approximation # etale and flat extensions; Henselization; Artin    13B40  
approximation # numerical    33F05  
approximation # Pad\'e    41A21  
approximation # simultaneous    41A28  
approximation # spline    41A15  
approximation # stochastic    62L20  
approximation # trigonometric    42A10  
approximation # uniqueness of best    41A52  
approximation (Bernstein, Jackson, Nikol'ski\u\i-type inequalities) # inequalities in    41A17  
approximation algorithms   68W25  
approximation and computational geometry (primarily algorithms) # numerical    65Dxx  
approximation and interpolation # trigonometric    65T40  
approximation by arbitrary linear expressions   41A45  
approximation by arbitrary nonlinear expressions; widths and entropy   41A46  
approximation by convex sets   52A27  
approximation by numbers from a fixed field   11J17  
approximation by operators (in particular, by integral operators)   41A35  
approximation by other special function classes   41A30  
approximation by polynomials   41A10  
approximation by positive operators   41A36  
approximation by rational functions   41A20  
approximation formulas # remainders in    41A80  
approximation in non-Archimedean valuations   11J61  
approximation in normed linear spaces and other abstract spaces) # abstract approximation theory (   41A65  
approximation in the complex domain   30E10  
approximation methods (nonlinear Galerkin, etc.)   37L65  
approximation methods and heuristics   90C59  
approximation methods and numerical treatment of dynamical systems   37Mxx  
approximation numbers, $s$-numbers, Kolmogorov numbers, entropy numbers, etc. of operators # Riesz operators; eigenvalue distributions;    47B06  
approximation of eigenvalues and of other parts of the spectrum # numerical    34L16  
approximation of invariant measures, computation of Lyapunov exponents, entropy) # computational methods for ergodic theory (   37M30  
approximation of solutions # numerical    34K28  
approximation of solutions # numerical    74G15  
approximation of solutions # numerical    74H15  
approximation of solutions # theoretical    34A45  
approximation of solutions # theoretical    34K07  
approximation of solutions # theoretical    45L05  
approximation of solutions (perturbation methods, asymptotic methods, series, etc.) # analytic    74G10  
approximation procedures, weak fields   83C25  
approximation properties # spaces of linear operators; topological tensor products;    46A32  
approximation properties # spaces of operators; tensor products;    46B28  
approximation solutions (perturbation methods, asymptotic methods, series, etc.) # analytic    74H10  
approximation theory # operator    47A58  
approximation theory (approximation in normed linear spaces and other abstract spaces) # abstract    41A65  
approximation to algebraic numbers   11J68  
approximation to limiting values (summation of series, etc.)   40A25  
approximation to one number # homogeneous    11J04  
approximation to solutions # theoretical    35A35  
approximation with constraints   41A29  
approximation, Chebyshev systems # best    41A50  
approximation, linear forms # simultaneous homogeneous    11J13  
approximation, ratio, proportion   512.924  
approximation, ratio, proportion   513.24  
approximation, Runge pairs, interpolation # holomorphic and polynomial    32E30  
approximation, transcendental number theory # Diophantine    11Jxx  
approximations   57Q55  
approximations # circle packings and conformal    52C26  
approximations # discrete    49M25  
approximations # methods of successive    49Mxx  
approximations # smooth    57R12  
approximations and expansions   511.4  
approximations and expansions   41-XX  
approximations to distributions (nonasymptotic)   62E17  
approximations, asymptotic expansions (steepest descent, etc.) # asymptotic    41A60  
Arakelov theory; heights # arithmetic varieties and schemes;    14G40  
arbitrary fields # linear algebraic groups over    20G15  
arbitrary genus or genus $\ne 1$ over global fields # curves of    11G30  
arbitrary intervals # sums over    11L26  
arbitrary linear expressions # approximation by    41A45  
arbitrary nonlinear expressions; widths and entropy # approximation by    41A46  
architecture # communications network    004.65  
architecture # computer    004.22  
architecture # general works on computer    004.3582  
architecture # mathematical problems of computer    68M07  
architectures # algorithms for specific classes of    65Y10  
areal metrics) # Finsler spaces and generalizations (   53B40  
areal metrics) # Finsler spaces and generalizations (   53C60  
areas # China and adjacent    951  
areas of application # equations of mathematical physics and other    35Qxx  
areas other than physics # applications of PDE in    35Q80  
areolar monogenic functions) # monogenic properties of complex functions (including polygenic and    30A05  
arguments # optimal control problems involving equations with retarded    49J25  
arguments # problems involving equations with retarded    49K25  
arising from non-commutative algebraic geometry # rings    16S38  
arising from the discretization of structural vibrations problems # systems    70J50  
arising in bifurcations # attractors and their bifurcations    37G35  
arising in fluid mechanics # other equations    35Q35  
arising in harmonic analysis # function spaces    42B35  
arising under various constructions # rings and algebras    16Sxx  
arithmetic   372.72  
arithmetic   513  
arithmetic # field    12E30  
arithmetic # interval and finite    65G30  
arithmetic # nonstandard    11U10  
arithmetic # nonstandard    12L15  
arithmetic # nonstandard models of    03H15  
arithmetic # symbols and    19F15  
arithmetic algebraic geometry (Diophantine geometry)   11Gxx  
arithmetic and algebra   513.12  
arithmetic and combinatorial problems   20D60  
arithmetic and fragments # first-order    03F30  
arithmetic and fragments # second- and higher-order    03F35  
arithmetic and geometric progressions   513.4  
arithmetic and geometry   513.13  
arithmetic and set theory # models of    03C62  
arithmetic aspects of modular and Shimura varieties   11G18  
arithmetic codes   94B40  
arithmetic combined with other branches of mathematics   513.1  
arithmetic functions   11K65  
arithmetic functions # asymptotic results on    11N37  
arithmetic functions # other results on the distribution of values or the characterization of    11N64  
arithmetic functions # rate of growth of    11N56  
arithmetic functions; related numbers; inversion formulas   11A25  
arithmetic functions; tables # values of    11Y70  
arithmetic ground fields   14H25  
arithmetic ground fields   14J20  
arithmetic ground fields   14K15  
arithmetic ground fields (finite, local, global)   14D10  
arithmetic groups # cohomology of    11F75  
arithmetic groups # structure of modular groups and generalizations;    11F06  
arithmetic operations   513.2  
arithmetic problems. Diophantine geometry   14Gxx  
arithmetic progressions   11B25  
arithmetic rings and other special rings   13Fxx  
arithmetic theory of algebraic function fields   11R58  
arithmetic theory of polynomial rings over finite fields   11T55  
arithmetic varieties and schemes; Arakelov theory; heights   14G40  
arithmetic, algebra and geometry   513.14  
arithmetic, separable algebras, Azumaya algebras # orders and    16H05  
arithmetic, zeta functions # quaternion and other division algebras:    11R52  
aro, Euler, N\"orlund and Hausdorff methods # Ces\`   40G05  
Aronszajn, de_Branges, # Hilbert subspaces; complementation (   46C07  
around obstacles # flow over and    532.53  
arrangements of hyperplanes # relations with    32S22  
arrangements of lines and pseudolines # planar    52C30  
arrangements of points, flats, hyperplanes   52C35  
arrays, Latin squares, Room squares # orthogonal    05B15  
articles # collections of reprinted    00B60  
articles of general interest # collections of    00B10  
articles of miscellaneous specific content # collections of    00B15  
artificial intelligence   006.3  
artificial intelligence   68Txx  
artificial intelligence # logic in    68T27  
artificial life and related topics # neural networks    92B20  
artificial radioactivity   539.753  
Artin approximation # etale and flat extensions; Henselization;    13B40  
Artin groups # braid groups;    20F36  
Artin rings # division rings and semisimple    16Kxx  
Artinian rings # representations of    16G10  
Artinian rings and modules   16P20  
Artinian rings and modules, finite-dimensional algebras   13E10  
ary compositions $(n \ge 3)$ # other $n$-   17A42  
ary systems # n$-   20N15  
Asia # Central    958  
Asia # Southeast    01A29  
Asia Far East # general history of    950  
Askey - Wilson polynomials, etc.) # basic orthogonal polynomials and functions (   33D45  
aspects # computational    33Fxx  
aspects # general    515.2  
aspects # general    515.82  
aspects # general    515.92  
aspects # general    516.1  
aspects # general    516.21  
aspects # nonanalytic    34M20  
aspects (differential-algebraic, hypertranscendence, group-theoretical) # algebraic    34M15  
aspects (motivation, anxiety, persistence, etc.) # affective    97C20  
aspects in algebraic geometry # computational    14Qxx  
aspects of associative rings # computational    16Z05  
aspects of Borel, analytic, projective, etc. sets) # descriptive set theory (topological    54H05  
aspects of commutative algebra # computational    13Pxx  
aspects of complex manifolds # topological    32Q55  
aspects of field theory and polynomials # computational    12Y05  
aspects of forcing and Boolean-valued models # other    03E40  
aspects of harmonic maps # differential geometric    53C43  
aspects of infinite or finite groups # special    20Fxx  
aspects of learning (culture, group interactions, equity issues, etc.) # sociological    97C60  
aspects of modular and Shimura varieties # arithmetic    11G18  
aspects of numerical algorithms # computer    65Yxx  
aspects of posets # algebraic    06A11  
aspects of quantum groups # ring-theoretic    16W35  
aspects of software engineering (specification, verification, metrics, requirements, etc.) # mathematical    68N30  
aspects related to convexity # computational    52B55  
aspects) # classical groups (geometric    14L35  
aspects) # connected and locally connected spaces (general    54D05  
aspects) # finite fields (field-theoretic    12E20  
aspects) # finite fields and commutative rings (number-theoretic    11Txx  
aspects) # foliations (differential geometric    53C12  
aspects) # other algebraic groups (geometric    14L40  
aspects) # superfluids (classical    76A25  
aspects: intersection cohomology, stratified sets, etc. # topological    35S35  
aspects: Lefschetz theorems, topological classification, invariants # topological    32S50  
assemblers   005.456  
assembly languages # machine and    005.136  
assessment (large scale assessment, validity, reliability, etc.)   97C40  
assessment, validity, reliability, etc.) # assessment (large scale    97C40  
assignment # discrete location and    90B80  
assisted instruction and programmed instruction # computer    97U50  
associated geometries   17C37  
associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics   13A30  
associated groups, automorphisms   17C30  
associated Lie structures   20F40  
associated manifolds   17C36  
associated to Drinfel'd modules # modular forms    11F52  
associated with additive and positive multiplicative functions # distribution functions    11N60  
associated with monads # algebras and Kleisli categories    18C20  
associated with other structures # Jordan structures    17C50  
associated with other structures (associative, Jordan, etc.) # Lie (super)algebras    17B60  
associated with root systems # basic hypergeometric functions    33D67  
associated with root systems # hypergeometric functions    33C67  
associated with root systems # orthogonal polynomials and functions    33C52  
associated with root systems (Macdonald polynomials, etc.) # basic orthogonal polynomials and functions    33D52  
association (correlation, canonical correlation, etc.) # measures of    62H20  
association schemes, strongly regular graphs   05E30  
association) analysis # correlation (   519.537  
associative rings # computational aspects of    16Z05  
associative rings and algebras   16-XX  
associative, Jordan, etc.) # Lie (super)algebras associated with other structures (   17B60  
astronomy   215.2  
astronomy # statistical    85A35  
astronomy and allied sciences   520  
astronomy and astrophysics   85-XX  
astrophysical flows # stability and instability of geophysical and    76E20  
astrophysics # astronomy and    85-XX  
asymptotic analysis   78M35  
asymptotic analysis   80M35  
asymptotic approximations, asymptotic expansions (steepest descent, etc.)   41A60  
asymptotic behavior   58K55  
asymptotic behavior of solutions   35B40  
asymptotic distribution of eigenvalues and eigenfunctions for PDO   35P20  
asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions   34L20  
asymptotic distribution theory   62E20  
asymptotic enumeration   05A16  
asymptotic expansions   34E05  
asymptotic expansions   35C20  
asymptotic methods, singular perturbations   76M45  
asymptotic procedures (radiation, news functions, $\scr H$-spaces, etc.)   83C30  
asymptotic properties   34D05  
asymptotic properties   62G20  
asymptotic properties of estimators   62F12  
asymptotic properties of groups   20F69  
asymptotic properties of tests   62F05  
asymptotic representations in the complex domain   30E15  
asymptotic results on arithmetic functions   11N37  
asymptotic results on counting functions for algebraic and topological structures   11N45  
asymptotic stability   93D20  
asymptotic theory   34Exx  
asymptotic theory   34K25  
asymptotics   45M05  
asymptotics # perturbations;    58J37  
asymptotics of difference equations, oscillatory and periodic solutions, etc. # stability and    39A11  
asymptotics, summation methods   34M30  
atmospheres # planetary    85A20  
atmospheric physics # meteorology and    86A10  
atmospheric waves   76B60  
atomic and nuclear physics   539.7  
atomic physics   81V45  
atomic structure   539.14  
atomic structure   541.24  
atomism   146.5  
atoms considered as particles # nuclei and    539.723  
attainable sets   93B03  
attitudes # social theologies and interreligious relations and    291.17  
attitudes # social theology and interreligious relations and    261  
attracting sets # inertial manifolds and other invariant    37L25  
attractors   34D45  
attractors   35B41  
attractors and repellers, topological structure   37C70  
attractors and their bifurcations arising in bifurcations   37G35  
attractors and their dimensions, Lyapunov exponents   37L30  
attractors, chaotic dynamics # strange    37D45  
attractors, repellers # Lyapunov functions and stability;    37B25  
auctions, bargaining, bidding, selling, etc.) # market models (   91B60  
audiovisual media and their use in instruction   97U80  
auroras   538.768  
Auslander - Reiten quivers # Auslander - Reiten sequences (almost split sequences) and    16G70  
Auslander - Reiten sequences (almost split sequences) and Auslander - Reiten quivers   16G70  
authentication and secret sharing   94A62  
automata # algebraic theory of languages and    68Q70  
automata # cellular    37B15  
automata # cellular    68Q80  
automata # formal languages and    68Q45  
automata and formal grammars in connection with logical questions   03D05  
automata sequences   11B85  
automata theory, linguistics, etc. # semigroups in    20M35  
automated information storage and retrieval systems   025.04  
automated information storage and retrieval systems   025.042  
automated information storage and retrieval systems   025.044  
automated information storage and retrieval systems devoted to specific disciplines and subjects   025.06  
automated systems (robots, etc.)   93C85  
automatic continuity   46H40  
automatic result verification # algorithm with    65G20  
automorphic $L$-series, periods of modular forms, cohomology, modular symbols # special values of    11F67  
automorphic forms   32N10  
automorphic forms # discontinuous groups and    11Fxx  
automorphic forms # Fourier coefficients of    11F30  
automorphic forms # Siegel modular groups and their modular and    11F46  
automorphic forms (several variables) # other groups and their modular and    11F55  
automorphic forms and functions) # analytic theory (Epstein zeta functions; relations with    11E45  
automorphic forms, one variable   11F12  
automorphic forms; Hilbert modular surfaces # Hilbert and Hilbert - Siegel modular groups and their modular and    11F41