# MSC2010

### From MSCwiki

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# Mathematics Subject Classification 2010 {Info & Stats}

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### Joint revision by Mathematical Reviews and Zentralblatt für Mathematik (done 2007 – 2009)

This wiki version of the current MSC was initialized in July 2007 with MSC2000 by Patrick Ion at MR/AMS. It was designed to be collaboratively editable by editorial staff of Mathematical Reviews and Zentralblatt für Mathematik so as to produce this joint draft of a proposed MSC2010 ready in January 2009. It now represents the final state of the revision process, namely our MSC2010 usable from July 2009.

**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 algebra~~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 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx}**42-XX**Harmonic analysis on Euclidean spaces~~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 57Nxx, 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