The current classification system, 2000 Mathematics Subject Classification (MSC2000), is a revision of the 1991 Mathematics Subject Classification, which is the classification that has been used by MR and Zbl since the beginning of 1991. MSC2000 is the result of a collaborative effort by the editors of MR and Zbl to update the classification. The editors acknowledge the many helpful suggestions from the mathematical community during the revision process.
00-XX General
01-XX History and biography [See also the classification number -03
in the other sections]
03-XX Mathematical logic and foundations
04-XX This section has been deleted {For set theory see 03Exx}
05-XX Combinatorics {For finite fields, see 11Txx}
06-XX Order, lattices, ordered algebraic structures [See also 18B35]
08-XX General algebraic systems
11-XX Number theory
12-XX Field theory and polynomials
13-XX Commutative rings and algebras
14-XX Algebraic geometry
15-XX Linear and multilinear algebra; matrix theory
16-XX Associative rings and algebras {For the commutative case, see 13-XX}
17-XX Nonassociative rings and algebras
18-XX Category 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}
19-XX $K$-theory [See also 16E20, 18F25]
20-XX Group theory and generalizations
22-XX Topological groups, Lie groups {For transformation groups, see
54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX}
26-XX Real functions [See also 54C30]
28-XX Measure and integration {For analysis on manifolds, see 58-XX}
30-XX Functions of a complex variable {For analysis on manifolds, see
58-XX}
31-XX Potential theory {For probabilistic potential theory, see 60J45}
32-XX Several complex variables and analytic spaces {For infinite-
dimensional holomorphy, see 46G20, 58B12}
33-XX Special 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-XX Ordinary differential equations
35-XX Partial differential equations
37-XX Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx,
34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
39-XX Difference and functional equations
40-XX Sequences, series, 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
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
46-XX Functional analysis {For manifolds modeled on topological linear
spaces, see 57N20, 58Bxx}
47-XX Operator theory
49-XX Calculus of variations and optimal control; optimization
[See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]
51-XX Geometry {For algebraic geometry, see 14-XX}
52-XX Convex and discrete geometry
53-XX Differential geometry {For differential topology, see 57Rxx. For
foundational questions of differentiable manifolds, see 58Axx}
54-XX General topology {For the topology of manifolds of all dimensions,
see 57Nxx}
55-XX Algebraic topology
57-XX Manifolds and cell complexes {For complex manifolds, see 32Qxx}
58-XX Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx,
32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory,
see 49Q15}
60-XX Probability theory and stochastic processes {For additional
applications, see 11Kxx, 62-XX, 90-XX, 91-XX,92-XX, 93-XX, 94-XX]
62-XX Statistics
65-XX Numerical analysis
68-XX Computer science {For papers involving machine computations and
programs in a specific mathematical area, see Section -04 in
that area}
70-XX Mechanics of particles and systems {For relativistic mechanics,
see 83A05 and 83C10; for statistical mechanics, see 82-XX}
73-XX This section has been deleted {For mechanics of solids, see 74-XX}
74-XX Mechanics of deformable solids
76-XX Fluid mechanics {For general continuum mechanics, see 74Axx, or
other parts of 74-XX}
78-XX Optics, electromagnetic theory {For quantum optics, see 81V80}
80-XX Classical thermodynamics, heat transfer {For thermodynamics of
solids, see 74A15}
81-XX Quantum theory
82-XX Statistical mechanics, structure of matter
83-XX Relativity and gravitational theory
85-XX Astronomy and astrophysics {For celestial mechanics, see 70F15}
86-XX Geophysics [See also 76U05, 76V05]
90-XX Operations research, mathematical programming
91-XX Game theory, economics, social and behavioral sciences
92-XX Biology and other natural sciences
93-XX Systems theory; control {For optimal control, see 49-XX}
94-XX Information and communication, circuits
97-XX Mathematics education
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