[

{

"code": "03",

"title": "Mathematical logic and foundations",

"descriptions": [

" Philosophical aspects of logic and foundations",

" General logic",

" Model theory",

" Computability and recursion theory",

" Set theory",

" Proof theory and constructive mathematics",

" Algebraic logic",

" Nonstandard models"

],

"prompt": "### Mathematical logic and foundations\n* Code: 03\n* Description: Philosophical aspects of logic and foundations; General logic; Model theory; Computability and recursion theory; Set theory; Proof theory and constructive mathematics; Algebraic logic; Nonstandard models"

},

{

"code": "05",

"title": "Combinatorics",

"descriptions": [

" Enumerative combinatorics",

" Designs and configurations",

" Graph theory",

" Extremal combinatorics",

" Algebraic combinatorics"

],

"prompt": "### Combinatorics\n* Code: 05\n* Description: Enumerative combinatorics; Designs and configurations; Graph theory; Extremal combinatorics; Algebraic combinatorics"

},

{

"code": "06",

"title": "Order, lattices, ordered algebraic structures",

"descriptions": [

" Ordered sets",

" Lattices",

" Modular lattices, complemented lattices",

" Distributive lattices",

" Boolean algebras (Boolean rings)",

" Ordered structures"

],

"prompt": "### Order, lattices, ordered algebraic structures\n* Code: 06\n* Description: Ordered sets; Lattices; Modular lattices, complemented lattices; Distributive lattices; Boolean algebras (Boolean rings); Ordered structures"

},

{

"code": "08",

"title": "General algebraic systems",

"descriptions": [

" Algebraic structures",

" Varieties",

" Other classes of algebras"

],

"prompt": "### General algebraic systems\n* Code: 08\n* Description: Algebraic structures; Varieties; Other classes of algebras"

},

{

"code": "11",

"title": "Number theory",

"descriptions": [

" Elementary number theory",

" Sequences and sets",

" Polynomials and matrices",

" Diophantine equations",

" Forms and linear algebraic groups",

" Discontinuous groups and automorphic forms",

" Arithmetic algebraic geometry (Diophantine geometry)",

" Geometry of numbers",

" Diophantine approximation, transcendental number theory",

" Probabilistic theory",

" Exponential sums and character sums",

" Zeta and $L$-functions",

" Multiplicative number theory",

" Additive number theory; partitions",

" Algebraic number theory",

" Algebraic number theory",

" Finite fields and commutative rings (number-theoretic aspects)",

" Connections with logic",

" Computational number theory",

" Miscellaneous applications of number theory"

],

"prompt": "### Number theory\n* Code: 11\n* Description: Elementary number theory; Sequences and sets; Polynomials and matrices; Diophantine equations; Forms and linear algebraic groups; Discontinuous groups and automorphic forms; Arithmetic algebraic geometry (Diophantine geometry); Geometry of numbers; Diophantine approximation, transcendental number theory; Probabilistic theory; Exponential sums and character sums; Zeta and $L$-functions; Multiplicative number theory; Additive number theory; partitions; Algebraic number theory; Algebraic number theory; Finite fields and commutative rings (number-theoretic aspects); Connections with logic; Computational number theory; Miscellaneous applications of number theory"

},

{

"code": "12",

"title": "Field theory and polynomials",

"descriptions": [

" Real and complex fields",

" General field theory",

" Field extensions",

" Homological methods (field theory)",

" Differential and difference algebra",

" Topological fields",

" Generalizations of fields",

" Connections with logic",

" Computational aspects of field theory and polynomials"

],

"prompt": "### Field theory and polynomials\n* Code: 12\n* Description: Real and complex fields; General field theory; Field extensions; Homological methods (field theory); Differential and difference algebra; Topological fields; Generalizations of fields; Connections with logic; Computational aspects of field theory and polynomials"

},

{

"code": "13",

"title": "Commutative algebra",

"descriptions": [

" General commutative ring theory",

" Ring extensions and related topics",

" Theory of modules and ideals",

" Homological methods",

" Chain conditions, finiteness conditions",

" Arithmetic rings and other special rings",

" Integral domains",

" Local rings and semilocal rings",

" Topological rings and modules",

" Applications of logic to commutative algebra",

" Finite commutative rings",

" Differential algebra",

" Computational aspects and applications"

],

"prompt": "### Commutative algebra\n* Code: 13\n* Description: General commutative ring theory; Ring extensions and related topics; Theory of modules and ideals; Homological methods; Chain conditions, finiteness conditions; Arithmetic rings and other special rings; Integral domains; Local rings and semilocal rings; Topological rings and modules; Applications of logic to commutative algebra; Finite commutative rings; Differential algebra; Computational aspects and applications"

},

{

"code": "14",

"title": "Algebraic geometry",

"descriptions": [

" Foundations",

" Local theory",

" Cycles and subschemes",

" Families, fibrations",

" Birational geometry",

" (Co)homology theory",

" Arithmetic problems. Diophantine geometry",

" Curves",

" Surfaces and higher-dimensional varieties",

" Abelian varieties and schemes",

" Algebraic groups",

" Special varieties",

" Projective and enumerative geometry",

" Real algebraic and real analytic geometry",

" Computational aspects in algebraic geometry",

" Affine geometry",

" Tropical geometry"

],

"prompt": "### Algebraic geometry\n* Code: 14\n* Description: Foundations; Local theory; Cycles and subschemes; Families, fibrations; Birational geometry; (Co)homology theory; Arithmetic problems. Diophantine geometry; Curves; Surfaces and higher-dimensional varieties; Abelian varieties and schemes; Algebraic groups; Special varieties; Projective and enumerative geometry; Real algebraic and real analytic geometry; Computational aspects in algebraic geometry; Affine geometry; Tropical geometry"

},

{

"code": "15",

"title": "Linear and multilinear algebra; matrix theory",

"descriptions": [

" Basic linear algebra",

" Special matrices"

],

"prompt": "### Linear and multilinear algebra; matrix theory\n* Code: 15\n* Description: Basic linear algebra; Special matrices"

},

{

"code": "16",

"title": "Associative rings and algebras",

"descriptions": [

" General and miscellaneous",

" Modules, bimodules and ideals",

" Homological methods",

" Representation theory of rings and algebras",

" Algebras and orders",

" Division rings and semisimple Artin rings",

" Local rings and generalizations",

" Radicals and radical properties of rings",

" Chain conditions, growth conditions, and other forms of finiteness",

" Rings with polynomial identity",

" Rings and algebras arising under various constructions",

" Hopf algebras, quantum groups and related topics",

" Conditions on elements",

" Rings and algebras with additional structure",

" Generalizations",

" Computational aspects of associative rings"

],

"prompt": "### Associative rings and algebras\n* Code: 16\n* Description: General and miscellaneous; Modules, bimodules and ideals; Homological methods; Representation theory of rings and algebras; Algebras and orders; Division rings and semisimple Artin rings; Local rings and generalizations; Radicals and radical properties of rings; Chain conditions, growth conditions, and other forms of finiteness; Rings with polynomial identity; Rings and algebras arising under various constructions; Hopf algebras, quantum groups and related topics; Conditions on elements; Rings and algebras with additional structure; Generalizations; Computational aspects of associative rings"

},

{

"code": "17",

"title": "Nonassociative rings and algebras",

"descriptions": [

" General nonassociative rings",

" Lie algebras and Lie superalgebras",

" Jordan algebras (algebras, triples and pairs)",

" Other nonassociative rings and algebras"

],

"prompt": "### Nonassociative rings and algebras\n* Code: 17\n* Description: General nonassociative rings; Lie algebras and Lie superalgebras; Jordan algebras (algebras, triples and pairs); Other nonassociative rings and algebras"

},

{

"code": "18",

"title": "Category theory; homological algebra",

"descriptions": [

" General theory of categories and functors",

" Special categories",

" Categories and theories",

" Categories with structure",

" Abelian categories",

" Categories and geometry",

" Homological algebra"

],

"prompt": "### Category theory; homological algebra\n* Code: 18\n* Description: General theory of categories and functors; Special categories; Categories and theories; Categories with structure; Abelian categories; Categories and geometry; Homological algebra"

},

{

"code": "19",

"title": "$K$-theory",

"descriptions": [

" Grothendieck groups and $K_0$",

" Whitehead groups and $K_1$",

" Steinberg groups and $K_2$",

" Higher algebraic $K$-theory",

" $K$-theory in geometry",

" $K$-theory in number theory",

" $K$-theory of forms",

" Obstructions from topology",

" $K$-theory and operator algebras",

" Topological $K$-theory",

" Miscellaneous applications of $K$-theory"

],

"prompt": "### $K$-theory\n* Code: 19\n* Description: Grothendieck groups and $K_0$; Whitehead groups and $K_1$; Steinberg groups and $K_2$; Higher algebraic $K$-theory; $K$-theory in geometry; $K$-theory in number theory; $K$-theory of forms; Obstructions from topology; $K$-theory and operator algebras; Topological $K$-theory; Miscellaneous applications of $K$-theory"

},

{

"code": "20",

"title": "Group theory and generalizations",

"descriptions": [

" Foundations",

" Permutation groups",

" Representation theory of groups",

" Abstract finite groups",

" Structure and classification of infinite or finite groups",

" Special aspects of infinite or finite groups",

" Linear algebraic groups and related topics",

" Other groups of matrices",

" Connections with homological algebra and category theory",

" Abelian groups",

" Groupoids (i.e. small categories in which all morphisms are isomorphisms)",

" Semigroups",

" Other generalizations of groups",

" Probabilistic methods in group theory"

],

"prompt": "### Group theory and generalizations\n* Code: 20\n* Description: Foundations; Permutation groups; Representation theory of groups; Abstract finite groups; Structure and classification of infinite or finite groups; Special aspects of infinite or finite groups; Linear algebraic groups and related topics; Other groups of matrices; Connections with homological algebra and category theory; Abelian groups; Groupoids (i.e. small categories in which all morphisms are isomorphisms); Semigroups; Other generalizations of groups; Probabilistic methods in group theory"

},

{

"code": "22",

"title": "Topological groups, Lie groups",

"descriptions": [

" Topological and differentiable algebraic systems",

" Locally compact abelian groups (LCA groups)",

" Compact groups",

" Locally compact groups and their algebras",

" Lie groups",

" Noncompact transformation groups"

],

"prompt": "### Topological groups, Lie groups\n* Code: 22\n* Description: Topological and differentiable algebraic systems; Locally compact abelian groups (LCA groups); Compact groups; Locally compact groups and their algebras; Lie groups; Noncompact transformation groups"

},

{

"code": "26",

"title": "Real functions",

"descriptions": [

" Functions of one variable",

" Functions of several variables",

" Polynomials, rational functions",

" Inequalities",

" Miscellaneous topics"

],

"prompt": "### Real functions\n* Code: 26\n* Description: Functions of one variable; Functions of several variables; Polynomials, rational functions; Inequalities; Miscellaneous topics"

},

{

"code": "28",

"title": "Measure and integration",

"descriptions": [

" Classical measure theory",

" Set functions, measures and integrals with values in abstract spaces",

" Set functions and measures on spaces with additional structure",

" Measure-theoretic ergodic theory",

" Miscellaneous topics in measure theory"

],

"prompt": "### Measure and integration\n* Code: 28\n* Description: Classical measure theory; Set functions, measures and integrals with values in abstract spaces; Set functions and measures on spaces with additional structure; Measure-theoretic ergodic theory; Miscellaneous topics in measure theory"

},

{

"code": "30",

"title": "Functions of a complex variable",

"descriptions": [

" General properties",

" Series expansions",

" Geometric function theory",

" Entire and meromorphic functions, and related topics",

" Miscellaneous topics of analysis in the complex domain",

" Riemann surfaces",

" Generalized function theory",

" Spaces and algebras of analytic functions",

" Function theory on the disc",

" Universal holomorphic functions",

" Analysis on metric spaces"

],

"prompt": "### Functions of a complex variable\n* Code: 30\n* Description: General properties; Series expansions; Geometric function theory; Entire and meromorphic functions, and related topics; Miscellaneous topics of analysis in the complex domain; Riemann surfaces; Generalized function theory; Spaces and algebras of analytic functions; Function theory on the disc; Universal holomorphic functions; Analysis on metric spaces"

},

{

"code": "31",

"title": "Potential theory",

"descriptions": [

" Two-dimensional theory",

" Higher-dimensional theory",

" Other generalizations",

" Axiomatic potential theory",

" Potential theory on metric spaces"

],

"prompt": "### Potential theory\n* Code: 31\n* Description: Two-dimensional theory; Higher-dimensional theory; Other generalizations; Axiomatic potential theory; Potential theory on metric spaces"

},

{

"code": "32",

"title": "Several complex variables and analytic spaces",

"descriptions": [

" Holomorphic functions of several complex variables",

" Local analytic geometry",

" Analytic spaces",

" Analytic continuation",

" Holomorphic convexity",

" Geometric convexity",

" Deformations of analytic structures",

" Holomorphic mappings and correspondences",

" Compact analytic spaces",

" Generalizations of analytic spaces (should also be assigned at least one other classification number from Section 32 describing the type of problem)",

" Holomorphic fiber spaces",

" Complex spaces with a group of automorphisms",

" Automorphic functions",

" Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)",

" Complex manifolds",

" Singularities",

" Pseudoconvex domains",

" Pluripotential theory",

" CR manifolds",

" Differential operators in several variables"

],

"prompt": "### Several complex variables and analytic spaces\n* Code: 32\n* Description: Holomorphic functions of several complex variables; Local analytic geometry; Analytic spaces; Analytic continuation; Holomorphic convexity; Geometric convexity; Deformations of analytic structures; Holomorphic mappings and correspondences; Compact analytic spaces; Generalizations of analytic spaces (should also be assigned at least one other classification number from Section 32 describing the type of problem); Holomorphic fiber spaces; Complex spaces with a group of automorphisms; Automorphic functions; Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem); Complex manifolds; Singularities; Pseudoconvex domains; Pluripotential theory; CR manifolds; Differential operators in several variables"

},

{

"code": "33",

"title": "Special functions (33-XX deals with the properties of functions as functions)",

"descriptions": [

" Elementary classical functions",

" Hypergeometric functions",

" Basic hypergeometric functions",

" Other special functions",

" Computational aspects"

],

"prompt": "### Special functions (33-XX deals with the properties of functions as functions)\n* Code: 33\n* Description: Elementary classical functions; Hypergeometric functions; Basic hypergeometric functions; Other special functions; Computational aspects"

},

{

"code": "34",

"title": "Ordinary differential equations",

"descriptions": [

" General theory",

" Boundary value problems",

" Qualitative theory",

" Stability theory",

" Asymptotic theory",

" Equations and systems with randomness",

" Differential equations in abstract spaces",

" Control problems",

" Functional-differential and differential-difference equations",

" Ordinary differential operators",

" Differential equations in the complex domain",

" Dynamic equations on time scales or measure chains"

],

"prompt": "### Ordinary differential equations\n* Code: 34\n* Description: General theory; Boundary value problems; Qualitative theory; Stability theory; Asymptotic theory; Equations and systems with randomness; Differential equations in abstract spaces; Control problems; Functional-differential and differential-difference equations; Ordinary differential operators; Differential equations in the complex domain; Dynamic equations on time scales or measure chains"

},

{

"code": "35",

"title": "Partial differential equations",

"descriptions": [

" General topics",

" Qualitative properties of solutions",

" Representations of solutions",

" Generalized solutions",

" Equations and systems with constant coefficients",

" General first-order equations and systems",

" General higher-order equations and systems",

" Close-to-elliptic equations and systems",

" Elliptic equations and systems",

" Parabolic equations and systems",

" Hyperbolic equations and systems",

" Equations and systems of special type (mixed, composite, etc.)",

" Overdetermined systems",

" Spectral theory and eigenvalue problems",

" Equations of mathematical physics and other areas of application",

" Miscellaneous topics",

" Pseudodifferential operators and other generalizations of partial differential operators"

],

"prompt": "### Partial differential equations\n* Code: 35\n* Description: General topics; Qualitative properties of solutions; Representations of solutions; Generalized solutions; Equations and systems with constant coefficients; General first-order equations and systems; General higher-order equations and systems; Close-to-elliptic equations and systems; Elliptic equations and systems; Parabolic equations and systems; Hyperbolic equations and systems; Equations and systems of special type (mixed, composite, etc.); Overdetermined systems; Spectral theory and eigenvalue problems; Equations of mathematical physics and other areas of application; Miscellaneous topics; Pseudodifferential operators and other generalizations of partial differential operators"

},

{

"code": "37",

"title": "Dynamical systems and ergodic theory",

"descriptions": [

" Ergodic theory",

" Topological dynamics",

" Smooth dynamical systems",

" Dynamical systems with hyperbolic behavior",

" Low-dimensional dynamical systems",

" Complex dynamical systems",

" Local and nonlocal bifurcation theory",

" Random dynamical systems",

" Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems",

" Infinite-dimensional Hamiltonian systems",

" Infinite-dimensional dissipative dynamical systems",

" Approximation methods and numerical treatment of dynamical systems",

" Applications",

" Arithmetic and non-Archimedean dynamical systems"

],

"prompt": "### Dynamical systems and ergodic theory\n* Code: 37\n* Description: Ergodic theory; Topological dynamics; Smooth dynamical systems; Dynamical systems with hyperbolic behavior; Low-dimensional dynamical systems; Complex dynamical systems; Local and nonlocal bifurcation theory; Random dynamical systems; Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems; Infinite-dimensional Hamiltonian systems; Infinite-dimensional dissipative dynamical systems; Approximation methods and numerical treatment of dynamical systems; Applications; Arithmetic and non-Archimedean dynamical systems"

},

{

"code": "39",

"title": "Difference and functional equations",

"descriptions": [

" Difference equations",

" Functional equations and inequalities"

],

"prompt": "### Difference and functional equations\n* Code: 39\n* Description: Difference equations; Functional equations and inequalities"

},

{

"code": "40",

"title": "Sequences, series, summability",

"descriptions": [

" Convergence and divergence of infinite limiting processes",

" Multiple sequences and series",

" General summability methods",

" Direct theorems on summability",

" Inversion theorems",

" Absolute and strong summability (should also be assigned at least one other classification number in Section 40)",

" Special methods of summability",

" Functional analytic methods in summability",

" Summability in abstract structures"

],

"prompt": "### Sequences, series, summability\n* Code: 40\n* Description: Convergence and divergence of infinite limiting processes; Multiple sequences and series; General summability methods; Direct theorems on summability; Inversion theorems; Absolute and strong summability (should also be assigned at least one other classification number in Section 40); Special methods of summability; Functional analytic methods in summability; Summability in abstract structures"

},

{

"code": "41",

"title": "Approximations and expansions",

"descriptions": [

" Approximations and expansions"

],

"prompt": "### Approximations and expansions\n* Code: 41\n* Description: Approximations and expansions"

},

{

"code": "42",

"title": "Harmonic analysis on Euclidean spaces",

"descriptions": [

" Harmonic analysis in one variable",

" Harmonic analysis in several variables",

" Nontrigonometric harmonic analysis"

],

"prompt": "### Harmonic analysis on Euclidean spaces\n* Code: 42\n* Description: Harmonic analysis in one variable; Harmonic analysis in several variables; Nontrigonometric harmonic analysis"

},

{

"code": "43",

"title": "Abstract harmonic analysis",

"descriptions": [

" Abstract harmonic analysis"

],

"prompt": "### Abstract harmonic analysis\n* Code: 43\n* Description: Abstract harmonic analysis"

},

{

"code": "44",

"title": "Integral transforms, operational calculus",

"descriptions": [

" Integral transforms, operational calculus"

],

"prompt": "### Integral transforms, operational calculus\n* Code: 44\n* Description: Integral transforms, operational calculus"

},

{

"code": "45",

"title": "Integral equations",

"descriptions": [

" Linear integral equations",

" Fredholm integral equations",

" Eigenvalue problems",

" Volterra integral equations",

" Singular integral equations",

" Systems of linear integral equations",

" Nonlinear integral equations",

" Miscellaneous special kernels",

" Integro-ordinary differential equations",

" Integro-partial differential equations",

" Theoretical approximation of solutions",

" Qualitative behavior",

" Abstract integral equations, integral equations in abstract spaces",

" Integral operators",

" Inverse problems",

" Random integral equations"

],

"prompt": "### Integral equations\n* Code: 45\n* Description: Linear integral equations; Fredholm integral equations; Eigenvalue problems; Volterra integral equations; Singular integral equations; Systems of linear integral equations; Nonlinear integral equations; Miscellaneous special kernels; Integro-ordinary differential equations; Integro-partial differential equations; Theoretical approximation of solutions; Qualitative behavior; Abstract integral equations, integral equations in abstract spaces; Integral operators; Inverse problems; Random integral equations"

},

{

"code": "46",

"title": "Functional analysis",

"descriptions": [

" Topological linear spaces and related structures",

" Normed linear spaces and Banach spaces; Banach lattices",

" Inner product spaces and their generalizations, Hilbert spaces",

" Linear function spaces and their duals",

" Distributions, generalized functions, distribution spaces",

" Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)",

" Topological algebras, normed rings and algebras, Banach algebras",

" Commutative Banach algebras and commutative topological algebras",

" Topological (rings and) algebras with an involution",

" Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.)",

" Methods of category theory in functional analysis",

" Miscellaneous applications of functional analysis",

" Other (nonclassical) types of functional analysis",

" Nonlinear functional analysis"

],

"prompt": "### Functional analysis\n* Code: 46\n* Description: Topological linear spaces and related structures; Normed linear spaces and Banach spaces; Banach lattices; Inner product spaces and their generalizations, Hilbert spaces; Linear function spaces and their duals; Distributions, generalized functions, distribution spaces; Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces); Topological algebras, normed rings and algebras, Banach algebras; Commutative Banach algebras and commutative topological algebras; Topological (rings and) algebras with an involution; Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.); Methods of category theory in functional analysis; Miscellaneous applications of functional analysis; Other (nonclassical) types of functional analysis; Nonlinear functional analysis"

},

{

"code": "47",

"title": "Operator theory",

"descriptions": [

" General theory of linear operators",

" Special classes of linear operators",

" Individual linear operators as elements of algebraic systems",

" Groups and semigroups of linear operators, their generalizations and applications",

" Ordinary differential operators",

" Partial differential operators",

" Integral, integro-differential, and pseudodifferential operators",

" Nonlinear operators and their properties",

" Equations and inequalities involving nonlinear operators",

" Linear spaces and algebras of operators",

" Miscellaneous applications of operator theory",

" Other (nonclassical) types of operator theory"

],

"prompt": "### Operator theory\n* Code: 47\n* Description: General theory of linear operators; Special classes of linear operators; Individual linear operators as elements of algebraic systems; Groups and semigroups of linear operators, their generalizations and applications; Ordinary differential operators; Partial differential operators; Integral, integro-differential, and pseudodifferential operators; Nonlinear operators and their properties; Equations and inequalities involving nonlinear operators; Linear spaces and algebras of operators; Miscellaneous applications of operator theory; Other (nonclassical) types of operator theory"

},

{

"code": "49",

"title": "Calculus of variations and optimal control; optimization",

"descriptions": [

" Existence theories",

" Optimality conditions",

" Hamilton-Jacobi theories, including dynamic programming",

" Numerical methods",

" Miscellaneous topics",

" Manifolds",

" Variational methods for eigenvalues of operators",

" Variational principles of physics"

],

"prompt": "### Calculus of variations and optimal control; optimization\n* Code: 49\n* Description: Existence theories; Optimality conditions; Hamilton-Jacobi theories, including dynamic programming; Numerical methods; Miscellaneous topics; Manifolds; Variational methods for eigenvalues of operators; Variational principles of physics"

},

{

"code": "51",

"title": "Geometry",

"descriptions": [

" Linear incidence geometry",

" Nonlinear incidence geometry",

" Ring geometry (Hjelmslev, Barbilian, etc.)",

" Geometric closure systems",

" Finite geometry and special incidence structures",

" Metric geometry",

" Ordered geometries (ordered incidence structures, etc.)",

" Topological geometry",

" Incidence groups",

" Distance geometry",

" Geometric order structures",

" Real and complex geometry",

" Analytic and descriptive geometry",

" Geometry and physics (should also be assigned at least one other classification number from Sections 70--86)"

],

"prompt": "### Geometry\n* Code: 51\n* Description: Linear incidence geometry; Nonlinear incidence geometry; Ring geometry (Hjelmslev, Barbilian, etc.); Geometric closure systems; Finite geometry and special incidence structures; Metric geometry; Ordered geometries (ordered incidence structures, etc.); Topological geometry; Incidence groups; Distance geometry; Geometric order structures; Real and complex geometry; Analytic and descriptive geometry; Geometry and physics (should also be assigned at least one other classification number from Sections 70--86)"

},

{

"code": "52",

"title": "Convex and discrete geometry",

"descriptions": [

" General convexity",

" Polytopes and polyhedra",

" Discrete geometry"

],

"prompt": "### Convex and discrete geometry\n* Code: 52\n* Description: General convexity; Polytopes and polyhedra; Discrete geometry"

},

{

"code": "53",

"title": "Differential geometry",

"descriptions": [

" Classical differential geometry",

" Local differential geometry",

" Global differential geometry",

" Symplectic geometry, contact geometry",

" Applications to physics"

],

"prompt": "### Differential geometry\n* Code: 53\n* Description: Classical differential geometry; Local differential geometry; Global differential geometry; Symplectic geometry, contact geometry; Applications to physics"

},

{

"code": "54",

"title": "General topology",

"descriptions": [

" Generalities",

" Basic constructions",

" Maps and general types of spaces defined by maps",

" Fairly general properties",

" Spaces with richer structures",

" Special properties",

" Peculiar spaces",

" Connections with other structures, applications",

" Nonstandard topology"

],

"prompt": "### General topology\n* Code: 54\n* Description: Generalities; Basic constructions; Maps and general types of spaces defined by maps; Fairly general properties; Spaces with richer structures; Special properties; Peculiar spaces; Connections with other structures, applications; Nonstandard topology"

},

{

"code": "55",

"title": "Algebraic topology",

"descriptions": [

" Classical topics",

" Homology and cohomology theories",

" Homotopy theory",

" Homotopy groups",

" Fiber spaces and bundles",

" Operations and obstructions",

" Spectral sequences",

" Applied homological algebra and category theory"

],

"prompt": "### Algebraic topology\n* Code: 55\n* Description: Classical topics; Homology and cohomology theories; Homotopy theory; Homotopy groups; Fiber spaces and bundles; Operations and obstructions; Spectral sequences; Applied homological algebra and category theory"

},

{

"code": "57",

"title": "Manifolds and cell complexes",

"descriptions": [

" Low-dimensional topology",

" Topological manifolds",

" Generalized manifolds",

" PL-topology",

" Differential topology",

" Topological transformation groups",

" Homology and homotopy of topological groups and related structures"

],

"prompt": "### Manifolds and cell complexes\n* Code: 57\n* Description: Low-dimensional topology; Topological manifolds; Generalized manifolds; PL-topology; Differential topology; Topological transformation groups; Homology and homotopy of topological groups and related structures"

},

{

"code": "58",

"title": "Global analysis, analysis on manifolds",

"descriptions": [

" General theory of differentiable manifolds",

" Infinite-dimensional manifolds",

" Calculus on manifolds; nonlinear operators",

" Spaces and manifolds of mappings (including nonlinear versions of 46Exx)",

" Variational problems in infinite-dimensional spaces",

" Pseudogroups, differentiable groupoids and general structures on manifolds",

" Partial differential equations on manifolds; differential operators",

" Theory of singularities and catastrophe theory",

" Applications to physics"

],

"prompt": "### Global analysis, analysis on manifolds\n* Code: 58\n* Description: General theory of differentiable manifolds; Infinite-dimensional manifolds; Calculus on manifolds; nonlinear operators; Spaces and manifolds of mappings (including nonlinear versions of 46Exx); Variational problems in infinite-dimensional spaces; Pseudogroups, differentiable groupoids and general structures on manifolds; Partial differential equations on manifolds; differential operators; Theory of singularities and catastrophe theory; Applications to physics"

},

{

"code": "60",

"title": "Probability theory and stochastic processes",

"descriptions": [

" Foundations of probability theory",

" Probability theory on algebraic and topological structures",

" Combinatorial probability",

" Geometric probability and stochastic geometry",

" Distribution theory",

" Limit theorems",

" Stochastic processes",

" Stochastic analysis",

" Markov processes",

" Special processes"

],

"prompt": "### Probability theory and stochastic processes\n* Code: 60\n* Description: Foundations of probability theory; Probability theory on algebraic and topological structures; Combinatorial probability; Geometric probability and stochastic geometry; Distribution theory; Limit theorems; Stochastic processes; Stochastic analysis; Markov processes; Special processes"

},

{

"code": "62",

"title": "Statistics",

"descriptions": [

" Foundational and philosophical topics",

" Sufficiency and information",

" Decision theory",

" Sampling theory, sample surveys",

" Distribution theory",

" Parametric inference",

" Nonparametric inference",

" Multivariate analysis",

" Linear inference, regression",

" Design of experiments",

" Sequential methods",

" Inference from stochastic processes",

" Survival analysis and censored data",

" Applications",

" Statistical tables"

],

"prompt": "### Statistics\n* Code: 62\n* Description: Foundational and philosophical topics; Sufficiency and information; Decision theory; Sampling theory, sample surveys; Distribution theory; Parametric inference; Nonparametric inference; Multivariate analysis; Linear inference, regression; Design of experiments; Sequential methods; Inference from stochastic processes; Survival analysis and censored data; Applications; Statistical tables"

},

{

"code": "65",

"title": "Numerical analysis",

"descriptions": [

" Tables",

" Acceleration of convergence",

" Probabilistic methods, simulation and stochastic differential equations",

" Numerical approximation and computational geometry (primarily algorithms)",

" Numerical methods in complex analysis (potential theory, etc.)",

" Numerical linear algebra",

" Error analysis and interval analysis",

" Nonlinear algebraic or transcendental equations",

" Numerical analysis in abstract spaces",

" Mathematical programming, optimization and variational techniques",

" Ordinary differential equations",

" Partial differential equations, initial value and time-dependent initial-boundary value problems",

" Partial differential equations, boundary value problems",

" Numerical problems in dynamical systems",

" Difference and functional equations, recurrence relations",

" Integral equations, integral transforms",

" Graphical methods",

" Numerical methods in Fourier analysis",

" Computer aspects of numerical algorithms",

" Applications to physics"

],

"prompt": "### Numerical analysis\n* Code: 65\n* Description: Tables; Acceleration of convergence; Probabilistic methods, simulation and stochastic differential equations; Numerical approximation and computational geometry (primarily algorithms); Numerical methods in complex analysis (potential theory, etc.); Numerical linear algebra; Error analysis and interval analysis; Nonlinear algebraic or transcendental equations; Numerical analysis in abstract spaces; Mathematical programming, optimization and variational techniques; Ordinary differential equations; Partial differential equations, initial value and time-dependent initial-boundary value problems; Partial differential equations, boundary value problems; Numerical problems in dynamical systems; Difference and functional equations, recurrence relations; Integral equations, integral transforms; Graphical methods; Numerical methods in Fourier analysis; Computer aspects of numerical algorithms; Applications to physics"

},

{

"code": "68",

"title": "Computer science",

"descriptions": [

" Computer system organization",

" Software",

" Theory of data",

" Theory of computing",

" Discrete mathematics in relation to computer science",

" Artificial intelligence",

" Computing methodologies and applications",

" Algorithms"

],

"prompt": "### Computer science\n* Code: 68\n* Description: Computer system organization; Software; Theory of data; Theory of computing; Discrete mathematics in relation to computer science; Artificial intelligence; Computing methodologies and applications; Algorithms"

},

{

"code": "70",

"title": "Mechanics of particles and systems",

"descriptions": [

" Axiomatics, foundations",

" Kinematics",

" Statics",

" Dynamics of a rigid body and of multibody systems",

" Dynamics of a system of particles, including celestial mechanics",

" General models, approaches, and methods",

" Hamiltonian and Lagrangian mechanics",

" Linear vibration theory",

" Nonlinear dynamics",

" Random vibrations",

" Orbital mechanics",

" Variable mass, rockets",

" Control of mechanical systems",

" Classical field theories"

],

"prompt": "### Mechanics of particles and systems\n* Code: 70\n* Description: Axiomatics, foundations; Kinematics; Statics; Dynamics of a rigid body and of multibody systems; Dynamics of a system of particles, including celestial mechanics; General models, approaches, and methods; Hamiltonian and Lagrangian mechanics; Linear vibration theory; Nonlinear dynamics; Random vibrations; Orbital mechanics; Variable mass, rockets; Control of mechanical systems; Classical field theories"

},

{

"code": "74",

"title": "Mechanics of deformable solids",

"descriptions": [

" Generalities, axiomatics, foundations of continuum mechanics of solids",

" Elastic materials",

" Plastic materials, materials of stress-rate and internal-variable type",

" Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)",

" Material properties given special treatment",

" Coupling of solid mechanics with other effects",

" Equilibrium (steady-state) problems",

" Dynamical problems",

" Waves",

" Thin bodies, structures",

" Special subfields of solid mechanics",

" Special kinds of problems",

" Phase transformations in solids",

" Optimization",

" Homogenization, determination of effective properties",

" Fracture and damage",

" Numerical methods"

],

"prompt": "### Mechanics of deformable solids\n* Code: 74\n* Description: Generalities, axiomatics, foundations of continuum mechanics of solids; Elastic materials; Plastic materials, materials of stress-rate and internal-variable type; Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials); Material properties given special treatment; Coupling of solid mechanics with other effects; Equilibrium (steady-state) problems; Dynamical problems; Waves; Thin bodies, structures; Special subfields of solid mechanics; Special kinds of problems; Phase transformations in solids; Optimization; Homogenization, determination of effective properties; Fracture and damage; Numerical methods"

},

{

"code": "76",

"title": "Fluid mechanics",

"descriptions": [

" Foundations, constitutive equations, rheology",

" Incompressible inviscid fluids",

" Incompressible viscous fluids",

" Hydrodynamic stability",

" Turbulence",

" General aerodynamics and subsonic flows",

" Transonic flows",

" Supersonic flows",

" Hypersonic flows",

" Shock waves and blast waves",

" Basic methods in fluid mechanics",

" Compressible fluids and gas dynamics, general",

" Rarefied gas flows, Boltzmann equation",

" Hydro- and aero-acoustics",

" Diffusion and convection",

" Flows in porous media; filtration; seepage",

" Two-phase and multiphase flows",

" Rotating fluids",

" Reaction effects in flows",

" Magnetohydrodynamics and electrohydrodynamics",

" Ionized gas flow in electromagnetic fields; plasmic flow",

" Quantum hydrodynamics and relativistic hydrodynamics",

" Biological fluid mechanics"

],

"prompt": "### Fluid mechanics\n* Code: 76\n* Description: Foundations, constitutive equations, rheology; Incompressible inviscid fluids; Incompressible viscous fluids; Hydrodynamic stability; Turbulence; General aerodynamics and subsonic flows; Transonic flows; Supersonic flows; Hypersonic flows; Shock waves and blast waves; Basic methods in fluid mechanics; Compressible fluids and gas dynamics, general; Rarefied gas flows, Boltzmann equation; Hydro- and aero-acoustics; Diffusion and convection; Flows in porous media; filtration; seepage; Two-phase and multiphase flows; Rotating fluids; Reaction effects in flows; Magnetohydrodynamics and electrohydrodynamics; Ionized gas flow in electromagnetic fields; plasmic flow; Quantum hydrodynamics and relativistic hydrodynamics; Biological fluid mechanics"

},

{

"code": "78",

"title": "Optics, electromagnetic theory",

"descriptions": [

" General",

" Basic methods"

],

"prompt": "### Optics, electromagnetic theory\n* Code: 78\n* Description: General; Basic methods"

},

{

"code": "80",

"title": "Classical thermodynamics, heat transfer",

"descriptions": [

" Thermodynamics and heat transfer",

" Basic methods"

],

"prompt": "### Classical thermodynamics, heat transfer\n* Code: 80\n* Description: Thermodynamics and heat transfer; Basic methods"

},

{

"code": "81",

"title": "Quantum theory",

"descriptions": [

" Axiomatics, foundations, philosophy",

" General mathematical topics and methods in quantum theory",

" Groups and algebras in quantum theory",

" General quantum mechanics and problems of quantization",

" Quantum field theory; related classical field theories",

" Scattering theory",

" Applications to specific physical systems"

],

"prompt": "### Quantum theory\n* Code: 81\n* Description: Axiomatics, foundations, philosophy; General mathematical topics and methods in quantum theory; Groups and algebras in quantum theory; General quantum mechanics and problems of quantization; Quantum field theory; related classical field theories; Scattering theory; Applications to specific physical systems"

},

{

"code": "82",

"title": "Statistical mechanics, structure of matter",

"descriptions": [

" Equilibrium statistical mechanics",

" Time-dependent statistical mechanics (dynamic and nonequilibrium)",

" Applications to specific types of physical systems"

],

"prompt": "### Statistical mechanics, structure of matter\n* Code: 82\n* Description: Equilibrium statistical mechanics; Time-dependent statistical mechanics (dynamic and nonequilibrium); Applications to specific types of physical systems"

},

{

"code": "83",

"title": "Relativity and gravitational theory",

"descriptions": [

" Special relativity",

" Observational and experimental questions",

" General relativity",

" Relativistic gravitational theories other than Einstein's, including asymmetric field theories",

" Unified, higher-dimensional and super field theories",

" Cosmology"

],

"prompt": "### Relativity and gravitational theory\n* Code: 83\n* Description: Special relativity; Observational and experimental questions; General relativity; Relativistic gravitational theories other than Einstein's, including asymmetric field theories; Unified, higher-dimensional and super field theories; Cosmology"

},

{

"code": "85",

"title": "Astronomy and astrophysics",

"descriptions": [

" Astronomy and astrophysics"

],

"prompt": "### Astronomy and astrophysics\n* Code: 85\n* Description: Astronomy and astrophysics"

},

{

"code": "86",

"title": "Geophysics",

"descriptions": [

" Geophysics"

],

"prompt": "### Geophysics\n* Code: 86\n* Description: Geophysics"

},

{

"code": "90",

"title": "Operations research, mathematical programming",

"descriptions": [

" Operations research and management science",

" Mathematical programming"

],

"prompt": "### Operations research, mathematical programming\n* Code: 90\n* Description: Operations research and management science; Mathematical programming"

},

{

"code": "91",

"title": "Game theory, economics, social and behavioral sciences",

"descriptions": [

" Game theory",

" Mathematical economics",

" Social and behavioral sciences",

" Mathematical sociology (including anthropology)",

" Mathematical psychology",

" Other social and behavioral sciences (mathematical treatment)",

" Mathematical finance"

],

"prompt": "### Game theory, economics, social and behavioral sciences\n* Code: 91\n* Description: Game theory; Mathematical economics; Social and behavioral sciences; Mathematical sociology (including anthropology); Mathematical psychology; Other social and behavioral sciences (mathematical treatment); Mathematical finance"

},

{

"code": "92",

"title": "Biology and other natural sciences",

"descriptions": [

" Mathematical biology in general",

" Physiological, cellular and medical topics",

" Genetics and population dynamics",

" Chemistry",

" Other natural sciences (should also be assigned at least one other classification number in this section)"

],

"prompt": "### Biology and other natural sciences\n* Code: 92\n* Description: Mathematical biology in general; Physiological, cellular and medical topics; Genetics and population dynamics; Chemistry; Other natural sciences (should also be assigned at least one other classification number in this section)"

},

{

"code": "93",

"title": "Systems theory; control",

"descriptions": [

" General",

" Controllability, observability, and system structure",

" Control systems",

" Stability",

" Stochastic systems and control"

],

"prompt": "### Systems theory; control\n* Code: 93\n* Description: General; Controllability, observability, and system structure; Control systems; Stability; Stochastic systems and control"

},

{

"code": "94",

"title": "Information and communication, circuits",

"descriptions": [

" Communication, information",

" Theory of error-correcting codes and error-detecting codes",

" Circuits, networks",

" Fuzzy sets and logic (in connection with questions of Section 94)"

],

"prompt": "### Information and communication, circuits\n* Code: 94\n* Description: Communication, information; Theory of error-correcting codes and error-detecting codes; Circuits, networks; Fuzzy sets and logic (in connection with questions of Section 94)"

},

{

"code": "97",

"title": "Mathematics education",

"descriptions": [

" General, mathematics and education",

" Educational policy and systems",

" Psychology of mathematics education, research in mathematics education",

" Education and instruction in mathematics",

" Foundations of mathematics",

" Arithmetic, number theory",

" Geometry",

" Algebra",

" Analysis",

" Combinatorics, graph theory, probability theory, statistics",

" Mathematical modeling, applications of mathematics",

" Numerical mathematics",

" Computer science",

" Computer science education",

" Computer science applications",

" Educational material and media, educational technology"

],

"prompt": "### Mathematics education\n* Code: 97\n* Description: General, mathematics and education; Educational policy and systems; Psychology of mathematics education, research in mathematics education; Education and instruction in mathematics; Foundations of mathematics; Arithmetic, number theory; Geometry; Algebra; Analysis; Combinatorics, graph theory, probability theory, statistics; Mathematical modeling, applications of mathematics; Numerical mathematics; Computer science; Computer science education; Computer science applications; Educational material and media, educational technology"

}

]