None of the above, but in this section

4=|51C05  Ring geometry (Hjelmslev, Barbilian, etc.)

2=|51Dxx  Geometric closure systems
3=|51D05  Abstract (Maeda) geometries
3=|51D10  Abstract geometries with exchange axiom
3=|51D15  Abstract geometries with parallelism
3=|51D20  Combinatorial geometries [See also 05B25, 05B35]
3=|51D25  Lattices of subspaces [See also 05B35]
3=|51D30  Continuous geometries and related topics [See also 06Cxx]
3=|51D99  None of the above, but in this section

2=|51Exx  Finite geometry and special incidence structures
3=|51E05  General block designs [See also 05B05]
3=|51E10  Steiner systems
3=|51E12  Generalized quadrangles, generalized polygons
3=|51E14  Finite partial geometries (general), nets, partial spreads
3=|51E15  Affine and projective planes
3=|51E20  Combinatorial structures in finite projective spaces
..........[See also 05Bxx]
3=|51E21  Blocking sets, ovals, $k$-arcs
3=|51E22  Linear codes and caps in Galois spaces [See also 94B05]
3=|51E23  Spreads and packing problems
3=|51E24  Buildings and the geometry of diagrams
3=|51E25  Other finite nonlinear geometries
3=|51E26  Other finite linear geometries
3=|51E30  Other finite incidence structures [See also 05B30]
3=|51E99  None of the above, but in this section

2=|51Fxx  Metric geometry
3=|51F05  Absolute planes
3=|51F10  Absolute spaces
3=|51F15  Reflection groups, reflection geometries 
..........[See also 20H10, 20H15; for Coxeter groups, see 20F55]
3=|51F20  Congruence and orthogonality [See also 20H05]
3=|51F25  Orthogonal and unitary groups [See also 20H05]
3=|51F99  None of the above, but in this section

4=|51G05  Ordered geometries (ordered incidence structures, etc.)

2=|51Hxx  Topological geometry
3=|51H05  General theory
3=|51H10  Topological linear incidence structures
3=|51H15  Topological nonlinear incidence structures
3=|51H20  Topological geometries on manifolds [See also 57-XX]
3=|51H25  Geometries with differentiable structure [See also 53Cxx, 53C70]
3=|51H30  Geometries with algebraic manifold structure [See also 14-XX]
3=|51H99  None of the above, but in this section

2=|51Jxx  Incidence groups
3=|51J05  General theory
3=|51J10  Projective incidence groups
3=|51J15  Kinematic spaces
3=|51J20  Representation by near-fields and near-algebras 
..........[See also 12K05, 16Y30]
3=|51J99  None of the above, but in this section

2=|51Kxx  Distance geometry
3=|51K05  General theory
3=|51K10  Synthetic differential geometry
3=|51K99  None of the above, but in this section

2=|51Lxx  Geometric order structures [See also 53C75]
3=|51L05  Geometry of orders of nondifferentiable curves
3=|51L10  Directly differentiable curves
3=|51L15  $n$-vertex theorems via direct methods
3=|51L20  Geometry of orders of surfaces
3=|51L99  None of the above, but in this section

2=|51Mxx  Real and complex geometry
3=|51M04  Elementary problems in Euclidean geometries
3=|51M05  Euclidean geometries (general) and generalizations
3=|51M09  Elementary problems in hyperbolic and elliptic geometries
3=|51M10  Hyperbolic and elliptic geometries (general) and generalizations
3=|51M15  Geometric constructions
3=|51M16  Inequalities and extremum problems {For convex problems, see 52A40}
3=|51M20  Polyhedra and polytopes; regular figures, division of spaces 
..........[See also 51F15]
3=|51M25  Length, area and volume [See also 26B15]
3=|51M30  Line geometries and their generalizations [See also 53A25]
3=|51M35  Synthetic treatment of fundamental manifolds in
..........projective geometries (Grassmannians, Veronesians and their 
..........generalizations) [See also 14M15]
3=|51M99  None of the above, but in this section

2=|51Nxx  Analytic and descriptive geometry
3=|51N05  Descriptive geometry [See also 65D17, 68U07]
3=|51N10  Affine analytic geometry
3=|51N15  Projective analytic geometry
3=|51N20  Euclidean analytic geometry
3=|51N25  Analytic geometry with other transformation groups
3=|51N30  Geometry of classical groups [See also 20Gxx, 14L35]
3=|51N35  Questions of classical algebraic geometry [See also 14Nxx]
3=|51N99  None of the above, but in this section

4=|51P05  Geometry and physics (should also be assigned at least
..........one other classification number from Sections 70--86)

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|52-XX  Convex and discrete geometry 
8=|52-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|52-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|52-02  Research exposition (monographs, survey articles)
8=|52-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|52-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|52-06  Proceedings, conferences, collections, etc. 

2=|52Axx  General convexity
3=|52A01  Axiomatic and generalized convexity
3=|52A05  Convex sets without dimension restrictions
3=|52A07  Convex sets in topological vector spaces [See also 46A55]
3=|52A10  Convex sets in $2$ dimensions (including convex curves) 
..........[See also 53A04]
3=|52A15  Convex sets in $3$ dimensions (including convex
..........surfaces) [See also 53A05, 53C45]
3=|52A20  Convex sets in $n$ dimensions (including convex
..........hypersurfaces) [See also 53A07, 53C45]
3=|52A21  Finite-dimensional Banach spaces (including special
..........norms, zonoids, etc.) [See also 46Bxx]
3=|52A22  Random convex sets and integral geometry [See also 53C65, 60D05]
3=|52A27  Approximation by convex sets
3=|52A30  Variants of convex sets (star-shaped, ($m, n$)-convex, etc.)
3>|52A35  Helly-type theorems and geometric transversal theory 
........../:> and geometric transversal theory
3=|52A37  Other problems of combinatorial convexity
3=|52A38  Length, area, volume [See also 26B15, 28A75, 49Q20]
3=|52A39  Mixed volumes and related topics
3=|52A40  Inequalities and extremum problems
3=|52A41  Convex functions and convex programs [See also 26B25, 90C25]
3=|52A55  Spherical and hyperbolic convexity
3=|52A99  None of the above, but in this section

2=|52Bxx  Polytopes and polyhedra
3=|52B05  Combinatorial properties (number of faces, shortest paths, etc.) 
..........[See also 05Cxx]
3=|52B10  Three-dimensional polytopes
3=|52B11  $n$-dimensional polytopes
3=|52B12  Special polytopes (linear programming, centrally symmetric, etc.)
3=|52B15  Symmetry properties of polytopes
3~|52B20  Lattice polytopes (including relations with commutative algebra 
..........and algebraic geometry) [See also 06A11, 13F20, 13Hxx] 
..........// 06A11 ~ 06A08 
3+|52B22  Shellability 
3-|52B30  arrangements of hyperplanes 
3=|52B35  Gale and other diagrams
3>|52B40  Matroids (realizations in the context of convex polytopes, 
..........convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx] 
........../:> 52Cxx
3>|52B45  Dissections and valuations (Hilbert's third problem, etc.) 
..........[See also 68-XX] /:> [See also 68-XX]
3~|52B55  Computational aspects related to convexity {For
..........computational geometry and algorithms, see 
..........68Q25, 68U05; for numerical algorithms, see 65Yxx}
..........[See also 68Uxx] /:< 68Q20,  /:> [See also 68Uxx]
3=|52B60  Isoperimetric problems for polytopes
3=|52B70  Polyhedral manifolds
3=|52B99  None of the above, but in this section

2=|52Cxx  Discrete geometry
3=|52C05  Lattices and convex bodies in $2$ dimensions [See also
..........11H06, 11H31, 11P21]
3=|52C07  Lattices and convex bodies in $n$ dimensions [See also
..........11H06, 11H31, 11P21]
3=|52C10  Erd\"os problems and related topics of discrete geometry 
..........[See also 11Hxx]
3=|52C15  Packing and covering in $2$ dimensions [See also 05B40, 11H31]
3=|52C17  Packing and covering in $n$ dimensions [See also 05B40, 11H31]
3=|52C20  Tilings in $2$ dimensions [See also 05B45, 51M20]
3=|52C22  Tilings in $n$ dimensions [See also 05B45, 51M20]
3+|52C23  Quasicrystals, aperiodic tilings 
3=|52C25  Rigidity and flexibility of structures [See also 70B15]
3+|52C26  Circle packings and conformal approximations 
3+|52C30  Planar arrangements of lines and pseudolines [See also 32S22] 
3+|52C35  Arrangements of points, flats, hyperplanes 
3+|52C40  Oriented matroids 
3+|52C45  Combinatorial complexity of geometric structures [See also 68U05] 
3=|52C99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|53-XX  Differential geometry 
..........{For differential topology, see 57Rxx. For foundational
..........questions of differentiable manifolds, see 58Axx} 
8=|53-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|53-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|53-02  Research exposition (monographs, survey articles)
8=|53-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|53-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|53-06  Proceedings, conferences, collections, etc.

2=|53Axx  Classical differential geometry
3=|53A04  Curves in Euclidean space
3=|53A05  Surfaces in Euclidean space
3=|53A07  Higher-dimension and -codimension surfaces in Euclidean $n$-space
3=|53A10  Minimal surfaces, surfaces with prescribed mean
..........curvature [See also 49Q05, 49Q10, 53C42]
3=|53A15  Affine differential geometry
3=|53A17  Kinematics
3=|53A20  Projective differential geometry
3=|53A25  Differential line geometry
3=|53A30  Conformal differential geometry
3=|53A35  Non-Euclidean differential geometry
3=|53A40  Other special differential geometries
3=|53A45  Vector and tensor analysis
3-|53A50  spinor analysis 
3=|53A55  Differential invariants (local theory), geometric objects
3=|53A60  Geometry of webs [See also 14C21, 20N05]
3=|53A99  None of the above, but in this section

2=|53Bxx  Local differential geometry
3=|53B05  Linear and affine connections
3=|53B10  Projective connections
3=|53B15  Other connections
3=|53B20  Local Riemannian geometry
3=|53B21  Methods of Riemannian geometry
3=|53B25  Local submanifolds [See also 53C40]
3=|53B30  Lorentz metrics, indefinite metrics
3=|53B35  Hermitian and K\"ahlerian structures [See also 32Cxx]
3=|53B40  Finsler spaces and generalizations (areal metrics)
3=|53B50  Applications to physics
3=|53B99  None of the above, but in this section

2=|53Cxx  Global differential geometry [See also 51H25, 58-XX;
..........for related bundle theory, see 55Rxx, 57Rxx]
3=|53C05  Connections, general theory
3~|53C07  Special connections and metrics on vector bundles
..........(Hermite-Einstein-Yang-Mills) [See also 32Q20] // 32Q20 ~ 32L07
3=|53C10  $G$-structures
3=|53C12  Foliations (differential geometric aspects) [See also 57R30, 57R32]
3<|53C15  General geometric structures on manifolds (almost complex, 
..........almost product structures, etc.) // (almost complex, 
..........almost product structures, etc.) ~ (almost complex, 
..........contact, symplectic, almost product structures, etc.)
3+|53C17  Sub-Riemannian geometry 
3=|53C20  Global Riemannian geometry, including pinching 
..........[See also 31C12, 58B20]
3~|53C21  Methods of Riemannian geometry, including PDE methods;
..........curvature restrictions [See also 58J60] // 58J60 ~ 58G30
3=|53C22  Geodesics [See also 58E10]
3=|53C23  Global topological methods (\`a la Gromov) 
3+|53C24  Rigidity results 
3=|53C25  Special Riemannian manifolds (Einstein, Sasakian, etc.)
3+|53C26  Hyper-K\"ahler and quaternionic K\"ahler geometry, 
..........``special'' geometry 
3+|53C27  Spin and Spin$^c$ geometry 
3+|53C28  Twistor methods [See also 32L25]
3+|53C29  Issues of holonomy 
3=|53C30  Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]
3=|53C35  Symmetric spaces [See also 32M15, 57T15]
3+|53C38  Calibrations and calibrated geometries 
3=|53C40  Global submanifolds [See also 53B25]
3=|53C42  Immersions (minimal, prescribed curvature, tight, etc.) 
..........[See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
3+|53C43  Differential geometric aspects of harmonic maps [See also 58E20]
3=|53C45  Global surface theory (convex surfaces \`a la A.D. Aleksandrov)
3=|53C50  Lorentz manifolds, manifolds with indefinite metrics
3=|53C55  Hermitian and K\"ahlerian manifolds [See also 32Cxx]
3=|53C56  Other complex differential geometry [See also 32Cxx]
3=|53C60  Finsler spaces and generalizations (areal metrics) [See also 58B20]
3=|53C65  Integral geometry [See also 52A22, 60D05]; differential forms, 
..........currents, etc. [See mainly 58Axx] 
3=|53C70  Direct methods ($G$-spaces of Busemann, etc.)
3=|53C75  Geometric orders, order geometry [See also 51Lxx]
3=|53C80  Applications to physics
3=|53C99  None of the above, but in this section

2+|53Dxx  Symplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx]
3+|53D05  Symplectic manifolds, general
3+|53D10  Contact manifolds, general
3+|53D12  Lagrangian submanifolds; Maslov index
3+|53D15  Almost contact and almost symplectic manifolds
3+|53D17  Poisson manifolds
3+|53D20  Momentum maps; symplectic reduction
3+|53D22  Canonical transformations
3+|53D25  Geodesic flows
3+|53D30  Symplectic structures of moduli spaces
3+|53D35  Global theory of symplectic and contact manifolds [See also 57Rxx]
3+|53D40  Floer homology and cohomology, symplectic aspects
3+|53D45  Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]
3+|53D50  Geometric quantization
3+|53D55  Deformation quantization, star products
3+|53D99  None of the above, but in this section

4+|53Z05  Applications to physics 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|54-XX  General topology 
..........{For the topology of manifolds of all dimensions, see 57Nxx} 
8=|54-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|54-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|54-02  Research exposition (monographs, survey articles)
8=|54-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|54-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|54-06  Proceedings, conferences, collections, etc.

2=|54Axx  Generalities
3=|54A05  Topological spaces and generalizations (closure spaces, etc.)
3=|54A10  Several topologies on one set (change of topology,
..........comparison of topologies, lattices of topologies)
3=|54A15  Syntopogeneous structures
3=|54A20  Convergence in general topology (sequences, filters,
..........limits, convergence spaces, etc.)
3<|54A25  Cardinality properties (cardinal functions and
..........inequalities, discrete subsets) [See also 03Exx]
..........{For ultrafilters, see 54D80} /:< , 04A30
3=|54A35  Consistency and independence results [See also 03E35]
3~|54A40  Fuzzy topology [See also 03E72] // 03E72 ~ 04A72
3=|54A99  None of the above, but in this section

2=|54Bxx  Basic constructions
3=|54B05  Subspaces
3=|54B10  Product spaces
3=|54B15  Quotient spaces, decompositions
3=|54B17  Adjunction spaces and similar constructions
3=|54B20  Hyperspaces
3=|54B30  Categorical methods [See also 18B30]
3=|54B35  Spectra
3=|54B40  Presheaves and sheaves [See also 18F20]
3=|54B99  None of the above, but in this section

2=|54Cxx  Maps and general types of spaces defined by maps
3=|54C05  Continuous maps
3=|54C08  Weak and generalized continuity
3=|54C10  Special maps on topological spaces (open, closed, perfect, etc.)
3=|54C15  Retraction
3=|54C20  Extension of maps
3=|54C25  Embedding
3=|54C30  Real-valued functions [See also 26-XX]
3=|54C35  Function spaces [See also 46Exx, 58D15]
3=|54C40  Algebraic properties of function spaces [See also 46J10]
3=|54C45  $C$- and $C^*$-embedding
3=|54C50  Special sets defined by functions [See also 26A21]
3=|54C55  Absolute neighborhood extensor, absolute extensor, absolute 
..........neighborhood retract (ANR), absolute retract spaces 
..........(general properties) [See also 55M15]
3=|54C56  Shape theory [See also 55P55, 57N25]
3=|54C60  Set-valued maps [See also 26E25, 28B20, 47H04, 58C06]
3=|54C65  Selections [See also 28B20]
3=|54C70  Entropy
3=|54C99  None of the above, but in this section

2=|54Dxx  Fairly general properties
3=|54D05  Connected and locally connected spaces (general aspects)
3=|54D10  Lower separation axioms, ($T_0$--$T_3$, etc.)
3=|54D15  Higher separation axioms (completely regular, normal,
..........perfectly or collectionwise normal, etc.)
3=|54D20  Noncompact covering properties (paracompact, Lindel\"of, etc.) 
3=|54D25  ``$P$-minimal'' and ``$P$-closed'' spaces
3=|54D30  Compactness
3=|54D35  Extensions of spaces (compactifications,
..........supercompactifications, completions, etc.)
3=|54D40  Remainders
3=|54D45  Local compactness, $sigma$-compactness
3=|54D50  $k$-spaces
3=|54D55  Sequential spaces
3=|54D60  Realcompactness and realcompactification
3=|54D65  Separability
3=|54D70  Base properties
3=|54D80  Special constructions of spaces (spaces of ultrafilters, etc.)
3=|54D99  None of the above, but in this section

2=|54Exx  Spaces with richer structures
3=|54E05  Proximity structures and generalizations
3=|54E15  Uniform structures and generalizations
3=|54E17  Nearness spaces
3=|54E18  $p$-spaces, $M$-spaces, $sigma$-spaces, etc.
3=|54E20  Stratifiable spaces, cosmic spaces, etc.
3=|54E25  Semimetric spaces
3=|54E30  Moore spaces
3=|54E35  Metric spaces, metrizability
3=|54E40  Special maps on metric spaces
3=|54E45  Compact (locally compact) metric spaces
3=|54E50  Complete metric spaces
3=|54E52  Baire category, Baire spaces
3=|54E55  Bitopologies
3=|54E70  Probabilistic metric spaces
3=|54E99  None of the above, but in this section

2=|54Fxx  Special properties
3>|54F05  Linearly ordered topological spaces, partially ordered spaces, and partially ordered spaces
..........[See also 06B30, 06F30] /:> Linearly /:> , and partially ordered spaces
3=|54F15  Continua and generalizations
3=|54F35  Higher-dimensional local connectedness [See also 55Mxx, 55Nxx]
3=|54F45  Dimension theory [See also 55M10]
3=|54F50  Spaces of dimension $\leq 1$; curves, dendrites [See also 26A03]
3=|54F55  Unicoherence, multicoherence
3=|54F65  Topological characterizations of particular spaces
3=|54F99  None of the above, but in this section

2=|54Gxx  Peculiar spaces
3=|54G05  Extremally disconnected spaces, $F$-spaces, etc.
3=|54G10  $P$-spaces
3=|54G12  Scattered spaces
3=|54G15  Pathological spaces
3=|54G20  Counterexamples
3=|54G99  None of the above, but in this section

2=|54Hxx  Connections with other structures, applications
3<|54H05  Descriptive set theory (topological aspects of Borel,
..........analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05] /:< 04A15, 
3=|54H10  Topological representations of algebraic systems [See also 22-XX]
3=|54H11  Topological groups [See also 22A05]
3=|54H12  Topological lattices, etc. [See also 06B30, 06F30]
3=|54H13  Topological fields, rings, etc. [See also 12Jxx] 
..........{For algebraic aspects, see 13Jxx, 16W80}
3=|54H15  Transformation groups and semigroups [See also 20M20, 22-XX, 57Sxx]
3~|54H20  Topological dynamics [See also 28Dxx, 37Bxx] 
........../:< 34C35,  // 37Bxx ~ 58Fxx
3=|54H25  Fixed-point and coincidence theorems [See also 47H10, 55M20]
3=|54H99  None of the above, but in this section

4=|54J05  Nonstandard topology [See also 03H05]

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|55-XX  Algebraic topology 
8=|55-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|55-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|55-02  Research exposition (monographs, survey articles)
8=|55-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|55-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|55-06  Proceedings, conferences, collections, etc.

2=|55Mxx  Classical topics {For the topology of Euclidean spaces
..........and manifolds, see 57Nxx} 
3=|55M05  Duality
3=|55M10  Dimension theory [See also 54F45]
3=|55M15  Absolute neighborhood retracts [See also 54C55]
3=|55M20  Fixed points and coincidences [See also 54H25]
3=|55M25  Degree, winding number
3=|55M30  Ljusternik-Schnirelman (Lyusternik-Shnirelman) category of a space
3=|55M35  Finite groups of transformations (including Smith theory) 
..........[See also 57S17]
3=|55M99  None of the above, but in this section

2=|55Nxx  Homology and cohomology theories [See also 57Txx]
3=|55N05  Cech types
3=|55N07  Steenrod-Sitnikov homologies
3=|55N10  Singular theory
3=|55N15  $K$-theory [See also 19Lxx] {For algebraic $K$-theory,
..........see 18F25, 19-XX}
3=|55N20  Generalized (extraordinary) homology and cohomology theories
3=|55N22  Bordism and cobordism theories, formal group laws 
..........[See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90] 
3=|55N25  Homology with local coefficients, equivariant cohomology
3=|55N30  Sheaf cohomology [See also 18F20, 32C35, 32L10]
3=|55N33  Intersection homology and cohomology
3+|55N34  Elliptic cohomology 
3=|55N35  Other homology theories
3=|55N40  Axioms for homology theory and uniqueness theorems
3=|55N45  Products and intersections
3=|55N91  Equivariant homology and cohomology [See also 19L47]
3=|55N99  None of the above, but in this section

2=|55Pxx  Homotopy theory {For simple homotopy type, see 57Q10}
3=|55P05  Homotopy extension properties, cofibrations
3=|55P10  Homotopy equivalences
3=|55P15  Classification of homotopy type
3=|55P20  Eilenberg-Mac Lane spaces
3=|55P25  Spanier-Whitehead duality
3=|55P30  Eckmann-Hilton duality
3=|55P35  Loop spaces
3=|55P40  Suspensions
3=|55P42  Stable homotopy theory, spectra
3+|55P43  Spectra with additional structure ($E_\infty$, $A_\infty$, 
..........ring spectra, etc.) 
3=|55P45  ${H}$-spaces and duals
3=|55P47  Infinite loop spaces
3+|55P48  Loop space machines, operads [See also 18D50] 
3=|55P50  Category and cocategory, etc.
3=|55P55  Shape theory [See also 54C56, 55Q07]
3+|55P57  Proper homotopy theory 
3=|55P60  Localization and completion
3=|55P62  Rational homotopy theory
3=|55P65  Homotopy functors
3=|55P91  Equivariant homotopy theory [See also 19L47]
3+|55P92  Relations between equivariant and nonequivariant homotopy theory 
3=|55P99  None of the above, but in this section

2=|55Qxx  Homotopy groups
3=|55Q05  Homotopy groups, general; sets of homotopy classes
3=|55Q07  Shape groups
3=|55Q10  Stable homotopy groups
3=|55Q15  Whitehead products and generalizations
3=|55Q20  Homotopy groups of wedges, joins, and simple spaces
3=|55Q25  Hopf invariants 
3-|55Q30  homotopy groups of triads, $n$-ads 
3=|55Q35  Operations in homotopy groups 
3=|55Q40  Homotopy groups of spheres
3=|55Q45  Stable homotopy of spheres
3=|55Q50  $J$-morphism [See also 19L20]
3+|55Q51  $v_n$-periodicity 
3=|55Q52  Homotopy groups of special spaces
3=|55Q55  Cohomotopy groups
3=|55Q70  Homotopy groups of special types [See also 55N05, 55N07]
3=|55Q91  Equivariant homotopy groups [See also 19L47]
3=|55Q99  None of the above, but in this section

2=|55Rxx  Fiber spaces and bundles [See also 18F15, 32Lxx, 46M20, 
..........57R20, 57R22, 57R25}
3=|55R05  Fiber spaces
3=|55R10  Fiber bundles
3=|55R12  Transfer
3=|55R15  Classification
3=|55R20  Spectral sequences and homology of fiber spaces [See also 55Txx]
3<|55R25  Sphere bundles and vector bundles 
.......... // vector bundles ~ vector space bundles
3=|55R35  Classifying spaces of groups and ${H}$-spaces
3+|55R37  Maps between classifying spaces 
3=|55R40  Homology of classifying spaces, characteristic classes
..........[See also 57Txx, 57R20]
3=|55R45  Homology and homotopy of $BO$ and $BU$; Bott periodicity
3=|55R50  Stable classes of vector space bundles, $K$-theory
..........[See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19-XX}
3=|55R55  Fiberings with singularities
3=|55R60  Microbundles and block bundles [See also 57N55, 57Q50]
3=|55R65  Generalizations of fiber spaces and bundles
3+|55R70  Fibrewise topology 
3+|55R80  Discriminantal varieties, configuration spaces 
3=|55R91  Equivariant fiber spaces and bundles [See also 19L47]
3=|55R99  None of the above, but in this section

2=|55Sxx  Operations and obstructions
3=|55S05  Primary cohomology operations
3=|55S10  Steenrod algebra
3=|55S12  Dyer-Lashof operations
3=|55S15  Symmetric products, cyclic products
3=|55S20  Secondary and higher cohomology operations
3=|55S25  $K$-theory operations and generalized cohomology
..........operations [See also 19D55, 19Lxx]
3=|55S30  Massey products
3=|55S35  Obstruction theory
3=|55S36  Extension and compression of mappings
3=|55S37  Classification of mappings
3=|55S40  Sectioning fiber spaces and bundles
3=|55S45  Postnikov systems, $k$-invariants
3=|55S91  Equivariant operations and obstructions [See also 19L47]
3=|55S99  None of the above, but in this section

2=|55Txx  Spectral sequences [See also 18G40, 55R20]
3=|55T05  General
3=|55T10  Serre spectral sequences
3=|55T15  Adams spectral sequences
3=|55T20  Eilenberg-Moore spectral sequences [See also 57T35]
3=|55T25  Generalized cohomology
3=|55T99  None of the above, but in this section

2=|55Uxx  Applied homological algebra and category theory [See also 18Gxx]
3=|55U05  Abstract complexes
3=|55U10  Semisimplicial complexes
3=|55U15  Chain complexes
3=|55U20  Universal coefficient theorems, Bockstein operator
3=|55U25  Homology of a product, K\"unneth formula
3=|55U30  Duality
3>|55U35  Abstract and axiomatic homotopy theory /:> and axiomatic 
3>|55U40  Topological categories, foundations of homotopy theory 
........../:> , foundations of homotopy theory
3=|55U99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1~|57-XX  Manifolds and cell complexes 
..........{For complex manifolds, see 32Qxx} // 32Qxx ~ 32C10 
8=|57-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|57-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|57-02  Research exposition (monographs, survey articles)
8=|57-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|57-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|57-06  Proceedings, conferences, collections, etc.

2=|57Mxx  Low-dimensional topology
3=|57M05  Fundamental group, presentations, free differential calculus
3=|57M07  Topological methods in group theory
3=|57M10  Covering spaces
3=|57M12  Special coverings, e.g. branched
3=|57M15  Relations with graph theory [See also 05Cxx]
3=|57M20  Two-dimensional complexes
3=|57M25  Knots and links in $S^3$ {For higher dimensions, see 57Q45}
3+|57M27  Invariants of knots and 3-manifolds 
3=|57M30  Wild knots and surfaces, etc., wild embeddings
3=|57M35  Dehn's lemma, sphere theorem, loop theorem, asphericity
3=|57M40  Characterizations of $E^3$ and $S^3$ (Poincar\'e conjecture) 
..........[See also 57N12]
3=|57M50  Geometric structures on low-dimensional manifolds
3=|57M60  Group actions in low dimensions
3=|57M99  None of the above, but in this section

2=|57Nxx  Topological manifolds
3=|57N05  Topology of $E^2$, $2$-manifolds
3=|57N10  Topology of general $3$-manifolds [See also 57Mxx]
3=|57N12  Topology of $E^3$ and $S^3$ [See also 57M40]
3=|57N13  Topology of $E^4$, $4$-manifolds [See also 14Jxx, 32Jxx]
3=|57N15  Topology of $E^n$, $n$-manifolds ($4 < n < \infty$)
3+|57N16  Geometric structures on manifolds [See also 57M50] 
3=|57N17  Topology of topological vector spaces
3=|57N20  Topology of infinite-dimensional manifolds [See also 58Bxx]
3=|57N25  Shapes [See also 54C56, 55P55, 55Q07]
3=|57N30  Engulfing
3=|57N35  Embeddings and immersions
3=|57N37  Isotopy and pseudo-isotopy
3=|57N40  Neighborhoods of submanifolds
3=|57N45  Flatness and tameness
3=|57N50  $S^{n-1}\subset E^n$, Schoenflies problem
3=|57N55  Microbundles and block bundles [See also 55R60, 57Q50]
3=|57N60  Cellularity
3=|57N65  Algebraic topology of manifolds
3=|57N70  Cobordism and concordance
3=|57N75  General position and transversality
3=|57N80  Stratifications
3=|57N99  None of the above, but in this section

2=|57Pxx  Generalized manifolds [See also 18F15]
3=|57P05  Local properties of generalized manifolds
3=|57P10  Poincar\'e duality spaces
3=|57P99  None of the above, but in this section

2=|57Qxx  PL-topology
3=|57Q05  General topology of complexes
3=|57Q10  Simple homotopy type, Whitehead torsion, Reidemeister-Franz 
..........torsion, etc. [See also 19B28]
3=|57Q12  Wall finiteness obstruction for CW-complexes
3=|57Q15  Triangulating manifolds
3=|57Q20  Cobordism
3=|57Q25  Comparison of PL-structures: classification, Hauptvermutung
3=|57Q30  Engulfing
3=|57Q35  Embeddings and immersions
3=|57Q37  Isotopy
3=|57Q40  Regular neighborhoods
3=|57Q45  Knots and links (in high dimensions) 
..........{For the low-dimensional case, see 57M25}
3=|57Q50  Microbundles and block bundles [See also 55R60, 57N55]
3=|57Q55  Approximations
3=|57Q60  Cobordism and concordance
3=|57Q65  General position and transversality
3=|57Q91  Equivariant PL-topology
3=|57Q99  None of the above, but in this section

2=|57Rxx  Differential topology {For foundational questions of
..........differentiable manifolds, see 58Axx; for infinite-dimensional
..........manifolds, see 58Bxx}
3=|57R05  Triangulating
3=|57R10  Smoothing
3=|57R12  Smooth approximations
3=|57R15  Specialized structures on manifolds (spin manifolds, 
..........framed manifolds, etc.)
3+|57R17  Symplectic and contact topology 
3=|57R19  Algebraic topology on manifolds
3=|57R20  Characteristic classes and numbers
3=|57R22  Topology of vector bundles and fiber bundles [See also 55Rxx]
3=|57R25  Vector fields, frame fields
3~|57R27  Controllability of vector fields on $C^\infty$ and real-analytic 
..........manifolds [See also 49Qxx, 37C10, 93B05] // 37C10 ~ 58F40
3=|57R30  Foliations; geometric theory
3=|57R32  Classifying spaces for foliations; Gelfand-Fuks
..........cohomology [See also 58H10]
3=|57R35  Differentiable mappings
3=|57R40  Embeddings
3=|57R42  Immersions
3=|57R45  Singularities of differentiable mappings
3=|57R50  Diffeomorphisms
3=|57R52  Isotopy
3=|57R55  Differentiable structures
3+|57R56  Topological quantum field theories 
3>|57R57  Applications of global analysis to structures on manifolds, 
..........Donaldson and Seiberg-Witten invariants [See also 58-XX] 
........../:> , Donaldson and Seiberg-Witten invariants 
3+|57R58  Floer homology 
3=|57R60  Homotopy spheres, Poincar\'e conjecture
3=|57R65  Surgery and handlebodies
3=|57R67  Surgery obstructions, Wall groups [See also 19J25]
3=|57R70  Critical points and critical submanifolds
3=|57R75  O- and SO-cobordism
3=|57R77  Complex cobordism (U- and SU-cobordism) [See also 55N22]
3=|57R80  $h$- and $s$-cobordism
3=|57R85  Equivariant cobordism
3=|57R90  Other types of cobordism [See also 55N22]
3=|57R91  Equivariant algebraic topology of manifolds
3=|57R95  Realizing cycles by submanifolds
3=|57R99  None of the above, but in this section

2=|57Sxx  Topological transformation groups [See also 20F34, 22-XX, 
..........54H15, 58D05]
3=|57S05  Topological properties of groups of homeomorphisms or diffeomorphisms
3=|57S10  Compact groups of homeomorphisms
3=|57S15  Compact Lie groups of differentiable transformations
3=|57S17  Finite transformation groups
3=|57S20  Noncompact Lie groups of transformations
3=|57S25  Groups acting on specific manifolds
3=|57S30  Discontinuous groups of transformations
3=|57S99  None of the above, but in this section

2=|57Txx  Homology and homotopy of topological groups and related structures
3=|57T05  Hopf algebras [See also 16W30]
3=|57T10  Homology and cohomology of Lie groups
3=|57T15  Homology and cohomology of homogeneous spaces of Lie groups
3=|57T20  Homotopy groups of topological groups and homogeneous spaces
3=|57T25  Homology and cohomology of ${H}$-spaces
3=|57T30  Bar and cobar constructions [See also 18G55, 55Uxx]
3=|57T35  Applications of Eilenberg-Moore spectral sequences
..........[See also 55R20, 55T20]
3=|57T99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|58-XX  Global analysis, analysis on manifolds 
..........[See also 32Cxx, 32Fxx, 46-XX, 47Hxx, 53Cxx] 
..........{For geometric integration theory, see 49Q15} 
8=|58-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|58-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|58-02  Research exposition (monographs, survey articles)
8=|58-03  Historical (must also be assigned at least one classification 
..........number from Section 01)
8=|58-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|58-06  Proceedings, conferences, collections, etc.

2=|58Axx  General theory of differentiable manifolds
3=|58A03  Topos-theoretic approach to differentiable manifolds
3=|58A05  Differentiable manifolds, foundations
3=|58A07  Real-analytic and Nash manifolds [See also 14P20, 32C07]
3=|58A10  Differential forms
3=|58A12  de Rham theory [See also 14Fxx]
3=|58A14  Hodge theory [See also 14C30, 14Fxx, 32J25, 32S35]
3=|58A15  Exterior differential systems (Cartan theory)
3=|58A17  Pfaffian systems
3=|58A20  Jets
3=|58A25  Currents [See also 32C30, 53C65]
3=|58A30  Vector distributions (subbundles of the tangent bundles)
3+|58A32  Natural bundles 
3<|58A35  Stratified sets [See also 32S60] /:< , 58C27
3=|58A40  Differential spaces
3=|58A50  Supermanifolds and graded manifolds [See also 14A22, 32C11]
3=|58A99  None of the above, but in this section

2=|58Bxx  Infinite-dimensional manifolds
3=|58B05  Homotopy and topological questions
3=|58B10  Differentiability questions
3=|58B12  Questions of holomorphy [See also 32-XX, 46G20]
3=|58B15  Fredholm structures [See also 47A53]
3=|58B20  Riemannian, Finsler and other geometric structures
..........[See also 53C20, 53C60]
3=|58B25  Group structures and generalizations on
..........infinite-dimensional manifolds [See also 22E65, 58D05]
3-|58B30  noncommutative differential geometry and topology [See also 46L30, 
..........46L87, 46L89]
3+|58B32  Geometry of quantum groups 
3+|58B34  Noncommutative geometry (\`a la Connes) 
3=|58B99  None of the above, but in this section

2>|58Cxx  Calculus on manifolds; nonlinear operators [See also 46Txx, 47Hxx] /:> 46Txx, 
3=|58C05  Real-valued functions
3=|58C06  Set valued and function-space valued mappings [See also 47H04, 54C60]
3=|58C07  Continuity properties of mappings
3=|58C10  Holomorphic maps [See also 32-XX]
3=|58C15  Implicit function theorems; global Newton methods
3=|58C20  Differentiation theory (Gateaux, Fr\'echet, etc.) 
..........[See also 26Exx, 46G05]
3=|58C25  Differentiable maps
3-|58C27  singularities of differentiable maps 
..........[See also 14B05, 14E15, 32Sxx] 
3-|58C28  catastrophes [See also 57R70, 58Exx] 
3=|58C30  Fixed point theorems on manifolds [See also 47H10]
3=|58C35  Integration on manifolds; measures on manifolds [See also 28Cxx]
3~|58C40  Spectral theory; eigenvalue problems [See also 47J10, 58E07] // 47J10 ~ 47H12
3=|58C50  Analysis on supermanifolds or graded manifolds
3=|58C99  None of the above, but in this section

2=|58Dxx  Spaces and manifolds of mappings (including nonlinear
..........versions of 46Exx)
3=|58D05  Groups of diffeomorphisms and homeomorphisms as manifolds 
..........[See also 22E65, 57S05]
3<|58D07  Groups and semigroups of nonlinear operators [See also
..........17B65, 47H20] /:< 47D03, 47D06, 
3=|58D10  Spaces of imbeddings and immersions
3>|58D15  Manifolds of mappings [See also 46T10, 54C35] /:> 46T10, 
3=|58D17  Manifolds of metrics (esp. Riemannian)
3=|58D19  Group actions and symmetry properties
3>|58D20  Measures (Gaussian, cylindrical, etc.) on manifolds of maps 
..........[See also 28Cxx, 46T12] /:> , 46T12
3~|58D25  Equations in function spaces; evolution equations 
..........[See also 34Gxx, 35K90, 35L90, 35R15, 37Lxx, 47Jxx]
.......... // 35K90, 35L90, 35R15, 37Lxx, 47Jxx ~ 35K22, 35R15, 47H15]
3=|58D27  Moduli problems for differential geometric structures
3=|58D29  Moduli problems for topological structures
3=|58D30  Applications (in quantum mechanics (Feynman path
..........integrals), relativity, fluid dynamics, etc.)
3=|58D99  None of the above, but in this section

2=|58Exx  Variational problems in infinite-dimensional spaces
3=|58E05  Abstract critical point theory (Morse theory,
..........Ljusternik-Schnirelman (Lyusternik-Shnirel'man) theory, etc.)
3=|58E07  Abstract bifurcation theory
3=|58E09  Group-invariant bifurcation theory
3=|58E10  Applications to the theory of geodesics (problems in one 
..........independent variable)
3=|58E11  Critical metrics
3>|58E12  Applications to minimal surfaces (problems in two
..........independent variables) [See also 49Q05] /:> [See also 49Q05]
3=|58E15  Application to extremal problems in several variables;
..........Yang-Mills functionals [See also 81T13], etc.
3>|58E17  Pareto optimality, etc., applications to economics [See also 90C29] /:> [See also 90C29]
3>|58E20  Harmonic maps [See also 53C43], etc. /:> [See also 53C43], etc.
3~|58E25  Applications to control theory  [See also 49-XX, 93-XX]
.......... // [See also 49-XX, 93-XX] ~ (optimal and nonoptimal)
3=|58E30  Variational principles
3=|58E35  Variational inequalities (global problems)
3=|58E40  Group actions
3=|58E50  Applications
3=|58E99  None of the above, but in this section

2-|58Fxx  Ordinary differential equations on manifolds; dynamical systems 
..........[See also 28D10, 34Cxx, 54H20] 
3-|58F03  one-dimensional dynamics, general symbolic dynamics 
..........[See also 26A18] 
3-|58F05  hamiltonian and Lagrangian systems; symplectic geometry 
..........[See also 70Hxx, 81S10] 
3-|58F06  geometric quantization (applications of representation theory) 
..........[See also 22E45, 81S10] 
3-|58F07  completely integrable systems (including systems with an infinite 
..........number of degrees of freedom) 
3-|58F08  point-mapping properties, iterations, completeness; dynamics of 
..........cellular automata [See also 26A18, 30D05] 
3-|58F09  Morse-Smale systems 
3-|58F10  stability theory 
3-|58F11  ergodic theory; invariant measures [See also 28Dxx] 
3-|58F12  structure of attractors (and repellors) 
3-|58F13  strange attractors; chaos and other pathologies [See also 70K50] 
3-|58F14  bifurcation theory and singularities 
3-|58F15  hyperbolic structures (expanding maps, Anosov systems, etc.) 
3-|58F17  geodesic and horocycle flows 
3-|58F18  relations with foliations 
3-|58F19  eigenvalue and spectral problems 
3-|58F20  periodic points and zeta functions 
3-|58F21  limit cycles, singular points, etc. 
3-|58F22  periodic solutions 
3-|58F23  holomorphic dynamics [See also 30D05] 
3-|58F25  flows 
3-|58F27  quasiperiodic flows 
3-|58F30  perturbations 
3-|58F32  functional-differential equations on manifolds 
3-|58F35  invariance properties 
3-|58F36  normal forms 
3-|58F37  correspondences and other transformation methods 
..........(e.g. Lie-B\"acklund) 
3-|58F39  dynamical systems treatment of PDE (should be assigned another 
..........number from 58F) [See also 35B32, 35K57] 
3-|58F40  applications 
3-|58F99  none of the above but in this section 

2-|58Gxx  Partial differential equations on manifolds; differential
..........operators [See also 35-XX] 
3-|58G03  elliptic equations on manifolds, general theory 
3-|58G05  differential complexes [See also 35Nxx]; elliptic complexes 
3-|58G07  relations with hyperfunctions 
3-|58G10  index theory and related fixed point theorems 
..........[See also 19K56, 46L80] 
3-|58G11  heat and other parabolic equation methods 
3-|58G12  exotic index theories [See also 19K56, 46L05, 46L10, 46L80, 46M20] 
3-|58G15  pseudodifferential and Fourier integral operators on manifolds 
..........[See also 35Sxx] 
3-|58G16  hyperbolic equations 
3-|58G17  propagation of singularities; initial value problems 
3-|58G18  perturbations; asymptotics 
3-|58G20  boundary value problems on manifolds 
3-|58G25  spectral problems; spectral geometry; scattering theory 
..........[See also 35Pxx] 
3-|58G26  determinants and determinant bundles 
3-|58G28  bifurcations [See also 35B32]
3-|58G30  relations with special manifold structures (Riemannian, 
..........Finsler, etc.) 
3-|58G32  diffusion processes and stochastic analysis on manifolds 
3-|58G35  invariance and symmetry properties [See also 35A30] 
3-|58G37  correspondences and other transformation methods 
..........(e.g. Lie-B\"acklund) [See also 35A22] 
3-|58G40  applications 
3-|58G99  none of the above but in this section 

2=|58Hxx  Pseudogroups, differentiable groupoids and general 
..........structures on manifolds
3=|58H05  Pseudogroups and differentiable groupoids [See also 22A22, 22E65]
3=|58H10  Cohomology of classifying spaces for pseudogroup
..........structures (Spencer, Gelfand-Fuks, etc.) [See also 57R32]
3~|58H15  Deformations of structures 
..........[See also 32Gxx, 58J10] // 58J10 ~ 58G05
3=|58H99  None of the above, but in this section

2+|58Jxx  Partial Differential equations on manifolds [See also 35-XX] 
3+|58J05  Elliptic equations on manifolds, general theory [See also 35-XX]
3+|58J10  Differential complexes [See also 35Nxx]; elliptic complexes
3+|58J15  Relations with hyperfunctions
3+|58J20  Index theory and related fixed point theorems [See also 19K56, 46L80]
3+|58J22  Exotic index theories [See also 19K56, 46L05, 46L10, 46L80, 46M20]
3+|58J26  Elliptic genera
3+|58J28  Eta-invariants, Chern-Simons invariants
3+|58J30  Spectral flows
3+|58J32  Boundary value problems on manifolds
3+|58J35  Heat and other parabolic equation methods
3+|58J37  Perturbations; asymptotics
3+|58J40  Pseudodifferential and Fourier integral operators on manifolds 
..........[See also 35Sxx]
3+|58J42  Noncommutative global analysis, noncommutative residues
3+|58J45  Hyperbolic equations [See also 35Lxx]
3+|58J47  Propagation of singularities; initial value problems
3+|58J50  Spectral problems; spectral geometry; scattering theory 
..........[See also 35Pxx]
3+|58J52  Determinants and determinant bundles, analytic torsion
3+|58J53  Isospectrality
3+|58J55  Bifurcation [See also 35B32]
3+|58J60  Relations with special manifold structures
..........(Riemannian, Finsler, etc.)
3+|58J65  Diffusion processes and stochastic analysis on manifolds 
..........[See also 35R60, 60H10, 60J60]
3+|58J70  Invariance and symmetry properties [See also 35A30]
3+|58J72  Correspondences and other transformation methods (e.g.
..........Lie-B\"acklund) [See also 35A22]
3+|58J90  Applications
3+|58J99  None of the above, but in this section

2+|58Kxx  Theory of singularities and catastrophe theory [See also 37-XX] 
3+|58K05  Critical points of functions and mappings
3+|58K10  Monodromy
3+|58K15  Topological properties of mappings
3+|58K20  Algebraic and analytic properties of mappings
3+|58K25  Stability
3+|58K30  Global theory
3+|58K35  Catastrophe theory
3+|58K40  Classification; finite determinacy of map germs
3+|58K45  Singularities of vector fields, topological aspects
3+|58K50  Normal forms
3+|58K55  Asymptotic behavior
3+|58K60  Deformation of singularities
3+|58K65  Topological invariants
3+|58K70  Symmetries, equivariance
3+|58K99  None of the above, but in this section

4=|58Z05  Applications to physics

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1~|60-XX  Probability theory and stochastic processes 
..........{For additional applications, see 11Kxx, 62-XX, 90-XX,
..........92-XX, 93-XX, 94-XX} // 94-XX} ~ . For numerical results, see 65U05} 
8=|60-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|60-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|60-02  Research exposition (monographs, survey articles)
8=|60-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|60-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|60-06  Proceedings, conferences, collections, etc.
8+|60-08  Computational methods (not classified at a more specific level) 
..........[See also 65C50] 

2=|60Axx  Foundations of probability theory
3=|60A05  Axioms; other general questions
3=|60A10  Probabilistic measure theory {For ergodic theory, see 28Dxx and 60Fxx}
3=|60A99  None of the above, but in this section

2=|60Bxx  Probability theory on algebraic and topological structures
3=|60B05  Probability measures on topological spaces
3=|60B10  Convergence of probability measures
3=|60B11  Probability theory on linear topological spaces [See also 28C20]
3=|60B12  Limit theorems for vector-valued random variables
..........(infinite-dimensional case)
3=|60B15  Probability measures on groups, Fourier transforms, factorization
3=|60B99  None of the above, but in this section

4=|60C05  Combinatorial probability

4=|60D05  Geometric probability, stochastic geometry, random sets 
..........[See also 52A22, 53C65]

2=|60Exx  Distribution theory [See also 62Exx, 62Hxx]
3=|60E05  Distributions: general theory
3=|60E07  Infinitely divisible distributions; stable distributions
3=|60E10  Characteristic functions; other transforms
3~|60E15  Inequalities; stochastic orderings /:< (Chebyshev, Kolmogorov, etc.) 
........../:> ; stochastic orderings
3=|60E99  None of the above, but in this section

2=|60Fxx  Limit theorems [See also 28Dxx, 60B12]
3=|60F05  Central limit and other weak theorems
3=|60F10  Large deviations
3=|60F15  Strong theorems
3=|60F17  Functional limit theorems; invariance principles
3=|60F20  Zero-one laws
3=|60F25  $L^p$-limit theorems
3=|60F99  None of the above, but in this section

2=|60Gxx  Stochastic processes
3=|60G05  Foundations of stochastic processes
3=|60G07  General theory of processes
3=|60G09  Exchangeability
3=|60G10  Stationary processes
3=|60G12  General second-order processes
3=|60G15  Gaussian processes
3=|60G17  Sample path properties
3=|60G18  Self-similar processes
3=|60G20  Generalized stochastic processes
3=|60G25  Prediction theory [See also 62M20]
3=|60G30  Continuity and singularity of induced measures
3=|60G35  Applications (signal detection, filtering, etc.) 
..........[See also 62M20, 93E10, 93E11, 94Axx]
3~|60G40  Stopping times; optimal stopping problems; gambling theory 
..........[See also 62L15, 91A60] // 91A60 ~ 90D60
3=|60G42  Martingales with discrete parameter
3=|60G44  Martingales with continuous parameter
3=|60G46  Martingales and classical analysis
3=|60G48  Generalizations of martingales
3>|60G50  Sums of independent random variables; random walks /:> ; random walks
3+|60G51  Processes with independent increments 
3+|60G52  Stable processes 
3=|60G55  Point processes
3=|60G57  Random measures
3=|60G60  Random fields
3=|60G70  Extreme value theory; extremal processes
3=|60G99  None of the above, but in this section

2~|60Hxx  Stochastic analysis [See also 58J65] // 58J65 ~ 58G32
3=|60H05  Stochastic integrals
3=|60H07  Stochastic calculus of variations and the Malliavin calculus
3=|60H10  Stochastic ordinary differential equations [See also 34F05]
3=|60H15  Stochastic partial differential equations [See also 35R60]
3=|60H20  Stochastic integral equations
3=|60H25  Random operators and equations [See also 47B80]
3=|60H30  Applications of stochastic analysis (to PDE, etc.)
3+|60H35  Computational methods for stochastic equations [See also 65C30] 
3+|60H40  White noise theory 
3=|60H99  None of the above, but in this section

2=|60Jxx  Markov processes
3=|60J05  Markov processes with discrete parameter
3=|60J10  Markov chains with discrete parameter
3-|60J15  random walks 
3~|60J20  Applications of discrete Markov processes (social
..........mobility, learning theory, industrial processes, etc.) 
..........[See also 90B30, 91D10, 91D35, 91E40] 
..........// 91D10, 91D35, 91E40 ~ 92H10, 92H35, 92J40
3+|60J22  Computational methods in Markov chains [See also 65C40] 
3=|60J25  Markov processes with continuous parameter
3=|60J27  Markov chains with continuous parameter
3-|60J30  processes with independent increments 
3=|60J35  Transition functions, generators and resolvents 
..........[See also 47D03, 47D07]
3=|60J40  Right processes
3=|60J45  Probabilistic potential theory [See also 31Cxx, 31D05]
3=|60J50  Boundary theory
3=|60J55  Local time and additive functionals
3=|60J57  Multiplicative functionals
3~|60J60  Diffusion processes [See also 58J65] // 58J65 ~ 58G32
3~|60J65  Brownian motion [See also 58J65] // 58J65 ~ 58G32
3=|60J70  Applications of diffusion theory (population genetics,
..........absorption problems, etc.) [See also 92Dxx]
3=|60J75  Jump processes
3=|60J80  Branching processes (Galton-Watson, birth-and-death, etc.)
3=|60J85  Applications of branching processes [See also 92Dxx]
3=|60J99  None of the above but in this section 

2=|60Kxx  Special processes
3=|60K05  Renewal theory
3=|60K10  Applications (reliability, demand theory, etc.)
3=|60K15  Markov renewal processes, semi-Markov processes
3=|60K20  Applications of Markov renewal processes (reliability, queueing 
..........networks, etc.) [See also 90Bxx]
3=|60K25  Queueing theory [See also 68M20, 90B22]
3=|60K30  Applications (congestion, allocation, storage, traffic, etc.) 
..........[See also 90Bxx]
3=|60K35  Interacting random processes; statistical mechanics
..........type models; percolation theory [See also 82B43, 82C43]
3+|60K37  Processes in random environments 
3=|60K40  Other physical applications of random processes
3=|60K99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1<|62-XX  Statistics /:< {For numerical methods, see 65U05} 
8=|62-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|62-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|62-02  Research exposition (monographs, survey articles)
8=|62-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|62-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|62-06  Proceedings, conferences, collections, etc.
8=|62-07  Data analysis
8=|62-09  Graphical methods

2-|62Axx  foundations 
4+|62A01  Foundational and philosophical topics 
3-|62A05  invariance and group considerations 
3-|62A10  the likelihood approach 
3-|62A15  the Bayesian approach 
3-|62A20  the classical approach 
3-|62A25  the structural approach 
3-|62A30  the fiducial approach 
3-|62A99  none of the above but in this section 

2=|62Bxx  Sufficiency and information
3=|62B05  Sufficient statistics and fields
3~|62B10  Information-theoretic topics [See also 94A17] 
..........// Information-theoretic topics ~ Statistical information theory
3=|62B15  Theory of statistical experiments
3-|62B20  measure-theoretic results, etc. 
3=|62B99  None of the above, but in this section

2~|62Cxx  Decision theory [See also 90B50, 91B05; for game theory, see 91A35] // 91B05 ~ 90A05 
.......... // 91A35 ~ 90D35
3=|62C05  General considerations
3=|62C07  Complete class results
3=|62C10  Bayesian problems; characterization of Bayes procedures
3=|62C12  Empirical decision procedures; empirical Bayes procedures
3=|62C15  Admissibility
3=|62C20  Minimax procedures
3=|62C25  Compound decision problems
3=|62C99  None of the above, but in this section

4=|62D05  Sampling theory, sample surveys

2=|62Exx  Distribution theory [See also 60Exx]
3=|62E10  Characterization and structure theory
3=|62E15  Exact distribution theory
3=|62E17  Approximations to distributions (nonasymptotic)
3=|62E20  Asymptotic distribution theory
3-|62E25  monte Carlo studies 
3-|62E30  formal computational methods (polykays, etc.) 
3=|62E99  None of the above, but in this section

2=|62Fxx  Parametric inference
3=|62F03  Hypothesis testing
3-|62F04  small sample properties of tests 
3=|62F05  Asymptotic properties of tests
3=|62F07  Ranking and selection
3=|62F10  Point estimation
3-|62F11  small sample properties of estimators 
3=|62F12  Asymptotic properties of estimators
3=|62F15  Bayesian inference
3=|62F25  Tolerance and confidence regions
3=|62F30  Inference under constraints
3=|62F35  Robustness and adaptive procedures
3+|62F40  Bootstrap, jackknife and other resampling methods 
3=|62F99  None of the above, but in this section

2=|62Gxx  Nonparametric inference
3=|62G05  Estimation
3~|62G07  Density estimation /~ Curve estimation (nonparametric regression, 
..........density estimation, etc.)
3+|62G08  Nonparametric regression 
3=|62G09  Resampling methods
3=|62G10  Hypothesis testing
3=|62G15  Tolerance and confidence regions
3=|62G20  Asymptotic properties
3=|62G30  Order statistics; empirical distribution functions
3+|62G32  Statistics of extreme values; tail inference 
3=|62G35  Robustness
3=|62G99  None of the above, but in this section

2=|62Hxx  Multivariate analysis [See also 60Exx]
3=|62H05  Characterization and structure theory
3=|62H10  Distribution of statistics
3=|62H11  Directional data; spatial statistics
3=|62H12  Estimation
3=|62H15  Hypothesis testing
3>|62H17  Contingency tables /:> tables
3=|62H20  Measures of association (correlation, canonical correlation, etc.)
3=|62H25  Factor analysis and principal components;
..........correspondence analysis
3=|62H30  Classification and discrimination; cluster analysis [See also 68T10]
3+|62H35  Image analysis 
3-|62H40  projection pursuit 
3=|62H99  None of the above, but in this section

2=|62Jxx  Linear inference, regression
3=|62J02  General nonlinear regression
3=|62J05  Linear regression
3~|62J07  Ridge regression; shrinkage estimators 
..........// shrinkage estimators ~ James-Stein estimators
3=|62J10  Analysis of variance and covariance
3=|62J12  Generalized linear models
3=|62J15  Paired and multiple comparisons
3=|62J20  Diagnostics
3=|62J99  None of the above, but in this section

2~|62Kxx  Design of experiments [See also 05Bxx]
..........// Design of experiment ~ Experimental design 
3=|62K05  Optimal designs
3=|62K10  Block designs
3=|62K15  Factorial designs
3+|62K20  Response surface designs 
3+|62K25  Robust parameter designs 
3=|62K99  None of the above, but in this section

2=|62Lxx  Sequential methods
3=|62L05  Sequential design
3=|62L10  Sequential analysis
3=|62L12  Sequential estimation
3~|62L15  Optimal stopping [See also 60G40, 91A60] // 91A60 ~ 90D60
3=|62L20  Stochastic approximation
3=|62L99  None of the above, but in this section

2=|62Mxx  Inference from stochastic processes
3=|62M02  Markov processes: hypothesis testing
3=|62M05  Markov processes: estimation
3=|62M07  Non-Markovian processes: hypothesis testing
3=|62M09  Non-Markovian processes: estimation
3~|62M10  Time series, auto-correlation, regression, etc. [See also 91B20] // 91B20 ~ 90A20
3=|62M15  Spectral analysis
3=|62M20  Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]
3=|62M30  Spatial processes
3>|62M40  Random fields; image analysis /:> ; image analysis
3+|62M45  Neural nets and related approaches 
3=|62M99  None of the above, but in this section

2~|62Nxx  Survival analysis and censored data /~ Engineering statistics
3+|62N01  Censored data models 
3+|62N02  Estimation 
3+|62N03  Testing 
3=|62N05  Reliability and life testing [See also 90B25]
3-|62N10  quality control 
3=|62N99  None of the above, but in this section

2>|62Pxx  Applications [See also 90-XX, 91-XX, 92-XX] /:> 91-XX,
3=|62P05  Applications to actuarial sciences and financial mathematics
3=|62P10  Applications to biology and medical sciences
3+|62P12  Applications to environmental and related topics 
3=|62P15  Applications to psychology
3~|62P20  Applications to economics [See also 91Bxx] // 91Bxx ~ 90Axx
3=|62P25  Applications to social sciences
3+|62P30  Applications in engineering and industry 
3+|62P35  Applications to physics 
3=|62P99  None of the above, but in this section

4=|62Q05  Statistical tables

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|65-XX  Numerical analysis 
8=|65-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|65-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|65-02  Research exposition (monographs, survey articles)
8=|65-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|65-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|65-05  Experimental papers
8=|65-06  Proceedings, conferences, collections, etc.

4=|65A05  Tables

2=|65Bxx  Acceleration of convergence
3=|65B05  Extrapolation to the limit, deferred corrections
3=|65B10  Summation of series
3=|65B15  Euler-Maclaurin formula
3=|65B99  None of the above, but in this section

2~|65Cxx  Probabilistic methods, simulation and stochastic differential equations {For theoretical ..........aspects, see 68U20 and 60H35} /~ Numerical simulation {For theoretical aspects, 
..........see 68U20}
3=|65C05  Monte Carlo methods
3=|65C10  Random number generation
3>|65C20  Models, numerical methods [See also 68U20] /:> [See also 68U20]
3+|65C30  Stochastic differential and integral equations 
3+|65C35  Stochastic particle methods [See also 82C80] 
3+|65C40  Computational Markov chains 
3+|65C50  Other computational problems in probability 
3+|65C60  Computational problems in statistics 
3=|65C99  None of the above, but in this section

2>|65Dxx  Numerical approximation and computational geometry {Primarily algorithms; for ..........theory, see 41-XX and 68Uxx} /:> and computational geometry /:> and 68Uxx 
3=|65D05  Interpolation
3=|65D07  Splines
3=|65D10  Smoothing, curve fitting
3=|65D15  Algorithms for functional approximation
3~|65D17  Computer aided design (modeling of curves and surfaces)
..........[See also 68U07] // 68U07 ~ 68U05
3+|65D18  Computer graphics and computational geometry 
..........[See also 51N05, 68U05] 
3>|65D20  Computation of special functions, construction of tables 
..........[See also 33F05] /:> [See also 33F05]
3=|65D25  Numerical differentiation
3=|65D30  Numerical integration
3=|65D32  Quadrature and cubature formulas
3=|65D99  None of the above, but in this section

4=|65E05  Numerical methods in complex analysis (potential theory, etc.) 
..........{For numerical methods in conformal mapping, see 30C30}

2=|65Fxx  Numerical linear algebra
3=|65F05  Direct methods for linear systems and matrix inversion
3=|65F10  Iterative methods for linear systems [See also 65N22]
3=|65F15  Eigenvalues, eigenvectors
3+|65F18  Inverse eigenvalue problems 
3=|65F20  Overdetermined systems, pseudoinverses
3+|65F22  Ill-posedness, regularization 
3=|65F25  Orthogonalization
3=|65F30  Other matrix algorithms
3=|65F35  Matrix norms, conditioning, scaling [See also 15A12, 15A60]
3=|65F40  Determinants
3=|65F50  Sparse matrices
3=|65F99  None of the above, but in this section

2>|65Gxx  Error analysis and interval analysis /:> and interval analysis
3-|65G05  Roundoff error
3-|65G10  interval and finite arithmetic
3+|65G20  Algorithm with automatic result verification
3+|65G30  Interval and finite arithmetic
3+|65G40  General methods in interval analysis
3+|65G50  Roundoff error
3=|65G99  None of the above, but in this section

2=|65Hxx  Nonlinear algebraic or transcendental equations
3=|65H05  Single equations
3=|65H10  Systems of equations
3~|65H17  Eigenvalues, eigenvectors [See also 58C40, 58E07, 47Hxx, 47Jxx, 
..........90C30] /~ Eigenvalues, eigenvectors and bifurcation problems 
..........[See also 58C40, 58E07, 58F14, 90C30]
3=|65H20  Global methods, including homotopy approaches 
..........[See also 58C30, 90C30]
3=|65H99  None of the above, but in this section

2=|65Jxx  Numerical analysis in abstract spaces
3=|65J05  General theory
3=|65J10  Equations with linear operators (do not use 65Fxx)
3=|65J15  Equations with nonlinear operators (do not use 65Hxx)
3>|65J20  Improperly posed problems; regularization /:> ; regularization
3+|65J22  Inverse problems 
3=|65J99  None of the above, but in this section

2=|65Kxx  Mathematical programming, optimization and variational techniques
3~|65K05  Mathematical programming [Algorithms; for theory see 90Cxx] 
..........// [Algorithms; for theory see 90Cxx] ~ [See also 90Cxx]
3=|65K10  Optimization and variational techniques [See also 49Mxx, 93B40]
3=|65K99  None of the above, but in this section

2=|65Lxx  Ordinary differential equations
3=|65L05  Initial value problems
3=|65L06  Multistep, Runge-Kutta and extrapolation methods
3=|65L07  Numerical investigation of stability of solutions
3=|65L08  Improperly posed problems
3+|65L09  Inverse problems 
3=|65L10  Boundary value problems
3=|65L12  Finite difference methods
3=|65L15  Eigenvalue problems
3>|65L20  Stability and convergence of numerical methods /:> and convergence
3=|65L50  Mesh generation and refinement
3=|65L60  Finite elements, Rayleigh-Ritz, Galerkin and collocation methods
3=|65L70  Error bounds
3+|65L80  Methods for differential-algebraic equations 
3=|65L99  None of the above, but in this section

2=|65Mxx  Partial differential equations, initial value and
..........time-dependent initial-boundary value problems
3=|65M06  Finite difference methods
3=|65M12  Stability and convergence of numerical methods
3=|65M15  Error bounds
3=|65M20  Method of lines
3=|65M25  Method of characteristics
3=|65M30  Improperly posed problems
3+|65M32  Inverse problems 
3=|65M50  Mesh generation and refinement
3=|65M55  Multigrid methods; domain decomposition
3=|65M60  Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
3=|65M70  Spectral, collocation and related methods
3=|65M99  None of the above, but in this section

2=|65Nxx  Partial differential equations, boundary value problems
3=|65N06  Finite difference methods
3=|65N12  Stability and convergence of numerical methods
3=|65N15  Error bounds
3+|65N21  Inverse problems 
3=|65N22  Solution of discretized equations [See also 65Fxx, 65Hxx]
3=|65N25  Eigenvalue problems
3=|65N30  Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
3=|65N35  Spectral, collocation and related methods
3=|65N38  Boundary element methods
3=|65N40  Method of lines
3=|65N45  Method of contraction of the boundary
3=|65N50  Mesh generation and refinement
3=|65N55  Multigrid methods; domain decomposition
3=|65N99  None of the above, but in this section

2+|65Pxx  Numerical problems in dynamical systems [See also 37Mxx] 
4-|65P05  partial differential equations, miscellanous problems 
3+|65P10  Hamiltonian systems including symplectic integrators 
3+|65P20  Numerical chaos 
3+|65P30  Bifurcation problems 
3+|65P40  Nonlinear stabilities 
3+|65P99  None of the above, but in this section 

4=|65Q05  Difference and functional equations, recurrence relations

2<|65Rxx  Integral equations, integral transforms /:< [See also 45Lxx]
3=|65R10  Integral transforms 
3=|65R20  Integral equations 
3=|65R30  Improperly posed problems 
3+|65R32  Inverse problems 
3=|65R99  None of the above but in this section 

4=|65S05  Graphical methods

2=|65Txx  Numerical methods in Fourier analysis
3-|65T10  trigonometric approximation and interpolation 
3-|65T20  discrete and fast Fourier transforms 
3+|65T40  Trigonometric approximation and interpolation 
3+|65T50  Discrete and fast Fourier transforms 
3+|65T60  Wavelets 
3=|65T99  None of the above, but in this section

4-|65U05  numerical methods in probability and statistics 

2=|65Yxx  Computer aspects of numerical algorithms
3=|65Y05  Parallel computation
3=|65Y10  Algorithms for specific classes of architectures
3=|65Y15  Packaged methods
3=|65Y20  Complexity and performance of numerical algorithms [See also 68Q25]
3-|65Y25  Computer graphics and computational geometry 
..........[See also 51N05, 68U05] 
3=|65Y99  None of the above, but in this section

4+|65Z05  Applications to physics 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|68-XX  Computer science 
..........{For papers involving machine computations and programs
..........in a specific mathematical area, see section -04 in that area} 
8=|68-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|68-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|68-02  Research exposition (monographs, survey articles)
8=|68-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|68-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|68-06  Proceedings, conferences, collections, etc.

2=|68Mxx  Computer system organization
3+|68M01  General 
3-|68M05  general 
3=|68M07  Mathematical problems of computer architecture
3~|68M10  Network design and communication [See also 90B18, 68R10] 
........../~ computer networks, [See also 90B12]
3+|68M12  Network protocols 
3+|68M14  Distributed systems 
3>|68M15  Reliability, testing and fault tolerance [See also 94C12] 
........../:> and fault tolerance [See also 94C12] 
3=|68M20  Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]
3=|68M99  None of the above, but in this section

2=|68Nxx  Software
3+|68N01  General 
3-|68N05  general theory of programming 
3=|68N15  Programming languages
3=|68N17  Logic programming
3+|68N18  Functional programming and lambda calculus [See also 03B40] 
3+|68N19  Other progamming techniques (object-oriented, sequential, 
..........concurrent, automatic, etc.) 
3~|68N20  Compilers and interpreters /~ Compilers and generators 
..........[See also 68Q52]
3~|68N25  Operating systems /~ Monitors and operating systems 
3+|68N30  Mathematical aspects of software engineering (specification, 
..........verification, metrics, requirements, etc.) 
3=|68N99  None of the above, but in this section

2=|68Pxx  Theory of data
3+|68P01  General 
3=|68P05  Data structures
3=|68P10  Searching and sorting
3=|68P15  Database theory
3=|68P20  Information storage and retrieval
3>|68P25  Data encryption [See also 94A60, 81P68] /:> , 81P68
3+|68P30  Coding and information theory (compaction, compression, models of 
..........communication, encoding schemes, etc.) [See also 94Axx] 
3=|68P99  None of the above, but in this section

2=|68Qxx  Theory of computing
3+|68Q01  General 
3~|68Q05  Models of computation (Turing machines, etc.) [See also 03D10, 81P68] 
........../~ Models of computation (abstract processors, Turing machines, etc.) 
..........[See also 03D10] 
3~|68Q10  Modes of computation (nondeterministic, parallel, interactive, 
..........probabilistic, etc.) [See also 68Q85] 
........../~ Modes of computation (concurrent, parallel, nondeterministic, 
..........etc.) [See also 68Q90]
3~|68Q15  Complexity classes (hierarchies, relations among complexity 
..........classes, etc.) [See also 03D15, 68Q17, 68Q19] 
........../~ Complexity classes [See also 03D15] 
3+|68Q17  Computational difficulty of problems (lower bounds, completeness, 
..........difficulty of approximation, etc.) [See also 68Q15] 
3+|68Q19  Descriptive complexity and finite models [See also 03C13]
3-|68Q22  parallel and distributed algorithms {for numerical algorithms, 
..........see 65Y05, 68Y10} 
3>|68Q25  Analysis of algorithms and problem complexity [See also 68W40] 
........../:> [See also 68W40]
3=|68Q30  Algorithmic information theory (Kolmogorov complexity, etc.)
3+|68Q32  Computational learning theory [See also 68T05] 
3-|68Q35  VLSI algorithms 
3-|68Q40  symbolic computation, algebraic computation [See also 11Yxx, 12Y05, 
..........13Pxx, 14Qxx, 16-08, 17-08] 
3>|68Q42  Grammars and rewriting systems /:> Grammars and 
3~|68Q45  Formal languages and automata [See also 03D05, 68Q70, 94A45] // 68Q70 ~ 20M35
........../:> and automata 
3-|68Q50  grammars [See also 03D05] 
3-|68Q52  parsing [See also 68N20] 
3>|68Q55  Semantics [See also 03B70, 06B35, 18C50] /:> , 18C50
3~|68Q60  Specification and verification (program logics, model checking, 
..........etc.) [See also 03B70]
........../~ Specification and verification of programs [See also 03B70]
3>|68Q65  Abstract data types; algebraic specification [See also 18C50] /:> [See also 18C50]
3-|68Q68  automata theory, general [See also 03D05] 
3>|68Q70  Algebraic theory of languages and automata [See also 18B20, 20M35] 
........../:> languages and
3-|68Q75  stochastic and nondeterministic automata 
3~|68Q80  Cellular automata [See also 37B15] /~ Tessellation automata, 
..........iterative arrays, cellular structures
3+|68Q85  Models and methods for concurrent and distributed 
..........computing (process algebras, bisimulation, transition nets, etc.) 
3-|68Q90  transition nets 
3=|68Q99  None of the above, but in this section

2=|68Rxx  Discrete mathematics in relation to computer science
3+|68R01  General 
3=|68R05  Combinatorics
3=|68R10  Graph theory [See also 05Cxx, 90B10, 90B35, 90C35]
3=|68R15  Combinatorics on words
3=|68R99  None of the above, but in this section

4-|68S05  mathematical linguistics [See also 03B65, 92K20] 

2<|68Txx  Artificial intelligence /:< [see also 92J40]
3=|68T01  General
3>|68T05  Learning and adaptive systems [See also 68Q32, 91E40] 
........../:> [See also 68Q32, 91E40]
3=|68T10  Pattern recognition, speech recognition {For cluster analysis, 
..........see 62H30}
3>|68T15  Theorem proving (deduction, resolution, etc.) [See also 03B35] 
........../:> (deduction, resolution, etc.)
3>|68T20  Problem solving (heuristics, search strategies, etc.) 
........../:> (heuristics, search strategies, etc)
3-|68T25  AI languages 
3~|68T27  Logic in artificial intelligence /~ AI logics 
3=|68T30  Knowledge representation
3~|68T35  Languages and software systems (knowledge-based systems, 
..........expert systems, etc.)
..........// Languages and software systems ~ AI software systems 
3+|68T37  Reasoning under uncertainty 
3+|68T40  Robotics [See also 93C85]
3+|68T45  Machine vision and scene understanding 
3+|68T50  Natural language processing  [See also 03B65]
3=|68T99  None of the above, but in this section

2>|68Uxx  Computing methodologies and applications /:> and applications 
3+|68U01  General 
3~|68U05  Computer graphics; computational geometry [See also 65D18] 
..........// 65D18 ~ 65Y25
3>|68U07  Computer-aided design [See also 65D17] /:> [See also 65D17]
3=|68U10  Image processing
3=|68U15  Text processing; mathematical typography
3=|68U20  Simulation [See also 65Cxx]
3-|68U30  other applications 
3+|68U35  Information systems (hypertext navigation, interfaces, 
..........decision support, etc.) 
3=|68U99  None of the above, but in this section

2+|68Wxx  Algorithms {For numerical algorithms, see 65-XX; for combinatorics 
..........and graph theory, see 68Rxx} 
3+|68W01  General 
3+|68W05  Nonnumerical algorithms 
3+|68W10  Parallel algorithms 
3+|68W15  Distributed algorithms 
3+|68W20  Randomized algorithms 
3+|68W25  Approximation algorithms 
3+|68W30  Symbolic computation and algebraic computation 
..........[See also 11Yxx, 12Y05, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10] 
3+|68W35  VLSI algorithms 
3+|68W40  Analysis of algorithms [See also 68Q25] 
3+|68W99  None of the above, but in this section 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1<|70-XX  Mechanics of particles and systems 
..........{For relativistic mechanics, see /:< 83-XX, -/ 83A05 and 83C10; 
..........for statistical mechanics, see 82-XX} 
8=|70-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|70-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|70-02  Research exposition (monographs, survey articles)
8=|70-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|70-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8~|70-05  Experimental work // work ~ papers
8=|70-06  Proceedings, conferences, collections, etc.
8=|70-08  Computational methods

4=|70A05  Axiomatics, foundations

2=|70Bxx  Kinematics [See also 53A17]
3=|70B05  Kinematics of a particle
3=|70B10  Kinematics of a rigid body
3~|70B15  Mechanisms, robots [See also 68T40, 70Q05, 93C85]
..........// 68T40, 70Q05, 93C85 ~ 73K05
3=|70B99  None of the above, but in this section

4=|70C20  Statics

2-|70Dxx  dynamics of a particle [See also 70Hxx] 
3-|70D05  newtonian dynamics 
3-|70D10  lagrangian dynamics 
3-|70D99  none of the above but in this section 

2>|70Exx  Dynamics of a rigid body and of multibody systems 
........../:> and of multibody systems
3=|70E05  Motion of the gyroscope
3-|70E10  motion of projectiles and rockets 
3~|70E15  Free motion of a rigid body [See also 70M20] /~ moton of rigid bodies
3+|70E17  Motion of a rigid body with a fixed point 
3+|70E18  Motion of a rigid body in contact with a solid surface 
..........[See also 70F25] 
3~|70E20  Perturbation methods for rigid body dynamics 
..........// rigid body dynamics ~ Euler's equations
3+|70E40  Integrable cases of motion 
3+|70E45  Higher-dimensional generalizations 
3+|70E50  Stability problems 
3+|70E55  Dynamics of multibody systems 
3+|70E60  Robot dynamics and control [See also 68T40, 70Q05, 93C85] 
3=|70E99  None of the above, but in this section

2=|70Fxx  Dynamics of a system of particles, including celestial
..........mechanics
3~|70F05  Two-body problems // problems ~ problem
3~|70F07  Three-body problems // problems ~ problem
3~|70F10  $n$-body problems // problems ~ problem
3=|70F15  Celestial mechanics
3+|70F16  Collisions in celestial mechanics, regularization 
3+|70F17  Inverse problems 
3=|70F20  Holonomic systems
3=|70F25  Nonholonomic systems
3-|70F30  impulsive motion 
3>|70F35  Collision of rigid or pseudo-rigid bodies 
........../:> of rigid or pseudo-rigid bodies
3+|70F40  Problems with friction 
3+|70F45  Infinite particle systems
3=|70F99  None of the above, but in this section

2~|70Gxx  General models, approaches, and methods [See also 37-XX] 
........../~ General representations of dynamical systems [See also 58Fxx]
3-|70G05  Riemannian geometry, tensorial methods 
..........[See also 53A45, 53A50, 53B20] 
3>|70G10  Generalized coordinates; event, impulse-energy,
..........configuration, state, or phase space 
........../:> ; event, impulse.energy, configuration, state, or phase space
3-|70G15  space of events 
3-|70G20  impulse-energy space 
3-|70G25  configuration space 
3-|70G30` state space 
3-|70G35  phase space 
3+|70G40  Topological and differential-topological methods 
3+|70G45  Differential-geometric methods (tensors, connections, symplectic, 
..........Poisson, contact, Riemannian, nonholonomic, etc.) [See also 53Cxx, 53Dxx, 58Axx]
3-|70G50  classical field theories (general) 
3+|70G55  Algebraic geometry methods 
3+|70G60  Dynamical systems methods 
3+|70G60  Symmetries, Lie-group and Lie-algebra methods 
3+|70G65  Functional-analytic methods 
3+|70G70  Variational methods 
3=|70G99  None of the above, but in this section

2~|70Hxx  Hamiltonian and Lagrangian mechanics [See also 37Jxx] 
..........// 37Jxx ~ 58F05
3+|70H03  Lagrange's equations
3=|70H05  Hamilton's equations
3+|70H06  Completely integrable systems and methods of integration 
3+|70H07  Nonintegrable systems 
3+|70H08  Nearly integrable Hamiltonian systems, KAM theory 
3+|70H09  Perturbation theories 
3-|70H10  Liouville's theorem 
3+|70H11  Adiabatic invariants 
3+|70H12  Periodic and almost periodic solutions 
3+|70H14  Stability problems 
3>|70H15  Canonical and symplectic transformations /:> and symplectic 
3=|70H20  Hamilton-Jacobi equations
3=|70H25  Hamilton's principle
3=|70H30  Other variational principles
3~|70H33  Symmetries and conservation laws, reverse symmetries, invariant 
..........manifolds and their bifurcations, reduction 
........../~ simmetries 
3-|70H35  Lagrange's equation of motion
3=|70H40  Relativistic dynamics
3+|70H45  Constrained dynamics, Dirac's theory of constraints 
..........[See also 70F20, 70F25, 70Gxx] 
3+|70H50  Higher-order theories 
3=|70H99  None of the above, but in this section

2<|70Jxx  Linear vibration theory /:< [See also 73D30]
3-|70J05  finite degree of freedom systems
3=|70J10  Modal analysis
3=|70J25  Stability
3=|70J30  Free motions
3=|70J35  Forced motions
3=|70J40  Parametric resonances
3+|70J50  Systems arising from the discretization of structural vibrations 
..........problems 
3=|70J99  None of the above, but in this section

2~|70Kxx  Nonlinear dynamics [See also 34Cxx, 37-XX] 
........../~ Nonlinear motions [See also 34Cxx, 58Fxx, 73D35, 73K12]
3>|70K05  Phase plane analysis, limit cycles /:> , limit cycles
3-|70K10  Limit cycles
3-|70K15  Lyapunov theorems
3=|70K20  Stability
3=|70K25  Free motions
3=|70K28  Parametric resonances
3=|70K30  Nonlinear resonances
3=|70K40  Forced motions
3+|70K42  Equilibria and periodic trajectories 
3+|70K43  Quasi-periodic motions and invariant tori 
3+|70K44  Homoclinic and heteroclinic trajectories 
3+|70K45  Normal forms 
3~|70K50  Bifurcations and instability /~ Transition to stochasticity 
..........(chaotic behaviour) [See also 58F13]
3+|70K55  Transition to stochasticity (chaotic behavior) [See also 37D50] 
3+|70K60  General perturbation schemes 
3+|70K65  Averaging of perturbations 
3+|70K70  Systems with slow and fast motions 
3+|70K75  Nonlinear modes 
3=|70K99  None of the above, but in this section

4<|70L05  Random vibrations [See also 74H50] // 74H50 ~ 73K35, 93Exx

4=|70M20  Orbital mechanics

4=|70P05  Variable mass, rockets

4<|70Q05  Control of mechanical systems [See also 49-XX, 93Cxx, 93Dxx] 
........../:< 73K50,

2+|70Sxx  Classical field theories [See also 37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX] 
3+|70S05  Lagrangian formalism and Hamiltonian formalism
3+|70S10  Symmetries and conservation laws
3+|70S15  Yang-Mills and other gauge theories
3+|70S20  More general nonquantum field theories
3+|70S99  None of the above, but in this section

%%-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1-|73-XX  Mechanics of solids 
8-|73-00  general reference works (handbooks, dictionaries, 
..........bibliographies, etc.) 
8-|73-01  instructional exposition (textbooks, tutorial papers, etc.) 
8-|73-02  research exposition (monographs, survey articles) 
8-|73-03  historical (must also be assigned at least one classification 
..........number from Section 01) 
8-|73-04  explicit machine computation and programs (not the theory 
..........of computation or programming) 
8-|73-05  experimental papers 
8-|73-06  proceedings, conferences, collections, etc. 

4-|73A05  axiomatics, foundations of solid mechanics 

2-|73Bxx  continuum mechanics of solids (constitutive description and
..........properties) 
3-|73B05  constitutive equations 
3-|73B10  symmetry groups 
3-|73B18  nonlocal theories 
3-|73B25  polar theories 
3-|73B27  nonhomogeneous materials; homogenization 
3-|73B30  thermodynamics of solids {For gases and fluids, See 80-XX} 
3-|73B35  random materials 
3-|73B40  anisotropic materials 
3-|73B50  stress concentrations 
3-|73B99  none of the above but in this section 

2-|73Cxx  elasticity {For the biharmonic equation, See 31A30, 31B30} 
3-|73C02  classical linear elasticity 
3-|73C05  stress functions 
3-|73C10  saint-Venant's principle 
3-|73C15  uniqueness theorems 
3-|73C35  mixed boundary value problems [See also 45F05] 
3-|73C50  nonlinear elasticity 
3-|73C99  none of the above but in this section 

2-|73Dxx  wave propagation in and vibrations of solids 
3-|73D05  impact and explosion problems [See also 76L05] 
3-|73D10  integral transforms 
3-|73D15  body waves 
3-|73D20  surface waves 
3-|73D25  wave diffraction and dispersion 
3-|73D30  linear vibrations [See also 70Jxx] 
3-|73D35  nonlinear vibrations [See also 70Kxx] 
3-|73D40  singular surfaces 
3-|73D50  inverse problems [See also 35Lxx, 35R30] 
3-|73D70  random waves 
3-|73D99  none of the above but in this section 

2-|73Exx  plasticity 
3-|73E05  constitutive specifications (yield criteria, flow rules, 
..........hardening, softening) 
3-|73E10  method of successive approximations 
3-|73E20  limit analysis 
3-|73E50  time-dependent problems 
3-|73E60  viscoplasticity 
3-|73E70  plastic waves 
3-|73E99  none of the above but in this section 

2-|73Fxx  viscoelasticity 
3-|73F05  creep and relaxation functions 
3-|73F10  correspondence principle 
3-|73F15  time-dependent problems 
3-|73F20  aging of materials 
3-|73F25  environmental-dependent materials 
3-|73F99  none of the above but in this section 

2-|73Gxx  finite deformations 
3-|73G05  finite elasticity 
3-|73G20  finite plasticity 
3-|73G25  finite viscoelasticity 
3-|73G99  none of the above but in this section 

2-|73Hxx  stability (linear and nonlinear) 
3-|73H05  buckling 
3-|73H10  dynamic stability 
3-|73H99  none of the above but in this section 

2-|73Kxx  mechanics of structures 
3-|73K03  strings 
3-|73K05  beams, columns, rods 
3-|73K10  plates, discs, membranes 
3-|73K12  dynamics of structures 
3-|73K15  shells 
3-|73K20  composite structures and materials 
3-|73K35  random vibrations 
3-|73K40  optimization [See also 90C90] 
3-|73K50  control of structures 
3-|73K70  aero- or hydromechanic structure interactions 
3-|73K99  none of the above but in this section 

4-|73M25  fracture mechanics

4-|73N20  geophysical solid mechanics [See also 86A15, 86A17] 

4-|73P05  biomechanics of solids [See also 92C10] 

4-|73Q05  soil and rock mechanics [See also 86A60] 

4-|73R05  electromagnetic elasticity 

4-|73S10  micromechanics of solids 

4-|73T05  contact and surface mechanics 

2-|73Vxx  basic methods in solid mechanics [See also 65-xx] 
3-|73V05  finite element methods 
3-|73V10  boundary element methods 
3-|73V15  finite difference methods 
3-|73V20  other numerical methods 
3-|73V25  variational methods 
3-|73V30  stochastic analysis 
3-|73V35  complex variable techniques 
3-|73V99  none of the above but in this section 

%%+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1+|74-XX  Mechanics of deformable solids 
8+|74-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.) 
8+|74-01  Instructional exposition (textbooks, tutorial papers, etc.) 
8+|74-02  Research exposition (monographs, survey articles) 
8+|74-03  Historical (must also be assigned at least one
..........classification number from Section 01) 
8+|74-04  Explicit machine computation and programs (not the
..........theory of computation or programming) 
8+|74-05  Experimental work 
8+|74-06  Proceedings, conferences, collections, etc. 

2+|74Axx  Generalities, axiomatics, foundations of continuum mechanics 
..........of solids 
3+|74A05  Kinematics of deformation 
3+|74A10  Stress 
3+|74A15  Thermodynamics 
3+|74A20  Theory of constitutive functions 
3+|74A25  Molecular, statistical, and kinetic theories 
3+|74A30  Nonsimple materials 
3+|74A35  Polar materials 
3+|74A40  Random materials and composite materials 
3+|74A45  Theories of fracture and damage 
3+|74A50  Structured surfaces and interfaces, coexistent phases 
3+|74A55  Theories of friction (tribology) 
3+|74A60  Micromechanical theories
3+|74A65  Reactive materials
3+|74A99  None of the above, but in this section 

2+|74Bxx  Elastic materials 
3+|74B05  Classical linear elasticity 
3+|74B10  Linear elasticity with initial stresses 
3+|74B15  Equations linearized about a deformed state (small deformations 
..........superposed on large) 
3+|74B20  Nonlinear elasticity 
3+|74B99  None of the above, but in this section 

2+|74Cxx  Plastic materials, materials of stress-rate and internal-variable 
..........type 
3+|74C05  Small-strain, rate-independent theories (including
..........rigid-plastic and elasto-plastic materials) 
3+|74C10  Small-strain, rate-dependent theories (including
..........theories of viscoplasticity) 
3+|74C15  Large-strain, rate-independent theories (including nonlinear 
..........plasticity) 
3+|74C20  Large-strain, rate-dependent theories 
3+|74C99  None of the above, but in this section 

2+|74Dxx  Materials of strain-rate type and history type, other
..........materials with memory (including elastic materials with
..........viscous damping, various viscoelastic materials) 
3+|74D05  Linear constitutive equations 
3+|74D10  Nonlinear constitutive equations 
3+|74D99  None of the above, but in this section 

2+|74Exx  Material properties given special treatment 
3+|74E05  Inhomogeneity 
3+|74E10  Anisotropy 
3+|74E15  Crystaline structure 
3+|74E20  Granularity 
3+|74E25  Texture 
3+|74E30  Composite and mixture properties 
3+|74E35  Random structure 
3+|74E40  Chemical structure 
3+|74E99  None of the above, but in this section 

2+|74Fxx  Coupling of solid mechanics with other effects 
3+|74F05  Thermal effects 
3+|74F10  Fluid-solid interactions (including aero- and hydro-elasticity, 
..........porosity, etc.) 
3+|74F15  Electromagnetic effects 
3+|74F20  Mixture effects 
3+|74F25  Chemical and reactive effects 
3+|74F99  None of the above, but in this section 

2+|74Gxx  Equilibrium (steady-state) problems 
3+|74G05  Explicit solutions 
3+|74G10  Analytic approximation of solutions (perturbation
..........methods, asymptotic methods, series, etc.) 
3+|74G15  Numerical approximation of solutions 
3+|74G20  Local existence of solutions (near a given solution) 
3+|74G25  Global existence of solutions 
3+|74G30  Uniqueness of solutions 
3+|74G35  Multiplicity of solutions 
3+|74G40  Regularity of solutions 
3+|74G45  Bounds for solutions 
3+|74G50  Saint-Venant's principle 
3+|74G55  Qualitative behavior of solutions 
3+|74G60  Bifurcation and buckling 
3+|74G65  Energy minimization 
3+|74G70  Stress concentrations, singularities 
3+|74G75  Inverse problems 
3+|74G99  None of the above, but in this section 

2+|74Hxx  Dynamical problems 
3+|74H05  Explicit solutions 
3+|74H10  Analytic approximation solutions (perturbation methods, 
..........asymptotic methods, series, etc.) 
3+|74H15  Numerical approximation of solutions 
3+|74H20  Existence of solutions 
3+|74H25  Uniqueness of solutions 
3+|74H30  Regularity of solutions 
3+|74H35  Singularities, blowup, stress concentrations 
3+|74H40  Long-time behavior of solutions 
3+|74H45  Vibrations 
3+|74H50  Random vibrations 
3+|74H55  Stability 
3+|74H60  Dynamical bifurcation 
3+|74H65  Chaotic behavior 
3+|74H99  None of the above, but in this section 

2+|74Jxx  Waves 
3+|74J05  Linear waves 
3+|74J10  Bulk waves 
3+|74J15  Surface waves 
3+|74J20  Wave scattering 
3+|74J25  Inverse problems 
3+|74J30  Nonlinear waves 
3+|74J35  Solitary waves 
3+|74J40  Shocks and related discontinuities 
3+|74J99  None of the above, but in this section 

2+|74Kxx  Thin bodies, structures 
3+|74K05  Strings 
3+|74K10  Rods (beams, columns, shafts, arches, rings, etc.) 
3+|74K15  Membranes 
3+|74K20  Plates 
3+|74K25  Shells 
3+|74K30  Junctions
3+|74K35  Thin films
3+|74K99  None of the above, but in this section 

2+|74Lxx  Special subfields of solid mechanics 
3+|74L05  Geophysical solid mechanics [See also 86-XX]
3+|74L10  Soil and rock mechanics 
3+|74L15  Biomechanical solid mechanics [See also 92C10]
3+|74L99  None of the above, but in this section 

2+|74Mxx  Special kinds of problems 
3+|74M05  Control, switches and devices (``smart materials'') [See also 93Cxx]
3+|74M10  Friction
3+|74M15  Contact
3+|74M20  Impact
3+|74M25  Micromechanics
3+|74M99  None of the above, but in this section 

2+|74Nxx  Phase transformations in solids [See also 74A50, 80Axx, 82B26, 82C26]
3+|74N05  Crystals
3+|74N10  Displacive transformations
3+|74N15  Analysis of microstructure
3+|74N20  Dynamics of phase boundaries
3+|74N25  Transformations involving diffusion
3+|74N30  Problems involving hysteresis
3+|74N99  None of the above, but in this section

2+|74Pxx  Optimization [See also 49Qxx]
3+|74P05  Compliance or weight optimization
3+|74P10  Optimization of other properties
3+|74P15  Topological methods
3+|74P20  Geometrical methods
3+|74P99  None of the above, but in this section

2+|74Qxx  Homogenization, determination of effective properties
3+|74Q05  Homogenization in equilibrium problems
3+|74Q10  Homogenization and oscillations in dynamical problems
3+|74Q15  Effective constitutive equations
3+|74Q20  Bounds on effective properties
3+|74Q99  None of the above, but in this section

2+|74Rxx  Fracture and damage
3+|74R05  Brittle damage
3+|74R10  Brittle fracture
3+|74R15  High-velocity fracture
3+|74R20  Anelastic fracture and damage
3+|74R99  None of the above, but in this section

2+|74Sxx  Numerical methods [See also 65-XX, 74G15, 74H15]
3+|74S05  Finite element methods
3+|74S10  Finite volume methods
3+|74S15  Boundary element methods
3+|74S20  Finite difference methods
3+|74S25  Spectral and related methods
3+|74S30  Other numerical methods
3+|74S99  None of the above, but in this section


%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1~|76-XX  Fluid mechanics {For general continuum mechanics, 
..........See 74Axx or other parts of 74-XX} // 74Axx ~ 73Bxx // 74-XX ~ 73-XX
8=|76-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|76-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|76-02  Research exposition (monographs, survey articles)
8=|76-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|76-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8~|76-05  Experimental work // work ~ papers
8=|76-06  Proceedings, conferences, collections, etc.

2=|76Axx  Foundations, constitutive equations, rheology
3=|76A02  Foundation of fluids mechanics
3=|76A05  Non-Newtonian fluids
3=|76A10  Viscoelastic fluids
3=|76A15  Liquid crystals [See also 82D30]
3+|76A20  Thin films 
3+|76A25  Superfluids (classical aspects) 
3=|76A99  None of the above but in this section

2<|76Bxx  Incompressible inviscid fluids /:< , potential theory
3+|76B03  Existence, uniqueness, and regularity theory [See also 35R35]
3-|76B05  airfoil theory 
3+|76B07  Free-surface potential flow 
3>|76B10  Jets and cavities, cavitation, free-streamline theory, water-entry 
..........problems, airfoil and hydrofoil theory, sloshing /:> airfoil and
3~|76B15  Water waves, gravity waves; dispersion and scattering, nonlinear 
..........interaction [See also 35Q30, 35Q53] // scattering ~ diffraction /:> , 35Q30
3=|76B20  Ship waves
3<|76B25  Solitary /:< and cnoidal -/ waves [See also 35Q51]
3-|76B35  Random waves, inviscid fluids
3-|76B40  added mass computations 
3>|76B45  Capillarity (surface tension) [See also 76D45] 
........../:> (surface tension) [See also 76D45]
3+|76B47  Vortex flows
3+|76B55  Internal waves 
3+|76B60  Atmospheric waves [See also 86A10] 
3+|76B65  Rossby waves [See also 86A05, 86A10]
3+|76B70  Stratification effects in inviscid fluids 
3+|76B75  Flow control and optimization [See also 49Q10, 93C20, 93C95]
3=|76B99  None of the above, but in this section

2-|76Cxx  incompressible inviscid fluids, vorticity flows 
3-|76C05  vorticity flows 
3-|76C10  internal waves 
3-|76C15  atmospheric waves 
3-|76C20  rossby waves 
3-|76C99  none of the above but in this section 

2=|76Dxx  Incompressible viscous fluids
3+|76D03  Existence, uniqueness, and regularity theory [See also 35Q30, 35Q35]
3=|76D05  Navier-Stokes equations [See also 35Q30]
3+|76D06  Statistical solutions of the Navier-Stokes  and related equations 
..........[See also 60H30, 76M35] 
3>|76D07  Stokes and related (Oseen, etc.) flows 
........../:> and related (Orseen, etc.)
3=|76D08  Lubrication theory
3+|76D09  Viscous-inviscid interaction 
3~|76D10  Boundary-layer theory, separation and reattachment,
..........higher-order effects 
........../~ boundary-layer theory 
3-|76D15  boundary-layer separation and reattachment 
3+|76D17  Viscous vortex flows
3-|76D20  higher-order effects in boundary layers 
3=|76D25  Wakes and jets
3+|76D27  Other free-boundary flows; Hele-Shaw flows 
3-|76D30  singular perturbation problems 
3=|76D33  Waves
3-|76D35  Random waves, viscous fluids
3>|76D45  Capillarity (surface tension) [See also 76B45] 
........../:> (surface tension)
3+|76D50  Stratification effects in viscous fluids 
3+|76D55  Flow control and optimization  [See also 49Q10, 93C20, 93C95]
3=|76D99  None of the above, but in this section

2=|76Exx  Hydrodynamic stability
3~|76E05  Parallel shear flows /~ Stability of parallel flows
3+|76E06  Convection 
3+|76E07  Rotation 
3+|76E09  Stability and instability of nonparallel flows 
3-|76E10  inertial instability 
3~|76E15  Absolute and convective instability and stability /~ Convective instability
3+|76E17  Interfacial stability and instability 
3+|76E19  Compressibility effects 
3>|76E20  Stability and instability of geophysical and astrophysical flows /:> Stability and
3~|76E25  Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
 .......... /~  Magnetohydrodynamic and electrohydrodynamic instabilities
3=|76E30  Nonlinear effects
3=|76E99  None of the above, but in this section

2<|76Fxx  Turbulence [See also 60Gxx, 60Jxx] /:< 58F13, 58F27,
3+|76F02  Fundamentals 
3~|76F05  Isotropic turbulence; homogeneous turbulence 
........../~ homogeneous isotropic turbolence
3+|76F06  Transition to turbulence 
3=|76F10  Shear flows
3~|76F20  Dynamical systems approach to turbulence [See also 37-XX] 
........../~ Turbolence via chaos techniques
3+|76F25  Turbulent transport, mixing 
3+|76F30  Renormalization and other field-theoretical methods 
..........[See also 81T99] 
3+|76F35  Convective turbulence [See also 76E15, 76Rxx] 
3+|76F40  Turbulent boundary layers 
3+|76F45  Stratification effects 
3+|76F50  Compressibility effects 
3+|76F55  Statistical turbulence modeling [See also 76M35] 
3+|76F60  k-epsilon modeling 
3+|76F65  Direct numerical and large eddy simulation of turbulence 
3+|76F70  Control of turbulent flows 
3=|76F99  None of the above, but in this section

4=|76G25  General aerodynamics and subsonic flows

4=|76H05  Transonic flows

4=|76J20  Supersonic flows

4=|76K05  Hypersonic flows

4<|76L05  Shock waves and blast waves [See also 35L67] /:< , 73D05

2=|76Mxx  Basic methods in fluid mechanics [See also 65-XX]
3=|76M10  Finite element methods
3+|76M12  Finite volume methods 
3=|76M15  Boundary element methods
3=|76M20  Finite difference methods
3+|76M22  Spectral methods 
3+|76M23  Vortex methods 
3=|76M25  Other numerical methods
3+|76M27  Visualization algorithms 
3+|76M28  Particle methods and lattice-gas methods 
3=|76M30  Variational methods
3=|76M35  Stochastic analysis
3+|76M40  Complex variable methods 
3+|76M45  Asymptotic methods, singular perturbations 
3+|76M50  Homogenization 
3+|76M55  Dimensional analysis and similarity 
3+|76M60  Symmetry analysis, Lie group and algebra methods 
3=|76M99  None of the above, but in this section

2=|76Nxx  Compressible fluids and gas dynamics, general
3~|76N10  Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30]
........... /~ Compressible fluids, general [See also 35Q30]
3=|76N15  Gas dynamics, general
3+|76N17  Viscous-inviscid interaction 
3=|76N20  Boundary-layer theory
3+|76N25  Flow control and optimization 
3=|76N99  None of the above, but in this section

4=|76P05  Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05]

4~|76Q05  Hydro- and aero-acoustics /~ Hydrodynamic sound, acoustic

2=|76Rxx  Diffusion and convection
3=|76R05  Forced convection
3=|76R10  Free convection
3=|76R50  Diffusion [See also 60J60]
3=|76R99  None of the above, but in this section

4=|76S05  Flows in porous media; filtration; seepage

2+|76Txx  Two-phase and multiphase flows 
4-|76T05  two-phase and multiphase flows 
3+|76T10  Liquid-gas two-phase flows, bubbly flows 
3+|76T15  Dusty-gas two-phase flows 
3+|76T20  Suspensions 
3+|76T25  Granular flows [See also 74A60, 74C99, 74E20]
3+|76T30  Three or more component flow 
3+|76T99  None of the above, but in this section 

4=|76U05  Rotating fluids

4~|76V05  Reaction effects in flows [See also 80A32] 
........../~ Stratified and reacting fluids

4=|76W05  Magnetohydrodynamics and electrohydrodynamics

4>|76X05  Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10] 
.......... /:> [See also 82D10]

4=|76Y05  Quantum hydrodynamics and relativistic hydrodynamics
..........[See also 83C55, 85A30]

2>|76Zxx  Biological fluid mechanics [See also 74F10, 74L10, 92Cxx] /:> 74F10, 74L10, 
3=|76Z05  Physiological flows [See also 92C35]
3=|76Z10  Biopropulsion in water and in air
3=|76Z99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|78-XX  Optics, electromagnetic theory {For quantum optics, see 81V80} 
8=|78-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|78-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|78-02  Research exposition (monographs, survey articles)
8=|78-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|78-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8~|78-05  Experimental work // work ~ papers
8=|78-06  Proceedings, conferences, collections, etc.
8-|78-08  computational methods 

2+|78Axx  General 
36|78A02  Foundations 
36|78A05  Geometric optics
36|78A10  Physical optics
36|78A15  Electron optics
36|78A20  Space charge waves
36|78A25  Electromagnetic theory, general
36|78A30  Electro- and magnetostatics
36|78A35  Motion of charged particles
36|78A40  Waves and radiation
36|78A45  Diffraction, scattering [See also 34E20 for WKB methods]
36|78A50  Antennas, wave-guides
36|78A55  Technical applications
36|78A60  Lasers, masers, optical bistability, nonlinear optics 
..........[See also 81V80]
3;|78A70  Biological applications [See also 92C30, 91D30] 
..........// 91D30 ~ 92J30
36|78A97  Mathematically heuristic optics and electromagnetic theory 
..........(must also be assigned at least one other classification number 
..........in this section)
36|78A99  Miscellaneous topics

2+|78Mxx  Basic methods 
3+|78M05  Method of moments
3+|78M10  Finite element methods
3+|78M15  Boundary element methods
3+|78M20  Finite difference methods
3+|78M25  Other numerical methods
3+|78M30  Variational methods
3+|78M35  Asymptotic analysis
3+|78M40  Homogenization
3+|78M50  Optimization
3+|78M99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1~|80-XX  Classical thermodynamics, heat transfer 
..........{For thermodynamics of solids, see 74A15} // 74A15 ~ 73B30
8=|80-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|80-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|80-02  Research exposition (monographs, survey articles)
8=|80-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|80-04  Explicit machine computation and programs (not the theory 
..........of computation or programming)
8~|80-05  Experimental work // work ~ papers
8=|80-06  Proceedings, conferences, collections, etc.
8-|80-08  computational methods 

2+|80Axx  Thermodynamics and heat transfer 
36|80A05  Foundations 
3:|80A10  Classical thermodynamics, including relativistic 
........../:> , including relativistic 
5-|80A15  thermodynamics of mixtures 
3+|80A17  Thermodynamics of continua [See also 74A15] 
36|80A20  Heat and mass transfer, heat flow 
3:|80A22  Stefan problems, phase changes, etc. [See also 74Nxx] /:>  [See also 74Nxx]
36|80A23  Inverse problems 
3!|80A25  Combustion /:< , interior ballistics 
3:|80A30  Chemical kinetics [See also 76V05, 92C45, 92E20] /:> 76V05,
36|80A32  Chemically reacting flows [See also 92C45, 92E20] 
36|80A50  Chemistry (general) [See mainly 92Exx] 
5-|80A97  mathematically heuristic classical thermodynamics (must also be 
..........assigned at least one other classification number in this section) 
3;|80A99  None of the above, but in this section /~ miscellaneous topics 

2+|80Mxx  Basic methods 
3+|80M10  Finite element methods
3+|80M15  Boundary element methods
3+|80M20  Finite difference methods
3+|80M25  Other numerical methods
3+|80M30  Variational methods
3+|80M35  Asymptotic analysis
3+|80M40  Homogenization
3+|80M50  Optimization
3+|80M99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|81-XX  Quantum Theory 
8=|81-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|81-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|81-02  Research exposition (monographs, survey articles)
8=|81-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|81-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|81-05  Experimental papers
8=|81-06  Proceedings, conferences, collections, etc.
8=|81-08  Computational methods

2=|81Pxx  Axiomatics, foundations, philosophy
3=|81P05  General and philosophical
3>|81P10  Logical foundations of quantum mechanics; quantum logic [See also 03G12, 06C15]
........../:> ; quantum logic /:> [See also 03G12, 06C15]
3=|81P15  Quantum measurement theory
3=|81P20  Stochastic mechanics (including stochastic electrodynamics)
3+|81P68  Quantum computation and quantum cryptography 
..........[See also 68Q05, 94A60] 
3=|81P99  None of the above, but in this section

2=|81Qxx  General mathematical topics and methods in quantum theory
3=|81Q05  Closed and approximate solutions to the Schr\"odinger, Dirac, 
..........Klein-Gordon and other quantum-mechanical equations
3=|81Q10  Selfadjoint operator theory in quantum theory,
..........including spectral analysis
3=|81Q15  Perturbation theories for operators and differential equations
3=|81Q20  Semiclassical techniques including WKB and Maslov methods
3=|81Q30  Feynman integrals and graphs; applications of algebraic 
..........topology and algebraic geometry [See also 14D05, 32S40]
3=|81Q40  Bethe-Salpeter and other integral equations
3~|81Q50  Quantum chaos [See also 37Dxx] // 37Dxx ~ 58F13
3=|81Q60  Supersymmetric quantum mechanics
3+|81Q70  Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.
3=|81Q99  None of the above, but in this section

2=|81Rxx  Groups and algebras in quantum theory
3~|81R05  Finite-dimensional groups and algebras motivated by physics 
..........and their representations [See also 20C35, 22E70]
........../~ Representations of Finite-dimensional groups and algebras 
..........motivated by physics [See also 20C35, 22E70]
3~|81R10  Infinite-dimensional groups and algebras motivated by physics, 
..........including Virasoro, Kac-Moody, 
..........$W$-algebras and other current algebras and their representations 
..........[See also 17B65, 17B67, 22E65, 22E67, 22E70] 
........../~ Representations of infinite-dimensional groups and algebras 
..........motivated by physics, including Virasoro, Kac-Moody 
..........and other current algebras and their representations 
..........[See also 17B65, 17B67, 22E65, 22E67, 22E70] 
3+|81R12  Relations with integrable systems [See also 17Bxx, 37J35] 
3+|81R15  Operator algebra methods [See also 46Lxx, 81T05] 
3=|81R20  Covariant wave equations
3=|81R25  Spinor and twistor methods [See also 32L25]
3>|81R30  Coherent states [See also 22E45]; squeezed states [See also 81V80] 
........../:> ; squeezed states [See also 81V80]
3=|81R40  Symmetry breaking
3=|81R50  Quantum groups and related algebraic methods [See also 16W30, 17B37]
3+|81R60  Noncommutative geometry 
3=|81R99  None of the above, but in this section

2=|81Sxx  General quantum mechanics and problems of quantization
3>|81S05  Commutation relations and statistics /:> and statistics
3~|81S10  Geometry and quantization, symplectic methods 
..........[See also 53D50] // Geometry and ~ Geometric // 53D50 ~ 58F06
3=|81S20  Stochastic quantization
3=|81S25  Quantum stochastic calculus
3=|81S30  Phase space methods including Wigner distributions, etc.
3=|81S40  Path integrals [See also 58D30]
3=|81S99  None of the above, but in this section

2>|81Txx  Quantum field theory; related classical field theories [See also 70Sxx] /:> [See also 70Sxx]
3=|81T05  Axiomatic quantum field theory; operator algebras
3=|81T08  Constructive quantum field theory
3=|81T10  Model quantum field theories
3=|81T13  Yang-Mills and other gauge theories [See also 53C07, 58E15]
3=|81T15  Perturbative methods of renormalization
3=|81T16  Nonperturbative methods of renormalization
3=|81T17  Renormalization group methods
3=|81T18  Feynman diagrams
3=|81T20  Quantum field theory on curved space backgrounds
3=|81T25  Quantum field theory on lattices
3=|81T27  Continuum limits
3>|81T30  String and superstring theories; other extended objects 
..........(e.g., branes) [See also 83E30] /:> (e.g. branes)
3=|81T40  Two-dimensional field theories, conformal field theories, etc.
3+|81T45  Topological field theories [See also 57R56, 58Dxx] 
3=|81T50  Anomalies
3=|81T60  Supersymmetric field theories
3~|81T70  Quantization in field theory; cohomological methods
..........[See also 58D29] // 58D29 ~ 58F06
3+|81T75  Noncommutative geometry methods [See also 46L85, 46L87, 58B34] 
3=|81T80  Simulation and numerical modeling
3=|81T99  None of the above, but in this section

2>|81Uxx  Scattering theory [See also 34A55, 34L25, 34L40, 35P25, 47A40] 
........../:> 34A55, 34L25, 34L40, 35P25, 
3=|81U05  $2$-body potential scattering theory [See also 34E20 for WKB methods]
3=|81U10  $n$-body potential scattering theory
3+|81U15  Exactly and quasi-solvable systems 
3=|81U20  $S$-matrix theory, etc.
3=|81U30  Dispersion theory, dispersion relations
3<|81U40  Inverse scattering problems /:< [See also 58F07, 37K15] 
3=|81U99  None of the above, but in this section

2=|81Vxx  Applications to specific physical systems
3=|81V05  Strong interaction, including quantum chromodynamics
3=|81V10  Electromagnetic interaction; quantum electrodynamics
3=|81V15  Weak interaction
3>|81V17  Gravitational interaction [See also 83Cxx] and 83Exx 
........../:> [See also 83Cxx] and 83Exx
3=|81V19  Other fundamental interactions
3=|81V22  Unified theories
3=|81V25  Other elementary particle theory
3=|81V35  Nuclear physics
3=|81V45  Atomic physics
3=|81V55  Molecular physics [See also 92E10]
3>|81V70  Many-body theory ; quantum Hall effect /:> ; quantum Hall effect
3=|81V80  Quantum optics
3=|81V99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|82-XX  Statistical mechanics, structure of matter 
8=|82-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|82-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|82-02  Research exposition (monographs, survey articles)
8=|82-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|82-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|82-05  Experimental papers
8=|82-06  Proceedings, conferences, collections, etc.
8=|82-08  Computational methods

2=|82Bxx  Equilibrium statistical mechanics
3=|82B03  Foundations
3=|82B05  Classical equilibrium statistical mechanics (general)
3=|82B10  Quantum equilibrium statistical mechanics (general)
3>|82B20  Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs 
........../:> ans systems on graphs
3=|82B21  Continuum models (systems of particles, etc.)
3>|82B23  Exactly solvable models; Bethe ansatz /:> ; Bethe ansatz
3>|82B24  Interface problems; diffusion-limited aggregation 
........../:> ; diffusion-limited aggregation 
3=|82B26  Phase transitions (general)
3=|82B27  Critical phenomena
3=|82B28  Renormalization group methods [See also 81T17]
3=|82B30  Statistical thermodynamics [See also 80-XX]
3=|82B31  Stochastic methods
3=|82B35  Irreversible thermodynamics, including Onsager-Machlup theory 
..........[See also 92E20]
3=|82B40  Kinetic theory of gases
3~|82B41  Random walks, random surfaces, lattice animals, etc. 
..........[See also 60G50, 82C41] // 60G50 ~ 60J15
3=|82B43  Percolation [See also 60K35]
3=|82B44  Disordered systems (random Ising models, random
..........Schr\"odinger operators, etc.)
3=|82B80  Numerical methods (Monte Carlo, series resummation, etc.) 
..........[See also 65-XX, 81T80]
3=|82B99  Miscellaneous topics

2=|82Cxx  Time-dependent statistical mechanics (dynamic and nonequilibrium)
3=|82C03  Foundations
3=|82C05  Classical dynamic and nonequilibrium statistical mechanics (general)
3=|82C10  Quantum dynamics and nonequilibrium statistical mechanics (general)
3>|82C20  Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs 
........../:> and systems on graphs
3=|82C21  Dynamic continuum models (systems of particles, etc.)
3=|82C22  Interacting particle systems [See also 60K35]
3~|82C23  Exactly solvable dynamic models [See also 37K60] // 37K60 ~ 58F07]
3>|82C24  Interface problems; diffusion-limited aggregation 
........../:> ; diffusion-limited aggrgation
3=|82C26  Dynamic and nonequilibrium phase transitions (general)
3=|82C27  Dynamic critical phenomena
3=|82C28  Dynamic renormalization group methods [See also 81T17]
3=|82C31  Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]
3~|82C32  Neural nets [See also 68T05, 92B20, 91E40] // 91E40 ~ 92J40
3=|82C35  Irreversible thermodynamics, including Onsager-Machlup theory
3=|82C40  Kinetic theory of gases
3~|82C41  Dynamics of random walks, random surfaces, lattice
..........animals, etc. [See also 60G50] // 60G50 ~ 60J15
3=|82C43  Time-dependent percolation [See also 60K35]
3=|82C44  Dynamics of disordered systems (random Ising systems, etc.)
3=|82C70  Transport processes
3=|82C80  Numerical methods (Monte Carlo, series resummation, etc.)
3=|82C99  None of the above, but in this section

2=|82Dxx  Applications to specific types of physical systems
3=|82D05  Gases
3=|82D10  Plasmas
3=|82D15  Liquids
3=|82D20  Solids
3=|82D25  Crystals {For crystallographic group theory, see 20H15}
3=|82D30  Random media, disordered materials (including liquid crystals 
..........and spin glasses)
3=|82D35  Metals
3+|82D37  Semiconductors 
3=|82D40  Magnetic materials
3=|82D45  Ferroelectrics
3=|82D50  Superfluids
3=|82D55  Superconductors
3=|82D60  Polymers
3>|82D75  Nuclear reactor theory; neutron transport /:> ; neutron transport
3=|82D99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|83-XX  Relativity and gravitational theory 
8=|83-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|83-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|83-02  Research exposition (monographs, survey articles)
8=|83-03  Historical (must also be assigned at least one classification number 
..........from Section 01)
8=|83-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8~|83-05  Experimental work // work ~ papers
8=|83-06  Proceedings, conferences, collections, etc.
8=|83-08  Computational methods

4=|83A05  Special relativity

4=|83B05  Observational and experimental questions

2=|83Cxx  General relativity
3=|83C05  Einstein's equations (general structure, canonical formalism, 
..........Cauchy problems)
3=|83C10  Equations of motion
3=|83C15  Exact solutions
3=|83C20  Classes of solutions; algebraically special solutions,
..........metrics with symmetries
3<|83C22  Einstein-Maxwell equations
........../~ Electromagnetics fields Einstein-Maxwell equations
3=|83C25  Approximation procedures, weak fields
3=|83C27  Lattice gravity, Regge calculus and other discrete methods
3=|83C30  Asymptotic procedures (radiation, news functions, 
..........{\scr H}-spaces, etc.)
3=|83C35  Gravitational waves
3=|83C40  Gravitational energy and conservation laws; groups of motions
3=|83C45  Quantization of the gravitational field
3~|83C47  Methods of quantum field theory[See also 81T20]
..........// Methods of quantum field theory ~ Quantum field theory aspects 
3=|83C50  Electromagnetic fields
3=|83C55  Macroscopic interaction of the gravitational field with matter 
..........(hydrodynamics, etc.)
3=|83C57  Black holes
3>|83C60  Spinor and twistor methods; Newman-Penrose formalism 
........../:> ; Newman-Penrose formalism
3+|83C65  Methods of noncommutative geometry [See also 58B34]
3=|83C75  Space-time singularities, cosmic censorship, etc.
3+|83C80  Analogues in lower dimensions 
3=|83C99  None of the above but in this section

4=|83D05  Relativistic gravitational theories other than
..........Einstein's, including asymmetric field theories

2=|83Exx  Unified, higher-dimensional and super field theories
3=|83E05  Geometrodynamics
3=|83E15  Kaluza-Klein and other higher-dimensional theories
3=|83E30  String and superstring theories [See also 81T30]
3=|83E50  Supergravity
3=|83E99  None of the above, but in this section

4=|83F05  Cosmology 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|85-XX  Astronomy and astrophysics 
..........{For celestial mechanics, see 70F15} 
8=|85-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|85-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|85-02  Research exposition (monographs, survey articles)
8=|85-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|85-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8~|85-05  Experimental work // work ~ papers
8=|85-06  Proceedings, conferences, collections, etc.
8=|85-08  Computational methods

5=|85A04  General
5=|85A05  Galactic and stellar dynamics
5=|85A15  Galactic and stellar structure
5~|85A20  Planetary atmospheres /~ Stellar atmospheres 
5=|85A25  Radiative transfer
5=|85A30  Hydrodynamic and hydromagnetic problems [See also 76Y05]
5=|85A35  Statistical astronomy
5=|85A40  Cosmology, {For relativistic cosmology, see 83F05}
5-|85A45  radio astronomy 
5=|85A99  Miscellaneous topics 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1<|86-XX  Geophysics [See also 76U05, 76V05] /:< 73N05, 
8=|86-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|86-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|86-02  Research exposition (monographs, survey articles)
8=|86-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|86-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8~|86-05  Experimental work // work ~ papers
8=|86-06  Proceedings, conferences, collections, etc.
8=|86-08  Computational methods

5=|86A04  General
5~|86A05  Hydrology, hydrography, oceanography [See also 76Bxx,
..........76E20, 76Q05, 76Rxx, 76U05] /:< 76C15, // 76Bxx ~ 76B15, 76B20, 76B25
5<|86A10  Meteorology and atmospheric physics [See also 76Bxx, 
..........76E20, 76N15, 76Q05, 76Rxx, 76U05] /:< 76C15, 76C20, 76V05
5<|86A15  Seismology /:< [See also 73Dxx, 73Fxx, 73M25, 73N20, 73Q05]
5=|86A17  Global dynamics, earthquake problems
5<|86A20  Potentials, prospecting /:< [See also 76S05, 76W05]
5=|86A22  Inverse problems [See also 35R30]
5>|86A25  Geo-electricity and geomagnetism [See also 76W05, 78A25] /:> 76W05, 
5=|86A30  Geodesy, mapping problems
5=|86A32  Geostatistics
5=|86A40  Glaciology
5=|86A60  Geological problems
5=|86A99  Miscellaneous topics 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1~|90-XX  Operations research, mathematical programming 
........../~ Economics, operations research, programming, games 
8=|90-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|90-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|90-02  Research exposition (monographs, survey articles)
8=|90-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|90-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|90-06  Proceedings, conferences, collections, etc.
8=|90-08  Computational methods

2-|90Axx  mathematical economics {for econometrics, see 62P20} 
3-|90A05  decision theory [See also 62Cxx, 90B50, 90D35] 
3-|90A06  individual preferences 
3-|90A07  group preferences 
3-|90A08  social choice 
3-|90A09  finance, portfolios, investment 
3-|90A10  utility theory 
3-|90A11  production theory, theory of the firm 
3-|90A12  price theory and market structure 
3-|90A14  equilibrium: general theory 
3-|90A15  general economic models, trade models 
3-|90A16  dynamic economic models, growth models 
3-|90A17  multisectoral models 
3-|90A19  statistical models; economic indexes and measures 
3-|90A20  economic time series analysis [see also 62M10] 
3-|90A25  spatial models 
3-|90A27  public goods 
3-|90A28  voting theory 
3-|90A30  environmental economics (natural resource models, harvesting, 
..........pollution, etc.) 
3-|90A35  informational economics 
3-|90A36  incentives theory 
3-|90A40  consumer behavior, demand theory 
3-|90A43  expected utility; risk-averse utility 
3-|90A46  risk theory 
3-|90A50  labor market 
3-|90A53  special types of economies 
3-|90A56  special types of equilibria 
3-|90A58  models of real-world systems; general macro-economic models, etc. 
3-|90A60  market models (auctions, bargaining, bidding, selling, etc.) 
3-|90A70  macro-economic policy-making, taxation 
3-|90A80  resource allocation 
3-|90A99  none of the above but in this section 

2=|90Bxx  Operations research and management science
3=|90B05  Inventory, storage, reservoirs
3=|90B06  Transportation, logistics
3~|90B10  Network models,deterministic // Network models, ~ Flows in networks, 
3-|90B12  communication network [See also 68M10, 94A05] 
3~|90B15  Network models, stochastic /~ Flows in networks, probabilistic
3+|90B18  Communication networks [See also 68M10, 94A05] 
3~|90B20  Traffic problems /~ Highway traffic
3=|90B22  Queues and service [See also 60K25, 68M20]
3=|90B25  Reliability, availability, maintenance, inspection 
..........[See also 60K10, 62N05]
3=|90B30  Production models
3>|90B35  Scheduling theory, deterministic [See also 68M20] 
........../:> , deterministic 
3+|90B36  Scheduling theory, stochastic [See also 68M20]
3=|90B40  Search theory
3~|90B50  Management decision making, including multiple
..........objectives [See also 90C31, 91A35, 91B05] // 91A35, 91B05 ~ 90D35, 90A05 
3=|90B60  Marketing, advertising [See also 90A60]
3~|90B70   Theory of organizations, manpower planning [See also 91D35] 
.......... /~ Theory of organizations, industrial and manpower planning [See also 92H25] 
3=|90B80  Discrete location and assignment [See also 90C10]
3=|90B85  Continuous location
3=|90B90  Case-oriented studies
3=|90B99  None of the above, but in this section

2<|90Cxx  Mathematical programming /:< [See also 49Mxx, 65Kxx]
3=|90C05  Linear programming
3=|90C06  Large-scale problems
3=|90C08  Special problems of linear programming (transportation, 
..........multi-index, etc.)
3=|90C09  Boolean programming
3=|90C10  Integer programming
3=|90C11  Mixed integer programming
3=|90C15  Stochastic programming
3=|90C20  Quadratic programming
3+|90C22  Semidefinite programming 
3=|90C25  Convex programming
3<|90C26  Nonconvex programming /:< , quasiconvex programming
3=|90C27  Combinatorial optimization
3-|90C28  geometric programming 
3<|90C29  Multi-objective and goal programming /:< ; vector optimization 
3=|90C30  Nonlinear programming
3=|90C31  Sensitivity, stability, parametric optimization
3=|90C32  Fractional programming
3=|90C33  Complementarity problems
3=|90C34  Semi-infinite programming
3>|90C35  Programming involving graphs or networks 
..........[See also 90C27] /:> [See also 90C27]
3=|90C39  Dynamic programming [See also 49L20]
3=|90C40  Markov and semi-Markov decision processes
3-|90C42  Markov programming and Markov renewal programming 
3-|90C45  continuous programming 
3+|90C46  Optimality conditions, duality [See also 49N15] 
3+|90C47  Minimax problems [See also 49K35] 
3=|90C48  Programming in abstract spaces
3+|90C50  Extreme-point and pivoting methods 
3+|90C51  Interior-point methods 
3+|90C52  Methods of reduced gradient type 
3+|90C53  Methods of quasi-Newton type 
3+|90C55  Methods of successive quadratic programming type 
3+|90C56  Derivative-free methods 
3+|90C57  Polyhedral combinatorics, branch-and-bound, branch-and-cut 
3+|90C59  Approximation methods and heuristics 
3=|90C60  Abstract computational complexity for mathematical programming 
..........problems [See also 68Q25]
3=|90C70  Fuzzy programming
3=|90C90  Applications of mathematical programming
3=|90C99  None of the above, but in this section

2-|90Dxx  game theory 
3-|90D05  $2$-person games 
3-|90D06  $n$-person games, $n>2$ 
3-|90D10  noncooperative games 
3-|90D12  cooperative games 
3-|90D13  games with infinitely many players 
3-|90D15  stochastic games [See also 93E05] 
3-|90D20  multistage and repeated games 
3-|90D25  differential games [see also 49N55] 
3-|90D26  pursuit and evasion games 
3-|90D35  decision theory for games [see also 62Cxx, 90A05, 90B50] 
3-|90D40  game-theoretic models [see also 65Cxx] 
3-|90D42  positional games 
3-|90D43  games involving graphs 
3-|90D44  games involving topology or set theory 
3-|90D46  combinatorial games 
3-|90D50  discrete-time games 
3-|90D55  games of timing 
3-|90D60  probabilistic games; gambling 
3-|90D65  hierarchical games 
3-|90D70  spaces of games 
3-|90D80  applications of game theory 
3-|90D99  none of the above but in this section 

%%+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1+|91-XX  Game theory, economic, social and behavioral sciences 
8+|91-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.) 
8+|91-01  Instructional exposition (textbooks, tutorial papers, etc.) 
8+|91-02  Research exposition (monographs, survey articles) 
8+|91-03  Historical (must also be assigned at least one 
..........classification number from section 01) 
8+|91-04  Explicit machine computation and programs (not the
..........theory of computation or programming) 
8+|91-06  Proceedings, conferences, collections, etc. 
8+|91-08  Computational methods 

2+|91Axx  Game theory 
3+|91A05  2-person games 
3+|91A06  $n$-person games, $n>2$ 
3+|91A10  Noncooperative games 
3+|91A12  Cooperative games 
3+|91A13  Games with infinitely many players 
3+|91A15  Stochastic games 
3+|91A18  Games in extensive form
3+|91A20  Multistage and repeated games 
3+|91A22  Evolutionary games 
3+|91A23  Differential games [See also 49N70]
3+|91A24  Positional games (pursuit and evasion, etc.) [See also 49N75]
3+|91A25  Dynamic games
3+|91A26  Rationality, learning
3+|91A28  Signaling, communication 
3+|91A30  Utility theory for games [See also 91B10] 
3+|91A35  Decision theory for games [See also 62Cxx, 91B05, 90B50] 
3+|91A40  Game-theoretic models 
3+|91A43  Games involving graphs 
3+|91A44  Games involving topology or set theory 
3+|91A46  Combinatorial games 
3+|91A50  Discrete-time games 
3+|91A55  Games of timing 
3+|91A60  Probabilistic games; gambling 
3+|91A65  Hierarchical games 
3+|91A70  Spaces of games 
3+|91A80  Applications of game theory 
3+|91A90  Experimental studies 
3+|91A99  None of the above, but in this section 

2+|91Bxx  Mathematical economics {For econometrics, see 62P20} 
3+|91B02  Fundamental topics (basic mathematics, methodology; applicable to economics in general)
3+|91B05  Decision theory [See also 62Cxx, 90B50, 91A35] 
3+|91B06  Individual preferences 
3+|91B07  Group preferences 
3+|91B08  Social choice 
3+|91B09  Finance, portfolios, investment 
3+|91B10  Utility theory 
3+|91B11  Production theory, theory of the firm 
3+|91B12  Price theory and market structure 
3+|91B14  Equilibrium: General theory 
3+|91B15  General economic models, trade models 
3+|91B16  Dynamic economic models, growth models 
3+|91B17  Multisectoral models 
3+|91B18  Matching models 
3+|91B19  Statistical models; economic indexes and measures 
3+|91B20  Economic time series analysis [See also 62M10] 
3+|91B21  Stochastic models 
3+|91B25  Spatial models 
3+|91B27  Public goods 
3+|91B28  Voting theory 
3+|91B30  Environmental economics (natural resource models, harvesting, 
..........pollution, etc.) 
3+|91B35  Informational economics 
3+|91B40  Consumer behavior, demand theory 
3+|91B46  Risk theory, insurance 
3+|91B50  Labor market, contracts 
3+|91B53  Special types of economies 
3+|91B56  Special types of equilibria 
3+|91B58  Models of real-world systems; general macro-economic models, etc. 
3+|91B60  Market models (auctions, bargaining, bidding, selling, etc.) 
3+|91B70  Macro-economic models (monetary models, models of taxation)
3+|91B80  Resource allocation 
3+|91B99  None of the above, but in this section 

2+|91Cxx  Social and behavioral sciences: methodology 
..........{For statistics, see 62-XX} 
3+|91C05  Measurement theory 
3+|91C15  One- and multi-dimensional scaling 
3+|91C20  Clustering [See also 62D30] 
3+|91C99  None of the above, but in this section 

2+|91Dxx  Mathematical sociology (including anthropology) 
3+|91D10  Models of societies, social and urban evolution 
3+|91D20  Mathematical geography and demography 
3+|91D25  Spatial models [See also 91B25] 
3+|91D30  Social networks 
3+|91D35  Manpower systems [See also 91B50, 90B70] 
3+|91D99  None of the above, but in this section 

2+|91Exx  Mathematical psychology 
3+|91E10  Cognitive psychology 
3+|91E30  Psychophysics and psychophysiology; perception 
3+|91E40  Memory and learning [See also 68T05] 
3+|91E45  Measurement and performance 
3+|91E99  None of the above, but in this section 

2+|91Fxx  Other social and behavioral sciences (mathematical treatment) 
3+|91F10  History, political science 
3+|91F20  Linguistics [See also 03B65, 68T50] 
3+|91F99  None of the above, but in this section 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1<|92-XX  Biology and other natural sciences /:< , behavioral sciences 
8=|92-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|92-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|92-02  Research exposition (monographs, survey articles)
8=|92-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|92-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|92-06  Proceedings, conferences, collections, etc.
8=|92-08  Computational methods

2=|92Bxx  Mathematical biology in general
3=|92B05  General biology and biomathematics
3=|92B10  Taxonomy, statistics
3=|92B15  General biostatistics [See also 62P10]
3>|92B20  Neural networks artificial life and related topics [See also 68T05, 82C32, 94Cxx]
........../:> artificial life and related topics
3=|92B99  None of the above, but in this section

2=|92Cxx  Physiological, cellular and medical topics
3=|92C05  Biophysics
3~|92C10  Biomechanics [See also 74L15] // 74L15 ~ 73P05
3=|92C15  Developmental biology, pattern formation
3+|92C17  Cell movement (chemotaxis, etc.) 
3=|92C20  Neural biology
3=|92C30  Physiology (general)
3=|92C35  Physiological flow [See also 76Z05]
3+|92C37  Cell biology 
3=|92C40  Biochemistry, molecular biology
3=|92C45  Kinetics in biochemical problems (pharmacokinetics, enzyme 
..........kinetics, etc.) [See also 80A30]
3=|92C50  Medical applications (general)
3=|92C55  Biomedical imaging and signal processing [See also 44A12, 65R10]
.......... // Biomedical imaging and signal processing  ~ Tomography
3=|92C60  Medical epidemiology
3+|92C80  Plant biology 
3=|92C99  None of the above, but in this section

2=|92Dxx  Genetics and population dynamics
3=|92D10  Genetics {For genetic algebras, see 17D92}
3=|92D15  Problems related to evolution
3=|92D20  Protein sequences, DNA sequences
3=|92D25  Population dynamics (general)
3=|92D30  Epidemiology
3=|92D40  Ecology
3=|92D50  Animal behavior
3=|92D99  None of the above, but in this section

2=|92Exx  Chemistry {For biochemistry, see 92C40}
3=|92E10  Molecular structure (graph-theoretic methods, methods
..........of differential topology, etc.)
3=|92E20  Classical flows, reactions, etc. [See also 80A30, 80A32]
3=|92E99  None of the above, but in this section

4=|92F05  Other natural sciences

2-|92Gxx  social and behavioral sciences: methodology {for statistics,
..........see 62-XX} 
3-|92G05  measurement theory 
3-|92G15  one- and multidimensional scaling 
3-|92G20  test theory 
3-|92G25  questionnaire analysis 
3-|92G30  clustering [see also 62H30} 
3-|92G40  Q-analysis 
3-|92G99  none of the above but in this section 

2-|92Hxx  mathematical sociology (including anthropology) 
3-|92H10  models of societies, social and urban evolution 
3-|92H20  mathematical geography and demography 
3-|92H25  spatial models [see also 90A25] 
3-|92H30  social networks 
3-|92H35  manpower systems [see also 90A50, 90B70] 
3-|92H99  none of the above but in this section 

2-|92Jxx  mathematical psychology 
3-|92J10  cognitive psychology 
3-|92J30  psychophysics and psychophysiology; perception 
3-|92J40  memory and learning [see also 68T05] 
3-|92J45  measurement and performance 
3-|92J99  none of the above but in this section 

2-|92Kxx  Other social and behavioral sciences (mathematical treatment) 
3-|92K10  history, political science 
3-|92K20  linguistics [see also 03B65, 68S05] 
3-|92K99  none of the above but in this section 

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|93-XX  Systems theory; control {For optimal control, see 49-XX} 
8=|93-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|93-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|93-02  Research exposition (monographs, survey articles)
8=|93-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|93-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|93-06  Proceedings, conferences, collections, etc.

2=|93Axx  General
3=|93A05  Axiomatic system theory
3=|93A10  General systems
3=|93A13  Hierarchical systems
3=|93A14  Decentralized systems
3=|93A15  Large scale systems
3-|93A20  cascaded systems 
3-|93A25  input-output systems 
3=|93A30  Mathematical modeling (models of systems, model-matching, etc.)
3=|93A99  None of the above, but in this section

2=|93Bxx  Controllability, observability, and system structure
3=|93B03  Attainable sets
3=|93B05  Controllability
3-|93B06  relations between controllability and optimal solutions 
3=|93B07  Observability
3=|93B10  Canonical structure
3=|93B11  System structure simplification
3=|93B12  Variable structure systems
3~|93B15  Realizations from input-output data 
..........// Realizations ~ realizability of systems 
3=|93B17  Transformations
3~|93B18  Linearizations /~ Linearizability
3=|93B20  Minimal systems representations
3=|93B25  Algebraic methods
3=|93B27  Geometric methods (including algebro-geometric)
3>|93B28  Operator-theoretic methods [See also 47A48, 47A57, 47B35, 47N70] /:> 47A48, 47B35,
3=|93B29  Differential-geometric methods
3=|93B30  System identification
3=|93B35  Sensitivity (robustness)
3=|93B36  $H^\infty$-control
3=|93B40  Computational methods
3=|93B50  Synthesis problems
3=|93B51  Design techniques (robust design, computer-aided design, etc.)
3=|93B52  Feedback control
3=|93B55  Pole and zero placement problems
3=|93B60  Eigenvalue problems
3=|93B99  None of the above, but in this section

2=|93Cxx  Control systems, guided systems
3>|93C05  Linear systems /:> systems
3>|93C10  Nonlinear systems /:> systems
3>|93C15  Systems governed by ordinary differential equations [See also 34H05] 
.......... /:> [See also 34H05]
3>|93C20  Systems governed by partial differential equations [See also 35B37]
.......... /:> [See also 35B37]
3-|93C22  systems governed by integral equations 
3+|93C23  Systems governed by functional differential equations [See also 34K35] 
3=|93C25  Systems in abstract spaces
3~|93C30  Systems governed by functional relations other than differential equations
..........// equations ~ or integral equations
3~|93C35   Multivariable systems /~ Multivariable, multidimensional systems
3<|93C40  Adaptive control /:< systems
3=|93C41  Problems with incomplete information
3=|93C42  Fuzzy control
3-|93C45  time-invariant 
3-|93C50  time-dependent 
3>|93C55  Discrete-time systems /:> systems
3>|93C57  Sampled-data systems /:> systems
3-|93C60  continuous-time 
3=|93C62  Digital systems
3+|93C65  Discrete event systems 
3~|93C70  Time-scale analysis and singular perturbations 
..........// singular perturbations ~ related topics 
3<|93C73  Perturbations /:< in control systems
3=|93C80  Frequency-response methods
3=|93C83  Control problems involving computers (process control, etc.)
3>|93C85  Automated systems (robots, etc.)  [See also 68T40, 70B15, 70Q05]
.......... /:>  [See also 68T40, 70B15, 70Q05]
3-|90C90  random disturbaces in control systems 
3<|93C95  Applications /:< of control systems
3=|93C99  None of the above, but in this section

2=|93Dxx  Stability
3=|93D05  Lyapunov and other classical stabilities (Lagrange, Poisson, 
..........$L^p, l^p$, etc.)
3=|93D09  Robust stability
3=|93D10  Popov-type stability of feedback systems
3=|93D15  Stabilization of systems by feedback
3=|93D20  Asymptotic stability
3=|93D21  Adaptive or robust stabilization
3-|93D22  interrelations between stability problems and optimization problems 
3=|93D25  Input-output approaches
3=|93D30  Scalar and vector Lyapunov functions
3=|93D99  None of the above, but in this section

2=|93Exx  Stochastic systems and control
3=|93E03  Stochastic systems, general
3-|93E05  stochastic games, stochastic differential games [See also 90D15] 
3=|93E10  Estimation and detection [See also 60G35]
3=|93E11  Filtering [See also 60G35]
3=|93E12  System identification
3=|93E14  Data smoothing
3=|93E15  Stochastic stability
3=|93E20  Optimal stochastic control
3-|93E23  stochastic gradient methods
3=|93E24  Least squares and related methods
3=|93E25  Other computational methods
3-|93E30  computer simulation of stochastic systems 
3=|93E35  Stochastic learning and adaptive control
3=|93E99  None of the above, but in this section

%%=%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1=|94-XX  Information and communication, circuits 
8=|94-00  General reference works (handbooks, dictionaries,
..........bibliographies, etc.)
8=|94-01  Instructional exposition (textbooks, tutorial papers, etc.)
8=|94-02  Research exposition (monographs, survey articles)
8=|94-03  Historical (must also be assigned at least one
..........classification number from Section 01)
8=|94-04  Explicit machine computation and programs (not the
..........theory of computation or programming)
8=|94-06  Proceedings, conferences, collections, etc.

2=|94Axx  Communication, information
3=|94A05  Communication theory [See also 60G35, 90B18]
3+|94A08  Image processing (compression, reconstruction, etc.) [See also 68U10]
3=|94A11  Application of orthogonal functions in communication
3=|94A12  Signal theory (characterization, reconstruction, etc.)
3=|94A13  Detection theory
3=|94A14  Modulation and demodulation
3=|94A15  Information theory, general [See also 62B10]
3=|94A17  Measures of information, entropy
3+|94A20  Sampling theory 
3=|94A24  Coding theorems (Shannon theory)
3>|94A29  Source coding [See also 68P30] /:> [See also 68P30]
3=|94A34  Rate-distortion theory
3=|94A40  Channel models
3=|94A45  Prefix, length-variable, comma-free codes [See also 20M35, 68Q45]
3=|94A50  Theory of questionnaires
3>|94A55  Shift register sequences and sequences over finite alphabets
........../:> and sequences over finite alphabets
3=|94A60  Cryptography [See also 11T71, 68P25]
3+|94A62  Authentication and secret sharing
3=|94A99  None of the above, but in this section

2>|94Bxx  Theory of error-correcting codes and error-detecting codes
.......... /:> and error-detecting codes 
3=|94B05  Linear codes, general
3=|94B10  Convolutional codes
3=|94B12  Combined modulation schemes (including trellis codes)
3=|94B15  Cyclic codes
3=|94B20  Burst-correcting codes
3=|94B25  Combinatorial codes
3=|94B27  Geometric methods (including applications of algebraic geometry) 
..........[See also 11T71]
3=|94B30  Majority codes
3=|94B35  Decoding
3=|94B40  Arithmetic codes [See also 11T71]
3=|94B50  Synchronization error-correcting codes
3=|94B60  Other types of codes
3=|94B65  Bounds on codes
3=|94B70  Error probability
3=|94B75  Applications of the theory of convex sets and geometry
..........of numbers (covering radius, etc.) [See also 11H31]
3=|94B99  None of the above, but in this section

2=|94Cxx  Circuits, networks
3=|94C05  Analytic circuit theory
3=|94C10  Switching theory, application of Boolean algebra;
..........Boolean functions [See also 06E30]
3=|94C12  Fault detection; testing
3=|94C15  Applications of graph theory [See also 05Cxx, 68R10]
3=|94C30  Applications of design theory [See also 05Bxx]
3=|94C99  None of the above, but in this section

4<|94D05  Fuzzy sets and logic (in connection with questions of
..........Section 94) [See also 03B52, 03E72, 28E10] /:< 04A72,

%%+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1+|97-XX  Mathematics education 
8+|97-00  General reference works (handbooks, dictionaries, 
..........bibliographies, etc.) 
8+|97-01  Instructional exposition (textbooks, tutorial papers, etc.) 
8+|97-02  Research exposition (monographs, survey articles) 
8+|97-03  Historical (must also be assigned at least one 
..........classification number from Section 01) 
8+|97-04  Explicit machine computation and programs (not the theory 
..........of computation or programming) 
8+|97-06  Proceedings, conferences, collections, etc. 

2+|97Axx  General 
3+|97A20  Recreational mathematics [See also 00A08] 
3+|97A40  Sociological issues [See also 97C60] 
3+|97A80  Standards [See also 97B70] 
3+|97A90  Fiction and games 

2+|97Bxx  Educational policy and educational systems 
3+|97B10  Educational research and planning 
3+|97B20  General education 
3+|97B30  Vocational education 
3+|97B40  Higher education 
3+|97B50  Teacher education {For research aspects see 97C70} 
3+|97B60  Out-of-school education. Adult and further education 
3+|97B70  Syllabuses. Curriculum guides, official documents [See also 97A80] 
3+|97B99  None of the above, but in this section 

2+|97Cxx  Psychology of and research in mathematics education 
3+|97C20  Affective aspects (motivation, anxiety, persistence, etc.) 
3+|97C30  Student learning and thinking (misconceptions,
..........cognitive development, problem solving, etc.) 
3+|97C40  Assessment (large scale assessment, validity, reliability, etc.) 
..........[See also 97D10] 
3+|97C50  Theoretical perspectives (learning theories, epistemology, 
..........philosophies of teaching and learning, etc.)
..........[See also 97D20] 
3+|97C60  Sociological aspects of learning (culture, group interactions, 
..........equity issues, etc.) 
3+|97C70  Teachers, and research on teacher education (teacher development, 
..........etc.) [See also 97B50] 
3+|97C80  Technological tools and other materials in teaching and learning 
..........(research on innovations, role in student learning, use of 
..........tools by teachers, etc.) 
3+|97C90  Teaching and curriculum (innovations, teaching practices, 
..........studies of curriculum materials, effective teaching, etc. ) 
3+|97C99  None of the above, but in this section 

2+|97Dxx  Education and instruction in mathematics 
3+|97D10  Comparative studies on mathematics education [See also 97C40] 
3+|97D20  Philosophical and theoretical contributions to mathematical 
..........education [See also 97C50] 
3+|97D30  Goals of mathematics teaching. Curriculum development 
3+|97D40  Teaching methods and classroom techniques. Lesson preparation. 
..........Educational principles {For research aspects see 97Cxx} 
3+|97D50  Teaching problem solving and heuristic strategies 
..........{For research aspects see 97Cxx} 
3+|97D60  Achievement control and rating 
3+|97D70  Diagnosis, analysis and remediation of learning difficulties 
..........and student errors 
3=|97D80  Teaching units, draft lessons and master lessons 
3+|97D99  None of the above, but in this section 

2+|97Uxx  Educational material and media. Educational technology 
3+|97U20  Analysis of textbooks, development and evaluation of textbooks. 
..........Textbook use in the classroom 
3+|97U30  Teacher manuals and planning aids 
3+|97U40  Problem books; students competitions, examination questions 
3+|97U50  Computer assisted instruction and programmed instruction 
3+|97U60  Manipulative materials and their use in the classroom
..........{For research aspects see 97C80} 
3+|97U70  Technological tools (computers, calculators, software, etc.) 
..........and their use in the classroom 
3+|97U80  Audiovisual media and their use in instruction 
3+|97U99  None of the above, but in this section