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MSC2010

2009-09-29

Mathematical Reviews (MR) and Zentralblatt MATH (Z-MATH) collaborate in maintaining the Mathematics Subject Classification (MSC), which is used by these reviewing services and many others to categorize items in the mathematical sciences literature. The MSC has undergone a general revision, with some additions, changes, and corrections, to create MSC2010, the successor to MSC2000, the scheme for the past 10 years. MR and Z-MATH carefully considered input received from the community in recent years, especially since the announcement of the projected revision in December 2006, and used it in the preparation of their joint MSC revision. As anticipated, there are no changes at the two-digit level but refinements have been made at the three- and five-digit levels. With July 2009 MR and Z-MATH started to use MSC2010 as their classification scheme.

MR and Z-MATH welcome and encourage community adoption of MSC2010. Comments can be submitted through the Web form found at http://msc2010.org/feedback or by email to feedback@msc2010.org. All information about MSC2010 is jointly shared by MR and Z-MATH.

The Editors and their staffs wish to express their gratitude to the numerous members of the community for their assistance in this lengthy revision process.

Bernd Wegner, Editor-in-Chief, Z-MATH

Table 1 MSC2000 Classification Codes-> MSC2010 Classification Codes

MSC2000

Description

MSC2010

 00-XX General _
 01-XX History and biography [See also the classification number ¨C03 in the other sections] _
 03-XX Mathematical logic and foundations _
 05-XX Combinatorics For finite fields, see 11Txx _ 05E20 Group actions on designs, geometries and codes 05E18 05E25 Group actions on posets and homology groups of posets [See also 06A11] 05E18 05E40 05E35 Orthogonal polynomials [See also 33C45, 33C50, 33D45] 05E30 33C45 33C50 33D45
 08-XX General algebraic systems _
 11-XX Number theory _
 12-XX Field theory and polynomials _
 13-XX Commutative rings and algebras _ 13A10 Radical theory 13A15 13B24 Going up; going down; going between 13B21 13D25 Complexes 13D02 13K05 Witt vectors and related rings 13F35
 14-XX Algebraic geometry _
 15-XX Linear and multilinear algebra; matrix theory _ 15A36 Matrices of integers [See also 11C20] 15B36 15A48 Positive matrices and their generalizations; cones of matrices 15B48 15A51 Stochastic matrices 15B51 15A52 Random matrices 15B52 15A57 Other types of matrices (Hermitian, skew-Hermitian, etc.) 15B57
 16-XX Associative rings and algebras For the commutative case, see 13-XX _ 16H05 Orders and arithmetic, separable algebras, Azumaya algebras [See also 11R52, 11R54, 11S45] 16Hxx 16W30 Coalgebras, bialgebras, Hopf algebras [See also 16S40, 57T05]; rings, modules, etc. on which these act 16Txx 16W35 Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50] 16Txx
 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 for algebraic topology _
 19-XX $K$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 _
 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 _ 30D50 Blaschke products, bounded mean oscillation, bounded characteristic, bounded functions, functions with positive real part 30J10 30D55 ${H}^p${H}^p -classes 30H10
 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 _ 34C30 Manifolds of solutions 34Cxx 34D40 Ultimate boundedness 34D05 34C11 34K12 34M20 Nonanalytic aspects 34Mxx 30Dxx 37Fxx 34M37 Resurgence phenomena 34Mxx 30Dxx 37Fxx
 35-XX Partial differential equations _ 35A05 General existence and uniqueness theorems 35A01 35A02 35A07 Local existence and uniqueness theorems [See also 35Hxx, 35Sxx] 35A01 35A02 35B37 PDE in connection with control problems [See also 49J20, 49K20, 93C20] 35Q93 35D05 Existence of generalized solutions 35Dxx 35D10 Regularity of generalized solutions 35Dxx 35J45 General theory of elliptic systems of PDE 35J46 35J47 35J48 35J55 Boundary value problems for elliptic systems 35J56 35J57 35J58 35J85 Unilateral problems and variational inequalities for elliptic PDE [See also 35R35, 49J40] 35J86 35J87 35K50 Boundary value problems for parabolic systems 35K51 35K52 35M20 PDE of composite type 35M10 35Q58 Other completely integrable equations [See also 37J35, 37K10] 35C05 35Q72 Other equations from mechanics 35Q70 35Q74
 37-XX Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] _
 39-XX Difference and functional equations _ 39A11 Stability and asymptotics of difference equations; oscillatory and periodic solutions, etc. 39A14 39A21 39A22 39A23 39A24 39A28 39A30 39A45 39A50
 40-XX Sequences, series, summability _
 41-XX Approximations and expansions For all approximation theory in the complex domain, see~; 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 . 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 _ 47H50 Potential operators 47G40 47N55 Applications in statistical physics 47N50
 49-XX Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] _ 49J22 Optimal control problems involving integral equations 49J21 49J24 Optimal control problems involving differential inclusions [See also 34A60] 49J21 49J25 Optimal control problems involving equations with retarded arguments [See also 34K35] 49J21 49K22 Problems involving integral equations 49K21 49K24 Problems involving differential inclusions [See also 34A60] 49K21 49K25 Problems involving equations with retarded arguments [See also 34K35] 49K21
 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 _
 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 _ 65Q05 Difference and functional equations, recurrence relations 65Q10 65Q20 65Q30
 68-XX Computer science For papers involving machine computations and programs in a specific mathematical area, see Section ¨C04 in that area _
 70-XX Mechanics of particles and systems For relativistic mechanics, see~; 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 _
 90-XX Operations research, mathematical programming _
 91-XX Game theory, economics, social and behavioral sciences _ 91B28 Finance, portfolios, investment 91Gxx
 92-XX Biology and other natural sciences _
 93-XX Systems theory; control For optimal control, see 49-XX _ 93B29 Differential-geometric methods 93B27
 94-XX Information and communication, circuits _
 97-XX Mathematics education _ 97C80 Technological tools and other materials in teaching and learning (research on innovations, role in student learning, use of tools by teachers, etc.) 97U70

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