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Index using "Encyclopedic Dictionary" System

Here are the top-level areas of mathematics and related fields classified according to the system used in the "Encyclopedic Dictionary of Mathematics", translated from the Japanese; Shôkichi Iyanaga and Yukiyoshi Kawada, eds. (MIT press, 1977, 1750pp, ISBN 0-262-09016-3). This is a fine encyclopedia, the second edition (1993) having 450 articles arranged alphabetically in three volumes, together with a fourth volume with appendices, tables, and name- and subject-indices. The articles are usually divided into labelled sub-themes, too. On the other hand, they are gathered into a systematic classification in an index table, reproduced below.

This classification systems is appropriate for indexing both new work and standard results together. However, it is not used as frequently among mathematicians as the Mathematics Subject Classification (MSC) scheme, which is the basis for the organization of materials at this site.

If someone would like to supply the headings of the named paragraphs within this classification system, they can be added to the list below. For the time being we offer no links to the materials at this site through this system.

The twenty-one groupings in this system are

  1. Logic and Foundations
  2. Sets, General Topology, and Categories
  3. Algebra
  4. Group Theory
  5. Number Theory
  6. Euclidean and Projective Geometry
  7. Differential Geometry
  8. Algebraic Geometry
  9. Topology
  10. Analysis
  11. Complex Analysis
  12. Functional Analysis
  13. Differential, Integral, and Functional Equations
  14. Special Functions
  15. Numerical Analysis
  16. Computer Science and Combinatorics
  17. Probability Theory
  18. Statistics
  19. Mathematical Programming and Operations Research
  20. Mechanics and Theoretical Physics
  21. History of Mathematics

Article headings are shown with their article number:

  1. Logic and Foundations
    1. Foundations of Mathematics [156]
    2. Axiom Systems [035]
    3. Paradoxes [319]
    4. Symbolic Logic [411]
    5. Axiomatic Set Theory [033]
    6. Model Theory [276]
    7. Nonstandard Analysis [293]
    8. Gödel Numbers [185]
    9. Recursive Functions [356]
    10. Decision Problem [097]
    11. Constructive Ordinal Numbers [081]
    12. Analytic Sets [022]
  2. Sets, General Topology, and Categories
    1. Sets [381]
    2. Relations [358]
    3. Equivalence Relations [135]
    4. Functions [165]
    5. Axiom of Choice and Equivalents [034]
    6. Cardinal Numbers [049]
    7. Structures [409]
    8. Permutations and Combinations [330]
    9. Numbers [294]
    10. Real Numbers [355]
    11. Complex Numbers [074]
    12. Ordering [311]
    13. Ordinal Numbers [312]
    14. Lattices [243]
    15. Boolean Algebras [042]
    16. Topological Spaces [425]
    17. Metric Spaces [273]
    18. Plane Domains [333]
    19. Convergence [087]
    20. Connectedness [079]
    21. Dimension Theory [117]
    22. Uniform Spaces [436]
    23. Uniform Convergence [435]
    24. Categories and Functors [052]
    25. Inductive Limits and Projective Limits [210]
    26. Sheaves [383]
  3. Algebra
    1. Algebra [008]
    2. Matrices [269]
    3. Determinants [103]
    4. Polynomials [337]
    5. Algebraic Equations [010]
    6. Fields [149]
    7. Galois Theory [172]
    8. Linear Spaces [256]
    9. Rings [368]
    10. Associative Algebras [029]
    11. Commutative Rings [067]
    12. Noetherian Rings [284]
    13. Rings of Polynomials [369]
    14. Rings of Power Series [370]
    15. Quadratic Forms [348]
    16. Clifford Algebras [061]
    17. Differential Rings [113]
    18. Witt Vectors [449]
    19. Valuations [439]
    20. Adèles and Idèles [006]
    21. Cayley Algebras [054]
    22. Jordan Algebras [231]
    23. Modules [277]
    24. Homological Algebra [200]
    25. Hopf Algebras [203]
  4. Group Theory
    1. Groups [190]
    2. Abelian Groups [002]
    3. Free Groups [161]
    4. Finite Groups [151]
    5. Classical Groups [060]
    6. Topological Groups [423]
    7. Topological Abelian Groups [422]
    8. Compact Groups [069]
    9. Lie Groups [249]
    10. Lie Algebras [248]
    11. Algebraics Groups [013]
    12. Homogeneous Spaces [199]
    13. Symmetric Riemannian Spaces and Real Forms [412]
    14. Discontinuous Groups [122]
    15. Crystallographic Groups [092]
    16. Representations [362]
    17. Unitary Representations [437]
    18. Invariants and Covariants [226]
  5. Number Theory
    1. Number Theory [296]
    2. Number Theory, Elementary [297]
    3. Continued Fractions [083]
    4. Number-Theoretic Functions [295]
    5. Additive Number Theory [004]
    6. Partitions of Numbers [328]
    7. Distributions of Prime Numbers [123]
    8. Lattice-Point Problems [242]
    9. Diophantine Equations [118]
    10. Geometry of Numbers [182]
    11. Transcendental Numbers [430]
    12. Quadratic Fields [347]
    13. Algebraic Number Fields [014]
    14. Class Field Theory [059]
    15. Complex Multiplication [073]
    16. Fermat's Problem [145]
    17. Local Fields [257]
    18. Arithmetic of Associative Algebras [027]
    19. Zeta Functions [450]
  6. Euclidean and Projective Geometry
    1. Geometry [181]
    2. Foundations of Geometry [155]
    3. Euclidean Geometry [139]
    4. Euclidean Spaces [140]
    5. Geometric Constructions [179]
    6. Regular Polyhedra [357]
    7. Pi [332]
    8. Trigonometry [432]
    9. Conic Sections [078]
    10. Quadric Surfaces [350]
    11. Convex Sets [089]
    12. Vectors [442]
    13. Coordinates [090]
    14. Projective Geometry [343]
    15. Affine Geometry [007]
    16. Non-Euclidean Geometry [285]
    17. Conformal Geometry [076]
    18. Erlangen Program [137]
    19. Continuous Geometry [085]
    20. Curves [093]
    21. Surfaces [410]
    22. Four-Color Problem [157]
  7. Differential Geometry
    1. Differential Geometry [109]
    2. Differentiable Manifolds [105]
    3. Riemannian Manifolds [364]
    4. Connections [080]
    5. Tensor Calculus [417]
    6. Geodesics [178]
    7. Symmetric Spaces [413]
    8. G-structures [191]
    9. Complex Manifolds [072]
    10. Kähler Manifolds [232]
    11. Harmonic Integrals [194]
    12. Differential Geometry of Curves and Surfaces [111]
    13. Riemannian Submanifolds [365]
    14. Minimal Submanifolds [275]
    15. Harmonic Mappings [195]
    16. Morse Theory [279]
    17. Differential Geometry in Specific Spaces [110]
    18. Finsler Spaces [152]
    19. Integral Geometry [218]
    20. Siegel Domains [384]
    21. Pseudoconformal Geometry [344]
    22. Spectral Geometry [391]
    23. Global Analysis [183]
  8. Algebraic Geometry
    1. Algebraic Geometry [012]
    2. Algebraic Curves [009]
    3. Algebraic Surfaces [015]
    4. Algebraic Varieties [016]
    5. Abelian Varieties [003]
    6. Riemann-Roch Theorems [366]
  9. Topology
    1. Topology [426]
    2. Fundamental Groups [170]
    3. Covering Spaces [091]
    4. Degree of Mapping [099]
    5. Complexes [070]
    6. Homology Theory [201]
    7. Fixed-Point Theorems [153]
    8. Cohomology Operations [064]
    9. Homotopy Theory [202]
    10. Fiber Spaces [148]
    11. Obstructions [305]
    12. Topology of Lie Groups and Homogeneous Spaces [427]
    13. Fiber Bundles [147]
    14. Characteristic Classes [056]
    15. K-Theory [237]
    16. Knot Theory [235]
    17. Combinatorial Manifolds [065]
    18. Differential Topology [114]
    19. Transformation Groups [431]
    20. Theory of Singularities [418]
    21. Foliations [154]
    22. Dynamical Systems [126]
    23. Shape Theory [382]
    24. Catastrophe Theory [051]
  10. Analysis
    1. Analysis [020]
    2. Continuous Functions [084]
    3. Inequalities [211]
    4. Convex Analysis [088]
    5. Functions of Bounded Variations [166]
    6. Differential Calculus [106]
    7. Implicit Functions [208]
    8. Elementary Functions [131]
    9. C^\infty-Functions and Quasi-Analytic Functions [058]
    10. Integral Calculus [216]
    11. Curvilinear Integrals and Surface Integrals [094]
    12. Measure Theory [270]
    13. Integration Theory [221]
    14. Invariant Measures [225]
    15. Set Functions [380]
    16. Length and Area [246]
    17. Denjoy Integrals [100]
    18. Series [379]
    19. Asymptotic Series [030]
    20. Polynomial Approximation [336]
    21. Orthogonal Functions [317]
    22. Fourier Series [159]
    23. Fourier Transform [160]
    24. Harmonic Analysis [192]
    25. Almost Periodic Functions [018]
    26. Laplace Transform [240]
    27. Integral Transforms [220]
    28. Potential Theory [338]
    29. Harmonic Functions and Subharmonic Functions [193]
    30. Dirichlet Problem [120]
    31. Capacity [048]
    32. Calculus of Variations [046]
    33. Plateau's Problem [334]
    34. Isoperimetric Problems [228]
    35. Variational Inequalities [440]
  11. Complex Analysis
    1. Holomorphic Functions [198]
    2. Power Series [339]
    3. Dirichlet Series [121]
    4. Bounded Functions [043]
    5. Univalent and Multivalent Functions [438]
    6. Transcendental Entire Functions [429]
    7. Meromorphic Functions [272]
    8. Distributions of Values of Functions of a Complex Variable [124]
    9. Cluster Sets [062]
    10. Algebraic Functions [011]
    11. Algebroidal Functions [017]
    12. Riemann Surfaces [367]
    13. Ideal Boundaries [207]
    14. Conformal Mappings [077]
    15. Quasiconformal Mappings [352]
    16. Teichmüller Spaces [416]
    17. Kleinian Groups [234]
    18. Extremal Length [143]
    19. Function-Theoretic Null Sets [169]
    20. Analytic Functions of Several Complex Variables [021]
    21. Analytic Spaces [023]
    22. Automorphic Functions [032]
  12. Functional Analysis
    1. Functional Analysis [162]
    2. Hilbert Spaces [197]
    3. Banach Spaces [037]
    4. Ordered Linear Spaces [310]
    5. Topological Linear Spaces [424]
    6. Function Spaces [168]
    7. Distributions and Hyperfunctions [125]
    8. Vector-Valued Integrals [443]
    9. Linear Operators [251]
    10. Compact and Nuclear Operators [068]
    11. Interpolation of Operators [224]
    12. Spectral Analysis of Operators [390]
    13. Perturbation of Linear Operators [331]
    14. Semigroups of Operators and Evolution Equations [378]
    15. Differential Operators [112]
    16. Microlocal Analysis [274]
    17. Banach Algebras [036]
    18. Function Algebras [164]
    19. Operator Algebras [308]
    20. Operational Calculus [306]
    21. Nonlinear Functional Analysis [286]
  13. Differential, Integral, and Functional Equations
    1. Differential Equations [107]
    2. Ordinary Differential Equations [313]
    3. Ordinary Differential Equations (Initial Value Problems) [316]
    4. Ordinary Differential Equations (Boundary Value Problems) [315]
    5. Ordinary Differential Equations (Asymptotic Behaviour of Solutions) [315]
    6. Linear Ordinary Differential Equations [252]
    7. Linear Ordinary Differential Equations (Local Theory) [254]
    8. Linear Ordinary Differential Equations (Global Theory) [253]
    9. Nonlinear Ordinary Differential Equations (Local Theory) [289]
    10. Nonlinear Ordinary Differential Equations (Global Theory) [288]
    11. Nonlinear Oscillation [290]
    12. Nonlinear Problems [291]
    13. Stability [394]
    14. Integral Invariants [219]
    15. Difference Equations [104]
    16. Functional-Differential Equations [163]
    17. Total Differential Equations [428]
    18. Contact Transformations [082]
    19. Partial Differential Equations [320]
    20. Partial Differential Equations (Methods of Integrations) [322]
    21. Partial Differential Equations (Initial Value Problems) [321]
    22. Partial Differential Equations of First Order [324]
    23. Monge-Ampère Equations [278]
    24. Partial Differential Equations of Elliptic Type [323]
    25. Partial Differential Equations of Hyperbolic Type [325]
    26. Partial Differential Equations of Parabolic Type [327]
    27. Partial Differential Equations of Mixed Type [326]
    28. Green's Functions [188]
    29. Green's Operators [189]
    30. Integral Equations [217]
    31. Integrodifferential Equations [222]
    32. Special Functional Equations [388]
    33. Pseudodifferential Operators [345]
  14. Special Functions
    1. Special Functions [389]
    2. Generating Functions [177]
    3. Elliptic Functions [134]
    4. Gamma Function [174]
    5. Hypergeometric Functions [206]
    6. Spherical Functions [393]
    7. Functions of Confluent Type [167]
    8. Bessel Functions [039]
    9. Ellipsoidal Harmonics [133]
    10. Mathieu Functions [268]
  15. Numerical Analysis
    1. Numerical Methods [300]
    2. Interpolations [223]
    3. Error Analysis [138]
    4. Numerical Solutions of Linear Equations [302]
    5. Numerical Solutions of Algebraic Equations [301]
    6. Numerical Computations of Eigenvalues [298]
    7. Numerical Integration [299]
    8. Numerical Solutions of Ordinary Differential Equations [303]
    9. Numerical Solutions of Partial Differential Equations [304]
    10. Analog Computation [019]
    11. Evaluation of Functions [142]
  16. Computer Science and Combinatorics
    1. Automata [031]
    2. Computers [075]
    3. Coding Theory [063]
    4. Cybernetics [095]
    5. Random Numbers [354]
    6. Simulations [385]
    7. Data Processing [096]
    8. Mathematical Models in Biology [263]
    9. Complexity of Computations [071]
    10. Combinatorics [066]
    11. Latin Squares [241]
    12. Graph Theory [186]
  17. Probability Theory
    1. Probability Theory [342]
    2. Probability Measures [341]
    3. Limit Theorems in Probability Theory [250]
    4. Stochastic Processes [407]
    5. Markov Processes [261]
    6. Markov Chains [260]
    7. Brownian Motion [045]
    8. Diffusion Processes [115]
    9. Additive Processes [005]
    10. Branching Processes [044]
    11. Martingales [262]
    12. Stationary Processes [395]
    13. Gaussian Processes [176]
    14. Stochastic Differential Equations [406]
    15. Ergodic Theory [136]
    16. Stochastic Control and Stochastic Filtering [405]
    17. Probabilistic Methods in Statistical Mechanics [340]
  18. Statistics
    1. Statistical Data Analysis [397]
    2. Statistical Inference [401]
    3. Statistic [396]
    4. Sampling Distributions [374]
    5. Statistical Models [403]
    6. Statistical Decision Functions [398]
    7. Statistical Estimation [399]
    8. Statistical Hypothesis Testing [400]
    9. Multivariable Analysis [280]
    10. Robust and Nonparametric Methods [371]
    11. Time Series Analysis [421]
    12. Design of Experiments [102]
    13. Sample Survey [373]
    14. Statistical Quality Control [404]
    15. Econometrics [128]
    16. Biometrics [040]
    17. Psychometrics [346]
    18. Insurance Mathematics [214]
  19. Mathematical Programming and Operations Research
    1. Mathematical Programming [264]
    2. Linear Programming [255]
    3. Quadratic Programming [349]
    4. Nonlinear Programming [292]
    5. Network Flow Problems [281]
    6. Integer Programming [215]
    7. Stochastic Programming [408]
    8. Dynamic Programming [127]
    9. Game Theory [173]
    10. Differential Games [108]
    11. Control Theory [086]
    12. Information Theory [213]
    13. Operations Research [307]
    14. Inventory Control [227]
    15. Scheduling and Production Planning [376]
  20. Mechanics and Theoretical Physics
    1. Systems of Units [414]
    2. Dimensional Analysis [116]
    3. Variational Principles [441]
    4. Mechanics [271]
    5. Spherical Astronomy [392]
    6. Celestial Mechanics [055]
    7. Orbit Determination [309]
    8. Three-Body Problem [420]
    9. Hydrodynamics [205]
    10. Hydrodynamical Equations [204]
    11. Magnetohydrodynamics [259]
    12. Turbulence and Chaos [433]
    13. Wave Propagation [446]
    14. Oscillations [318]
    15. Geometric Optics [180]
    16. Electromagnetism [130]
    17. Networks [282]
    18. Thermodynamics [419]
    19. Statistical Mechanics [402]
    20. Boltzman Equation [041]
    21. Relativity [359]
    22. Unified Field Theory [434]
    23. Quantum Mechanics [351]
    24. Lorentz Group [258]
    25. Racah Algebra [353]
    26. Scattering Theory [375]
    27. Second Quantization [377]
    28. Field Theory [150]
    29. S-Matrices [386]
    30. Feynman Integrals [146]
    31. Elementary Particles [132]
    32. Renormalization Group [361]
    33. Nonlinear Lattice Dynamics [287]
    34. Solitons [387]
    35. Approximation Methods in Physics [025]
    36. Inequalities in Physics [212]
  21. History of Mathematics
    1. Ancient Mathematics [024]
    2. Greek Mathematics [187]
    3. Roman and Medieval Mathematics [372]
    4. Arab Mathematics [026]
    5. Indian Mathematics [209]
    6. Chinese Mathematics [057]
    7. Japanese Mathematics (Wasan) [230]
    8. Renaissance Mathematics [360]
    9. Mathematics in the 17th Century [265]
    10. Mathematics in the 18th Century [266]
    11. Mathematics in the 19th Century [267]
    12. Abel, Niels Henrik [001]
    13. Artin, Emil [028]
    14. Bernoulli Family [038]
    15. Cantor, Georg [047]
    16. Cartan, Élie [050]
    17. Cauchy, Augustin Louis [053]
    18. Dedekind, Julius Wilhelm Richard [098]
    19. Descartes, René [101]
    20. Dirichlet, Peter Gustav Lejeune [119]
    21. Einstein, Albert [129]
    22. Euler, Leonhard [141]
    23. Fermat, Pierre de [144]
    24. Fourier, Jean Baptiste Joseph [158]
    25. Galois, Évariste [171]
    26. Gauss, Carl Friedrich [175]
    27. Gödel, Kurt [184]
    28. Hilbert, David [196]
    29. Jacobi, Carl Gustav Jacob [229]
    30. Klein, Felix [233]
    31. Kronecker, Leopold [236]
    32. Lagrange, Joseph Louis [238]
    33. Laplace, Pierre Simon [239]
    34. Lebesgue, Henri Leon [244]
    35. Leibniz, Gottfried Wilhelm [245]
    36. Lie, Marius Sophus [247]
    37. Newton, Isaac [283]
    38. Pascal, Blaise [329]
    39. Poincaré, Henri [335]
    40. Riemann, Georg Friedrich Bernhard [363]
    41. Takagi, Teiji [415]
    42. Viète, François [444]
    43. Von Neumann, John [445]
    44. Weierstrass, Karl [447]
    45. Weyl, Hermann [448]

There are two appendices (A, B) containing tables relevant to these sections:

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Last modified 2000/01/18 by Dave Rusin. Mail: