01-XX	history and biography    908   920
01A16	Egyptian    932
01A17	Babylonian    935
01A20	Greek, Roman    937   938
01A25	China    931   951
01A27	Japan    952
01A30	Islam (Medieval)    955   956   958   960
01A32	India    934
03-XX	mathematical logic and foundations    511.3
03A05	philosophical and critical    510.1   511.2
03B52	fuzzy logic; logic of vagueness    511.324
03Bxx	general logic    511.3
03Cxx	model theory    511.3
03Dxx	computability and recursion theory    511.35
03E20	other classical set theory (including functions, relations, and set algebra)    511.6
03E72	fuzzy set theory    511.324
03Exx	set theory    511.322
03Fxx	proof theory and constructive mathematics    511.3
03Gxx	algebraic logic    511.33
03Hxx	nonstandard models    511.3
05-XX	combinatorics    511.6
05A05	combinatorial choice problems (subsets, representatives, permutations)    511.64   511.65
05A16	asymptotic enumeration    511.62
05A17	partitions of integers    512.73
05Axx	classical combinatorial problems    511.6
05B05	block designs    516.13
05B25	finite geometries    516.13
05B30	other designs, configurations    516.13
05B35	matroids, geometric lattices    516.13
05B40	packing and covering    516.13
05B45	tessellation and tiling problems    516.13
05Bxx	designs and configurations    511.6
05C25	graphs and groups    512.2
05C55	generalized Ramsey theory    511.6
05Cxx	graph theory    511.5
05Dxx	extremal combinatorics    511.6
05E10	tableaux, representations of the symmetric group    512.2
05E15	combinatorial problems concerning the classical groups    512.2
05E35	orthogonal polynomials    515.9
05Exx	algebraic combinatorics    511.6
06-XX	order, lattices, ordered algebraic structures    511.33
06Axx	ordered sets    511.33
06B30	topological lattices, order topologies    512.55
06B35	continuous lattices and posets, applications    512.55
06Bxx	lattices    511.33
06Cxx	modular lattices, complemented lattices    511.33
06Dxx	distributive lattices    511.33
06E20	ring-theoretic properties    512.55
06Exx	Boolean algebras (Boolean rings)    511.324
06F15	ordered groups    512.2
06F20	ordered Abelian groups, Riesz groups, ordered linear spaces    512.2
06F25	ordered rings, algebras, modules    512.4   512.55
06Fxx	ordered structures    511.33   512.2
08-XX	general algebraic systems    511.3   512.02
08Axx	algebraic structures    512.2
08Bxx	varieties    511.33   512.02
08C05	categories of algebras    512.55
08Cxx	other classes of algebras    511.3   512.02
11-XX	number theory    512.7
11Axx	elementary number theory    512.72
11Bxx	sequences and sets    512.72
11C20	matrices, determinants    512.943
11Cxx	polynomials and matrices    512.5
11Dxx	Diophantine equations    512.72
11E04	quadratic forms over general fields    512.74
11E08	quadratic forms over local rings and fields    512.74
11E10	forms over real fields    512.74
11E12	quadratic forms over global rings and fields    512.74
11E16	general binary quadratic forms    512.74
11E20	general ternary and quaternary quadratic forms; forms of more than two variables    512.74
11E25	sums of squares and representations by other particular quadratic forms    512.74
11E39	bilinear and Hermitian forms    512.5
11E70	$K$-theory of quadratic and Hermitian forms    512.55
11Exx	forms and linear algebraic groups    512.944
11Fxx	discontinuous groups and automorphic forms    512.73   515.98
11Gxx	arithmetic algebraic geometry (Diophantine geometry)    512.7   516.35
11Hxx	geometry of numbers    512.75
11Jxx	Diophantine approximation, transcendental number theory    512.73
11Kxx	probabilistic theory: distribution modulo $1$; metric theory of algorithms    512.76
11Lxx	exponential sums and character sums    512.7
11Mxx	zeta and $L$-functions: analytic theory    512.73
11Nxx	multiplicative number theory    512.73
11P81	elementary theory of partitions    511.6   515.243
11P82	analytic theory of partitions    515.243
11P83	partitions; congruences and congruential restrictions    515.243
11Pxx	additive number theory; partitions    512.74
11R32	Galois theory    512.3
11R33	integral representations related to algebraic numbers; Galois module structure of rings of integers    512.3
11R34	Galois cohomology    512.3
11R52	quaternion and other division algebras: arithmetic, zeta functions    512.5
11Rxx	algebraic number theory: global fields    512.74
11S20	Galois theory    512.3
11S25	Galois cohomology    512.3
11S45	algebras and orders, and their zeta functions    511.33
11S70	$K$-theory of local fields    512.3
11Sxx	algebraic number theory: local and $p$-adic fields    512.74
11Txx	finite fields and commutative rings (number-theoretic aspects)    512.74
11Uxx	connections with logic    511.3
11Z05	miscellaneous applications of number theory    512.7
12-XX	field theory and polynomials    512.3   512.94
12Dxx	real and complex fields    512.3
12Exx	general field theory    512.3
12Fxx	field extensions    512.3   512.74
12Gxx	homological methods (field theory)    512.55
12Hxx	differential and difference algebra    512.56
12Jxx	topological fields    512.55   512.74
12Kxx	generalizations of fields    512.02
12Lxx	connections with logic    511.3
13-XX	commutative rings and algebras    512.4
13Axx	general commutative ring theory    512.2   512.4
13Bxx	ring extensions and related topics    512.4
13Cxx	theory of modules and ideals    512.4
13Dxx	homological methods    512.55
13Exx	chain conditions, finiteness conditions    512.4
13Fxx	arithmetic rings and other special rings    512.4
13G05	integral domains    512.4
13Hxx	local rings and semilocal rings    512.4
13Jxx	topological rings and modules    512.55
13K05	Witt vectors and related rings    512.5
13L05	applications of logic to commutative algebra    511.3
13Mxx	finite commutative rings    512.4   512.74
13Nxx	differential algebra    512.56
14-XX	algebraic geometry    516.35
14Axx	foundations    516.35
14Bxx	local theory    516.35
14Cxx	cycles and subschemes    516.35
14Dxx	families, fibrations    516.35
14Exx	birational geometry    516.35
14F30	$p$-adic cohomology, crystalline cohomology    512.74
14G15	finite ground fields    512.3
14G20	local ground fields    512.3   512.74
14G25	global ground fields    512.3
14Gxx	arithmetic problems. Diophantine geometry    512.72
14Hxx	curves    516.352
14Jxx	surfaces and higher-dimensional varieties    516.353
14K15	arithmetic ground fields    512.74
14Kxx	Abelian varieties and schemes    516.35
14Lxx	algebraic groups    512.2   516.35
14M05	varieties defined by ring conditions (factorial, Cohen - Macaulay, seminormal)    512.4
14Mxx	special varieties    516.35
14Nxx	projective and enumerative geometry    516.4   516.5   516.6
15-XX	linear and multilinear algebra; matrix theory    512.5
15A03	vector spaces, linear dependence, rank    512.52
15A04	linear transformations, semilinear transformations    512.52
15A06	linear equations    512.943
15A09	matrix inversion, generalized inverses    512.943
15A12	conditioning of matrices    512.943
15A15	determinants, permanents, other special matrix functions    512.943
15A18	eigenvalues, singular values, and eigenvectors    512.943
15A21	canonical forms, reductions, classification    512.943
15A22	matrix pencils    512.943
15A23	factorization of matrices    512.943
15A24	matrix equations and identities    512.943
15A27	commutativity    512.943
15A30	algebraic systems of matrices    512.943
15A33	matrices over special rings (quaternions, finite fields, etc.)    512.943
15A36	matrices of integers    512.943
15A39	linear inequalities    512.943
15A42	inequalities involving eigenvalues and eigenvectors    512.943
15A45	miscellaneous inequalities involving matrices    512.943
15A48	positive matrices and their generalizations; cones of matrices    512.943
15A51	stochastic matrices    512.943
15A52	random matrices    512.943
15A54	matrices over function rings in one or more variables    512.943
15A57	other types of matrices (Hermitian, skew-Hermitian, etc.)    512.943
15A60	norms of matrices, numerical range, applications of functional analysis to matrix theory    512.943
15A63	quadratic and bilinear forms, inner products    512.74
15A66	Clifford algebras, spinors    512.57
15A69	multilinear algebra, tensor products    512.57
15A72	vector and tensor algebra, theory of invariants    512.57
15A75	exterior algebra, Grassmann algebras    512.57
16-XX	associative rings and algebras    512.4
16B50	category-theoretic methods and results    512.55
16B70	applications of logic    511.3
16Dxx	modules, bimodules and ideals    512.4
16Exx	homological methods    512.55
16Gxx	representation theory of rings and algebras    512.4
16H05	orders and arithmetic, separable algebras, Azumaya algebras    512.74
16Kxx	division rings and semisimple Artin rings    512.4
16Lxx	local rings and generalizations    512.4
16Nxx	radicals and radical properties of rings    512.4
16Pxx	chain conditions, growth conditions, and other forms of finiteness    512.4
16Rxx	rings with polynomial identity    512.944
16Sxx	rings and algebras arising under various constructions    512.4
16Uxx	conditions on elements    512.4
16Wxx	rings and algebras with additional structure    512.4
16Yxx	generalizations    512.4
17-XX	nonassociative rings and algebras    512.24
17Axx	general nonassociative rings    512.24
17Bxx	Lie algebras and Lie superalgebras    512.55
17Cxx	Jordan algebras (algebras, triples and pairs)    512.24
17Dxx	other nonassociative rings and algebras    512.24
18-XX	category theory; abstract homological algebra    512.55
18A15	foundations, relations to logic and deductive systems    511.3
18Axx	general theory of categories and functors    512.55
18Bxx	special categories    512.55
18Cxx	categories and theories    512.55
18Dxx	categories with structure    512.55
18F15	abstract manifolds and fiber bundles    514.224
18F20	presheaves and sheaves    514.224
18F25	algebraic $K$-theory and $L$-theory    514.23
18Fxx	categories and geometry    512.55
18Gxx	abstract homological algebra    512.55
19-XX	$K$-theory    512.55
19Axx	Grothendieck groups and $K_0$    512.55
19Bxx	Whitehead groups and $K_1$    512.55
19Cxx	Steinberg groups and $K_2$    512.55
19D10	algebraic $K$-theory of spaces    512.55
19Exx	$K$-theory in geometry    512.55
19Fxx	$K$-theory in number theory    512.74
19Gxx	$K$-theory of forms    512.55
19Jxx	obstructions from topology    514.2
19Kxx	$K$-theory and operator algebras    512.55
19Lxx	topological $K$-theory    514.2
20-XX	group theory and generalizations    512.2
20Axx	foundations    511.3   512.2
20Bxx	permutation groups    512.2
20C11	$p$-adic representations of finite groups    512.74
20Cxx	representation theory of groups    512.2
20D60	arithmetic and combinatorial problems    511.6   512.74
20Dxx	abstract finite groups    512.2
20Exx	structure and classification of infinite or finite groups    512.2
20F10	word problems, other decision problems, connections with logic and automata    511.3
20F36	braid groups; Artin groups    514.224
20F38	other groups related to topology or analysis    512.55   514.2
20F40	associated Lie structures    512.55
20Fxx	special aspects of infinite or finite groups    512.2
20Gxx	linear algebraic groups (classical groups)    512.2   512.5
20Jxx	connections with homological algebra and category theory    512.55
20Kxx	Abelian groups    512.2
20L05	groupoids (i.e. small categories in which all morphisms are isomorphisms)    512.55
20M05	free semigroups, generators and relations, word problems    511.3
20Mxx	semigroups    512.2
20Nxx	other generalizations of groups    512.02   512.2
20P05	probabilistic methods in group theory    519.26
22-XX	topological groups, Lie groups    512.55
22Axx	topological and differentiable algebraic systems    512.55
22Bxx	locally compact Abelian groups (LCA groups)    512.55
22Dxx	locally compact groups and their algebras    512.55
22Exx	Lie groups    512.55
26-XX	real functions    515   515.8
26Axx	functions of one variable    515.83
26Bxx	functions of several variables    515.84
26Cxx	polynomials, rational functions    515.825
26Dxx	inequalities    515.826
26Exx	miscellaneous topics    515.8
28-XX	measure and integration    515   515.42
28A60	measures on Boolean rings, measure algebras    511.324
28A80	fractals    515.35
28Bxx	set functions, measures and integrals with values in abstract spaces    515.783
28Cxx	set functions and measures on spaces with additional structure    515.783
28Dxx	measure-theoretic ergodic theory    515.42
28E10	fuzzy measure theory    511.324
28Exx	miscellaneous topics in measure theory    511.3   515.42
30-XX	functions of a complex variable    515   515.9   515.93
30A10	inequalities in the complex domain    515.926
30Bxx	series expansions    515.9234
30Cxx	geometric function theory    516.35
30Dxx	entire and meromorphic functions, and related topics    515.98
30E10	approximation in the complex domain    511.4
30E20	integration, integrals of Cauchy type, integral representations of analytic functions    515.43
30E25	boundary value problems    515.35
30F35	Fuchsian groups and automorphic functions    515.98
30Fxx	Riemann surfaces    515.9223
30Gxx	generalized function theory    515.98
30H05	spaces and algebras of analytic functions    515.9223
31-XX	potential theory    515   515.9
31Axx	two-dimensional theory    515.9
31Bxx	higher-dimensional theory    515.9
31Cxx	other generalizations    515.9
31D05	axiomatic potential theory    515.9
32-XX	several complex variables and analytic spaces    515   515.9   515.94
32A05	power series, series of functions    515.9243
32A15	entire functions    515.98
32A17	special families of functions    515.98
32A20	meromorphic functions    515.982
32A22	Nevanlinna theory (local); growth estimates; other inequalities    515.926
32Bxx	local analytic geometry    515.94
32Cxx	analytic spaces    515.9223
32Fxx	geometric convexity    515.7242
32Gxx	deformations of analytic structures    515.98
32H04	meromorphic mappings    515.982
32Jxx	compact analytic spaces    515.9223
32Kxx	generalizations of analytic spaces    515.9223
32Lxx	holomorphic fiber spaces    514.224   515.9223
32Mxx	complex spaces with a group of automorphisms    512.55   515.9223
32Nxx	automorphic functions    515.9
32S25	surface and hypersurface singularities    515.35
32Sxx	singularities    515.35   515.36   515.9
33-XX	special functions    515   515.5
33B10	exponential and trigonometric functions    516.34
33Bxx	elementary classical functions    515.52
33Cxx	hypergeometric functions    515.55
33D05	$q$-gamma functions, $q$-beta functions and integrals    515.984
33Dxx	basic hypergeometric functions    515.55
33E05	elliptic functions and integrals    515.983
33E10	Lam\'e, Mathieu, and spheroidal wave functions    515.54
33Exx	other special functions    515.5
34-XX	ordinary differential equations    515   515.352
34A40	differential inequalities    515.36
34Axx	general theory    515.35
34Bxx	boundary value problems    515.35
34Cxx	qualitative theory    515.352
34Dxx	stability theory    515.35
34Exx	asymptotic theory    515.35
34F05	equations and systems with randomness    519.2
34Gxx	differential equations in abstract spaces    515.35
34H05	control problems    515.64   629.8312
34Kxx	functional-differential and differential-difference equations    515.35   515.38
34Lxx	ordinary differential operators    515.7242
35-XX	partial differential equations    515   515.353
35Axx	general theory    515.35
35Bxx	qualitative properties of solutions    515.35
35Cxx	representations of solutions    515.35
35Dxx	generalized solutions of partial differential equations    515.353
35Exx	equations and systems with constant coefficients    515.353
35Fxx	general first-order equations and systems    515.353
35Gxx	general higher-order equations and systems    515.353
35Hxx	close-to-elliptic equations    515.353
35J85	unilateral problems and variational inequalities for elliptic PDE    515.36
35Jxx	partial differential equations of elliptic type    515.353
35Kxx	parabolic equations and systems    515.353
35Lxx	partial differential equations of hyperbolic type    515.353
35Mxx	partial differential equations of special type (mixed, composite, etc.)    515.353
35Pxx	spectral theory and eigenvalue problems for partial differential operators    515.7222   515.724
35Rxx	miscellaneous topics involving partial differential equations    515.353   515.38
35Sxx	pseudodifferential operators and other generalizations of partial differential operators    515.7242
37-XX	dynamical systems and ergodic theory    515
39-XX	difference and functional equations    515   515.625
39Axx	difference equations    515.625
40-XX	sequences, series, summability    515   515.24
40Axx	convergence and divergence of infinite limiting processes    515.24
40Cxx	general summability methods    515.243
40Dxx	direct theorems on summability    515.243
40Exx	inversion theorems    515.24
40Gxx	special methods of summability    515.243
40H05	functional analytic methods in summability    515.243
40J05	summability in abstract structures    515.243
41-XX	approximations and expansions    511.4   515   515.234
42-XX	Fourier analysis    515   515.2433
43-XX	abstract harmonic analysis    515.785
44-XX	integral transforms, operational calculus    515   515.72
44A05	general transforms    515.723
44A10	Laplace transform    515.723
44A12	Radon transform    515.723
44A15	special transforms (Legendre, Hilbert, etc.)    515.723
44A20	transforms of special functions    515.723
44A30	multiple transforms    515.723
45-XX	integral equations    515   515.45
45J05	integro-ordinary differential equations    515.38
45K05	integro-partial differential equations    515.38
46-XX	functional analysis    515   515.7
46Axx	topological linear spaces and related structures    515.73
46Bxx	normed linear spaces and Banach spaces; Banach lattices    515.732
46Cxx	inner product spaces and their generalizations, Hilbert spaces    515.733
46Exx	linear function spaces and their duals    515.73   515.782
46Fxx	distributions, generalized functions, distribution spaces    515.782
46Gxx	measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)    515.42
46Hxx	topological algebras, normed rings and algebras, Banach algebras    512.55
46Jxx	commutative Banach algebras and commutative topological algebras    512.55
46Kxx	topological (rings and) algebras with an involution    512.55
46Lxx	selfadjoint operator algebras ($C^*$-algebras, von_Neumann ($W^*$-) algebras, etc.)    512.55
46Mxx	methods of category theory in functional analysis    512.55
47-XX	operator theory    515   515.724   515.7242
47Axx	general theory of linear operators    515.7246
47Bxx	special classes of linear operators    515.7246
47Cxx	individual linear operators as elements of algebraic systems    512.55   515.723
47Dxx	groups and semigroups of linear operators, their generalizations and applications    512.55   515.7246
47E05	ordinary differential operators    515.7242
47F05	partial differential operators    515.7242
47Gxx	integral, integro-differential, and pseudodifferential operators    515.723
47Hxx	nonlinear operators and their properties    515.7248
47Nxx	miscellaneous applications of operator theory    515.724
47S50	operator theory in probabilistic metric linear spaces    519.2
47Sxx	other (nonclassical) types of operator theory    515.724
49-XX	calculus of variations and optimal control; optimization    515   515.64
49Jxx	existence theories    515.64
49Kxx	necessary conditions and sufficient conditions for optimality    515.64
49Lxx	Hamilton - Jacobi theories, including dynamic programming    515.7
49M37	methods of nonlinear programming type    519.76
49Mxx	methods of successive approximations    515.64
51-XX	geometry    516
51Axx	linear incidence geometry    516.12
51Bxx	nonlinear incidence geometry    516.12
51D20	combinatorial geometries    511.6   516.13
51Dxx	geometric closure systems    516.35
51Exx	finite geometry and special incidence structures    511.6   516.13
51F25	orthogonal and unitary groups    512.2
51Fxx	metric geometry    516.1
51G05	ordered geometries (ordered incidence structures, etc.)    511.33
51H10	topological linear incidence structures    516.12
51H15	topological nonlinear incidence structures    516.12
51H20	topological geometries on manifolds    516.07   516.36
51H25	geometries with differentiable structure    516.07   516.36
51H30	geometries with algebraic manifold structure    516.07   516.36
51Hxx	topological geometry    516
51J10	projective incidence groups    516.5
51Jxx	incidence groups    512.2   516.12
51Kxx	distance geometry    516.36
51Lxx	geometric order structures    516.36
51M04	elementary problems in Euclidean geometries    516.2
51M05	Euclidean geometries (general) and generalizations    516.2   516.3
51M09	elementary problems in hyperbolic and elliptic geometries    516.9
51M10	hyperbolic and elliptic geometries (general) and generalizations    516.9
51M16	inequalities and extremum problems    516.17
51M20	polyhedra and polytopes; regular figures, division of spaces    516.15   516.35
51M25	length, area and volume    515.4
51M30	line geometries and their generalizations    516.183
51M35	synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations)    516.07   516.36   516.5
51Mxx	real and complex geometry    516.2   516.3   516.9
51N05	descriptive geometry    516.6
51N10	affine analytic geometry    516.4
51N15	projective analytic geometry    516.5
51N20	Euclidean analytic geometry    516.3
51N25	analytic geometry with other transformation groups    512.2   512.55   516.35
51N30	geometry of classical groups    512.2   512.55   516.35
51N35	questions of classical algebraic geometry    512.2   516.35
51Nxx	analytic and descriptive geometry    516.3   516.6
52-XX	convex and discrete geometry    516.08
52A07	convex sets in topological vector spaces    515.73
52A10	convex sets in $2$ dimensions (including convex curves)    515.36
52A15	convex sets in $3$ dimensions (including convex surfaces)    515.36
52A20	convex sets in $n$ dimensions (including convex hypersurfaces)    515.36
52A21	finite-dimensional Banach spaces (including special norms, zonoids, etc.)    515.732
52A22	random convex sets and integral geometry    516.362   519.2
52A37	other problems of combinatorial convexity    511.6
52A38	length, area, volume    515.4
52A40	inequalities and extremum problems    516.17
52A41	convex functions and convex programs    516.362   519.76
52A55	spherical and hyperbolic convexity    516.362
52B05	combinatorial properties (number of faces, shortest paths, etc.)    511.6   516.13
52Bxx	polytopes and polyhedra    516.15   516.35
52Cxx	discrete geometry    512.75   516.35
53-XX	differential geometry    516.36   516.37
53A04	curves in Euclidean space    516.372
53A05	surfaces in Euclidean space    516.372
53A07	higher-dimension and higher-codimension surfaces in Euclidean $n$-space    516.372
53A45	vector and tensor analysis    515.63   516.182
53Axx	classical differential geometry    516.182
53Bxx	local differential geometry    516.36   516.37
53C12	foliations (differential geometric aspects)    514.72
53C15	general geometric structures on manifolds (almost complex, almost product structures, etc.)    516.07
53C20	global Riemannian geometry, including pinching    516.373
53C21	methods of Riemannian geometry, including PDE methods; curvature restrictions    516.373
53C25	special Riemannian manifolds (Einstein, Sasakian, etc.)    516.373
53C60	Finsler spaces and generalizations (areal metrics)    516.375
53C65	integral geometry    516.362
53Cxx	global differential geometry    516.36   516.37
54-XX	general topology    511.33   514
54A25	cardinality properties (cardinal functions and inequalities, discrete subsets)    511.32
54Axx	generalities    514
54B30	categorical methods    512.55   514.224
54B40	presheaves and sheaves    512.55   514.224
54C15	retraction    514.24
54C35	function spaces    515.73
54C40	algebraic properties of function spaces    512.55
54C55	absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)    514.24
54C56	shape theory    516.15
54Cxx	maps and general types of spaces defined by maps    511.33
54Dxx	fairly general properties    514
54Exx	spaces with richer structures    514
54F05	linearly ordered topological spaces, partially ordered spaces, and partially ordered spaces    511.33
54F45	dimension theory    516
54Fxx	special properties    514
54Gxx	peculiar spaces    514
54H05	descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)    511.3
54H10	topological representations of algebraic systems    512.55
54H11	topological groups    512.55
54H13	topological fields, rings, etc.    512.55
54H15	transformation groups and semigroups    512.55
54H20	topological dynamics    515.352
55-XX	algebraic topology    514.2
55M10	dimension theory    516
55Mxx	classical topics    514.2
55Nxx	homology and cohomology theories    514.23
55P55	shape theory    516.15
55Pxx	homotopy theory    514.24
55Qxx	homotopy groups    512.55   514.24
55Rxx	fiber spaces and bundles    514.224
55Sxx	operations and obstructions    514.23
55Txx	spectral sequences    514.23
55Uxx	applied homological algebra and category theory    512.55   514.23
57-XX	manifolds and cell complexes    514.223   514.3
57M05	fundamental group, presentations, free differential calculus    512.55
57M07	topological methods in group theory    512.55
57M15	relations with graph theory    511.5
57Mxx	low-dimensional topology    514.223
57Nxx	topological manifolds    514.223   514.3
57Pxx	generalized manifolds    514.223   514.3
57Qxx	PL-topology    514.223   514.3
57Rxx	differential topology    514.72
57Sxx	topological transformation groups    512.55
57Txx	homology and homotopy of topological groups and related structures    512.55   514.23   514.24
58-XX	global analysis, analysis on manifolds    514.7   514.74   515
58Cxx	calculus on manifolds; nonlinear operators    515.7248
58D05	groups of diffeomorphisms and homeomorphisms as manifolds    512.55   515.73
58D07	groups and semigroups of nonlinear operators    512.55   515.73
58Dxx	spaces and manifolds of mappings    515.73
58Exx	variational problems in infinite-dimensional spaces    515.64   515.73
58Hxx	pseudogroups, differentiable groupoids and general structures on manifolds    512.55
60-XX	probability theory and stochastic processes    519.2
60Axx	foundations of probability theory    519.2
60Bxx	probability theory on algebraic and topological structures    519.26
60C05	combinatorial probability    511.6   519.2
60D05	geometric probability, stochastic geometry, random sets    519.2
60Exx	distribution theory    519.24
60G10	stationary processes    519.232
60G42	martingales with discrete parameter    519.287
60G44	martingales with continuous parameter    519.287
60G46	martingales and classical analysis    519.287
60G50	sums of independent random variables; random walks    519.282
60Gxx	stochastic processes    519.23
60Hxx	stochastic analysis    519.2
60J80	branching processes (Galton - Watson, birth-and-death, etc.)    519.24
60J85	applications of branching processes    519.24
60Jxx	Markov processes    519.233   519.282
60K05	renewal theory    519.287
60K10	applications (reliability, demand theory, etc.)    519.287
60K15	Markov renewal processes, semi-Markov processes    519.287
60K20	applications of Markov renewal processes (reliability, queueing networks, etc.)    519.287
60K25	queueing theory    519.82
60K30	applications (congestion, allocation, storage, traffic, etc.)    519.82
62-07	data analysis    001.4225
62-XX	statistics    519.5
62A01	foundational and philosophical topics    519.5
62Bxx	sufficiency and information    519.54
62Cxx	decision theory    519.542
62D05	sampling theory, sample surveys    519.52
62Exx	distribution theory    519.24   519.532
62F03	hypothesis testing    519.56
62F10	point estimation    519.544
62F12	asymptotic properties of estimators    519.544
62Fxx	parametric inference    519.54   519.544
62G05	estimation    519.544
62G07	density estimation    519.544
62G10	hypothesis testing    519.56
62G30	order statistics; empirical distribution functions    519.532
62Gxx	nonparametric inference    519.54
62H12	estimation    519.544
62H15	hypothesis testing    519.56
62H20	measures of association (correlation, canonical correlation, etc.)    519.537
62H25	factor analysis and principal components; correspondence analysis    519.5354
62H30	classification and discrimination; cluster analysis    519.53
62Hxx	multivariate analysis    519.535
62J10	analysis of variance and covariance    519.538
62Jxx	linear inference, regression    519.536
62Kxx	design of experiments    511.6
62Lxx	sequential methods    519.54
62M02	Markov processes: hypothesis testing    519.233   519.56
62M05	Markov processes: estimation    519.233   519.544
62M07	non-Markovian processes: hypothesis testing    519.23   519.56
62M09	non-Markovian processes: estimation    519.23   519.544
62M10	time series, auto-correlation, regression, etc.    519.55
62M20	prediction    519.287
62Mxx	inference from stochastic processes    519.54
62N05	reliability and life testing    519.287
62Nxx	survival analysis and censored data    519.287   519.86
62Q05	statistical tables    001.422
65-XX	numerical analysis    511.4
65Bxx	acceleration of convergence    515.243
65Cxx	probabilistic methods, simulation and stochastic differential equations    519.4
65D20	computation of special functions, construction of tables    515.5
65D25	numerical differentiation    515.623
65D30	numerical integration    515.624
65Dxx	numerical approximation and computational geometry (primarily algorithms)    511.4
65E05	numerical methods in complex analysis (potential theory, etc.)    515.9232
65Fxx	numerical linear algebra    512.5
65Gxx	error analysis and interval analysis    511.43
65Hxx	nonlinear algebraic or transcendental equations    512.94
65J10	equations with linear operators    515.7242
65J15	equations with nonlinear operators    515.7246
65Jxx	numerical analysis in abstract spaces    515.724
65Kxx	mathematical programming, optimization and variational techniques    515.64   519.7
65Lxx	ordinary differential equations    515.352
65Mxx	partial differential equations, initial value and time-dependent initial-boundary value problems    515.353
65Nxx	partial differential equations, boundary value problems    515.353
65Pxx	numerical problems in dynamical systems    515.353
65Q05	difference and functional equations, recurrence relations    515.38   515.625
65R10	integral transforms    515.45
65R20	integral equations    515.723
65Rxx	integral equations, integral transforms    515.45   515.723
65S05	graphical methods    511.5
65T50	discrete and fast Fourier transforms    515.723
65Txx	numerical methods in Fourier analysis    515.2433
68-XX	computer science    004   005   006
68M01	general    004.0151
68M07	mathematical problems of computer architecture    004.22
68M10	network design and communication    004.65   004.68
68M15	reliability, testing and fault tolerance    004.24
68M20	performance evaluation; queueing; scheduling    004.21
68Mxx	computer system organization    004
68N01	general    005.101
68N15	programming languages    005.13   005.133   005.136
68N17	logic programming    005.11   005.115   005.131
68N18	functional programming and lambda calculus    005.11   005.114
68N19	other progamming techniques (object-oriented, sequential, concurrent, automatic, etc.)    005.11   005.112   005.113   005.117   005.118
68N20	compilers and interpreters    005.45
68N25	operating systems    005.43   005.44
68N30	mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)    005.131
68N99	none of the above, but in this section    005.12
68Nxx	software    005
68P05	data structures    005.73
68P10	searching and sorting    005.741
68P15	database theory    005.74
68P20	information storage and retrieval    005.74
68P25	data encryption    005.82
68Q05	models of computation (Turing machines, etc.)    511.3
68Q10	modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)    005.13
68Q15	complexity classes (hierarchies, relations among complexity classes, etc.)    511.3
68Q25	analysis of algorithms and problem complexity    005.13
68Q30	algorithmic information theory (Kolmogorov complexity, etc.)    005.13   519.2
68Q42	grammars and rewriting systems    005.131   511.3
68Q45	formal languages and automata    005.131   511.3   519.2
68Q55	semantics    511.3
68Q60	specification and verification (program logics, model checking, etc.)    005.14   005.15
68Q65	abstract data types; algebraic specification    005.13   511.3
68Q70	algebraic theory of languages and automata    005.131   511.3
68Q80	cellular automata    005.131
68R05	combinatorics    511.6
68R10	graph theory    511.5
68R15	combinatorics on words    511.6
68Rxx	discrete mathematics in relation to computer science    005
68T05	learning and adaptive systems    006.31
68T10	pattern recognition, speech recognition    006.4
68T15	theorem proving (deduction, resolution, etc.)    511.3
68T20	problem solving (heuristics, search strategies, etc.)    006.33
68T27	logic in artificial intelligence    006.33   511.3
68T30	knowledge representation    006.33
68T35	languages and software systems (knowledge-based systems, expert systems, etc.)    006.33
68T50	natural language processing    006.35   410.151   415
68Txx	artificial intelligence    006.3
68U05	computer graphics; computational geometry    006.6
68U07	computer-aided design    006.6
68U10	image processing    006.42
68U20	simulation    519.4
68Uxx	computing methodologies and applications    006
70-XX	mechanics of particles and systems    531
74-XX	mechanics of deformable solids    531
76-XX	fluid mechanics    532
78-XX	optics, electromagnetic theory    535.14   535.2
80-XX	classical thermodynamics, heat transfer    536   536.2   536.7   541.36
81-XX	quantum theory    530.12   530.133   535.15
81R25	spinor and twistor methods    515.63
81S25	quantum stochastic calculus    530.133
82-XX	statistical mechanics, structure of matter    530.13
82B41	random walks, random surfaces, lattice animals, etc.    519.282
82C41	dynamics of random walks, random surfaces, lattice animals, etc.    519.282
83-XX	relativity and gravitational theory    530.11
83C60	spinor and twistor methods; Newman - Penrose formalism    515.63
85-XX	astronomy and astrophysics    520
86-XX	geophysics    551
90-XX	operations research, mathematical programming    519   519.2   658.4034
90B05	inventory, storage, reservoirs    519.83
90B18	communication networks    004.5   004.68
90B22	queues and service    004.24   519.82
90B25	reliability, availability, maintenance, inspection    519.86
90B35	scheduling theory, deterministic    004.24
90B50	management decision making, including multiple objectives    658.40301
90B60	marketing, advertising    339
90B80	discrete location and assignment    519.7
90B85	continuous location    519.7
90Bxx	operations research and management science    003
90C05	linear programming    519.72
90C20	quadratic programming    519.76
90C25	convex programming    519.76
90C30	nonlinear programming    519.76
90Cxx	mathematical programming    519.7
91-XX	game theory, economic, social and behavioral sciences    519.3
91Axx	game theory    519.3
91B05	decision theory    519.542   658.40301
91B19	statistical models; economic indexes and measures    519.5
91B50	labor market, contracts    332
91B53	special types of economies    339
91B56	special types of equilibria    339
91B58	models of real-world systems; general macro-economic models, etc.    339
91B60	market models (auctions, bargaining, bidding, selling, etc.)    339
91B70	macro-economic models (monetary models, models of taxation)    339
91Bxx	mathematical economics    330.0151   330.015195   330.1543   332   338   339
92-XX	biology and other natural sciences    570
93-XX	systems theory; control    003.5   658.4032
94-XX	information and communication, circuits    003.5   003.54
97-XX	mathematics education    372.7