00-XX General
00Axx General and miscellaneous specific topics
00Bxx Conference proceedings and collections of papers
01-XX History and biography [See also the classification number -03 in the other sections]
01Axx History of mathematics and mathematicians
03-XX Mathematical logic and foundations
03Bxx General logic
03Cxx Model theory
03Dxx Computability and recursion theory
/:> Computability and
03Exx Set theory
/:< [See also 04-XX]
03Fxx Proof theory and constructive mathematics
03Gxx Algebraic logic
03Hxx Nonstandard models [See also 03C62]
04-XX
Set theory [See also 03Exx] %% this section has been deleted {For set theory, see 03Exx}
05-XX Combinatorics {For finite fields, see 11Txx}
05Axx Classical combinatorial problems
05Bxx Designs and configurations {For applications of design theory, see 94C30}
05Cxx Graph theory {For applications of graphs, see 68R10, 90C35, 94C15}
/:< 68Q90,
05Dxx Extremal combinatorics
05Exx Algebraic combinatorics
06-XX Order, lattices, ordered algebraic structures [See also 18B35]
06Axx Ordered sets
06Bxx Lattices [See also 03G10]
06Cxx Modular lattices, complemented lattices
06Dxx Distributive lattices
06Exx Boolean algebras (Boolean rings) [See also 03G05]
06Fxx Ordered structures
08-XX General algebraic systems
08Axx Algebraic structures [See also 03C05]
08Bxx Varieties
08Cxx Other classes of algebras
11-XX Number theory
11Axx Elementary number theory {For analogues in number fields, see 11R04}
11Bxx Sequences and sets
11Cxx Polynomials and matrices
11Dxx Diophantine equations [See also 11Gxx, 14Gxx]
11Exx Forms and linear algebraic groups [See also 19Gxx] {For quadratic forms in linear algebra, see 15A63}
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}
11Gxx Arithmetic algebraic geometry (Diophantine geometry) [See also 11Dxx, 14-XX, 14Gxx, 14Kxx]
11Hxx Geometry of numbers {For applications in coding theory, see 94B75}
11Jxx Diophantine approximation, transcendental number theory [See also 11K60]
11Kxx Probabilistic theory: distribution modulo $1$; metric theory of algorithms
11Lxx Exponential sums and character sums {For finite fields, see 11Txx}
11Mxx Zeta and $L$-functions: analytic theory
11Nxx Multiplicative number theory
11Pxx Additive number theory; partitions
11Rxx Algebraic number theory: global fields {For complex multiplication, see 11G15}
11Sxx Algebraic number theory: local and $p$-adic fields
11Txx Finite fields and commutative rings (number-theoretic aspects)
11Uxx Connections with logic
11Yxx Computational number theory [See also 11-04]
12-XX Field theory and polynomials
12Dxx Real and complex fields
12Exx General field theory
12Fxx Field extensions
12Gxx Homological methods (field theory)
12Hxx Differential and difference algebra
12Jxx Topological fields
12Kxx Generalizations of fields
12Lxx Connections with logic
13-XX Commutative rings and algebras
13Axx General commutative ring theory
13Bxx Ring extensions and related topics
13Cxx Theory of modules and ideals
13Dxx Homological methods {For noncommutative rings, see 16Exx; for general categories, see 18Gxx}
(Co)homological methods
13Exx Chain conditions, finiteness conditions
13Fxx Arithmetic rings and other special rings
/:< [See also 12-XX]
13Hxx Local rings and semilocal rings
13Jxx Topological rings and modules [See also 16W60, 16W80]
13Mxx Finite commutative rings {For number-theoretic aspects, see 11Txx}
13Nxx Differential algebra [See also 12H05, 14F10]
13Pxx Computational aspects of commutative algebra [See also 68W30]
// 68W30 ~ 68Q40
14-XX Algebraic geometry
14Axx Foundations
14Bxx Local theory
/:< [See also 32Sxx]
14Cxx Cycles and subschemes
14Dxx Families, fibrations
14Exx Birational geometry
Mappings and correspondences
14Fxx (Co)homology theory [See also 13Dxx]
14Gxx Arithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx]
14Hxx Curves
14Jxx Surfaces and higher-dimensional varieties {For analytic theory, see 32Jxx}
14Kxx Abelian varieties and schemes
14Lxx Algebraic groups {For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45}
// Algebraic groups ~ group schemes
14Mxx Special varieties
14Nxx Projective and enumerative geometry [See also 51-XX]
Classical methods and problems [See also 51-XX]
14Pxx Real algebraic and real analytic geometry
14Qxx Computational aspects in algebraic geometry [See also 12Y05, 13Pxx, 68W30]
// 12Y05, 13Pxx, 68W30 ~ 12-04, 68Q40
14Rxx Affine geometry
15-XX Linear and multilinear algebra; matrix theory
/:< (Finite and infinite)
16-XX Associative rings and algebras {For the commutative case, see 13-XX}
16Bxx General and miscellaneous
16Dxx Modules, bimodules and ideals
16Exx Homological methods {For commutative rings, see 13Dxx; for general categories, see 18Gxx}
Homological methods and results [See also 18Gxx]
16Gxx Representation theory of rings and algebras
16Kxx Division rings and semisimple Artin rings [See also 12E15, 15A30]
16Lxx Local rings and generalizations
16Nxx Radicals and radical properties of rings
16Pxx Chain conditions, growth conditions, and other forms of finiteness
16Rxx Rings with polynomial identity
16Sxx Rings and algebras arising under various constructions
16Uxx Conditions on elements
/:< (Including elements of matrix rings, etc.)
16Wxx Rings and algebras with additional structure
16Yxx Generalizations {For nonassociative rings, see 17-XX}
17-XX Nonassociative rings and algebras
17Axx General nonassociative rings
17Bxx Lie algebras and Lie superalgebras {For Lie groups, see 22Exx}
/:> And Lie superalgebras
17Cxx Jordan algebras (algebras, triples and pairs)
17Dxx Other nonassociative rings and algebras
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
18Axx General theory of categories and functors
18Bxx Special categories
18Cxx Categories and theories
Categories and algebraic theories
18Dxx Categories with structure
18Exx Abelian categories
18Fxx Categories and geometry
18Gxx Abstract homological algebra [See also 13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx]
/:> Abstract /:> 20Jxx, 55Nxx, 57Txx,
19-XX $K$-theory [See also 16E20, 18F25]
19Axx Grothendieck groups and $K_0$ [See also 13D15, 18F30]
19Bxx Whitehead groups and $K_1$
19Cxx Steinberg groups and $K_2$
19Dxx Higher algebraic $K$-theory
19Exx $K$-theory in geometry
19Fxx $K$-theory in number theory [See also 11R70, 11S70]
19Gxx $K$-theory of forms [See also 11Exx]
19Jxx Obstructions from topology
19Kxx $K$-theory and operator algebras [See mainly 46L80, and also 46M20]
19Lxx Topological $K$-theory [See also 55N15, 55R50, 55S25]
20-XX Group theory and generalizations
20Axx Foundations
20Bxx Permutation groups
20Cxx Representation theory of groups {For representation rings and Burnside rings, see also 19A22}
20Dxx Abstract finite groups
20Exx Structure and classification of infinite or finite groups
20Fxx Special aspects of infinite or finite groups
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
20Hxx Other groups of matrices [See also 15A30]
20Jxx Connections with homological algebra and category theory
20Kxx Abelian groups
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}
20Mxx Semigroups
20Nxx Other generalizations of groups
22-XX Topological groups, Lie groups {For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX}
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
22Bxx Locally compact Abelian groups (LCA groups)
22Dxx Locally compact groups and their algebras
22Exx Lie groups {For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis theorem, see 43A80, 43A85, 43A90}
22Fxx Noncompact transformation groups
26-XX Real functions [See also 54C30]
26Axx Functions of one variable
26Bxx Functions of several variables
26Cxx Polynomials, rational functions
26Dxx Inequalities {For maximal function inequalities, see 42B25; for functional inequalities, see 39B72; for probabilistic inequalities, see 60E15}
26Exx Miscellaneous topics [See also 58Cxx]
28-XX Measure and integration {For analysis on manifolds, see 58-XX}
28Axx Classical measure theory
28Bxx Set functions, measures and integrals with values in abstract spaces
28Cxx Set functions and measures on spaces with additional structure [See also 46G12, 58C35, 58D20]
28Dxx Measure-theoretic ergodic theory [See also 11K50, 11K55, 22D40, 47A35, 54H20, 37Axx, 60Fxx, 60G10]
// 37Axx ~ 58Fxx
28Exx Miscellaneous topics in measure theory
30-XX Functions of a complex variable {For analysis on manifolds, see 58-XX}
30Axx General properties
30Bxx Series expansions
30Cxx Geometric function theory
30Dxx Entire and meromorphic functions, and related topics
30Exx Miscellaneous topics of analysis in the complex domain
30Fxx Riemann surfaces
30Gxx Generalized function theory
31-XX Potential theory {For probabilistic potential theory, see 60J45}
31Axx Two-dimensional theory
31Bxx Higher-dimensional theory
31Cxx Other generalizations
32-XX Several complex variables and analytic spaces {For infinite-dimensional holomorphy, see also 46G20, 58B12}
32Axx Holomorphic functions of several complex variables
32Bxx Local analytic geometry [See also 13-XX and 14-XX]
32Cxx Analytic spaces
General theory of analytic spasec
32Dxx Analytic continuation
32Exx Holomorphic convexity
32Fxx Geometric convexity
/:< Partial differential operators
32Gxx Deformations of analytic structures
32Hxx Holomorphic mappings and correspondences
32Jxx Compact analytic spaces {For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic theory, see 14Jxx}
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
32Lxx Holomorphic fiber spaces [See also 55Rxx]
32Mxx Complex spaces with a group of automorphisms
32Nxx Automorphic functions [See also 11Fxx, 20H10, 22E40, 30F35]
32Qxx Complex manifolds
32Sxx Singularities
32Txx Pseudoconvex domains
32Uxx Pluripotential theory
32Vxx $CR$ manifolds
32Wxx Differential operators in several variables
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}
33Bxx Elementary classical functions
33Cxx Hypergeometric functions
33Dxx Basic hypergeometric functions
33Exx Other special functions
33Fxx Computational aspects
34-XX Ordinary differential equations
34Axx General theory
34Bxx Boundary value problems {For ordinary differential operators, see 34Lxx}
34Cxx Qualitative theory [See also 37-XX]
// 37-XX ~ 58Fxx
34Dxx Stability theory [See also 37C75, 93Dxx]
// 37C75 ~ 58F10
34Exx Asymptotic theory
34Gxx Differential equations in abstract spaces [See also 37Kxx, 34Lxx, 47Dxx, 47Hxx, 47Jxx, 58D25]
/:> 37Kxx, 34Lxx, 47Dxx, 47Hxx, 47Jxx,
34Kxx Functional-differential and differential-difference equations [See also 37-XX]
/:< , With or without deviating arguments /:> [See also 37-XX]
34Lxx Ordinary differential operators [See also 47E05]
34Mxx Differential equations in the complex domain [See also 30Dxx, 32G34]
35-XX Partial differential equations
35Axx General theory
35Bxx Qualitative properties of solutions
35Cxx Representations of solutions
35Dxx Generalized solutions of partial differential equations
35Exx Equations and systems with constant coefficients [See also 35N05]
35Fxx General first-order equations and systems
35Gxx General higher-order equations and systems
35Hxx Close-to-elliptic equations
35Jxx Partial differential equations of elliptic type [See also 58Jxx, 58J10, 58J20]
// 58Jxx, 58J10, 58J20 ~ 58G05, 58G10
35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35]
// 58J35 ~ 58G11
35Lxx Partial differential equations of hyperbolic type [See also 58J45]
// 58J45 ~ 58G16
35Mxx Partial differential equations of special type (mixed, composite, etc.) {For degenerate types, see 35J70, 35K65, 35L80}
35Nxx Overdetermined systems [See also 58Jxx, 58J10, 58J15, 58Hxx]
// 58Jxx, 58J10, 58J15 ~ 58G05, 58G07
35Pxx Spectral theory and eigenvalue problems for partial differential operators [See also 47Axx, 47Bxx, 47F05]
35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05]
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
35Sxx Pseudodifferential operators and other generalizations of partial differential operators [See also 47G30, 58J40]
// 58J40 ~ 58G15
37-XX Dynamical systems and ergodic theory [See also 26A18, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
37Axx Ergodic theory
37Bxx Topological dynamics [See also 54H20]
37Cxx Smooth dynamical systems: general theory [See also 34Cxx, 34Dxx]
37Dxx Dynamical systems with hyperbolic behavior
37Exx Low-dimensional dynamical systems
37Fxx Complex dynamical systems [See also 30D05, 32Hxx]
37Gxx Local and global bifurcation theory
37Hxx Random dynamical systems
37Jxx Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also 53Dxx, 70Hxx]
37Kxx Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx]
37Lxx Infinite-dimensional dissipative dynamical systems [See also 35Bxx, 35Qxx]
37Mxx Approximation methods and numerical treatment of dynamical systems [See also 65Pxx]
37Nxx Applications
39-XX Difference and functional equations
// Difference ~ finite differences
39Axx Difference equations {For dynamical systems, see 37-XX}
// 37-XX ~ 58Fxx
39Bxx Functional equations and inequalities [See also 30D05]
/:> And inequalities
40-XX Sequences, series, summability
40Axx Convergence and divergence of infinite limiting processes
40Cxx General summability methods
40Dxx Direct theorems on summability
40Exx Inversion theorems
40Gxx Special methods of summability
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
42-XX Fourier analysis
42Axx Fourier analysis in one variable
42Bxx Fourier analysis in several variables {For automorphic theory, see mainly 11F30}
42Cxx Nontrigonometric Fourier analysis
43-XX Abstract harmonic analysis {For other analysis on topological and Lie groups, see 22Exx}
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}
45-XX Integral equations
45Exx Singular integral equations [See also 30Exx, 44-XX, 30E20, 30E25, 44A15, 44A35]
/:> 30Exx, 44-XX,
45Fxx Systems of linear integral equations
45Gxx Nonlinear integral equations [See also 47H30, 47Jxx]
// 47H30, 47Jxx ~ 47H15
45Lxx
Approximation of solutions
45Mxx Qualitative behavior
46-XX Functional analysis {For manifolds modeled on topological linear spaces, see 57N20, 58Bxx}
46Axx Topological linear spaces and related structures {For function spaces, see 46Exx}
46Bxx Normed linear spaces and Banach spaces; Banach lattices {For function spaces, see 46Exx}
46Cxx Inner product spaces and their generalizations, Hilbert spaces {For function spaces, see 46Exx}
46Exx Linear function spaces and their duals [See also 30H05, 32A38, 46F05] {For function algebras, see 46J10}
// 32A38 ~ 32E25
46Fxx Distributions, generalized functions, distribution spaces [See also 46T30]
// [See also 46T30] ~ {For distribution theory on monolinear spaces, see 58Cxx}
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
46Hxx Topological algebras, normed rings and algebras, Banach algebras {For group algebras, convolution algebras and measure algebras, see 43A10, 43A20}
46Jxx Commutative Banach algebras and commutative topological algebras [See also 46E25]
46Kxx Topological (rings and) algebras with an involution [See also 16W10]
46Lxx Selfadjoint operator algebras ($C^*$-algebras, von_Neumann ($W^*$-) algebras, etc.) [See also 22D25]
46Mxx Methods of category theory in functional analysis [See also 18-XX]
46Nxx Miscellaneous applications of functional analysis [See also 47Nxx]
46Sxx Other (nonclassical) types of functional analysis [See also 47Sxx]
46Txx Nonlinear functional analysis [See also 47Hxx, 47Jxx, 58Cxx, 58Dxx]
47-XX Operator theory
47Axx General theory of linear operators
47Bxx Special classes of linear operators
47Cxx Individual linear operators as elements of algebraic systems
47Dxx Groups and semigroups of linear operators, their generalizations and applications
Algebraic systems of linear operators [See also 46Lxx]
47Gxx Integral, integro-differential, and pseudodifferential operators [See also 58Jxx]
/:> [See also 58Jxx]
47Hxx Nonlinear operators and their properties {For global and geometric aspects, see 58-XX, especially 58Cxx}
/:> And their properties
47Jxx Equations and inequalities involving linear operators
47Lxx Linear spaces and algebras of operators [See also 46Lxx]
47Nxx Miscellaneous applications of operator theory [See also 46Nxx]
47Sxx Other (nonclassical) types of operator theory [See also 46Sxx]
49-XX Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]
/:> 34K35
49Jxx Existence theories
49Kxx Necessary conditions and sufficient conditions for optimality
49Lxx Hamilton-Jacobi theories, including dynamic programming
Carath\'eodory, Hamilton-Jacobi theories, including dynamic programming
49Mxx Methods of successive approximations [See also 90Cxx, 65Kxx]
// [See also 90Cxx, 65Kxx] ~ {For discrete problems, see 90Cxx; see also 65Kxx}
49Nxx Miscellaneous topics
49Qxx Manifolds [See also 58Exx]
// 58Exx ~ 58Fxx
49Rxx
Variational methods {For eigenvalues of operators, see 47A75}
51-XX Geometry {For algebraic geometry, see 14-XX}
51Axx Linear incidence geometry
51Bxx Nonlinear incidence geometry
51Dxx Geometric closure systems
51Exx Finite geometry and special incidence structures
51Fxx Metric geometry
51Hxx Topological geometry
51Jxx Incidence groups
51Kxx Distance geometry
51Lxx Geometric order structures [See also 53C75]
51Mxx Real and complex geometry
51Nxx Analytic and descriptive geometry
52-XX Convex and discrete geometry
52Axx General convexity
52Bxx Polytopes and polyhedra
52Cxx Discrete geometry
53-XX Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx}
53Axx Classical differential geometry
53Bxx Local differential geometry
53Cxx Global differential geometry [See also 51H25, 58-XX] {For related bundle theory, see 55Rxx, 57Rxx}
53Dxx Symplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx]
54-XX General topology {For the topology of manifolds of all dimensions, see 57Nxx}
54Axx Generalities
54Bxx Basic constructions
54Cxx Maps and general types of spaces defined by maps
54Dxx Fairly general properties
54Exx Spaces with richer structures
54Fxx Special properties
54Gxx Peculiar spaces
54Hxx Connections with other structures, applications
55-XX Algebraic topology
55Mxx Classical topics {For the topology of Euclidean spaces and manifolds, see 57Nxx}
55Nxx Homology and cohomology theories [See also 57Txx]
55Pxx Homotopy theory {For simple homotopy type, see 57Q10}
55Qxx Homotopy groups
55Rxx Fiber spaces and bundles [See also 18F15, 32Lxx, 46M20, 57R20, 57R22, 57R25]
55Sxx Operations and obstructions
55Txx Spectral sequences [See also 18G40, 55R20]
55Uxx Applied homological algebra and category theory [See also 18Gxx]
57-XX Manifolds and cell complexes {For complex manifolds, see 32Qxx}
// 32Qxx ~ 32C10
57Mxx Low-dimensional topology
57Nxx Topological manifolds
57Pxx Generalized manifolds [See also 18F15]
57Qxx PL-topology
57Rxx Differential topology {For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimensional manifolds, see 58Bxx}
57Sxx Topological transformation groups [See also 20F34, 22-XX, 54H15, 58D05]
57Txx Homology and homotopy of topological groups and related structures
58-XX Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15}
58Axx General theory of differentiable manifolds
58Bxx Infinite-dimensional manifolds
58Cxx Calculus on manifolds; nonlinear operators [See also 46Txx, 47Hxx]
/:> 46Txx,
58Dxx Spaces and manifolds of mappings {!including nonlinear versions of 46Exx}
58Exx Variational problems in infinite-dimensional spaces
58Fxx
Ordinary differential equations on manifolds; dynamical systems [See also 28D10, 34Cxx, 54H20]
58Gxx
Partial differential equations on manifolds; differential operators [See also 35-XX]
58Hxx Pseudogroups, differentiable groupoids and general structures on manifolds
58Jxx Partial differential equations on manifolds [See also 35-XX]
58Kxx Theory of singularities and catastrophe theory [See also 37-XX]
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}
60Axx Foundations of probability theory
60Bxx Probability theory on algebraic and topological structures
60Exx Distribution theory [See also 62Exx, 62Hxx]
60Fxx Limit theorems [See also 28Dxx, 60B12]
60Gxx Stochastic processes
60Hxx Stochastic analysis [See also 58J65]
// 58J65 ~ 58G32
60Jxx Markov processes
60Kxx Special processes
62-XX Statistics
/:< {For numerical methods, see 65U05}
62Axx
Foundations
62Bxx Sufficiency and information
62Cxx Decision theory [See also 90B50, 91B05] {For game theory, see 91A35}
// 91B05 ~ 90A05 // 91A35 ~ 90D35
62Exx Distribution theory [See also 60Exx]
62Fxx Parametric inference
62Gxx Nonparametric inference
62Hxx Multivariate analysis [See also 60Exx]
62Jxx Linear inference, regression
62Kxx Design of experiments [See also 05Bxx]
// Design of experiment ~ experimental design
62Lxx Sequential methods
62Mxx Inference from stochastic processes
62Nxx Survival analysis and censored data
Engineering statistics
62Pxx Applications [See also 90-XX, 91-XX, 92-XX]
/:> 91-XX,
65-XX Numerical analysis
65Bxx Acceleration of convergence
65Cxx Probabilistic methods, simulation and stochastic differential equations {For theoretical aspects, see 68U20 and 60H35}
Numerical simulation {For theoretical aspects, see 68U20}
65Dxx Numerical approximation and computational geometry (primarily algorithms) {For theory, see 41-XX and 68Uxx}
/:> And computational geometry /:> and 68Uxx
65Fxx Numerical linear algebra
65Gxx Error analysis and interval analysis
/:> And interval analysis
65Hxx Nonlinear algebraic or transcendental equations
65Jxx Numerical analysis in abstract spaces
65Kxx Mathematical programming, optimization and variational techniques
65Lxx Ordinary differential equations
65Mxx Partial differential equations, initial value and time-dependent initial-boundary value problems
65Nxx Partial differential equations, boundary value problems
65Pxx Numerical problems in dynamical systems [See also 37Mxx]
65Rxx Integral equations, integral transforms
/:< [See also 45Lxx]
65Txx Numerical methods in Fourier analysis
65Yxx Computer aspects of numerical algorithms
68-XX Computer science {For papers involving machine computations and programs in a specific mathematical area, see section -04 in that area}
68Mxx Computer system organization
68Nxx Software
68Pxx Theory of data
68Qxx Theory of computing
68Rxx Discrete mathematics in relation to computer science
68Txx Artificial intelligence
/:< [See also 92J40]
68Uxx Computing methodologies and applications
/:> And applications
68Wxx Algorithms {For numerical algorithms, see 65-XX; for combinatorics and graph theory, see 68Rxx}
70-XX Mechanics of particles and systems {For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX}
// See 83A05 ~ see 83-XX, 83A05
70Bxx Kinematics [See also 53A17]
70Dxx
Dynamics of a particle [See also 70Hxx]
70Exx Dynamics of a rigid body and of multibody systems
/:> And of multibody systems
70Fxx Dynamics of a system of particles, including celestial mechanics
70Gxx General models, approaches, and methods [See also 37-XX]
General representations of dynamical systems [See also 58Fxx]
70Hxx Hamiltonian and Lagrangian mechanics [See also 37Jxx]
// 37Jxx ~ 58F05
70Jxx Linear vibration theory
/:< [See also 73D30]
70Kxx Nonlinear dynamics [See also 34Cxx, 37-XX]
Nonlinear motions [See also 34Cxx, 58Fxx, 73D35, 73K12]
70Sxx Classical field theories [See also 37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX]
73-XX
Mechanics of solids
73Bxx
Continuum mechanics of solids (constitutive description and properties)
73Cxx
Elasticity {For the biharmonic equation, see 31A30, 31B30}
73Dxx
Wave propagation in and vibrations of solids
73Exx
Plasticity
73Fxx
Viscoelasticity
73Gxx
Finite deformations
73Hxx
Stability (linear and nonlinear)
73Kxx
Mechanics of structures
73Vxx
Basic methods in solid mechanics [See also 65-xx]
74-XX Mechanics of deformable solids
74Axx Generalities, axiomatics, foundations of continuum mechanics of solids
74Bxx Elastic materials
74Cxx Plastic materials, materials of stress-rate and internal-variable type
74Dxx Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
74Exx Material properties given special treatment
74Fxx Coupling of solid mechanics with other effects
74Gxx Equilibrium (steady-state) problems
74Hxx Dynamical problems
74Jxx Waves
74Kxx Thin bodies, structures
74Lxx Special subfields of solid mechanics
74Mxx Special kinds of problems
74Nxx Phase transformations in solids [See also 74A50, 80Axx, 82B26, 82C26]
74Pxx Optimization [See also 49Qxx]
74Qxx Homogenization, determination of effective properties
74Rxx Fracture and damage
74Sxx Numerical methods [See also 65-XX, 74G15, 74H15]
76-XX Fluid mechanics {For general continuum mechanics, see 74Axx or other parts of 74-XX}
// 74Axx ~ 73Bxx // 74-XX ~ 73-XX
76Axx Foundations, constitutive equations, rheology
76Bxx Incompressible inviscid fluids
/:< , Potential theory
76Cxx
Incompressible inviscid fluids, vorticity flows
76Dxx Incompressible viscous fluids
76Exx Hydrodynamic stability
76Fxx Turbulence [See also 60Gxx, 60Jxx]
/:< 58F13, 58F27,
76Mxx Basic methods in fluid mechanics [See also 65-XX]
76Nxx Compressible fluids and gas dynamics, general
76Rxx Diffusion and convection
76Txx Two-phase and multiphase flows
76Zxx Biological fluid mechanics [See also 74F10, 74L10, 92Cxx]
/:> 74F10, 74L10,
78-XX Optics, electromagnetic theory {For quantum optics, see 81V80}
78Axx General
78Mxx Basic methods
80-XX Classical thermodynamics, heat transfer {For thermodynamics of solids, see 74A15}
// 74A15 ~ 73B30
80Axx Thermodynamics and heat transfer
80Mxx Basic methods
81-XX Quantum theory
81Pxx Axiomatics, foundations, philosophy
81Qxx General mathematical topics and methods in quantum theory
81Rxx Groups and algebras in quantum theory
81Sxx General quantum mechanics and problems of quantization
81Txx Quantum field theory; related classical field theories [See also 70Sxx]
/:> [See also 70Sxx]
81Uxx Scattering theory [See also 34A55, 34L25, 34L40, 35P25, 47A40]
/:> 34A55, 34L25, 34L40, 35P25,
81Vxx Applications to specific physical systems
82-XX Statistical mechanics, structure of matter
82Bxx Equilibrium statistical mechanics
82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium)
82Dxx Applications to specific types of physical systems
83-XX Relativity and gravitational theory
83Cxx General relativity
83Exx Unified, higher-dimensional and super field theories
85-XX Astronomy and astrophysics {For celestial mechanics, see 70F15}
86-XX Geophysics [See also 76U05, 76V05]
/:< 73N05,
90-XX Operations research, mathematical programming
Economics, operations research, programming, games
90Axx
Mathematical economics {For econometrics, see 62P20}
90Bxx Operations research and management science
90Cxx Mathematical programming
/:< [See also 49Mxx, 65Kxx]
90Dxx
Game theory
91-XX Game theory, economic, social and behavioral sciences
91Axx Game theory
91Bxx Mathematical economics {For econometrics, see 62P20}
91Cxx Social and behavioral sciences: methodology {For statistics, see 62-XX}
91Dxx Mathematical sociology (including anthropology)
91Exx Mathematical psychology
91Fxx Other social and behavioral sciences (mathematical treatment)
92-XX Biology and other natural sciences
/:< , Behavioral sciences
92Bxx Mathematical biology in general
92Cxx Physiological, cellular and medical topics
92Dxx Genetics and population dynamics
92Exx Chemistry {For biochemistry, see 92C40}
92Gxx
Social and behavioral sciences: methodology {For statistics, see 62-XX}
92Hxx
Mathematical sociology (including anthropology)
92Jxx
Mathematical psychology
92Kxx
Other social and behavioral sciences (mathematical treatment)
93-XX Systems theory; control {For optimal control, see 49-XX}
93Axx General
93Bxx Controllability, observability, and system structure
93Cxx Control systems, guided systems
93Dxx Stability
93Exx Stochastic systems and control
94-XX Information and communication, circuits
94Axx Communication, information
94Bxx Theory of error-correcting codes and error-detecting codes
/:> And error-detecting codes
94Cxx Circuits, networks
97-XX Mathematics education
97Axx General
97Bxx Educational policy and educational systems
97Cxx Psychology of and research in mathematics education
97Dxx Education and instruction in mathematics
97Uxx Educational material and media. Educational technology