00-XX
| General
| 01-XX
| History and biography [See also the classification number -03 in the other sections]
| 03-XX
| Mathematical logic and foundations
| 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; abstract 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, 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}
| 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
| |