数学主题分类 - 英文(下)

        
* 43-XX Abstract harmonic analysis, {For other analysis on topological and Lie groups, See 22Exx}
    43-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    43-01 Instructional exposition (textbooks, tutorial papers, etc.)
    43-02 Research exposition (monographs, survey articles)
    43-03 Historical (must be assigned at least one classification number from 01-XX)
    43-04 Explicit machine computation and programs (not the theory of computation or programming)
    43-06 Proceedings, conferences, collections, etc.
    43A05 Measures on groups and semigroups, etc.
    43A07 Means on groups, semigroups, etc.; amenable groups
    43A10 Measure algebras on groups, semigroups, etc.
    43A15 $L^p$-spaces and other function spaces on groups, semigroups, etc.
    43A17 Analysis on ordered groups, ${H}^p$-theory
    43A20 $L^1$-algebras on groups, semigroups, etc.
    43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
    43A25 Fourier and Fourier-Stieltjes transforms on locally compact abelian groups
    43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
    43A32 Other transforms and operators of Fourier type
    43A35 Positive definite functions on groups, semigroups, etc.
    43A40 Character groups and dual objects
    43A45 Spectral synthesis on groups, semigroups, etc.
    43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
    43A50 Convergence of Fourier series and of inverse transforms
    43A55 Summability methods on groups, semigroups, etc., See Also { 40J05}
    43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
    43A62 Hypergroups
    43A65 Representations of groups, semigroups, etc., See Also {22A10, 22A20, 22Dxx, 22E45}
    43A70 Analysis on specific locally compact abelian groups, See also {11R56, 22B05}
    43A75 Analysis on specific compact groups
    43A77 Analysis on general compact groups
    43A80 Analysis on other specific Lie groups, See also {22Exx}
    43A85 Analysis on homogeneous spaces
    43A90 Spherical functions, See also {22E45, 22E46, 33C65, 33D55}
    43A95 Categorical methods, See also {46Mxx}
    43A99 Miscellaneous topics
* 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}
    44-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    44-01 Instructional exposition (textbooks, tutorial papers, etc.)
    44-02 Research exposition (monographs, survey articles)
    44-03 Historical (must be assigned at least one classification number from 01-XX)
    44-04 Explicit machine computation and programs (not the theory of computation or programming)
    44-06 Proceedings, conferences, collections, etc.
    44A05 General transforms, See also {42A38}
    44A10 Laplace transform
    44A12 Radon transform, See also {92C55}
    44A15 Special transforms (Legendre, Hilbert, etc.)
    44A20 Transforms of special functions
    44A30 Multiple transforms
    44A35 Convolution
    44A40 Calculus of Mikusinski and other operational calculi
    44A45 Classical operational calculus
    44A55 Discrete operational calculus
    44A60 Moment problems
    44A99 Miscellaneous topics
* 45-XX Integral equations
    45-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    45-01 Instructional exposition (textbooks, tutorial papers, etc.)
    45-02 Research exposition (monographs, survey articles)
    45-03 Historical (must be assigned at least one classification number from 01-XX)
    45-04 Explicit machine computation and programs (not the theory of computation or programming)
    45-06 Proceedings, conferences, collections, etc.
    45A05 Linear integral equations
    45B05 Fredholm integral equations
    45C05 Eigenvalue problems, See also {34Lxx, 35Pxx, 45P05, 47A75}
    45D05 Volterra integral equations, See also {34A12}
    45Exx Singular integral equations, see also {{30Exx, 44-XX} {30E20, 30E25, 44A15, 44A35}}
        45E05 Integral equations with kernels of Cauchy type, See Also { 35J15}
        45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), See also {47B35}
        45E99 None of the above but in this section
    45Fxx Systems of linear integral equations
        45F05 Systems of nonsingular linear integral equations
        45F10 Dual, triple, etc., integral and series equations
        45F15 Systems of singular linear integral equations
        45F99 None of the above but in this section
    45Gxx Nonlinear integral equations, see also {47H15}
        45G05 Singular nonlinear integral equations
        45G10 Other nonlinear integral equations
        45G15 Systems of nonlinear integral equations
    45H05 Miscellaneous special kernels, See also {44A15}
    45J05 Integro-ordinary differential equations
    45K05 Integro-partial differential equations
    45Lxx Approximation of solutions
        45L05 Theoretical approximation of solutions
        45L10 Numerical approximation of solutions, {For numerical analysis, See 65R20}
        45L99 None of the above but in this section    
    45Mxx Qualitative behavior
        45M05 Asymptotics
        45M10 Stability theory
        45M15 Periodic solutions
        45M20 Positive solutions
        45M99 None of the above but in this section    
    45N05 Abstract integral equations, integral equations in abstract spaces
    45P05 Integral operators, See also {47B38, 47G10}
* 46-XX Functional analysis, {For manifolds modeled on topological linear spaces, See 57N20, 58Bxx}
    46-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    46-01 Instructional exposition (textbooks, tutorial papers, etc.)
    46-02 Research exposition (monographs, survey articles)
    46-03 Historical (must be assigned at least one classification number from 01-XX)
    46-04 Explicit machine computation and programs (not the theory of computation or programming)
    46-06 Proceedings, conferences, collections, etc.
    46Axx Topological linear spaces and related structures, {For function spaces, see 46Exx}
        46A03 General theory of locally convex spaces
        46A04 Locally convex Frechet spaces and (DF)-spaces
        46A08 Barrelled spaces, bornological spaces
        46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
        46A13 Spaces defined by inductive or projective limits (LB, LF, etc.), See also {46M40}
        46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
        46A17 Bornologies and related structures; Mackey convergence, etc.
        46A19 Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than ${R}$, etc.)
        46A20 Duality theory
        46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators, See also {46M10}
        46A25 Reflexivity and semi-reflexivity, See also {46B10}
        46A30 Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness)
        46A32 Spaces of linear operators; topological tensor products; approximation properties, See also {46B28, 46M05, 47D15, 47D50}
        46A35 Summability and bases, See also {46B15}
        46A40 Ordered topological linear spaces, vector lattices, See also {06F20, 46B40, 46B42}
        46A45 Sequence spaces (including Kothe sequence spaces), See also {46B45}
        46A50 Compactness in topological linear spaces; angelic spaces, etc.
        46A55 Convex sets in topological linear spaces; Choquet theory, See also {52A07}
        46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
        46A80 Modular spaces
        46A99 None of the above but in this section
    46Bxx Normed linear spaces and Banach spaces; Banach lattices, {For function spaces, see 46Exx}
        46B03 Isomorphic theory (including renorming) of Banach spaces
        46B04 Isometric theory of Banach spaces
        46B07 Local theory of Banach spaces
        46B08 Ultraproduct techniques in Banach space theory, See Also { 46M07}
        46B09 Probabilistic methods in Banach space theory, See Also { 60Bxx}
        46B10 Duality and reflexivity, See also {46A25}
        46B15 Summability and bases, See also {46A35}
        46B20 Geometry and structure of normed linear spaces
        46B22 Radon-Nikodym, Kreuin-Milman and related properties, See also {46G10}
        46B25 Classical Banach spaces in the general theory
        46B26 Nonseparable Banach spaces
        46B28 Spaces of operators; tensor products; approximation properties, See also {46A32, 46M05, 47D15, 47D50}
        46B40 Ordered normed spaces, See also {46A40, 46B42}
        46B42 Banach lattices, See also {46A40, 46B40}
        46B45 Banach sequence spaces, See also {46A45}
        46B70 Interpolation between normed linear spaces, See Also { 46M35}
        46B99 None of the above but in this section
    46Cxx Inner product spaces and their generalizations, Hilbert spaces , {For function spaces, see 46Exx}
        46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
        46C15 Characterizations of Hilbert spaces
        46C20 Spaces with indefinite inner product
        46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.)
        46C99 None of the above but in this section
    46Exx Linear function spaces and their duals, see also {30H05, 32E25, 46F05; for function algebras, See 46J10}
        46E05 Lattices of continuous, differentiable or analytic functions
        46E10 Topological linear spaces of continuous, differentiable or analytic functions
        46E15 Banach spaces of continuous, differentiable or analytic functions
        46E20 Hilbert spaces of continuous, differentiable or analytic functions
        46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces)
        46E25 Rings and algebras of continuous, differentiable or analytic functions, {For Banach function algebras, See 46J10, 46J15}
        46E27 Spaces of measures, See also {28A33, 46Gxx}
        46E30 Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
        46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
        46E39 Sobolev (and similar kinds of) spaces of functions of discrete variables
        46E40 Spaces of vector- and operator-valued functions
        46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces, See also {46G20}
        46E99 None of the above but in this section
    46Fxx Distributions, generalized functions, distribution spaces, {For distribution theory on nonlinear spaces, See 58Cxx}
        46F05 Topological linear spaces of test functions, distributions and ultradistributions, See also {46E10, 46E35}
        46F10 Operations with distributions
        46F12 Integral transforms in distribution spaces, See Also {42-XX, 44-XX}
        46F15 Hyperfunctions, analytic functionals, See also {32A25, 32A45, 32C35, 58G07}
        46F20 Distributions and ultradistributions as boundary values of analytic functions, See also {30D40, 30E25, 32A40}
        46F25 Distributions on infinite-dimensional spaces, See Also { 58C35}
        46F99 None of the above but in this section
    46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces), see Also {28-XX} {For nonlinear functional analysis, See 47Hxx, 58-XX, especially 58Cxx}
        46G05 Derivatives, See also {58C20, 58C25}
        46G10 Vector-valued measures and integration, See also {28Bxx, 46B22}
        46G12 Measures and integration on abstract linear spaces, See also {28C20}
        46G15 Functional analytic lifting theory, See also {28A51}
        46G20 Infinite-dimensional holomorphy, See also {32-XX, 46E50, 58B12, 58C10}
        46G99 None of the above but in this section
    46Hxx Topological algebras, normed rings and algebras, Banach algebras, {For group algebras, convolution algebras and measure algebras, see 43A10, 43A20}
        46H05 General theory of topological algebras
        46H10 Ideals and subalgebras
        46H15 Representations of topological algebras
        46H20 Structure, classification of topological algebras
        46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
        46H30 Functional calculus in topological algebras, See Also { 47A60}
        46H35 Topological algebras of operators [See mainly 47D30, and also 47D25, 47D50]
        46H40 Automatic continuity
        46H70 Nonassociative topological algebras, See also {46K70, 46L70}
        46H99 None of the above but in this section
    46Jxx Commutative Banach algebras and commutative topological algebras, see also {46E25}
        46J05 General theory of commutative topological algebras
        46J10 Banach algebras of continuous functions, function algebras, See also {46E25}
        46J15 Banach algebras of differentiable or analytic functions, ${H}^p$-spaces, See also {30D55, 30H05, 32A35, 32A37, 32E25, 42B30}
        46J20 Ideals, maximal ideals, boundaries
        46J25 Representations of commutative topological algebras
        46J30 Subalgebras
        46J40 Structure, classification of commutative topological algebras
        46J45 Radical Banach algebras
        46J99 None of the above but in this section
    46Kxx Topological (rings and) algebras with an involution, see also {16W10}
        46K05 General theory of topological algebras with involution
        46K10 Representations of topological algebras with involution
        46K15 Hilbert algebras
        46K50 Nonselfadjoint (sub)algebras in algebras with involution
        46K70 Nonassociative topological algebras with an involution, See also {46H70, 46L70}
        46K99 None of the above but in this section
    46Lxx Selfadjoint operator algebras ($C$*-algebras, von Neumann ($W$*-) algebras, etc.), See also {22D25}
        46L05 General theory of $C$*-algebras
        46L10 General theory of von Neumann algebras
        46L30 States
        46L35 Classifications of $C^*$-algebras, factors
        46L37 Subfactors and their classification
        46L40 Automorphisms
        46L45 Decomposition theory for $C^*$-algebras
        46L50 Noncommutative measure, integration and probability
        46L55 Noncommutative dynamical systems, See also {28Dxx, 54H20, 58Fxx}
        46L57 Derivations, dissipations and positive semigroups in $C^*$-algebras
        46L60 Applications of selfadjoint operator algebras to physics, See also {46N50, 46N55, 47D45, 81T05, 82B10, 82C10}
        46L70 Nonassociative selfadjoint operator algebras, See Also {46H70, 46K70}
        46L80 $K$-theory and operator algebras (including cyclic theory), See also {18F25, 19Kxx, 46M20, 55Rxx, 58G12}
        46L85 Noncommutative topology, See also {58B30, 58G12}
        46L87 Noncommutative differential geometry, See also {58B30, 58G12}
        46L89 Other ``noncommutative'' mathematics based on $C^*$-algebra theory, See also {58B30, 58G12}
        46L99 None of the above but in this section
    46Mxx Methods of category theory in functional analysis, see Also { 18-XX}
        46M05 Tensor products, See also {46A32, 46B28, 47A80}
        46M07 Ultraproducts, See also {46B08, 46S20}
        46M10 Projective and injective objects, See also {46A22}
        46M15 Functors, {For $K$-theory and EXT, See 19K33, 46L80, 46M20}
        46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.), See also {14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 55Rxx}
        46M35 Abstract interpolation of topological vector spaces, See also {46B70}
        46M40 Inductive and projective limits, See also {46A13}
        46M99 None of the above but in this section
    46Nxx Miscellaneous applications of functional analysis, see Also { 47Nxx}
        46N10 Applications in optimization, convex analysis, mathematical programming, economics
        46N20 Applications to differential and integral equations
        46N30 Applications in probability theory and statistics
        46N40 Applications in numerical analysis, See also {65Jxx}
        46N50 Applications in quantum physics
        46N55 Applications in statistical physics
        46N60 Applications in biology and other sciences
        46N99 None of the above but in this section
    46Sxx Other (nonclassical) types of functional analysis, see Also { 47Sxx}
        46S10 Functional analysis over fields other than ${R}$ or ${C}$ or the quaternions; non-Archimedean functional analysis, See also {12J25, 32P05}
        46S20 Nonstandard functional analysis, See also {03H05}
        46S30 Constructive functional analysis, See also {03F65}
        46S40 Fuzzy functional analysis, See also {04A72}
        46S50 Functional analysis in probabilistic metric linear spaces
        46S99 None of the above but in this section
* 47-XX Operator theory
    47-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    47-01 Instructional exposition (textbooks, tutorial papers, etc.)
    47-02 Research exposition (monographs, survey articles)
    47-03 Historical (must be assigned at least one classification number from 01-XX)
    47-04 Explicit machine computation and programs (not the theory of computation or programming)
    47-06 Proceedings, conferences, collections, etc.
    47Axx General theory of linear operators
        47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
        47A10 Spectrum, resolvent
        47A11 Local spectral properties
        47A12 Numerical range
        47A13 Several-variable spectral theory
        47A15 Invariant subspaces
        47A20 Dilations, extensions, compressions
        47A25 Spectral sets
        47A30 Norms (inequalities, more than one norm, etc.)
        47A35 Ergodic theory, See also {28Dxx}
        47A40 Scattering theory, See also {34L25, 35P25, 81Uxx}
        47A45 Canonical models for contractions and nonselfadjoint operators
        47A48 Operator colligations (= nodes)
        47A50 Equations and inequalities involving linear operators, with vector unknowns
        47A53 (Semi-) Fredholm operators; index theories, See Also {58B10, 58G12}
        47A55 Perturbation theory
        47A56 Functions whose values are linear operators (operator and matrix pencils, etc.)
        47A57 Operator methods in interpolation, moment and extension problems, See also {30E05, 42A70, 42A82}
        47A58 Operator approximation theory
        47A60 Functional calculus
        47A62 Equations involving linear operators, with operator unknowns
        47A63 Operator inequalities, operator means, shorted operators, etc.
        47A65 Structure theory
        47A66 (Non)quasitriangular, (non)quasidiagonal operators
        47A67 Representation theory
        47A68 Factorization theory (including Wiener-Hopf and spectral factorizations)
        47A70 (Generalized) eigenfunction expansions; rigged Hilbert spaces
        47A75 Eigenvalue problems, See also {49Rxx}
        47A80 Tensor products of operators, See also {46M05}
        47A99 None of the above but in this section    
    47Bxx Special classes of linear operators
        47B06 Riesz operators; eigenvalue distributions; approximation numbers, $s$-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
        47B07 Operators defined by compactness properties
        47B10 Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.), See also {47D50}
        47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
        47B20 Subnormal operators, hyponormal operators, etc.
        47B25 Symmetric and selfadjoint operators (unbounded)
        47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators, See also {45P05, 47G10 for other integral operators; See also 32H10, 32M15}
        47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
        47B38 Operators on function spaces (including composition operators, kernel operators)
        47B39 Difference operators, See also {39A70}
        47B40 Spectral operators, decomposable operators, well-bounded operators, etc.
        47B44 Accretive operators, dissipative operators, etc.
        47B47 Commutators, derivations, elementary operators, etc.
        47B48 Operators on Banach algebras
        47B49 Transformers (= operators on spaces of operators)
        47B50 Operators on spaces with an indefinite metric
        47B60 Operators on ordered spaces
        47B65 Positive operators and order-bounded operators
        47B80 Random operators, See also {60H25}
        47B99 None of the above but in this section    
    47Cxx Individual linear operators as elements of algebraic systems
        47C05 Operators in algebras
        47C10 Operators in *-algebras
        47C15 Operators in $C$*- or von Neumann algebras
        47C99 None of the above but in this section    
    47Dxx Algebraic systems of linear operators, see also {46Lxx}
        47D03 (Semi)groups of linear operators, {For nonlinear operators, See 47H20; See also 20M20}
        47D06 One-parameter semigroups and linear evolution equations
        47D07 Markov semigroups, {For Markov processes, See 60Jxx}
        47D09 Operator cosine functions and higher-order Cauchy problems
        47D15 Linear spaces of operators, See also {46A32, 46B28}
        47D20 Convex sets and cones of operators, See also {90C25, 90C31}
        47D25 Operator algebras on Hilbert space
        47D27 Dual operator algebras
        47D30 Operator algebras on Banach spaces and other linear topological spaces
        47D35 Dual spaces of operator algebras and topological groups
        47D40 Algebras of unbounded operators
        47D45 Applications of operator algebras to physics, See Also {46L60, 46N50, 46N55, 47N50, 47N55}
        47D50 Operator ideals
        47D99 None of the above but in this section    
    47E05 Ordinary differential operators, See also {34Bxx, 34Lxx, 58F19}
    47F05 Partial differential operators, See also {35Pxx, 58G05}
    47Gxx Integral, integro-differential, and pseudodifferential operators
        47G10 Integral operators, See also {45P05}
        47G20 Integro-differential operators, See also {45J05, 45K05}
        47G30 Pseudodifferential operators, See also {35Sxx, 58G15}
        47G99 None of the above but in this section    
    47Hxx Nonlinear operators, {For global and geometric aspects, see 58-XX, especially 58Cxx}
        47H04 Set-valued operators, See also {28B20, 54C60, 58C06}
        47H05 Monotone operators (with respect to duality)
        47H06 Accretive operators, dissipative operators, etc.
        47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
        47H09 Nonexpansive mappings, and their generalizations (ultimately compact mappings, measures of noncompactness, $A$-proper mappings, $K$-set contractions, etc.)
        47H10 Fixed-point theorems, See also {54H25, 55M20, 58C30}
        47H11 Degree theory, See also {55M25, 58C30}
        47H12 Spectral theory of nonlinear operators, See also {58C40}
        47H15 Equations involving nonlinear operators, See also {58E07 for abstract bifurcation theory}
        47H17 Methods for solving equations involving nonlinear operators, See also {58C15}, {For numerical analysis, See 65J15}
        47H19 Inequalities involving nonlinear operators, See Also {49J27, 49J40, 49K27}
        47H20 Semigroups of nonlinear operators and nonlinear evolution equations, See also {58D07}
        47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiui, Uryson, hysteresis operators, etc.), See also {45P05}
        47H40 Random operators, See also {60H25}
        47H99 None of the above but in this section    
    47Nxx Miscellaneous applications of operator theory, see Also { 46Nxx}
        47N10 Applications in optimization, convex analysis, mathematical programming, economics
        47N20 Applications to differential and integral equations
        47N30 Applications in probability theory and statistics
        47N40 Applications in numerical analysis, See also {65Jxx}
        47N50 Applications in quantum physics
        47N55 Applications in statistical physics
        47N60 Applications in biology and other sciences
        47N70 Applications in systems theory, circuits, etc.
        47N99 None of the above but in this section    
    47Sxx Other (nonclassical) types of operator theory, see Also { 46Sxx}
        47S10 Operator theory over fields other than ${R}$, ${C}$ or the quaternions; non-Archimedean operator theory
        47S20 Nonstandard operator theory, See also {03H05}
        47S30 Constructive operator theory, See also {03F65}
        47S40 Fuzzy operator theory, See also {04A72}
        47S50 Operator theory in probabilistic metric linear spaces
        47S99 None of the above but in this section    
* 49-XX Calculus of variations and optimal control; optimization, See also {34H05, 65Kxx, 90Cxx, 93-XX}
    49-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    49-01 Instructional exposition (textbooks, tutorial papers, etc.)
    49-02 Research exposition (monographs, survey articles)
    49-03 Historical (must be assigned at least one classification number from 01-XX)
    49-04 Explicit machine computation and programs (not the theory of computation or programming)
    49-06 Proceedings, conferences, collections, etc.
    49Jxx Existence theory for optimal solutions
        49J05 Free problems in one independent variable
        49J10 Free problems in two or more independent variables
        49J15 Optimal control problems involving ordinary differential equations
        49J20 Optimal control problems involving partial differential equations
        49J22 Optimal control problems involving integral equations
        49J24 Optimal control problems involving differential inclusions
        49J25 Optimal control problems involving equations with retarded arguments, See also {34K35}
        49J27 Problems in abstract spaces [see 90C48]
        49J30 Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
        49J35 Minimax problems
        49J40 Variational methods including variational inequalities
        49J45 Problems involving semicontinuity and convergence
        49J50 Frechet and Gateaux differentiability, See also {46G05, 58C20}
        49J52 Nonsmooth analysis (other weak concepts of optimality), See also {58C20, 90C48}
        49J55 Problems involving randomness, See also {93E20}
        49J99 None of the above but in this section    
    49Kxx Necessary conditions and sufficient conditions for optimality
        49K05 Free problems in one independent variable
        49K10 Free problems in two or more independent variables
        49K15 Problems involving ordinary differential equations
        49K20 Problems involving partial differential equations
        49K22 Problems involving integral equations
        49K24 Problems involving differential inclusions
        49K25 Problems involving equations with retarded arguments, See also {34K35}
        49K27 Problems in abstract spaces [See 90C48, 93C25]
        49K30 Optimal solutions belonging to restricted classes
        49K35 Minimax problems
        49K40 Sensitivity of optimal solutions in the presence of perturbations
        49K45 Problems involving randomness, See also {93E20}
        49K99 None of the above but in this section
    49Lxx Caratheodory, Hamilton-Jacobi theories, including dynamic programming
        49L05 Free problems and problems involving ordinary differential equations
        49L10 Free problems and problems involving partial differential equations
        49L15 Problems in abstract spaces or problems involving functional relations other than differential equations
        49L20 Dynamic programming method
        49L25 Viscosity solutions
        49L99 None of the above but in this section
    49Mxx Methods of successive approximations, {For discrete problems, see 90Cxx; See also 65Kxx}
        49M05 Methods based on necessary conditions
        49M07 Gradient methods
        49M10 Methods of steepest descent type
        49M15 Methods of Newton-Raphson, Galerkin and Ritz types
        49M20 Methods of relaxation type
        49M25 Finite difference methods
        49M27 Decomposition methods
        49M29 Multiplier methods
        49M30 Other methods, not based on necessary conditions (penalty function, etc.)
        49M35 Methods of linear programming type, See also {90C05}
        49M37 Nonlinear programming, See also {90C30}
        49M39 Semi-infinite programming, See also {90C34}
        49M40 Methods of quadratic programming type, See also {90C20}
        49M45 Methods of convex programming type, See also {90C25}
        49M49 Geometric programming, See also {90C28}
        49M99 None of the above but in this section
    49Nxx Miscellaneous topics
        49N05 Linear optimal control problems, See also {93C05}
        49N10 Linear-quadratic problems
        49N15 Duality theory
        49N20 Periodic optimization
        49N25 Impulsive optimal control problems, See also {93C57}
        49N30 Problems with incomplete information, See also {93C41}
        49N35 Closed-loop controls
        49N40 Open-loop controls
        49N45 Inverse problems in calculus of variations
        49N50 Inverse problems in optimal control theory
        49N55 Noneconomic applications of optimal control theory and differential games, See also {90D25}
        49N60 Regularity of solutions in the calculus of variations
        49N65 Applications of measurable selections to control theory, See also {28B20, 26E25}
        49N99 None of the above but in this section    
    49Qxx Manifolds, see also {58Fxx}
        49Q05 Minimal surfaces, See also {53A10, 58E12}
        49Q10 Optimization of the shape other than minimal surfaces, See also {73K40, 90C90}
        49Q12 Sensitivity analysis
        49Q15 Geometric measure and integration theory, integral and normal currents, See also {28A75, 32C30, 58A25, 58C35}
        49Q20 Variational problems in a geometric measure-theoretic setting
        49Q25 Surface area
        49Q99 None of the above but in this section    
    49Rxx Variational methods, {For eigenvalues of operators, see 47A75}
        49R05 Variational approach to eigenvalues
        49R10 Rayleigh-Ritz methods
        49R15 Weinstein and Aronszajn methods, intermediate problems
        49R20 Linear operators in Hilbert spaces
        49R99 None of the above but in this section    
    49S05 Variational principles of physics
* 51-XX Geometry, {For algebraic geometry, See 14-XX}
    51-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    51-01 Instructional exposition (textbooks, tutorial papers, etc.)
    51-02 Research exposition (monographs, survey articles)
    51-03 Historical (must be assigned at least one classification number from 01-XX)
    51-04 Explicit machine computation and programs (not the theory of computation or programming)
    51-06 Proceedings, conferences, collections, etc.
    51Axx Linear incidence geometry
        51A05 General theory and projective geometries
        51A10 Homomorphism, automorphism and dualities
        51A15 Structures with parallelism
        51A20 Configuration theorems
        51A25 Algebraization, See also {12Kxx, 20N05}
        51A30 Desarguesian and Pappian geometries
        51A35 Non-Desarguesian affine and projective planes
        51A40 Translation planes and spreads
        51A45 Incidence structures imbeddable into projective geometries
        51A50 Polar geometry, symplectic spaces, orthogonal spaces
        51A99 None of the above but in this section    
    51Bxx Nonlinear incidence geometry
        51B05 General theory
        51B10 Mobius geometries
        51B15 Laguerre geometries
        51B20 Minkowski geometries
        51B25 Lie geometries
        51B99 None of the above but in this section    
    51C05 Ring geometry (Hjelmslev, Barbilian, etc.)
    51Dxx Geometric closure systems
        51D05 Abstract (Maeda) geometries
        51D10 Abstract geometries with exchange axiom
        51D15 Abstract geometries with parallelism
        51D20 Combinatorial geometries, See also {05B25, 05B35}
        51D25 Lattices of subspaces, See also {05B35}
        51D30 Continuous geometries and related topics, See also {06Cxx}
        51D99 None of the above but in this section    
    51Exx Finite geometry and special incidence structures
        51E05 General block designs, See also {05B05}
        51E10 Steiner systems
        51E12 Generalized quadrangles, generalized polygons
        51E14 Finite partial geometries (general), nets, partial spreads
        51E15 Affine and projective planes
        51E20 Combinatorial structures in finite projective spaces, See also {05Bxx}
        51E21 Blocking sets, ovals, $k$-arcs
        51E22 Linear codes and caps in Galois spaces, See also {94B05}
        51E23 Spreads and packing problems
        51E24 Buildings and the geometry of diagrams
        51E25 Other finite nonlinear geometries
        51E26 Other finite linear geometries
        51E30 Other finite incidence structures, See also {05B30}
        51E99 None of the above but in this section    
    51Fxx Metric geometry
        51F05 Absolute planes
        51F10 Absolute spaces
        51F15 Reflection groups, reflection geometries, See also {20H10, 20H15; for Coxeter groups, See 20F55}
        51F20 Congruence and orthogonality, See also {20H05}
        51F25 Orthogonal and unitary groups, See also {20H05}
        51F99 None of the above but in this section    
    51G05 Ordered geometries (ordered incidence structures, etc.)
    51Hxx Topological geometry
        51H05 General theory
        51H10 Topological linear incidence structures
        51H15 Topological nonlinear incidence structures
        51H20 Topological geometries on manifolds, See also {57-XX}
        51H25 Geometries with differentiable structure, See also {53Cxx, 53C70}
        51H30 Geometries with algebraic manifold structure, See Also { 14-XX}
        51H99 None of the above but in this section    
    51Jxx Incidence groups
        51J05 General theory
        51J10 Projective incidence groups
        51J15 Kinematic spaces
        51J20 Representation by near-fields and near-algebras, See Also {12K05, 16Y30}
        51J99 None of the above but in this section    
    51Kxx Distance geometry
        51K05 General theory
        51K10 Synthetic differential geometry
        51K99 None of the above but in this section    
    51Lxx Geometric order structures, see also {53C75}
        51L05 Geometry of orders of nondifferentiable curves
        51L10 Directly differentiable curves
        51L15 $n$-vertex theorems via direct methods
        51L20 Geometry of orders of surfaces
        51L99 None of the above but in this section    
    51Mxx Real and complex geometry
        51M04 Elementary problems in Euclidean geometries
        51M05 Euclidean geometries (general) and generalizations
        51M09 Elementary problems in hyperbolic and elliptic geometries
        51M10 Hyperbolic and elliptic geometries (general) and generalizations
        51M15 Geometric constructions
        51M16 Inequalities and extremum problems, {For convex problems, See 52A40}
        51M20 Polyhedra and polytopes; regular figures, division of spaces, See also {51F15}
        51M25 Length, area and volume, See also {26B15}
        51M30 Line geometries and their generalizations, See also {53A25}
        51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations), See also {14M15}
        51M99 None of the above but in this section    
    51Nxx Analytic and descriptive geometry
        51N05 Descriptive geometry, See also {65D17, 68U07}
        51N10 Affine analytic geometry
        51N15 Projective analytic geometry
        51N20 Euclidean analytic geometry
        51N25 Analytic geometry with other transformation groups
        51N30 Geometry of classical groups, See also {20Gxx, 14L35}
        51N35 Questions of classical algebraic geometry, See also {14Nxx}
        51N99 None of the above but in this section    
    51P05 Geometry and physics (should also be assigned at least one other classification number from Sections 70--86)
* 52-XX Convex and discrete geometry
    52-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    52-01 Instructional exposition (textbooks, tutorial papers, etc.)
    52-02 Research exposition (monographs, survey articles)
    52-03 Historical (must be assigned at least one classification number from 01-XX)
    52-04 Explicit machine computation and programs (not the theory of computation or programming)
    52-06 Proceedings, conferences, collections, etc.
    52Axx General convexity
        52A01 Axiomatic and generalized convexity
        52A05 Convex sets without dimension restrictions
        52A07 Convex sets in topological vector spaces, See also {46A55}
        52A10 Convex sets in $2$ dimensions (including convex curves), See also {53A04}
        52A15 Convex sets in $3$ dimensions (including convex surfaces), See also {53A05, 53C45}
        52A20 Convex sets in $n$ dimensions (including convex hypersurfaces), See also {53A07, 53C45}
        52A21 Finite-dimensional Banach spaces (including special norms, zonoids, etc.), See also {46Bxx}
        52A22 Random convex sets and integral geometry, See also {53C65, 60D05}
        52A27 Approximation by convex sets
        52A30 Variants of convex sets (star-shaped, ($m, n$)-convex, etc.)
        52A35 Helly-type theorems
        52A37 Other problems of combinatorial convexity
        52A38 Length, area, volume, See also {26B15, 28A75, 49Q20}
        52A39 Mixed volumes and related topics
        52A40 Inequalities and extremum problems
        52A41 Convex functions and convex programs, See also {26B25, 90C25}
        52A55 Spherical and hyperbolic convexity
        52A99 None of the above but in this section    
    52Bxx Polytopes and polyhedra
        52B05 Combinatorial properties (number of faces, shortest paths, etc.), See also {05Cxx}
        52B10 Three-dimensional polytopes
        52B11 $n$-dimensional polytopes
        52B12 Special polytopes (linear programming, centrally symmetric, etc.)
        52B15 Symmetry properties of polytopes
        52B20 Lattice polytopes (including relations with commutative algebra and algebraic geometry), See also {06A08, 13F20, 13Hxx}
        52B30 Arrangements of hyperplanes
        52B35 Gale and other diagrams
        52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.), See Also { 05B35}
        52B45 Dissections and valuations (Hilbert's third problem, etc.)
        52B55 Computational aspects related to convexity, {For computational geometry and algorithms, See 68Q20, 68Q25, 68U05; for numerical algorithms, See 65Yxx}
        52B60 Isoperimetric problems for polytopes
        52B70 Polyhedral manifolds
        52B99 None of the above but in this section    
    52Cxx Discrete geometry
        52C05 Lattices and convex bodies in $2$ dimensions, See Also {11H06, 11H31, 11P21}
        52C07 Lattices and convex bodies in $n$ dimensions, See Also {11H06, 11H31, 11P21}
        52C10 Erdos problems and related topics of discrete geometry, See also {11Hxx}
        52C15 Packing and covering in $2$ dimensions, See also {05B40, 11H31}
        52C17 Packing and covering in $n$ dimensions, See also {05B40, 11H31}
        52C20 Tilings in $2$ dimensions, See also {05B45, 51M20}
        52C22 Tilings in $n$ dimensions, See also {05B45, 51M20}
        52C25 Rigidity and flexibility of structures, See also {70B15}
        52C99 None of the above but in this section    
* 53-XX Differential geometry, {For differential topology, See 57Rxx. For foundational questions of differentiable manifolds, See 58Axx}
    53-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    53-01 Instructional exposition (textbooks, tutorial papers, etc.)
    53-02 Research exposition (monographs, survey articles)
    53-03 Historical (must be assigned at least one classification number from 01-XX)
    53-04 Explicit machine computation and programs (not the theory of computation or programming)
    53-06 Proceedings, conferences, collections, etc.
    53Axx Classical differential geometry
        53A04 Curves in Euclidean space
        53A05 Surfaces in Euclidean space
        53A07 Higher-dimension and -codimension surfaces in Euclidean $n$-space
        53A10 Minimal surfaces, surfaces with prescribed mean curvature, See also {49Q05, 49Q10, 53C42}
        53A15 Affine differential geometry
        53A17 Kinematics
        53A20 Projective differential geometry
        53A25 Differential line geometry
        53A30 Conformal differential geometry
        53A35 Non-Euclidean differential geometry
        53A40 Other special differential geometries
        53A45 Vector and tensor analysis
        53A50 Spinor analysis
        53A55 Differential invariants (local theory), geometric objects
        53A60 Geometry of webs, See also {14C21, 20N05}
        53A99 None of the above but in this section    
    53Bxx Local differential geometry
        53B05 Linear and affine connections
        53B10 Projective connections
        53B15 Other connections
        53B20 Local Riemannian geometry
        53B21 Methods of Riemannian geometry
        53B25 Local submanifolds, See also {53C40}
        53B30 Lorentz metrics, indefinite metrics
        53B35 Hermitian and Kahlerian structures, See also {32Cxx}
        53B40 Finsler spaces and generalizations (areal metrics)
        53B50 Applications to physics
        53B99 None of the above but in this section    
    53Cxx Global differential geometry, see also {51H25, 58-XX; for related bundle theory, See 55Rxx, 57Rxx}
        53C05 Connections, general theory
        53C07 Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills), See also {32L07}
        53C10 $G$-structures
        53C12 Foliations (differential geometric aspects), See Also {57R30, 57R32}
        53C15 General geometric structures on manifolds (almost complex, contact, symplectic, almost product structures, etc.)
        53C20 Global Riemannian geometry, including pinching, See Also {31C12, 58B20}
        53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions, See also {58G30}
        53C22 Geodesics, See also {58E10}
        53C23 Global topological methods (a la Gromov)
        53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
        53C30 Homogeneous manifolds, See also {14M15, 14M17, 32M10, 57T15}
        53C35 Symmetric spaces, See also {32M15, 57T15}
        53C40 Global submanifolds, See also {53B25}
        53C42 Immersions (minimal, prescribed curvature, tight, etc.), See also {49Q05, 49Q10, 53A10, 57R40, 57R42}
        53C45 Global surface theory (convex surfaces a la A. D. Aleksandrov)
        53C50 Lorentz manifolds, manifolds with indefinite metrics
        53C55 Hermitian and Kahlerian manifolds, See also {32Cxx}
        53C56 Other complex differential geometry, See also {32Cxx}
        53C60 Finsler spaces and generalizations (areal metrics), See also {58B20}
        53C65 Integral geometry, See also {52A22, 60D05}; differential forms, currents, etc. See mainly{58Axx}
        53C70 Direct methods ($G$-spaces of Busemann, etc.)
        53C75 Geometric orders, order geometry, See also {51Lxx}
        53C80 Applications to physics
        53C99 None of the above but in this section
* 54-XX General topology, {For the topology of manifolds of all dimensions, See 57Nxx}
    54-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    54-01 Instructional exposition (textbooks, tutorial papers, etc.)
    54-02 Research exposition (monographs, survey articles)
    54-03 Historical (must be assigned at least one classification number from 01-XX)
    54-04 Explicit machine computation and programs (not the theory of computation or programming)
    54-06 Proceedings, conferences, collections, etc.
    54Axx Generalities
        54A05 Topological spaces and generalizations (closure spaces, etc.)
        54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
        54A15 Syntopogeneous structures
        54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
        54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets), See also {03Exx, 04A30}, {For ultrafilters, See 54D80}
        54A35 Consistency and independence results, See also {03E35}
        54A40 Fuzzy topology, See also {04A72}
        54A99 None of the above but in this section    
    54Bxx Basic constructions
        54B05 Subspaces
        54B10 Product spaces
        54B15 Quotient spaces, decompositions
        54B17 Adjunction spaces and similar constructions
        54B20 Hyperspaces
        54B30 Categorical methods, See also {18B30}
        54B35 Spectra
        54B40 Presheaves and sheaves, See also {18F20}
        54B99 None of the above but in this section    
    54Cxx Maps and general types of spaces defined by maps
        54C05 Continuous maps
        54C08 Weak and generalized continuity
        54C10 Special maps on topological spaces (open, closed, perfect, etc.)
        54C15 Retraction
        54C20 Extension of maps
        54C25 Embedding
        54C30 Real-valued functions, See also {26-XX}
        54C35 Function spaces, See also {46Exx, 58D15}
        54C40 Algebraic properties of function spaces, See also {46J10}
        54C45 $C$- and $C$*-embedding
        54C50 Special sets defined by functions, See also {26A21}
        54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties), See also {55M15}
        54C56 Shape theory, See also {55P55, 57N25}
        54C60 Set-valued maps, See also {26E25, 28B20, 47H04, 58C06}
        54C65 Selections, See also {28B20}
        54C70 Entropy
        54C99 None of the above but in this section    
    54Dxx Fairly general properties
        54D05 Connected and locally connected spaces (general aspects)
        54D10 Lower separation axioms, ($T_0$--$T_3$, etc.)
        54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
        54D20 Noncompact covering properties (paracompact, Lindelof, etc.)
        54D25 ``$P$-minimal'' and ``$P$-closed'' spaces
        54D30 Compactness
        54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
        54D40 Remainders
        54D45 Local compactness, $sigma$-compactness
        54D50 $k$-spaces
        54D55 Sequential spaces
        54D60 Realcompactness and realcompactification
        54D65 Separability
        54D70 Base properties
        54D80 Special constructions of spaces (spaces of ultrafilters, etc.)
        54D99 None of the above but in this section    
    54Exx Spaces with richer structures
        54E05 Proximity structures and generalizations
        54E15 Uniform structures and generalizations
        54E17 Nearness spaces
        54E18 $p$-spaces, $M$-spaces, $sigma$-spaces, etc.
        54E20 Stratifiable spaces, cosmic spaces, etc.
        54E25 Semimetric spaces
        54E30 Moore spaces
        54E35 Metric spaces, metrizability
        54E40 Special maps on metric spaces
        54E45 Compact (locally compact) metric spaces
        54E50 Complete metric spaces
        54E52 Baire category, Baire spaces
        54E55 Bitopologies
        54E70 Probabilistic metric spaces
        54E99 None of the above but in this section    
    54Fxx Special properties
        54F05 Ordered topological spaces, partially ordered spaces, See also {06B30, 06F30}
        54F15 Continua and generalizations
        54F35 Higher-dimensional local connectedness, See also {55Mxx, 55Nxx}
        54F45 Dimension theory, See also {55M10}
        54F50 Spaces of dimension $\leq 1$; curves, dendrites, See Also { 26A03}
        54F55 Unicoherence, multicoherence
        54F65 Topological characterizations of particular spaces
        54F99 None of the above but in this section    
    54Gxx Peculiar spaces
        54G05 Extremally disconnected spaces, $F$-spaces, etc.
        54G10 $P$-spaces
        54G12 Scattered spaces
        54G15 Pathological spaces
        54G20 Counterexamples
        54G99 None of the above but in this section    
    54Hxx Connections with other structures, applications
        54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), See also {03E15, 04A15, 26A21, 28A05}
        54H10 Topological representations of algebraic systems, See Also { 22-XX}
        54H11 Topological groups, See also {22A05}
        54H12 Topological lattices, etc., See also {06B30, 06F30}
        54H13 Topological fields, rings, etc., See also {12Jxx}, {For algebraic aspects, See 13Jxx, 16W80}
        54H15 Transformation groups and semigroups, See also {20M20, 22-XX, 57Sxx}
        54H20 Topological dynamics, See also {28Dxx, 34C35, 58Fxx}
        54H25 Fixed-point and coincidence theorems, See also {47H10, 55M20}
        54H99 None of the above but in this section    
    54J05 Nonstandard topology, See also {03H05}
* 55-XX Algebraic topology
    55-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    55-01 Instructional exposition (textbooks, tutorial papers, etc.)
    55-02 Research exposition (monographs, survey articles)
    55-03 Historical (must be assigned at least one classification number from 01-XX)
    55-04 Explicit machine computation and programs (not the theory of computation or programming)
    55-06 Proceedings, conferences, collections, etc.
    55Mxx Classical topics, {For the topology of Euclidean spaces and manifolds, see {57Nxx} {57Nxx}}
        55M05 Duality
        55M10 Dimension theory, See also {54F45}
        55M15 Absolute neighborhood retracts, See also {54C55}
        55M20 Fixed points and coincidences, See also {54H25}
        55M25 Degree, winding number
        55M30 Ljusternik-Schnirelman (Lyusternik-Shnirelman) category of a space
        55M35 Finite groups of transformations (including Smith theory), See also {57S17}
        55M99 None of the above but in this section
    55Nxx Homology and cohomology theories, see also {57Txx}
        55N05 Cech types
        55N07 Steenrod-Sitnikov homologies
        55N10 Singular theory
        55N15 $K$-theory, See also {19Lxx}, {For algebraic $K$-theory, See 18F25, 19-XX}
        55N20 Generalized (extraordinary) homology and cohomology theories
        55N22 Bordism and cobordism theories, formal group laws, See also {14L05, 19L41, 57R75, 57R77, 57R85, 57R90}
        55N25 Homology with local coefficients, equivariant cohomology
        55N30 Sheaf cohomology, See also {18F20, 32C35, 32L10}
        55N33 Intersection homology and cohomology
        55N35 Other homology theories
        55N40 Axioms for homology theory and uniqueness theorems
        55N45 Products and intersections
        55N91 Equivariant homology and cohomology, See also {19L47}
        55N99 None of the above but in this section    
    55Pxx Homotopy theory, {For simple homotopy type, see 57Q10}
        55P05 Homotopy extension properties, cofibrations
        55P10 Homotopy equivalences
        55P15 Classification of homotopy type
        55P20 Eilenberg-Mac Lane spaces
        55P25 Spanier-Whitehead duality
        55P30 Eckmann-Hilton duality
        55P35 Loop spaces
        55P40 Suspensions
        55P42 Stable homotopy theory, spectra
        55P45 ${H}$-spaces and duals
        55P47 Infinite loop spaces
        55P50 Category and cocategory, etc.
        55P55 Shape theory, See also {54C56, 55Q07}
        55P60 Localization and completion
        55P62 Rational homotopy theory
        55P65 Homotopy functors
        55P91 Equivariant homotopy theory, See also {19L47}
        55P99 None of the above but in this section    
    55Qxx Homotopy groups
        55Q05 Homotopy groups, general; sets of homotopy classes
        55Q07 Shape groups
        55Q10 Stable homotopy groups
        55Q15 Whitehead products and generalizations
        55Q20 Homotopy groups of wedges, joins, and simple spaces
        55Q25 Hopf invariants
        55Q30 Homotopy groups of triads, $n$-ads
        55Q35 Operations in homotopy groups
        55Q40 Homotopy groups of spheres
        55Q45 Stable homotopy of spheres
        55Q50 $J$-morphism, See also {19L20}
        55Q52 Homotopy groups of special spaces
        55Q55 Cohomotopy groups
        55Q70 Homotopy groups of special types, See also {55N05, 55N07}
        55Q91 Equivariant homotopy groups, See also {19L47}
        55Q99 None of the above but in this section    
    55Rxx Fiber spaces and bundles, see also {18F15, 32Lxx, 46M20, { 57Rxx} {57R20, 57R22, 57R25}}
        55R05 Fiber spaces
        55R10 Fiber bundles
        55R12 Transfer
        55R15 Classification
        55R20 Spectral sequences and homology of fiber spaces, See Also { 55Txx}
        55R25 Sphere bundles and vector space bundles
        55R35 Classifying spaces of groups and ${H}$-spaces
        55R40 Homology of classifying spaces, characteristic classes, See also {57Txx, 57R20}
        55R45 Homology and homotopy of $BO$ and $BU$; Bott periodicity
        55R50 Stable classes of vector space bundles, $K$-theory, See also {19Lxx}, {For algebraic $K$-theory, See 18F25, 19-XX}
        55R55 Fiberings with singularities
        55R60 Microbundles and block bundles, See also {57N55, 57Q50}
        55R65 Generalizations of fiber spaces and bundles
        55R91 Equivariant fiber spaces and bundles, See also {19L47}
        55R99 None of the above but in this section
    55Sxx Operations and obstructions
        55S05 Primary cohomology operations
        55S10 Steenrod algebra
        55S12 Dyer-Lashof operations
        55S15 Symmetric products, cyclic products
        55S20 Secondary and higher cohomology operations
        55S25 $K$-theory operations and generalized cohomology operations, See also {19D55, 19Lxx}
        55S30 Massey products
        55S35 Obstruction theory
        55S36 Extension and compression of mappings
        55S37 Classification of mappings
        55S40 Sectioning fiber spaces and bundles
        55S45 Postnikov systems, $k$-invariants
        55S91 Equivariant operations and obstructions, See also {19L47}
        55S99 None of the above but in this section
    55Txx Spectral sequences, see also {18G40, 55R20}
        55T05 General
        55T10 Serre spectral sequences
        55T15 Adams spectral sequences
        55T20 Eilenberg-Moore spectral sequences, See also {57T35}
        55T25 Generalized cohomology
        55T99 None of the above but in this section
    55Uxx Applied homological algebra and category theory, see Also { 18Gxx}
        55U05 Abstract complexes
        55U10 Semisimplicial complexes
        55U15 Chain complexes
        55U20 Universal coefficient theorems, Bockstein operator
        55U25 Homology of a product, Kunneth formula
        55U30 Duality
        55U35 Abstract homotopy theory
        55U40 Topological categories
        55U99 None of the above but in this section    
* 57-XX Manifolds and cell complexes, {For complex manifolds, See 32C10}
    57-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    57-01 Instructional exposition (textbooks, tutorial papers, etc.)
    57-02 Research exposition (monographs, survey articles)
    57-03 Historical (must be assigned at least one classification number from 01-XX)
    57-04 Explicit machine computation and programs (not the theory of computation or programming)
    57-06 Proceedings, conferences, collections, etc.
    57Mxx Low-dimensional topology
        57M05 Fundamental group, presentations, free differential calculus
        57M07 Topological methods in group theory
        57M10 Covering spaces
        57M12 Special coverings, e.g. branched
        57M15 Relations with graph theory, See also {05Cxx}
        57M20 Two-dimensional complexes
        57M25 Knots and links in $S^3$, {For higher dimensions, See 57Q45}
        57M30 Wild knots and surfaces, etc., wild embeddings
        57M35 Dehn's lemma, sphere theorem, loop theorem, asphericity
        57M40 Characterizations of $E^3$ and $S^3$ (Poincare conjecture), See also {57N12}
        57M50 Geometric structures on low-dimensional manifolds
        57M60 Group actions in low dimensions
        57M99 None of the above but in this section    
    57Nxx Topological manifolds
        57N05 Topology of $E^2$, $2$-manifolds
        57N10 Topology of general $3$-manifolds, See also {57Mxx}
        57N12 Topology of $E^3$ and $S^3$, See also {57M40}
        57N13 Topology of $E^4$, $4$-manifolds, See also {14Jxx, 32Jxx}
        57N15 Topology of $E^n$, $n$-manifolds ($4 \less n \less \infty$)
        57N17 Topology of topological vector spaces
        57N20 Topology of infinite-dimensional manifolds, See Also { 58Bxx}
        57N25 Shapes, See also {54C56, 55P55, 55Q07}
        57N30 Engulfing
        57N35 Embeddings and immersions
        57N37 Isotopy and pseudo-isotopy
        57N40 Neighborhoods of submanifolds
        57N45 Flatness and tameness
        57N50 $S^{n-1}\subset E^n$, Schoenflies problem
        57N55 Microbundles and block bundles, See also {55R60, 57Q50}
        57N60 Cellularity
        57N65 Algebraic topology of manifolds
        57N70 Cobordism and concordance
        57N75 General position and transversality
        57N80 Stratifications
        57N99 None of the above but in this section    
    57Pxx Generalized manifolds, see also {18F15}
        57P05 Local properties of generalized manifolds
        57P10 Poincare duality spaces
        57P99 None of the above but in this section    
    57Qxx PL-topology
        57Q05 General topology of complexes
        57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc., See also {19B28}
        57Q12 Wall finiteness obstruction for CW-complexes
        57Q15 Triangulating manifolds
        57Q20 Cobordism
        57Q25 Comparison of PL-structures: classification, Hauptvermutung
        57Q30 Engulfing
        57Q35 Embeddings and immersions
        57Q37 Isotopy
        57Q40 Regular neighborhoods
        57Q45 Knots and links (in high dimensions), {For the low-dimensional case, See 57M25}
        57Q50 Microbundles and block bundles, See also {55R60, 57N55}
        57Q55 Approximations
        57Q60 Cobordism and concordance
        57Q65 General position and transversality
        57Q91 Equivariant PL-topology
        57Q99 None of the above but in this section    
    57Rxx Differential topology, {For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimensional manifolds, See 58Bxx}
        57R05 Triangulating
        57R10 Smoothing
        57R12 Smooth approximations
        57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
        57R19 Algebraic topology on manifolds
        57R20 Characteristic classes and numbers
        57R22 Topology of vector bundles and fiber bundles, See Also { 55Rxx}
        57R25 Vector fields, frame fields
        57R27 Controllability of vector fields on $C^\infty$ and real-analytic manifolds, See also {49Qxx, 58F40, 93B05}
        57R30 Foliations; geometric theory
        57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology, See also {58H10}
        57R35 Differentiable mappings
        57R40 Embeddings
        57R42 Immersions
        57R45 Singularities of differentiable mappings
        57R50 Diffeomorphisms
        57R52 Isotopy
        57R55 Differentiable structures
        57R57 Applications of global analysis to structures on manifolds, See also {58-XX}
        57R60 Homotopy spheres, Poincare conjecture
        57R65 Surgery and handlebodies
        57R67 Surgery obstructions, Wall groups, See also {19J25}
        57R70 Critical points and critical submanifolds
        57R75 O- and SO-cobordism
        57R77 Complex cobordism (U- and SU-cobordism), See also {55N22}
        57R80 $h$- and $s$-cobordism
        57R85 Equivariant cobordism
        57R90 Other types of cobordism See{55N22}
        57R91 Equivariant algebraic topology of manifolds
        57R95 Realizing cycles by submanifolds
        57R99 None of the above but in this section
    57Sxx Topological transformation groups, see also {20F34, 22-XX, 54H15, 58D05}
        57S05 Topological properties of groups of homeomorphisms or diffeomorphisms
        57S10 Compact groups of homeomorphisms
        57S15 Compact Lie groups of differentiable transformations
        57S17 Finite transformation groups
        57S20 Noncompact Lie groups of transformations
        57S25 Groups acting on specific manifolds
        57S30 Discontinuous groups of transformations
        57S99 None of the above but in this section
    57Txx Homology and homotopy of topological groups and related structures
        57T05 Hopf algebras, See also {16W30}
        57T10 Homology and cohomology of Lie groups
        57T15 Homology and cohomology of homogeneous spaces of Lie groups
        57T20 Homotopy groups of topological groups and homogeneous spaces
        57T25 Homology and cohomology of ${H}$-spaces
        57T30 Bar and cobar constructions, See also {18G55, 55Uxx}
        57T35 Applications of Eilenberg-Moore spectral sequences, See also {55R20, 55T20}
        57T99 None of the above but in this section
* 58-XX Global analysis, analysis on manifolds, See also {{32-XX} {32Cxx, 32Fxx}, 46-XX, 47Hxx, 53Cxx; for geometric integration theory, See {49Fxx} {49Q15}}
    58-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    58-01 Instructional exposition (textbooks, tutorial papers, etc.)
    58-02 Research exposition (monographs, survey articles)
    58-03 Historical (must be assigned at least one classification number from 01-XX)
    58-04 Explicit machine computation and programs (not the theory of computation or programming)
    58-06 Proceedings, conferences, collections, etc.
    58Axx General theory of differentiable manifolds
        58A03 Topos-theoretic approach to differentiable manifolds
        58A05 Differentiable manifolds, foundations
        58A07 Real-analytic and Nash manifolds, See also {14P20, 32C07}
        58A10 Differential forms
        58A12 de Rham theory, See also {14Fxx}
        58A14 Hodge theory, See also {14C30, 14Fxx, 32J25, 32S35}
        58A15 Exterior differential systems (Cartan theory)
        58A17 Pfaffian systems
        58A20 Jets
        58A25 Currents, See also {32C30, 53C65}
        58A30 Vector distributions (subbundles of the tangent bundles)
        58A35 Stratified sets, See also {32S60, 58C27}
        58A40 Differential spaces
        58A50 Supermanifolds and graded manifolds, See also {14A22, 32C11}
        58A99 None of the above but in this section
    58Bxx Infinite-dimensional manifolds
        58B05 Homotopy and topological questions
        58B10 Differentiability questions
        58B12 Questions of holomorphy, See also {32-XX, 46G20}
        58B15 Fredholm structures, See also {47A53}
        58B20 Riemannian, Finsler and other geometric structures, See also {53C20, 53C60}
        58B25 Group structures and generalizations on infinite-dimensional manifolds, See also {22E65, 58D05}
        58B30 Noncommutative differential geometry and topology, See also {46L30, 46L87, 46L89}
        58B99 None of the above but in this section
    58Cxx Calculus on manifolds; nonlinear operators, see also {47Hxx}
        58C05 Real-valued functions
        58C06 Set valued and function-space valued mappings, See Also {47H04, 54C60}
        58C07 Continuity properties of mappings
        58C10 Holomorphic maps, See also {32-XX}
        58C15 Implicit function theorems; global Newton methods
        58C20 Differentiation theory (Gateaux, Frechet, etc.), See also {26Exx, 46G05}
        58C25 Differentiable maps
        58C27 Singularities of differentiable maps, See also {14B05, 14E15, 32Sxx}
        58C28 Catastrophes, See also {57R70, 58Exx}
        58C30 Fixed point theorems on manifoldsSee also {47H10}
        58C35 Integration on manifolds; measures on manifolds, See Also { 28Cxx}
        58C40 Spectral theory; eigenvalue problems, See also {47H12, 58E07}
        58C50 Analysis on supermanifolds or graded manifolds
        58C99 None of the above but in this section
    58Dxx Spaces and manifolds of mappings {(including nonlinear versions of 46Exx)}
        58D05 Groups of diffeomorphisms and homeomorphisms as manifolds, See also {22E65, 57S05}
        58D07 Groups and semigroups of nonlinear operators, See Also {17B65, 47D03, 47D06, 47H20}
        58D10 Spaces of imbeddings and immersions
        58D15 Manifolds of mappings, See also {54C35}
        58D17 Manifolds of metrics (esp. Riemannian)
        58D19 Group actions and symmetry properties
        58D20 Measures (Gaussian, cylindrical, etc.) on manifolds of maps See{28Cxx}
        58D25 Equations in function spaces; evolution equations, See also {34Gxx, 35K22, 35R15, 47H15}
        58D27 Moduli problems for differential geometric structures
        58D29 Moduli problems for topological structures
        58D30 Applications (in quantum mechanics (Feynman path integrals), relativity, fluid dynamics, etc.)
        58D99 None of the above but in this section
    58Exx Variational problems in infinite-dimensional spaces
        58E05 Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirelman) theory, etc.)
        58E07 Abstract bifurcation theory
        58E09 Group-invariant bifurcation theory
        58E10 Applications to the theory of geodesics (problems in one independent variable)
        58E11 Critical metrics
        58E12 Applications to minimal surfaces (problems in two independent variables)
        58E15 Application to extremal problems in several variables; Yang-Mills functionals, See also {81T13}, etc.
        58E17 Pareto optimality, etc., applications to economics
        58E20 Harmonic maps
        58E25 Applications to control theory (optimal and nonoptimal)
        58E30 Variational principles
        58E35 Variational inequalities (global problems)
        58E40 Group actions
        58E50 Applications
        58E99 None of the above but in this section
    58Fxx Ordinary differential equations on manifolds; dynamical systems, see also {28D10, 34Cxx, {34Cxx} {54H20}}
        58F03 One-dimensional dynamics, general symbolic dynamics, See also {26A18}
        58F05 Hamiltonian and Lagrangian systems; symplectic geometry, See also {70Hxx, 81S10}
        58F06 Geometric quantization (applications of representation theory), See also {22E45, 81S10}
        58F07 Completely integrable systems (including systems with an infinite number of degrees of freedom)
        58F08 Point-mapping properties, iterations, completeness; dynamics of cellular automata, See also {26A18, 30D05}
        58F09 Morse-Smale systems
        58F10 Stability theory
        58F11 Ergodic theory; invariant measures, See also {28Dxx}
        58F12 Structure of attractors (and repellors)
        58F13 Strange attractors; chaos and other pathologies, See Also { 70K50}
        58F14 Bifurcation theory and singularities
        58F15 Hyperbolic structures (expanding maps, Anosov systems, etc.)
        58F17 Geodesic and horocycle flows
        58F18 Relations with foliations
        58F19 Eigenvalue and spectral problems
        58F20 Periodic points and zeta functions
        58F21 Limit cycles, singular points, etc.
        58F22 Periodic solutions
        58F23 Holomorphic dynamics, See also {30D05}
        58F25 Flows
        58F27 Quasiperiodic flows
        58F30 Perturbations
        58F32 Functional-differential equations on manifolds
        58F35 Invariance properties
        58F36 Normal forms
        58F37 Correspondences and other transformation methods (e.g. Lie-Backlund)
        58F39 Dynamical systems treatment of PDE (should be assigned another number from 58F), See also {35B32, 35K57}
        58F40 Applications
        58F99 None of the above but in this section
    58Gxx Partial differential equations on manifolds; differential operators, see also {35-XX}
        58G03 Elliptic equations on manifolds, general theory
        58G05 Differential complexes, See also {35Nxx}; elliptic complexes
        58G07 Relations with hyperfunctions
        58G10 Index theory and related fixed point theorems, See Also {19K56, 46L80}
        58G11 Heat and other parabolic equation methods
        58G12 Exotic index theories, See also {19K56, 46L05, 46L10, 46L80, 46M20}
        58G15 Pseudodifferential and Fourier integral operators on manifolds, See also {35Sxx}
        58G16 Hyperbolic equations
        58G17 Propagation of singularities; initial value problems
        58G18 Perturbations; asymptotics
        58G20 Boundary value problems on manifolds
        58G25 Spectral problems; spectral geometry; scattering theory, See also {35Pxx}
        58G26 Determinants and determinant bundles
        58G28 Bifurcations, See also {35B32}
        58G30 Relations with special manifold structures (Riemannian, Finsler, etc.)
        58G32 Diffusion processes and stochastic analysis on manifolds
        58G35 Invariance and symmetry properties, See also {35A30}
        58G37 Correspondences and other transformation methods (e.g. Lie-Backlund), See also {35A22}
        58G40 Applications
        58G99 None of the above but in this section
    58Hxx Pseudogroups, differentiable groupoids and general structures on manifolds
        58H05 Pseudogroups and differentiable groupoids, See also {22A22, 22E65}
        58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.), See also {57R32}
        58H15 Deformations of structures, See also {32Gxx, 58G05}
        58H99 None of the above but in this section
    58Z05 Applications to physics
* 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}
    60-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    60-01 Instructional exposition (textbooks, tutorial papers, etc.)
    60-02 Research exposition (monographs, survey articles)
    60-03 Historical (must be assigned at least one classification number from 01-XX)
    60-04 Explicit machine computation and programs (not the theory of computation or programming)
    60-06 Proceedings, conferences, collections, etc.
    60Axx Foundations of probability theory
        60A05 Axioms; other general questions
        60A10 Probabilistic measure theory, {For ergodic theory, See 28Dxx and 60Fxx}
    60Bxx Probability theory on algebraic and topological structures
        60B05 Probability measures on topological spaces
        60B10 Convergence of probability measures
        60B11 Probability theory on linear topological spaces, See Also { 28C20}
        60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
        60B15 Probability measures on groups, Fourier transforms, factorization
        60B99 None of the above but in this section
    60C05 Combinatorial probability
    60D05 Geometric probability, stochastic geometry, random sets, See also {52A22, 53C65}
    60Exx Distribution theory, see also {62Exx, 62Hxx}
        60E05 Distributions: general theory
        60E07 Infinitely divisible distributions; stable distributions
        60E10 Characteristic functions; other transforms
        60E15 Inequalities (Chebyshev, Kolmogorov, etc.)
        60E99 None of the above but in this section
    60Fxx Limit theorems, see also {28Dxx, 60B12}
        60F05 Central limit and other weak theorems
        60F10 Large deviations
        60F15 Strong theorems
        60F17 Functional limit theorems; invariance principles
        60F20 Zero-one laws
        60F25 $L^p$-limit theorems
        60F99 None of the above but in this section
    60Gxx Stochastic processes
        60G05 Foundations of stochastic processes
        60G07 General theory of processes
        60G09 Exchangeability
        60G10 Stationary processes
        60G12 General second-order processes
        60G15 Gaussian processes
        60G17 Sample path properties
        60G18 Self-similar processes
        60G20 Generalized stochastic processes
        60G25 Prediction theory, See also {62M20}
        60G30 Continuity and singularity of induced measures
        60G35 Applications (signal detection, filtering, etc.), See Also {62M20, 93E10, 93E11, 94Axx}
        60G40 Stopping times; optimal stopping problems; gambling theory, See also {62L15, 90D60}
        60G42 Martingales with discrete parameter
        60G44 Martingales with continuous parameter
        60G46 Martingales and classical analysis
        60G48 Generalizations of martingales
        60G50 Sums of independent random variables
        60G55 Point processes
        60G57 Random measures
        60G60 Random fields
        60G70 Extreme value theory; extremal processes
        60G99 None of the above but in this section
    60Hxx Stochastic analysis, see also {58G32}
        60H05 Stochastic integrals
        60H07 Stochastic calculus of variations and the Malliavin calculus
        60H10 Stochastic ordinary differential equations, See Also { 34F05}
        60H15 Stochastic partial differential equations, See also {35R60}
        60H20 Stochastic integral equations
        60H25 Random operators and equations, See also {47B80}
        60H30 Applications of stochastic analysis (to PDE, etc.)
        60H99 None of the above but in this section    
    60Jxx Markov processes
        60J05 Markov processes with discrete parameter
        60J10 Markov chains with discrete parameter
        60J15 Random walks
        60J20 Applications of discrete Markov processes (social mobility, learning theory, industrial processes, etc.), See Also {90B30, 92H10, 92H35, 92J40}
        60J25 Markov processes with continuous parameter
        60J27 Markov chains with continuous parameter
        60J30 Processes with independent increments
        60J35 Transition functions, generators and resolvents, See Also {47D03, 47D07}
        60J40 Right processes
        60J45 Probabilistic potential theory, See also {31Cxx, 31D05}
        60J50 Boundary theory
        60J55 Local time and additive functionals
        60J57 Multiplicative functionals
        60J60 Diffusion processes, See also {58G32}
        60J65 Brownian motion, See also {58G32}
        60J70 Applications of diffusion theory (population genetics, absorption problems, etc.), See also {92Dxx}
        60J75 Jump processes
        60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
        60J85 Applications of branching processes, See also {92Dxx}
        60J99 None of the above but in this section
    60Kxx Special processes
        60K05 Renewal theory
        60K10 Applications (reliability, demand theory, etc.)
        60K15 Markov renewal processes, semi-Markov processes
        60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.), See also {90Bxx}
        60K25 Queueing theory, See also {68M20, 90B22}
        60K30 Applications (congestion, allocation, storage, traffic, etc.), See also {90Bxx}
        60K35 Interacting random processes; statistical mechanics type models; percolation theory, See also {82B43, 82C43}
        60K40 Other physical applications of random processes
        60K99 None of the above but in this section    
* 62-XX Statistics, {For numerical methods, See 65U05}
    62-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    62-01 Instructional exposition (textbooks, tutorial papers, etc.)
    62-02 Research exposition (monographs, survey articles)
    62-03 Historical (must be assigned at least one classification number from 01-XX)
    62-04 Explicit machine computation and programs (not the theory of computation or programming)
    62-06 Proceedings, conferences, collections, etc.
    62-07 Data analysis
    62-09 Graphical methods
    62Axx Foundations
        62A05 Invariance and group considerations
        62A10 The likelihood approach
        62A15 The Bayesian approach
        62A20 The classical approach
        62A25 The structural approach
        62A30 The fiducial approach
        62A99 None of the above but in this section    
    62Bxx Sufficiency and information
        62B05 Sufficient statistics and fields
        62B10 Statistical information theory, See also {94A17}
        62B15 Theory of statistical experiments
        62B20 Measure-theoretic results, etc.
        62B99 None of the above but in this section    
    62Cxx Decision theory, see also {90A05, 90B50; for game theory, See 90D35}
        62C05 General considerations
        62C07 Complete class results
        62C10 Bayesian problems; characterization of Bayes procedures
        62C12 Empirical decision procedures; empirical Bayes procedures
        62C15 Admissibility
        62C20 Minimax procedures
        62C25 Compound decision problems
        62C99 None of the above but in this section    
    62D05 Sampling theory, sample surveys
    62Exx Distribution theory, see also {60Exx}
        62E10 Characterization and structure theory
        62E15 Exact distribution theory
        62E17 Approximations to distributions (nonasymptotic)
        62E20 Asymptotic distribution theory
        62E25 Monte Carlo studies
        62E30 Formal computational methods (polykays, etc.)
        62E99 None of the above but in this section    
    62Fxx Parametric inference
        62F03 Hypothesis testing
        62F04 Small sample properties of tests
        62F05 Asymptotic properties of tests
        62F07 Ranking and selection
        62F10 Point estimation
        62F11 Small sample properties of estimators
        62F12 Asymptotic properties of estimators
        62F15 Bayesian inference
        62F25 Tolerance and confidence regions
        62F30 Inference under constraints
        62F35 Robustness and adaptive procedures
        62F99 None of the above but in this section    
    62Gxx Nonparametric inference
        62G05 Estimation
        62G07 Curve estimation (nonparametric regression, density estimation, etc.)
        62G09 Resampling methods
        62G10 Hypothesis testing
        62G15 Tolerance and confidence regions
        62G20 Asymptotic properties
        62G30 Order statistics; empirical distribution functions
        62G35 Robustness
        62G99 None of the above but in this section    
    62Hxx Multivariate analysis, see also {60Exx}
        62H05 Characterization and structure theory
        62H10 Distribution of statistics
        62H11 Directional data; spatial statistics
        62H12 Estimation
        62H15 Hypothesis testing
        62H17 Contingency
        62H20 Measures of association (correlation, canonical correlation, etc.)
        62H25 Factor analysis and principal components; correspondence analysis
        62H30 Classification and discrimination; cluster analysis, See also {68T10}
        62H40 Projection pursuit
        62H99 None of the above but in this section    
    62Jxx Linear inference, regression
        62J02 General nonlinear regression
        62J05 Linear regression
        62J07 Ridge regression; James-Stein estimators
        62J10 Analysis of variance and covariance
        62J12 Generalized linear models
        62J15 Paired and multiple comparisons
        62J20 Diagnostics
        62J99 None of the above but in this section    
    62Kxx Experimental design, see also {05Bxx}
        62K05 Optimal designs
        62K10 Block designs
        62K15 Factorial designs
        62K99 None of the above but in this section    
    62Lxx Sequential methods
        62L05 Sequential design
        62L10 Sequential analysis
        62L12 Sequential estimation
        62L15 Optimal stopping, See also {60G40, 90D60}
        62L20 Stochastic approximation
        62L99 None of the above but in this section    
    62Mxx Inference from stochastic processes
        62M02 Markov processes: hypothesis testing
        62M05 Markov processes: estimation
        62M07 Non-Markovian processes: hypothesis testing
        62M09 Non-Markovian processes: estimation
        62M10 Time series, auto-correlation, regression, etc., See Also { 90A20}
        62M15 Spectral analysis
        62M20 Prediction, See also {60G25}; filtering, See also {60G35, 93E10, 93E11}
        62M30 Spatial processes
        62M40 Random fields
        62M99 None of the above but in this section    
    62Nxx Engineering statistics
        62N05 Reliability and life testing, See also {90B25}
        62N10 Quality control
        62N99 None of the above but in this section    
    62Pxx Applications, see also {90-XX, 92-XX}
        62P05 Applications to actuarial sciences and financial mathematics
        62P10 Applications to biology
        62P15 Applications to psychology
        62P20 Applications to economics, See also {90Axx}
        62P25 Applications to social sciences
        62P99 None of the above but in this section    
    62Q05 Statistical tables
* 65-XX Numerical analysis
    65-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    65-01 Instructional exposition (textbooks, tutorial papers, etc.)
    65-02 Research exposition (monographs, survey articles)
    65-03 Historical (must be assigned at least one classification number from 01-XX)
    65-04 Explicit machine computation and programs (not the theory of computation or programming)
    65-05 Experimental papers
    65-06 Proceedings, conferences, collections, etc.
    65A05 Tables
    65Bxx Acceleration of convergence
        65B05 Extrapolation to the limit, deferred corrections
        65B10 Summation of series
        65B15 Euler-Maclaurin formula
        65B99 None of the above but in this section    
    65Cxx Numerical simulation, {For theoretical aspects, see 68U20}
        65C05 Monte Carlo methods
        65C10 Random number generation
        65C20 Models, numerical methods
        65C99 None of the above but in this section    
    65Dxx Numerical approximation, {Primarily algorithms; for theory, see 41-XX}
        65D05 Interpolation
        65D07 Splines
        65D10 Smoothing, curve fitting
        65D15 Algorithms for functional approximation
        65D17 Computer aided design (modeling of curves and surfaces), See also {68U05}
        65D20 Computation of special functions, construction of tables
        65D25 Numerical differentiation
        65D30 Numerical integration
        65D32 Quadrature and cubature formulas
        65D99 None of the above but in this section
    65E05 Numerical methods in complex analysis (potential theory, etc.), {For numerical methods in conformal mapping, See 30C30}
    65Fxx Numerical linear algebra
        65F05 Direct methods for linear systems and matrix inversion
        65F10 Iterative methods for linear systems, See also {65N22}
        65F15 Eigenvalues, eigenvectors
        65F20 Overdetermined systems, pseudoinverses
        65F25 Orthogonalization
        65F30 Other matrix algorithms
        65F35 Matrix norms, conditioning, scaling, See also {15A12, 15A60}
        65F40 Determinants
        65F50 Sparse matrices
        65F99 None of the above but in this section    
    65Gxx Error analysis
        65G05 Roundoff error
        65G10 Interval and finite arithmetic
        65G99 None of the above but in this section    
    65Hxx Nonlinear algebraic or transcendental equations
        65H05 Single equations
        65H10 Systems of equations
        65H17 Eigenvalues, eigenvectors and bifurcation problems, See also {58C40, 58E07, 58F14, 90C30}
        65H20 Global methods, including homotopy approaches, See Also {58C30, 90C30}
        65H99 None of the above but in this section    
    65Jxx Numerical analysis in abstract spaces
        65J05 General theory
        65J10 Equations with linear operators (do not use 65Fxx)
        65J15 Equations with nonlinear operators (do not use 65Hxx)
        65J20 Improperly posed problems
        65J99 None of the above but in this section
    65Kxx Mathematical programming, optimization and variational techniques
        65K05 Mathematical programming, See also {90Cxx}
        65K10 Optimization and variational techniques, See also {49Mxx, 93B40}
        65K99 None of the above but in this section
    65Lxx Ordinary differential equations
        65L05 Initial value problems
        65L06 Multistep, Runge-Kutta and extrapolation methods
        65L07 Numerical investigation of stability of solutions
        65L08 Improperly posed problems
        65L10 Boundary value problems
        65L12 Finite difference methods
        65L15 Eigenvalue problems
        65L20 Stability of numerical methods
        65L50 Mesh generation and refinement
        65L60 Finite elements, Rayleigh-Ritz, Galerkin and collocation methods
        65L70 Error bounds
        65L99 None of the above but in this section
    65Mxx Partial differential equations, initial value and time-dependent initial-boundary value problems
        65M06 Finite difference methods
        65M12 Stability and convergence of numerical methods
        65M15 Error bounds
        65M20 Method of lines
        65M25 Method of characteristics
        65M30 Improperly posed problems
        65M50 Mesh generation and refinement
        65M55 Multigrid methods; domain decomposition
        65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
        65M70 Spectral, collocation and related methods
        65M99 None of the above but in this section
    65Nxx Partial differential equations, boundary value problems
        65N06 Finite difference methods
        65N12 Stability and convergence of numerical methods
        65N15 Error bounds
        65N22 Solution of discretized equations, See also {65Fxx, 65Hxx}
        65N25 Eigenvalue problems
        65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
        65N35 Spectral, collocation and related methods
        65N38 Boundary element methods
        65N40 Method of lines
        65N45 Method of contraction of the boundary
        65N50 Mesh generation and refinement
        65N55 Multigrid methods; domain decomposition
        65N99 None of the above but in this section
    65P05 Partial differential equations, miscellaneous problems
    65Q05 Difference and functional equations, recurrence relations
    65Rxx Integral equations, integral transforms, see also {45Lxx}
        65R10 Integral transforms
        65R20 Integral equations
        65R30 Improperly posed problems
        65R99 None of the above but in this section
    65S05 Graphical methods
    65Txx Numerical methods in Fourier analysis
        65T10 Trigonometric approximation and interpolation
        65T20 Discrete and fast Fourier transforms
        65T99 None of the above but in this section
    65U05 Numerical methods in probability and statistics
    65Yxx Computer aspects of numerical algorithms
        65Y05 Parallel computation
        65Y10 Algorithms for specific classes of architectures
        65Y15 Packaged methods
        65Y20 Complexity and performance of numerical algorithms, See also {68Q25}
        65Y25 Computer graphics and computational geometry, See Also {51N05, 68U05}
        65Y99 None of the above but in this section
* 68-XX Computer science, {For papers involving machine computations and programs in a specific mathematical area, See {Section --04 in} that area}
    68-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    68-01 Instructional exposition (textbooks, tutorial papers, etc.)
    68-02 Research exposition (monographs, survey articles)
    68-03 Historical (must be assigned at least one classification number from 01-XX)
    68-04 Explicit machine computation and programs (not the theory of computation or programming)
    68-06 Proceedings, conferences, collections, etc.
    68Mxx Computer system organization
        68M05 General
        68M07 Mathematical problems of computer architecture
        68M10 Computer networks, See also {90B12}
        68M15 Reliability and testing
        68M20 Performance evaluation; queueing; scheduling, See Also {60K25, 90Bxx}
        68M99 None of the above but in this section
    68Nxx Software
        68N05 General theory of programming
        68N15 Programming languages
        68N17 Logic programming
        68N20 Compilers and generators, See also {68Q52}
        68N25 Monitors and operating systems
        68N99 None of the above but in this section    
    68Pxx Theory of data
        68P05 Data structures
        68P10 Searching and sorting
        68P15 Database theory
        68P20 Information storage and retrieval
        68P25 Data encryption, See also {94A60}
        68P99 None of the above but in this section    
    68Qxx Theory of computing
        68Q05 Models of computation (abstract processors, Turing machines, etc.), See also {03D10}
        68Q10 Modes of computation (concurrent, parallel, nondeterministic, etc.), See also {68Q90}
        68Q15 Complexity classes, See also {03D15}
        68Q20 Nonnumerical algorithms, {For numerical algorithms, See 65-XX; for combinatorics and graph theory, See 68Rxx}
        68Q22 Parallel and distributed algorithms, {For numerical algorithms, See 65Y05, 65Y10}
        68Q25 Analysis of algorithms and problem complexity
        68Q30 Algorithmic information theory (Kolmogorov complexity, etc.)
        68Q35 VLSI algorithms
        68Q40 Symbolic computation, algebraic computation, See Also {11Yxx, 12Y05, 13Pxx, 14Qxx, 16-08, 17-08}
        68Q42 Rewriting systems
        68Q45 Formal languages, See also {03D05, 20M35, 94A45}
        68Q50 Grammars, See also {03D05}
        68Q52 Parsing, See also {68N20}
        68Q55 Semantics, See also {03B70, 06B35}
        68Q60 Specification and verification of programs, See Also { 03B70}
        68Q65 Abstract data types; algebraic specification
        68Q68 Automata theory, general, See also {03D05}
        68Q70 Algebraic theory of automata, See also {18B20, 20M35}
        68Q75 Stochastic and nondeterministic automata
        68Q80 Tessellation automata, iterative arrays, cellular structures
        68Q90 Transition nets
        68Q99 None of the above but in this section    
    68Rxx Discrete mathematics in relation to computer science
        68R05 Combinatorics
        68R10 Graph theory, See also {05Cxx, 90B10, 90B35, 90C35}
        68R15 Combinatorics on words
        68R99 None of the above but in this section
    68S05 Mathematical linguistics, See also {03B65, 92K20}
    68Txx Artificial intelligence, see also {92J40}
        68T01 General
        68T05 Learning and adaptive systems
        68T10 Pattern recognition, speech recognition, {For cluster analysis, See 62H30}
        68T15 Theorem proving, See also {03B35}
        68T20 Problem solving
        68T25 AI languages
        68T27 AI logics
        68T30 Knowledge representation
        68T35 AI software systems (knowledge-based systems, expert systems, etc.)
        68T99 None of the above but in this section    
    68Uxx Computing methodologies
        68U05 Computer graphics; computational geometry, See also {65Y25}
        68U07 Computer-aided design
        68U10 Image processing
        68U15 Text processing; mathematical typography
        68U20 Simulation, See also {65Cxx}
        68U30 Other applications
        68U99 None of the above but in this section    
* 70-XX Mechanics of particles and systems, {For relativistic mechanics, See {83-XX} {83A05 and 83C10}; for statistical mechanics, See 82-XX}
    70-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    70-01 Instructional exposition (textbooks, tutorial papers, etc.)
    70-02 Research exposition (monographs, survey articles)
    70-03 Historical (must be assigned at least one classification number from 01-XX)
    70-04 Explicit machine computation and programs (not the theory of computation or programming)
    70-05 Experimental papers
    70-06 Proceedings, conferences, collections, etc.
    70-08 Computational methods
    70A05 Axiomatics, foundations
    70Bxx Kinematics, see also {53A17}
        70B05 Kinematics of a particle
        70B10 Kinematics of a rigid body
        70B15 Mechanisms, robots, See also {73K05}
        70B99 None of the above but in this section    
    70C20 Statics
    70Dxx Dynamics of a particle, see also {70Hxx}
        70D05 Newtonian dynamics
        70D10 Lagrangian dynamics
        70D99 None of the above but in this section    
    70Exx Dynamics of a rigid body
        70E05 Motion of the gyroscope
        70E10 Motion of projectiles and rockets
        70E15 Motion of rigid bodies
        70E20 Perturbation methods for Euler's equations
        70E99 None of the above but in this section    
    70Fxx Dynamics of a system of particles, including celestial mechanics
        70F05 Two-body problem
        70F07 Three-body problem
        70F10 $n$-body problem
        70F15 Celestial mechanics
        70F20 Holonomic systems
        70F25 Nonholonomic systems
        70F30 Impulsive motion
        70F35 Collisions
        70F99 None of the above but in this section    
    70Gxx General representations of dynamical systems, see Also { 58Fxx}
        70G05 Riemannian geometry, tensorial methods, See also {53A45, 53A50, 53B20}
        70G10 Generalized coordinates
        70G15 Space of events
        70G20 Impulse-energy space
        70G25 Configuration space
        70G30 State space
        70G35 Phase space
        70G50 Classical field theories (general)
        70G99 None of the above but in this section    
    70Hxx Hamiltonian and Lagrangian mechanics, see also {58F05}
        70H05 Hamilton's equations
        70H10 Liouville's theorem
        70H15 Canonical transformations
        70H20 Hamilton-Jacobi equations
        70H25 Hamilton's principle
        70H30 Other variational principles
        70H33 Symmetries
        70H35 Lagrange's equation of motion
        70H40 Relativistic dynamics
        70H99 None of the above but in this section    
    70Jxx Linear vibration theory, see also {73D30}
        70J05 Finite degree of freedom systems
        70J10 Modal analysis
        70J25 Stability
        70J30 Free motions
        70J35 Forced motions
        70J40 Parametric resonances
        70J99 None of the above but in this section    
    70Kxx Nonlinear motions, see also {34Cxx, 58Fxx, 73D35, 73K12}
        70K05 Phase plane analysis
        70K10 Limit cycles
        70K15 Lyapunov theorems
        70K20 Stability
        70K25 Free motions
        70K28 Parametric resonances
        70K30 Nonlinear resonances
        70K40 Forced motions
        70K50 Transition to stochasticity (chaotic behavior), See Also { 58F13}
        70K99 None of the above but in this section    
    70L05 Random vibrations, See also {73K35, 93Exx}
    70M20 Orbital mechanics
    70P05 Variable mass, rockets
    70Q05 Control of mechanical systems, See also {49-XX, 73K50, 93Cxx, 93Dxx}
* 73-XX Mechanics of solids
    73-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    73-01 Instructional exposition (textbooks, tutorial papers, etc.)
    73-02 Research exposition (monographs, survey articles)
    73-03 Historical (must be assigned at least one classification number from 01-XX)
    73-04 Explicit machine computation and programs (not the theory of computation or programming)
    73-05 Experimental papers
    73-06 Proceedings, conferences, collections, etc.
    73A05 Axiomatics, foundations of solid mechanics
    73Bxx Continuum mechanics of solids (constitutive description and properties)
        73B05 Constitutive equations
        73B10 Symmetry groups
        73B18 Nonlocal theories
        73B25 Polar theories
        73B27 Nonhomogeneous materials; homogenization
        73B30 Thermodynamics of solids, {For gases and fluids, See 80-XX}
        73B35 Random materials
        73B40 Anisotropic materials
        73B50 Stress concentrations
        73B99 None of the above but in this section    
    73Cxx Elasticity, {For the biharmonic equation, see 31A30, 31B30}
        73C02 Classical linear elasticity
        73C05 Stress functions
        73C10 Saint-Venant's principle
        73C15 Uniqueness theorems
        73C35 Mixed boundary value problems, See also {45F05}
        73C50 Nonlinear elasticity
        73C99 None of the above but in this section    
    73Dxx Wave propagation in and vibrations of solids
        73D05 Impact and explosion problems, See also {76L05}
        73D10 Integral transforms
        73D15 Body waves
        73D20 Surface waves
        73D25 Wave diffraction and dispersion
        73D30 Linear vibrations, See also {70Jxx}
        73D35 Nonlinear vibrations, See also {70Kxx}
        73D40 Singular surfaces
        73D50 Inverse problems, See also {35Lxx, 35R30}
        73D70 Random waves
        73D99 None of the above but in this section    
    73Exx Plasticity
        73E05 Constitutive specifications (yield criteria, flow rules, hardening, softening)
        73E10 Method of successive approximations
        73E20 Limit analysis
        73E50 Time-dependent problems
        73E60 Viscoplasticity
        73E70 Plastic waves
        73E99 None of the above but in this section    
    73Fxx Viscoelasticity
        73F05 Creep and relaxation functions
        73F10 Correspondence principle
        73F15 Time-dependent problems
        73F20 Aging of materials
        73F25 Environmental-dependent materials
        73F99 None of the above but in this section    
    73Gxx Finite deformations
        73G05 Finite elasticity
        73G20 Finite plasticity
        73G25 Finite viscoelasticity
        73G99 None of the above but in this section    
    73Hxx Stability (linear and nonlinear)
        73H05 Buckling
        73H10 Dynamic stability
        73H99 None of the above but in this section    
    73Kxx Mechanics of structures
        73K03 Strings
        73K05 Beams, columns, rods
        73K10 Plates, discs, membranes
        73K12 Dynamics of structures
        73K15 Shells
        73K20 Composite structures and materials
        73K35 Random vibrations
        73K40 Optimization, See also {90C90}
        73K50 Control of structures
        73K70 Aero- or hydromechanic structure interactions
        73K99 None of the above but in this section    
    73M25 Fracture mechanics
    73N20 Geophysical solid mechanics, See also {86A15, 86A17}
    73P05 Biomechanics of solids, See also {92C10}
    73Q05 Soil and rock mechanics, See also {86A60}
    73R05 Electromagnetic elasticity
    73S10 Micromechanics of solids
    73T05 Contact and surface mechanics
    73Vxx Basic methods in solid mechanics, see also {65-XX}
        73V05 Finite element methods
        73V10 Boundary element methods
        73V15 Finite difference methods
        73V20 Other numerical methods
        73V25 Variational methods
        73V30 Stochastic analysis
        73V35 Complex variable techniques
        73V99 None of the above but in this section    
* 76-XX Fluid mechanics, {For general continuum mechanics, See 73Bxx, or other parts of 73-XX}
    76-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    76-01 Instructional exposition (textbooks, tutorial papers, etc.)
    76-02 Research exposition (monographs, survey articles)
    76-03 Historical (must be assigned at least one classification number from 01-XX)
    76-04 Explicit machine computation and programs (not the theory of computation or programming)
    76-05 Experimental papers
    76-06 Proceedings, conferences, collections, etc.
    76Axx Foundations, constitutive equations, rheology
        76A02 Foundations of fluid mechanics
        76A05 Non-Newtonian fluids
        76A10 Viscoelastic fluids
        76A15 Liquid crystals, See also {82D30}
        76A99 None of the above but in this section
    76Bxx Incompressible inviscid fluids, potential theory
        76B05 Airfoil theory
        76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, hydrofoil theory, sloshing
        76B15 Water waves, gravity waves; dispersion and diffraction, nonlinear interaction, See also {35Q53}
        76B20 Ship waves
        76B25 Solitary and cnoidal waves, See also {35Q51}
        76B35 Random waves, inviscid fluids
        76B40 Added mass computations
        76B45 Capillarity
        76B99 None of the above but in this section    
    76Cxx Incompressible inviscid fluids, vorticity flows
        76C05 Vorticity flows
        76C10 Internal waves
        76C15 Atmospheric waves
        76C20 Rossby waves
        76C99 None of the above but in this section    
    76Dxx Incompressible viscous fluids
        76D05 Navier-Stokes equations, See also {35Q30}
        76D07 Stokes flows
        76D08 Lubrication theory
        76D10 Boundary-layer theory
        76D15 Boundary-layer separation and reattachment
        76D20 Higher-order effects in boundary layers
        76D25 Wakes and jets
        76D30 Singular perturbation problems
        76D33 Waves
        76D35 Random waves, viscous fluids
        76D45 Capillarity, See also {76B45}
        76D99 None of the above but in this section    
    76Exx Hydrodynamic stability
        76E05 Stability of parallel flows
        76E10 Inertial instability
        76E15 Convective instability
        76E20 Instability of geophysical and astrophysical flows
        76E25 Magnetohydrodynamic and electrohydrodynamic instabilities
        76E30 Nonlinear effects
        76E99 None of the above but in this section    
    76Fxx Turbulence, see also {58F13, 58F27, 60Gxx, 60Jxx}
        76F05 Homogeneous isotropic turbulence
        76F10 Shear flows
        76F20 Turbulence via chaos techniques
        76F99 None of the above but in this section    
    76G25 General aerodynamics and subsonic flows
    76H05 Transonic flows
    76J20 Supersonic flows
    76K05 Hypersonic flows
    76L05 Shock waves and blast waves, See also {35L67, 73D05}
    76Mxx Basic methods in fluid mechanics, see also {65-XX}
        76M10 Finite element methods
        76M15 Boundary element methods
        76M20 Finite difference methods
        76M25 Other numerical methods
        76M30 Variational methods
        76M35 Stochastic analysis
        76M99 None of the above but in this section    
    76Nxx Compressible fluids and gas dynamics, general
        76N10 Compressible fluids, general, See also {35Q30}
        76N15 Gas dynamics, general
        76N20 Boundary-layer theory
        76N99 None of the above but in this section    
    76P05 Rarefied gas flows, Boltzmann equation, See also {82B40, 82C40, 82D05}
    76Q05 Hydrodynamic sound, acoustics
    76Rxx Diffusion and convection
        76R05 Forced convection
        76R10 Free convection
        76R50 Diffusion, See also {60J60}
        76R99 None of the above but in this section    
    76S05 Flows in porous media; filtration; Seepage
    76T05 Two-phase and multiphase flows
    76U05 Rotating fluids
    76V05 Stratified and reacting fluids
    76W05 Magnetohydrodynamics and electrohydrodynamics
    76X05 Ionized gas flow in electromagnetic fields; plasmic flow
    76Y05 Quantum hydrodynamics and relativistic hydrodynamics, See also {83C55, 85A30}
    76Zxx Biological fluid mechanics, see also {92Cxx}
        76Z05 Physiological flows, See also {92C35}
        76Z10 Biopropulsion in water and in air
        76Z99 None of the above but in this section    
* 78-XX Optics, electromagnetic theory, {For quantum optics, See 81V80}
    78-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    78-01 Instructional exposition (textbooks, tutorial papers, etc.)
    78-02 Research exposition (monographs, survey articles)
    78-03 Historical (must be assigned at least one classification number from 01-XX)
    78-04 Explicit machine computation and programs (not the theory of computation or programming)
    78-05 Experimental papers
    78-06 Proceedings, conferences, collections, etc.
    78-08 Computational methods
    78A02 Foundations
    78A05 Geometric optics
    78A10 Physical optics
    78A15 Electron optics
    78A20 Space charge waves
    78A25 Electromagnetic theory, general
    78A30 Electro- and magnetostatics
    78A35 Motion of charged particles
    78A40 Waves and radiation
    78A45 Diffraction, scattering, See also {34E20 for WKB methods}
    78A50 Antennas, wave-guides
    78A55 Technical applications
    78A60 Lasers, masers, optical bistability, nonlinear optics, See also {81V80}
    78A70 Biological applications, See also {92C30, 92J30}
    78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned at least one other classification number in this section)
    78A99 Miscellaneous topics
* 80-XX Classical thermodynamics, heat transfer, {For thermodynamics of solids, See 73B30}
    80-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    80-01 Instructional exposition (textbooks, tutorial papers, etc.)
    80-02 Research exposition (monographs, survey articles)
    80-03 Historical (must be assigned at least one classification number from 01-XX)
    80-04 Explicit machine computation and programs (not the theory of computation or programming)
    80-05 Experimental papers
    80-06 Proceedings, conferences, collections, etc.
    80-08 Computational methods
    80A05 Foundations
    80A10 Classical thermodynamics
    80A15 Thermodynamics of mixtures
    80A20 Heat and mass transfer, heat flow
    80A22 Stefan problems, phase changes, etc.
    80A23 Inverse problems
    80A25 Combustion, interior ballistics
    80A30 Chemical kinetics, See also {92C45, 92E20}
    80A32 Chemically reacting flows, See also {92C45, 92E20}
    80A50 Chemistry (general) See mainly{92Exx}
    80A97 Mathematically heuristic classical thermodynamics (must also be assigned at least one other classification number in this section)
    80A99 Miscellaneous topics
* 81-XX Quantum Theory
    81-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    81-01 Instructional exposition (textbooks, tutorial papers, etc.)
    81-02 Research exposition (monographs, survey articles)
    81-03 Historical (must be assigned at least one classification number from 01-XX)
    81-04 Explicit machine computation and programs (not the theory of computation or programming)
    81-05 Experimental papers
    81-06 Proceedings, conferences, collections, etc.
    81-08 Computational methods
    81Pxx Axiomatics, foundations, philosophy
        81P05 General and philosophical
        81P10 Logical foundations of quantum mechanics
        81P15 Quantum measurement theory
        81P20 Stochastic mechanics (including stochastic electrodynamics)
        81P99 None of the above but in this section    
    81Qxx General mathematical topics and methods in quantum theory
        81Q05 Closed and approximate solutions to the Schrodinger, Dirac, Klein-Gordon and other quantum-mechanical equations
        81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
        81Q15 Perturbation theories for operators and differential equations
        81Q20 Semiclassical techniques including WKB and Maslov methods
        81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry, See also {14D05, 32S40}
        81Q40 Bethe-Salpeter and other integral equations
        81Q50 Quantum chaos, See also {58F13}
        81Q60 Supersymmetric quantum mechanics
        81Q99 None of the above but in this section    
    81Rxx Groups and algebras in quantum theory
        81R05 Representations of finite-dimensional groups and algebras motivated by physics, See also {20C35, 22E70}
        81R10 Representations of infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody and other current algebras, See also {17B65, 17B67, 22E65, 22E67, 22E70}
        81R20 Covariant wave equations
        81R25 Spinor and twistor methods, See also {32L25}
        81R30 Coherent states, See also {22E45}
        81R40 Symmetry breaking
        81R50 Quantum groups and related algebraic methods, See Also {16W30, 17B37}
        81R99 None of the above but in this section    
    81Sxx General quantum mechanics and problems of quantization
        81S05 Commutation relations
        81S10 Geometric quantization, symplectic methods, See Also { 58F06}
        81S20 Stochastic quantization
        81S25 Quantum stochastic calculus
        81S30 Phase space methods including Wigner distributions, etc.
        81S40 Path integrals, See also {58D30}
        81S99 None of the above but in this section    
    81Txx Quantum field theory; related classical field theories
        81T05 Axiomatic quantum field theory; operator algebras
        81T08 Constructive quantum field theory
        81T10 Model quantum field theories
        81T13 Yang-Mills and other gauge theories, See also {53C07, 58E15}
        81T15 Perturbative methods of renormalization
        81T16 Nonperturbative methods of renormalization
        81T17 Renormalization group methods
        81T18 Feynman diagrams
        81T20 Quantum field theory on curved space backgrounds
        81T25 Quantum field theory on lattices
        81T27 Continuum limits
        81T30 String and superstring theories; other extended objects , See also {83E30}
        81T40 Two-dimensional field theories, conformal field theories, etc.
        81T50 Anomalies
        81T60 Supersymmetric field theories
        81T70 Quantization in field theory; cohomological methods, See also {58F06}
        81T80 Simulation and numerical modeling
        81T99 None of the above but in this section    
    81Uxx Scattering theory, see also {47A40}
        81U05 $2$-body potential scattering theory, See also {34E20 for WKB methods}
        81U10 $n$-body potential scattering theory
        81U20 $S$-matrix theory, etc.
        81U30 Dispersion theory, dispersion relations
        81U40 Inverse scattering problems, See also {58F07, 58F19}
        81U99 None of the above but in this section    
    81Vxx Applications to specific physical systems
        81V05 Strong interaction, including quantum chromodynamics
        81V10 Electromagnetic interaction; quantum electrodynamics
        81V15 Weak interaction
        81V17 Gravitational interaction
        81V19 Other fundamental interactions
        81V22 Unified theories
        81V25 Other elementary particle theory
        81V35 Nuclear physics
        81V45 Atomic physics
        81V55 Molecular physics, See also {92E10}
        81V70 Many-body theory
        81V80 Quantum optics
        81V99 None of the above but in this section    
* 82-XX Statistical mechanics, structure of matter
    82-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    82-01 Instructional exposition (textbooks, tutorial papers, etc.)
    82-02 Research exposition (monographs, survey articles)
    82-03 Historical (must be assigned at least one classification number from 01-XX)
    82-04 Explicit machine computation and programs (not the theory of computation or programming)
    82-05 Experimental papers
    82-06 Proceedings, conferences, collections, etc.
    82-08 Computational methods
    82Bxx Equilibrium statistical mechanics
        82B03 Foundations
        82B05 Classical equilibrium statistical mechanics (general)
        82B10 Quantum equilibrium statistical mechanics (general)
        82B20 Lattice systems (Ising, dimer, Potts, etc.)
        82B21 Continuum models (systems of particles, etc.)
        82B23 Exactly solvable models
        82B24 Interface problems
        82B26 Phase transitions (general)
        82B27 Critical phenomena
        82B28 Renormalization group methods, See also {81T17}
        82B30 Statistical thermodynamics, See also {80-XX}
        82B31 Stochastic methods
        82B35 Irreversible thermodynamics, including Onsager-Machlup theory, See also {92E20}
        82B40 Kinetic theory of gases
        82B41 Random walks, random surfaces, lattice animals, etc., See also {60J15, 82C41}
        82B43 Percolation, See also {60K35}
        82B44 Disordered systems (random Ising models, random Schrodinger operators, etc.)
        82B80 Numerical methods (Monte Carlo, series resummation, etc.), See also {65-XX, 81T80}
        82B99 Miscellaneous topics    
    82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium)
        82C03 Foundations
        82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
        82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
        82C20 Dynamic lattice systems (kinetic Ising, etc.)
        82C21 Dynamic continuum models (systems of particles, etc.)
        82C22 Interacting particle systems, See also {60K35}
        82C23 Exactly solvable dynamic models, See also {58F07}
        82C24 Interface problems
        82C26 Dynamic and nonequilibrium phase transitions (general)
        82C27 Dynamic critical phenomena
        82C28 Dynamic renormalization group methods, See also {81T17}
        82C31 Stochastic methods (Fokker-Planck, Langevin, etc.), See also {60H10}
        82C32 Neural nets, See also {68T05, 92B20, 92J40}
        82C35 Irreversible thermodynamics, including Onsager-Machlup theory
        82C40 Kinetic theory of gases
        82C41 Dynamics of random walks, random surfaces, lattice animals, etc., See also {60J15}
        82C43 Time-dependent percolation, See also {60K35}
        82C44 Dynamics of disordered systems (random Ising systems, etc.)
        82C70 Transport processes
        82C80 Numerical methods (Monte Carlo, series resummation, etc.)
        82C99 None of the above but in this section    
    82Dxx Applications to specific types of physical systems
        82D05 Gases
        82D10 Plasmas
        82D15 Liquids
        82D20 Solids
        82D25 Crystals, {For crystallographic group theory, See 20H15}
        82D30 Random media, disordered materials (including liquid crystals and spin glasses)
        82D35 Metals
        82D40 Magnetic materials
        82D45 Ferroelectrics
        82D50 Superfluids
        82D55 Superconductors
        82D60 Polymers
        82D75 Nuclear reactor theory
        82D99 None of the above but in this section    
* 83-XX Relativity and gravitational theory
    83-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    83-01 Instructional exposition (textbooks, tutorial papers, etc.)
    83-02 Research exposition (monographs, survey articles)
    83-03 Historical (must be assigned at least one classification number from 01-XX)
    83-04 Explicit machine computation and programs (not the theory of computation or programming)
    83-05 Experimental papers
    83-06 Proceedings, conferences, collections, etc.
    83-08 Computational methods
    83A05 Special relativity
    83B05 Observational and experimental questions
    83Cxx General relativity
        83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
        83C10 Equations of motion
        83C15 Exact solutions
        83C20 Classes of solutions; algebraically special solutions, metrics with symmetries
        83C22 Electromagnetic fields, Einstein-Maxwell equations
        83C25 Approximation procedures, weak fields
        83C27 Lattice gravity, Regge calculus and other discrete methods
        83C30 Asymptotic procedures (radiation, news functions, {H}-spaces, etc.)
        83C35 Gravitational waves
        83C40 Gravitational energy and conservation laws; groups of motions
        83C45 Quantization of the gravitational field
        83C47 Quantum field theory aspects, See also {81T20}
        83C50 Electromagnetic fields
        83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
        83C57 Black holes
        83C60 Spinor and twistor methods
        83C75 Space-time singularities, cosmic censorship, etc.
        83C99 None of the above but in this section    
    83D05 Relativistic gravitational theories other than Einstein's, including asymmetric field theories
    83Exx Unified, higher-dimensional and super field theories
        83E05 Geometrodynamics
        83E15 Kaluza-Klein and other higher-dimensional theories
        83E30 String and superstring theories, See also {81T30}
        83E50 Supergravity
        83E99 None of the above but in this section    
    83F05 Cosmology
* 85-XX Astronomy and astrophysics, {For celestial mechanics, See 70F15}
    85-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    85-01 Instructional exposition (textbooks, tutorial papers, etc.)
    85-02 Research exposition (monographs, survey articles)
    85-03 Historical (must be assigned at least one classification number from 01-XX)
    85-04 Explicit machine computation and programs (not the theory of computation or programming)
    85-05 Experimental papers
    85-06 Proceedings, conferences, collections, etc.
    85-08 Computational methods
    85A04 General
    85A05 Galactic and stellar dynamics
    85A15 Galactic and stellar structure
    85A20 Stellar atmospheres
    85A25 Radiative transfer
    85A30 Hydrodynamic and hydromagnetic problems, See also {76Y05}
    85A35 Statistical astronomy
    85A40 Cosmology, {For relativistic cosmology, See 83F05}
    85A45 Radio astronomy
    85A99 Miscellaneous topics
* 86-XX Geophysics, See also {73N05, 76U05, 76V05}
    86-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    86-01 Instructional exposition (textbooks, tutorial papers, etc.)
    86-02 Research exposition (monographs, survey articles)
    86-03 Historical (must be assigned at least one classification number from 01-XX)
    86-04 Explicit machine computation and programs (not the theory of computation or programming)
    86-05 Experimental papers
    86-06 Proceedings, conferences, collections, etc.
    86-08 Computational methods
    86A04 General
    86A05 Hydrology, hydrography, oceanography, See also {76B15, 76B20, 76B25, 76C15, 76E20, 76Q05, 76Rxx, 76U05}
    86A10 Meteorology and atmospheric physics, See also {76Bxx, 76C15, 76C20, 76E20, 76N15, 76Q05, 76Rxx, 76U05, 76V05}
    86A15 Seismology, See also {73Dxx, 73Fxx, 73M25, 73N20, 73Q05}
    86A17 Global dynamics, earthquake problems
    86A20 Potentials, prospecting, See also {76S05, 76W05}
    86A22 Inverse problems, See also {35R30}
    86A25 Geo-electricity and geomagnetism, See also {78A25}
    86A30 Geodesy, mapping problems
    86A32 Geostatistics
    86A40 Glaciology
    86A60 Geological problems
    86A99 Miscellaneous topics
* 90-XX Economics, operations research, programming, games
    90-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    90-01 Instructional exposition (textbooks, tutorial papers, etc.)
    90-02 Research exposition (monographs, survey articles)
    90-03 Historical (must be assigned at least one classification number from 01-XX)
    90-04 Explicit machine computation and programs (not the theory of computation or programming)
    90-06 Proceedings, conferences, collections, etc.
    90-08 Computational methods
    90Axx Mathematical economics, {For econometrics, see 62P20}
        90A05 Decision theory, See also {62Cxx, 90B50, 90D35}
        90A06 Individual preferences
        90A07 Group preferences
        90A08 Social choice
        90A09 Finance, portfolios, investment
        90A10 Utility theory
        90A11 Production theory, theory of the firm
        90A12 Price theory and market structure
        90A14 Equilibrium: general theory
        90A15 General economic models, trade models
        90A16 Dynamic economic models, growth models
        90A17 Multisectoral models
        90A19 Statistical models; economic indexes and measures
        90A20 Economic time series analysis, See also {62M10}
        90A25 Spatial models
        90A27 Public goods
        90A28 Voting theory
        90A30 Environmental economics (natural resource models, harvesting, pollution, etc.)
        90A35 Informational economics
        90A36 Incentives theory
        90A40 Consumer behavior, demand theory
        90A43 Expected utility; risk-averse utility
        90A46 Risk theory
        90A50 Labor market
        90A53 Special types of economies
        90A56 Special types of equilibria
        90A58 Models of real-world systems; general macro-economic models, etc.
        90A60 Market models (auctions, bargaining, bidding, selling, etc.)
        90A70 Macro-economic policy-making, taxation
        90A80 Resource allocation
        90A99 None of the above but in this section    
    90Bxx Operations research and management science
        90B05 Inventory, storage, reservoirs
        90B06 Transportation, logistics
        90B10 Flows in networks, deterministic
        90B12 Communication networks, See also {68M10, 94A05}
        90B15 Flows in networks, probabilistic
        90B20 Highway traffic
        90B22 Queues and service, See also {60K25, 68M20}
        90B25 Reliability, availability, maintenance, inspection, See also {60K10, 62N05}
        90B30 Production models
        90B35 Scheduling theory, See also {68M20}
        90B40 Search theory
        90B50 Management decision-making, including multiple objectives, See also {90A05, 90C31, 90D35}
        90B60 Marketing, advertising, See also {90A60}
        90B70 Theory of organizations, industrial and manpower planning, See also {92H35}
        90B80 Discrete location and assignment, See also {90C10}
        90B85 Continuous location
        90B90 Case-oriented studies
        90B99 None of the above but in this section    
    90Cxx Mathematical programming, see also {49Mxx, 65Kxx}
        90C05 Linear programming
        90C06 Large-scale problems
        90C08 Special problems of linear programming (transportation, multi-index, etc.)
        90C09 Boolean programming
        90C10 Integer programming
        90C11 Mixed integer programming
        90C15 Stochastic programming
        90C20 Quadratic programming
        90C25 Convex programming
        90C26 Nonconvex programming, quasiconvex programming
        90C27 Combinatorial optimization
        90C28 Geometric programming
        90C29 Multi-objective and goal programming; vector optimization
        90C30 Nonlinear programming
        90C31 Sensitivity, stability, parametric optimization
        90C32 Fractional programming
        90C33 Complementarity problems
        90C34 Semi-infinite programming
        90C35 Programming involving graphs or networks
        90C39 Dynamic programming, See also {49L20}
        90C40 Markov and semi-Markov decision processes
        90C42 Markov programming and Markov renewal programming
        90C45 Continuous programming
        90C48 Programming in abstract spaces
        90C60 Abstract computational complexity for mathematical programming problems, See also {68Q25}
        90C70 Fuzzy programming
        90C90 Applications of mathematical programming
        90C99 None of the above but in this section    
    90Dxx Game theory
        90D05 $2$-person games
        90D06 $n$-person games, $n>2$
        90D10 Noncooperative games
        90D12 Cooperative games
        90D13 Games with infinitely many players
        90D15 Stochastic games, See also {93E05}
        90D20 Multistage and repeated games
        90D25 Differential games, See also {49N55}
        90D26 Pursuit and evasion games
        90D35 Decision theory for games, See also {62Cxx, 90A05, 90B50}
        90D40 Game-theoretic models, See also {65Cxx}
        90D42 Positional games
        90D43 Games involving graphs
        90D44 Games involving topology or set theory
        90D46 Combinatorial games
        90D50 Discrete-time games
        90D55 Games of timing
        90D60 Probabilistic games; gambling
        90D65 Hierarchical games
        90D70 Spaces of games
        90D80 Applications of game theory
        90D99 None of the above but in this section    
* 92-XX Biology and other natural sciences, behavioral sciences
    92-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    92-01 Instructional exposition (textbooks, tutorial papers, etc.)
    92-02 Research exposition (monographs, survey articles)
    92-03 Historical (must be assigned at least one classification number from 01-XX)
    92-04 Explicit machine computation and programs (not the theory of computation or programming)
    92-06 Proceedings, conferences, collections, etc.
    92-08 Computational methods
    92Bxx Mathematical biology in general
        92B05 General biology and biomathematics
        92B10 Taxonomy, statistics
        92B15 General biostatistics, See also {62P10}
        92B20 Neural networks, See also {68T05, 82C32, 94Cxx}
        92B99 None of the above but in this section    
    92Cxx Physiological, cellular and medical topics
        92C05 Biophysics
        92C10 Biomechanics, See also {73P05}
        92C15 Developmental biology, pattern formation
        92C20 Neural biology
        92C30 Physiology (general)
        92C35 Physiological flow, See also {76Z05}
        92C40 Biochemistry, molecular biology
        92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.), See also {80A30}
        92C50 Medical applications (general)
        92C55 Tomography, See also {44A12, 65R10}
        92C60 Medical epidemiology
        92C99 None of the above but in this section    
    92Dxx Genetics and population dynamics
        92D10 Genetics, {For genetic algebras, See 17D92}
        92D15 Problems related to evolution
        92D20 Protein sequences, DNA sequences
        92D25 Population dynamics (general)
        92D30 Epidemiology
        92D40 Ecology
        92D50 Animal behavior
        92D99 None of the above but in this section    
    92Exx Chemistry, {For biochemistry, see 92C40}
        92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
        92E20 Classical flows, reactions, etc., See also {80A30, 80A32}
        92E99 None of the above but in this section    
    92F05 Other natural sciences
    92Gxx Social and behavioral sciences: methodology, {For statistics, see 62-XX}
        92G05 Measurement theory
        92G15 One- and multidimensional scaling
        92G20 Test theory
        92G25 Questionnaire analysis
        92G30 Clustering, See also {62H30}
        92G40 Q-analysis
        92G99 None of the above but in this section    
    92Hxx Mathematical sociology (including anthropology)
        92H10 Models of societies, social and urban evolution
        92H20 Mathematical geography and demography
        92H25 Spatial models, See also {90A25}
        92H30 Social networks
        92H35 Manpower systems, See also {90A50, 90B70}
        92H99 None of the above but in this section    
    92Jxx Mathematical psychology
        92J10 Cognitive psychology
        92J30 Psychophysics and psychophysiology; perception
        92J40 Memory and learning, See also {68T05}
        92J45 Measurement and performance
        92J99 None of the above but in this section    
    92Kxx Other social and behavioral sciences (mathematical treatment)
        92K10 History, political science
        92K20 Linguistics, See also {03B65, 68S05}
        92K99 None of the above but in this section    
* 93-XX Systems theory; control, {For optimal control, See 49-XX}
    93-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    93-01 Instructional exposition (textbooks, tutorial papers, etc.)
    93-02 Research exposition (monographs, survey articles)
    93-03 Historical (must be assigned at least one classification number from 01-XX)
    93-04 Explicit machine computation and programs (not the theory of computation or programming)
    93-06 Proceedings, conferences, collections, etc.
    93Axx General
        93A05 Axiomatic system theory
        93A10 General systems
        93A13 Hierarchical systems
        93A14 Decentralized systems
        93A15 Large scale systems
        93A20 Cascaded systems
        93A25 Input-output systems
        93A30 Mathematical modeling (models of systems, model-matching, etc.)
        93A99 None of the above but in this section
    93Bxx Controllability, observability, and system structure
        93B03 Attainable sets
        93B05 Controllability
        93B06 Relations between controllability and optimal solutions
        93B07 Observability
        93B10 Canonical structure
        93B11 System structure simplification
        93B12 Variable structure systems
        93B15 Realizability of systems from input-output data
        93B17 Transformation
        93B18 Linearizability
        93B20 Minimal systems representations
        93B25 Algebraic methods
        93B27 Geometric methods (including algebro-geometric)
        93B28 Operator-theoretic methods, See also {47A57, 47N70}
        93B29 Differential-geometric methods
        93B30 System identification
        93B35 Sensitivity (robustness)
        93B36 ${H}^ \infty$-control
        93B40 Computational methods
        93B50 Synthesis problems
        93B51 Design techniques (robust design, computer-aided design, etc.)
        93B52 Feedback control
        93B55 Pole and zero placement problems
        93B60 Eigenvalue problems
        93B99 None of the above but in this section    
    93Cxx Control systems, guided systems
        93C05 Linear
        93C10 Nonlinear
        93C15 Systems governed by ordinary differential equations
        93C20 Systems governed by partial differential equations
        93C22 Systems governed by integral equations
        93C25 Systems in abstract spaces
        93C30 Systems governed by functional relations other than differential or integral equations
        93C35 Multivariable, multidimensional systems
        93C40 Adaptive control systems
        93C41 Problems with incomplete information
        93C42 Fuzzy control
        93C45 Time-invariant
        93C50 Time-dependent
        93C55 Discrete-time
        93C57 Sampled-data
        93C60 Continuous-time
        93C62 Digital systems
        93C70 Time-scale analysis and related topics
        93C73 Perturbations in control systems
        93C80 Frequency-response methods
        93C83 Control problems involving computers (process control, etc.)
        93C85 Automated systems (robots, etc.)
        93C90 Random disturbances in control systems
        93C95 Applications of control theory
        93C99 None of the above but in this section    
    93Dxx Stability
        93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $L^p, l^p$, etc.)
        93D09 Robust stability
        93D10 Popov-type stability of feedback systems
        93D15 Stabilization of systems by feedback
        93D20 Asymptotic stability
        93D21 Adaptive and robust stabilization
        93D22 Interrelations between stability problems and optimization problems
        93D25 Input-output approaches
        93D30 Scalar and vector Lyapunov functions
        93D99 None of the above but in this section    
    93Exx Stochastic systems and control
        93E03 Stochastic systems, general
        93E05 Stochastic games, stochastic differential games, See Also { 90D15}
        93E10 Estimation and detection, See also {60G35}
        93E11 Filtering, See also {60G35}
        93E12 System identification
        93E14 Data smoothing
        93E15 Stochastic stability
        93E20 Optimal stochastic control
        93E23 Stochastic gradient methods
        93E24 Least squares and related methods
        93E25 Other computational methods
        93E30 Computer simulations of stochastic systems
        93E35 Stochastic learning and adaptive control
        93E99 None of the above but in this section    
* 94-XX Information and communication, circuits
    94-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
    94-01 Instructional exposition (textbooks, tutorial papers, etc.)
    94-02 Research exposition (monographs, survey articles)
    94-03 Historical (must be assigned at least one classification number from 01-XX)
    94-04 Explicit machine computation and programs (not the theory of computation or programming)
    94-06 Proceedings, conferences, collections, etc.
    94Axx Communication, information
        94A05 Communication theory, See also {60G35, 90B12}
        94A11 Application of orthogonal functions in communication
        94A12 Signal theory (characterization, reconstruction, etc.)
        94A13 Detection theory
        94A14 Modulation and demodulation
        94A15 Information theory, general, See also {62B10}
        94A17 Measures of information, entropy
        94A24 Coding theorems (Shannon theory)
        94A29 Source coding
        94A34 Rate-distortion theory
        94A40 Channel models
        94A45 Prefix, length-variable, comma-free codes, See also {20M35, 68Q45}
        94A50 Theory of questionnaires
        94A55 Shift register sequences
        94A60 Cryptography, See also {11T71, 68P25}
        94A99 None of the above but in this section    
    94Bxx Theory of error-correcting codes
        94B05 Linear codes, general
        94B10 Convolutional codes
        94B12 Combined modulation schemes (including trellis codes)
        94B15 Cyclic codes
        94B20 Burst-correcting codes
        94B25 Combinatorial codes
        94B27 Geometric methods (including applications of algebraic geometry), See also {11T71}
        94B30 Majority codes
        94B35 Decoding
        94B40 Arithmetic codes, See also {11T71}
        94B50 Synchronization error-correcting codes
        94B60 Other types of codes
        94B65 Bounds on codes
        94B70 Error probability
        94B75 Applications of the theory of convex sets and geometry of numbers (covering radius, etc.), See also {11H31}
        94B99 None of the above but in this section    
    94Cxx Circuits, networks
        94C05 Analytic circuit theory
        94C10 Switching theory, application of Boolean algebra; Boolean functions, See also {06E30}
        94C12 Fault detection; testing
        94C15 Applications of graph theory, See also {05Cxx, 68R10}
        94C30 Applications of design theory, See also {05Bxx}
        94C99 None of the above but in this section    
    94D05 Fuzzy sets and logic {(in connection with questions of Section 94)}, See also {03B52, 03E72, 04A72, 28E10}

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