2000 Mathematics Subject Classification

(IM PAN version, the original one is at www.ams.org/msc)

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01-XXHistory and biography
[See also the classification number -03 in the other sections]
03-XXMathematical logic and foundations
{For finite fields, see 11Txx}
06-XXOrder, lattices, ordered algebraic structures
[See also 18B35]
08-XXGeneral algebraic systems
11-XXNumber theory
12-XXField theory and polynomials
13-XXCommutative rings and algebras
14-XXAlgebraic geometry
15-XXLinear and multilinear algebra; matrix theory
16-XXAssociative rings and algebras
{For the commutative case, see 13-XX}
17-XXNonassociative rings and algebras
18-XXCategory theory; homological algebra
{For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for algebraic topology}
[See also 16E20, 18F25]
20-XXGroup theory and generalizations
22-XXTopological groups, Lie groups
{For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX}
26-XXReal functions
[See also 54C30]
28-XXMeasure and integration
{For analysis on manifolds, see 58-XX}
30-XXFunctions of a complex variable
{For analysis on manifolds, see 58-XX}
31-XXPotential theory
{For probabilistic potential theory, see 60J45}
32-XXSeveral complex variables and analytic spaces
{For infinite- dimensional holomorphy, see 46G20, 58B12}
33-XXSpecial functions (33-XX deals with the properties of functions as functions)
{For orthogonal functions, see 42Cxx; for aspects of combinatorics, see 05Axx; for number-theoretic aspects, see 11-XX; for representation theory, see 22Exx}
34-XXOrdinary differential equations
35-XXPartial differential equations
37-XXDynamical systems and ergodic theory
[See also 26A18, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
39-XXDifference and functional equations
40-XXSequences, series, summability
41-XXApproximations and expansions
{For all approximation theory in the complex domain, see 30Exx, 30E05and 30E10; for all trigonometric approximation and interpolation, see 42Axx, 42A10and 42A15; for numerical approximation, see 65Dxx}
42-XXFourier analysis
43-XXAbstract harmonic analysis
{For other analysis on topological and Lie groups, see 22Exx}
44-XXIntegral 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-XXIntegral equations
46-XXFunctional analysis
{For manifolds modeled on topological linear spaces, see 57N20, 58Bxx}
47-XXOperator theory
49-XXCalculus of variations and optimal control; optimization
[See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]
{For algebraic geometry, see 14-XX}
52-XXConvex and discrete geometry
53-XXDifferential geometry
{For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx}
54-XXGeneral topology
{For the topology of manifolds of all dimensions, see 57Nxx}
55-XXAlgebraic topology
57-XXManifolds and cell complexes
{For complex manifolds, see 32Qxx}
58-XXGlobal analysis, analysis on manifolds
[See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx]
{For geometric integration theory, see 49Q15}
60-XXProbability theory and stochastic processes
{For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX,92-XX, 93-XX, 94-XX]
65-XXNumerical analysis
68-XXComputer science
{For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area}
70-XXMechanics of particles and systems
{For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX}
74-XXMechanics of deformable solids
76-XXFluid mechanics
{For general continuum mechanics, see 74Axx, or other parts of 74-XX}
78-XXOptics, electromagnetic theory
{For quantum optics, see 81V80}
80-XXClassical thermodynamics, heat transfer
{For thermodynamics of solids, see 74A15}
81-XXQuantum theory
82-XXStatistical mechanics, structure of matter
83-XXRelativity and gravitational theory
85-XXAstronomy and astrophysics
{For celestial mechanics, see 70F15}
[See also 76U05, 76V05]
90-XXOperations research, mathematical programming
91-XXGame theory, economics, social and behavioral sciences
92-XXBiology and other natural sciences
93-XXSystems theory; control
{For optimal control, see 49-XX}
94-XXInformation and communication, circuits
97-XXMathematics education

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