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 |
