The following mathematics subject classification, MSC2000, is the proposed revision of the 1991 Mathematics Subject Classification (MSC), which is the classification that has been used by the two reviewing journals Mathematical Reviews (MR) and Zentralblatt für Mathematik (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. MR and Zbl plan to start using the new classification MSC2000 in January of the year 2000.

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; 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}
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

Version of December 15, 1998