1991 Mathematics Subject Classification

An introduction to the current (1991) MSC, and instructions on how to use it, are available.

• 00-XX General
• 01-XX History and biography
• 03-XX Mathematical logic and foundations
• 04-XX Set theory, see also {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 {(finite and infinite)}
• 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
• 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 also 46G20, 58B12}
• 33-XX Special functions, {33-XX deals with the properties of functions as functions. For orthogonal functions, See also 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
• 39-XX Finite differences 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, 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 32C10}
• 58-XX Global analysis, analysis on manifolds, see also {{32-XX} {32Cxx, 32Fxx}, 46-XX, 47Hxx, 53Cxx; for geometric integration theory, See {49Fxx} {49Q15}}
• 60-XX Probability theory and stochastic processes, {For additional applications, See 11Kxx, 62-XX, 90-XX, 92-XX, 93-XX, 94-XX. For numerical results, See 65U05}
• 62-XX Statistics, {For numerical methods, see 65U05}
• 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 {83-XX} {83A05 and 83C10}; for statistical mechanics, See 82-XX}
• 73-XX Mechanics of solids
• 76-XX Fluid mechanics, {For general continuum mechanics, see 73Bxx, or other parts of 73-XX}
• 78-XX Optics, electromagnetic theory, {For quantum optics, See 81V80}
• 80-XX Classical thermodynamics, heat transfer,{For thermodynamics of solids, See 73B30}
• 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 {73N05, 76U05, 76V05}
• 90-XX Economics, operations research, programming, games
• 92-XX Biology and other natural sciences, behavioral sciences
• 93-XX Systems theory; control, {For optimal control, see 49-XX}
• 94-XX Information and communication, circuits