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
|
03Exx
|
Set theory
|
03Fxx
|
Proof theory and constructive mathematics
|
03Gxx
|
Algebraic logic
|
03Hxx
|
Nonstandard models
[See also
03C62]
|
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}
|
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}
|
13Exx
|
Chain conditions, finiteness conditions
|
13Fxx
|
Arithmetic rings and other special rings
|
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]
|
14-XX
|
Algebraic geometry
|
14Axx
|
Foundations
|
14Bxx
|
Local theory
|
14Cxx
|
Cycles and subschemes
|
14Dxx
|
Families, fibrations
|
14Exx
|
Birational geometry
|
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}
|
14Mxx
|
Special varieties
|
14Nxx
|
Projective and enumerative geometry
[See also
51-XX]
|
14Pxx
|
Real algebraic and real analytic geometry
|
14Qxx
|
Computational aspects in algebraic geometry
[See also
12Y05,
13Pxx,
68W30]
|
14Rxx
|
Affine geometry
|
15-XX
|
Linear and multilinear algebra; matrix theory
|
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}
|
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
|
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}
|
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}
|
18Axx
|
General theory of categories and functors
|
18Bxx
|
Special categories
|
18Cxx
|
Categories and theories
|
18Dxx
|
Categories with structure
|
18Exx
|
Abelian categories
|
18Fxx
|
Categories and geometry
|
18Gxx
|
Abstract homological algebra
[See also
13Dxx,
16Exx,
20Jxx,
55Nxx,
55Uxx,
57Txx]
|
19-XX
|
K-theory
[See also
16E20,
18F25]
|
19Axx
|
Grothendieck groups and K0
[See also
13D15,
18F30]
|
19Bxx
|
Whitehead groups and K1
|
19Cxx
|
Steinberg groups and K2
|
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}
|
20Hxx
|
Other groups of matrices
[See also
15A30]
|
20Jxx
|
Connections with homological algebra and category theory
|
20Kxx
|
Abelian groups
|
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}
|
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]
|
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
|
32Dxx
|
Analytic continuation
|
32Exx
|
Holomorphic convexity
|
32Fxx
|
Geometric convexity
|
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}
|
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]
|
34Dxx
|
Stability theory
[See also
37C75,
93Dxx]
|
34Exx
|
Asymptotic theory
|
34Gxx
|
Differential equations in abstract spaces
[See also
37Kxx,
34Lxx,
47Dxx,
47Hxx,
47Jxx,
58D25]
|
34Kxx
|
Functional-differential and differential-difference equations
[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]
|
35Kxx
|
Parabolic equations and systems
[See also
35Bxx,
35Dxx,
35R30,
35R35,
58J35]
|
35Lxx
|
Partial differential equations of hyperbolic type
[See also
58J45]
|
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]
|
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}
|
35Sxx
|
Pseudodifferential operators and other generalizations of partial differential operators
[See also
47G30,
58J40]
|
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
|
39Axx
|
Difference equations
{For dynamical systems, see
37-XX}
|
39Bxx
|
Functional equations and inequalities
[See also
30D05]
|
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}
|
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]
|
45Fxx
|
Systems of linear integral equations
|
45Gxx
|
Nonlinear integral equations
[See also
47H30,
47Jxx]
|
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}
|
46Fxx
|
Distributions, generalized functions, distribution spaces
[See also
46T30]
|
46Gxx
|
Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
[See also
28-XX,
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
|
47Gxx
|
Integral, integro-differential, and pseudodifferential operators
[See also
58Jxx]
|
47Hxx
|
Nonlinear operators and their properties
{For global and geometric aspects, see
58-XX,
especially
58Cxx}
|
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]
|
49Jxx
|
Existence theories
|
49Kxx
|
Necessary conditions and sufficient conditions for optimality
|
49Lxx
|
Hamilton - Jacobi theories, including dynamic programming
|
49Mxx
|
Methods of successive approximations
[See also
90Cxx,
65Kxx]
|
49Nxx
|
Miscellaneous topics
|
49Qxx
|
Manifolds
[See also
58Exx]
|
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}
|
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]
|
58Dxx
|
Spaces and manifolds of mappings {!including nonlinear versions of
46Exx}
|
58Exx
|
Variational problems in infinite-dimensional spaces
|
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}
|
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]
|
60Jxx
|
Markov processes
|
60Kxx
|
Special processes
|
62-XX
|
Statistics
|
62Bxx
|
Sufficiency and information
|
62Cxx
|
Decision theory
[See also
90B50,
91B05]
{For game theory, see
91A35}
|
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]
|
62Lxx
|
Sequential methods
|
62Mxx
|
Inference from stochastic processes
|
62Nxx
|
Survival analysis and censored data
|
62Pxx
|
Applications
[See also
90-XX,
91-XX,
92-XX]
|
65-XX
|
Numerical analysis
|
65Bxx
|
Acceleration of convergence
|
65Cxx
|
Probabilistic methods, simulation and stochastic differential equations
{For theoretical aspects, see
68U20
and
60H35}
|
65Dxx
|
Numerical approximation and computational geometry (primarily algorithms)
{For theory, see
41-XX
and
68Uxx}
|
65Fxx
|
Numerical linear algebra
|
65Gxx
|
Error 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
|
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
|
68Uxx
|
Computing methodologies 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}
|
70Bxx
|
Kinematics
[See also
53A17]
|
70Exx
|
Dynamics of a rigid body and of multibody systems
|
70Fxx
|
Dynamics of a system of particles, including celestial mechanics
|
70Gxx
|
General models, approaches, and methods
[See also
37-XX]
|
70Hxx
|
Hamiltonian and Lagrangian mechanics
[See also
37Jxx]
|
70Jxx
|
Linear vibration theory
|
70Kxx
|
Nonlinear dynamics
[See also
34Cxx,
37-XX]
|
70Sxx
|
Classical field theories
[See also
37Kxx,
37Lxx,
78-XX,
81Txx,
83-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}
|
76Axx
|
Foundations, constitutive equations, rheology
|
76Bxx
|
Incompressible inviscid fluids
|
76Dxx
|
Incompressible viscous fluids
|
76Exx
|
Hydrodynamic stability
|
76Fxx
|
Turbulence
[See also
60Gxx,
60Jxx]
|
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]
|
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}
|
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]
|
81Uxx
|
Scattering theory
[See also
34A55,
34L25,
34L40,
35P25,
47A40]
|
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]
|
90-XX
|
Operations research, mathematical programming
|
90Bxx
|
Operations research and management science
|
90Cxx
|
Mathematical programming
|
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
|
92Bxx
|
Mathematical biology in general
|
92Cxx
|
Physiological, cellular and medical topics
|
92Dxx
|
Genetics and population dynamics
|
92Exx
|
Chemistry
{For biochemistry, see
92C40}
|
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
|
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
|