Classifications AMS

La Classificaction AMS, appelée aussi Mathematics Subject Classification (MSC) est une classification établie par l'American Mathematical Society.

• 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 Spécial 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 Différence 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

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