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Graduate Texts in Mathematics (GTM) is a series of graduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are small yellow books of a standard size. This particular series is easily identified by a white band at the top of the book.

List of books

[edit]
  • 1 Introduction to Axiomatic Set Theory, Gaisi Takeuti, W. M. Zaring
  • 2 Measure and Category, John C. Oxtoby (1997, ISBN 978-0-387-90508-2)
  • 3 Topological Vector Spaces, Schaefer, Wolff (1999, ISBN 978-0-387-98726-2)
  • 4 A Course in Homological Algebra, Peter Hilton, Urs Stammbach (1997, ISBN 978-0-387-94823-2)
  • 5 Categories for the Working Mathematician, Saunders Mac Lane (1998, ISBN 978-0-387-98403-2)
  • 6 Projective Planes, Hughes, Piper
  • 7 A Course in Arithmetic, Jean-Pierre Serre (1996, ISBN 978-0-387-90040-7)
  • 8 Axiomatic Set Theory, Gaisi Takeuti, Zaring
  • 9 Introduction to Lie Algebras and Representation Theory, James E. Humphreys (1997, ISBN 978-0-387-90053-7)
  • 10 A Course in Simple-Homotopy Theory, M. M. Cohen
  • 11 Functions of One Complex Variable I, John B. Conway (1995, ISBN 978-0-387-90328-6)
  • 12 Advanced Mathematical Analysis, R. Beals (1973, ISBN 978-0-387-90065-0)
  • 13 Rings and Categories of Modules, Anderson, Fuller (1992, ISBN 978-0-387-97845-1)
  • 14 Stable Mappings and Their Singularities, Golubitsky, Guillemin
  • 15 Lectures in Functional Analysis and Operator Theory, S. K. Berberian
  • 16 The Structure of Fields, D. Winter
  • 17 Random Processes, M. Rosenblatt
  • 18 Measure Theory, Paul R. Halmos (1974, ISBN 978-0-387-90088-9)
  • 19 A Hilbert Space Problem Book, P. R. Halmos (1982, ISBN 978-0-387-90685-0)
  • 20 Fibre Bundles, Dale Husemoller (1994, ISBN 978-0-387-94087-8)
  • 21 Linear Algebraic Groups, James E. Humphreys (1998, ISBN 978-0-387-90108-4)
  • 22 An Algebraic Introduction to Mathematical Logic, Barnes, Mack
  • 23 Linear Algebra, Werner H. Greub (1981, ISBN 978-0-387-90110-7)
  • 24 Geometric Functional Analysis and Its Applications, Holmes
  • 25 Real and Abstract Analysis, Hewitt, Stromberg (1975, ISBN 978-0-387-90138-1)
  • 26 Algebraic Theories, Manes
  • 27 General Topology, John L. Kelley (1975, ISBN 978-0-387-90125-1)
  • 28 Commutative Algebra I, Oscar Zariski, Pierre Samuel, Cohen (1975, ISBN 978-0-387-90089-6)
  • 29 Commutative Algebra II, Oscar Zariski, Pierre Samuel
  • 30 Lectures in Abstract Algebra I, Nathan Jacobson
  • 31 Lectures in Abstract Algebra II, Nathan Jacobson
  • 32 Lectures in Abstract Algebra III, Nathan Jacobson
  • 33 Differential Topology, Morris W. Hirsch
  • 34 Principles of Random Walk, Frank Spitzer
  • 35 Several Complex Variables and Banach Algebras, Alexander, Wermer
  • 36 A Course in Robust Control Theory, Dullerud, Paganini
  • 37 Mathematical Logic, Monk
  • 38 Geometric Methods and Applications, Jean Gallier
  • 39 An Invitation to -Algebras, William Arveson
  • 40 Denumerable Markov Chains, John George Kemeny, Snell, Knapp et al.
  • 41 Modular Functions and Dirichlet Series in Number Theory, Tom M. Apostol
  • 42 Linear Representations of Finite Groups, Jean-Pierre Serre, Scott
  • 43 Rings of Continuous Functions, Gillman, Jerison
  • 44 Elementary Algebraic Geometry, K. Kendig
  • 45 Probability Theory I, I M. Loeve
  • 46 Probability Theory II, I M. Loeve
  • 47 Geometric Topology in Dimensions 2 and 3, Moise
  • 48 General Relativity for Mathematicians, Sachs, Wu
  • 49 Linear Geometry, Gruenberg, Weir
  • 50 Fermat's Last Theorem, Harold M. Edwards
  • 51 A Course in Differential Geometry, Klingenberg
  • 52 Algebraic Geometry, Robin Hartshorne
  • 53 A Course in Mathematical Logic, Yu. I. Manin, Neal Koblitz
  • 54 Combinatorics with Emphasis on the Theory of Graphs, Graver, Watkins
  • 55 Introduction to Operator Theory I, Brown, Pearcy
  • 56 Algebraic Topology: An Introduction, William S. Massey
  • 57 Introduction to Knot Theory, Richard H. Crowell, Ralph H. Fox (1977, ISBN 978-0-387-90272-2)
  • 58 P-adic Numbers, p-adic Analysis, and Zeta-Functions, Neal Koblitz
  • 59 Cyclotomic Fields, Serge Lang
  • 60 Mathematical Methods of Classical Mechanics, V. I. Arnold
  • 61 Elements of Homotopy Theory, George W. Whitehead
  • 62 Fundamentals of the Theory of Groups, Kargapolov, Merzljakov, Burns
  • 63 Graph Theory, Bollobas
  • 64 Fourier Series I, Edwards
  • 65 Differential Analysis on Complex Manifolds, R.O. Wells Jr.
  • 66 Introduction to Affine Group Schemes, W.C. Waterhouse
  • 67 Local Fields, Jean-Pierre Serre, Greenberg
  • 68 Linear Operators on Hilbert Spaces, Weidmann, Szuecs
  • 69 Cyclotomic Fields II, Serge Lang
  • 70 Singular Homology Theory, William S. Massey
  • 71 Riemann Surfaces, Herschel Farkas, Irwin Kra
  • 72 Classical Topology and Combinatorial Group Theory. John Stillwell
  • 73 Algebra, Thomas W. Hungerford
  • 74 Multiplicative Number Theory, Davenport, Montgomery
  • 75 Basic Theory of Algebraic Groups and Lie Algebras, G. P. Hochschild
  • 76 Algebraic Geometry, Iitaka
  • 77 Lectures on the Theory of Algebraic Numbers, Hecke, Brauer, Goldman et al.
  • 78 A Course in Universal Algebra, Burris, Sankappanavar (Online [1])
  • 79 An Introduction to Ergodic Theory, Peter Walters
  • 80 A Course in the Theory of Groups, Derek J.S. Robinson
  • 81 Lectures on Riemann Surfaces, Forster, Gilligan
  • 82 Differential Forms in Algebraic Topology, Raoul Bott, Loring Tu
  • 83 Introduction to Cyclotomic Fields, Lawrence C. Washington
  • 84 A Classical Introduction to Modern Number Theory, Ireland, Rosen (1995, ISBN 0-387-97329-X)
  • 85 Fourier Series A Modern Introduction, R. E. Edwards
  • 86 Introduction to Coding Theory, J.H. van Lint
  • 87 Cohomology of Groups, Kenneth S. Brown
  • 88 Associative Algebras, R.S. Pierce
  • 89 Introduction to Algebraic and Abelian Functions, Serge Lang
  • 90 An Introduction to Convex Polytopes, Arne Brondsted
  • 91 The Geometry of Discrete Groups, Alan F. Beardon, Beardon
  • 92 Sequences and Series in Banach Spaces, J. Diestel
  • 93 Modern Geometry - Methods and Applications I, Dubrovin, Fomenko, Novikov et al.
  • 94 Foundations of Differentiable Manifolds and Lie Groups, Frank W. Warner
  • 95 Probability, Shiryaev, Boas
  • 96 A Course in Functional Analysis, John B. Conway
  • 97 Introduction to Elliptic Curves and Modular Forms, Neal Koblitz
  • 98 Representations of Compact Lie Groups, Broecker, Dieck
  • 99 Finite Reflection Groups, Grove, Benson
  • 100 Harmonic Analysis on Semigroups, Berg, Christensen, Ressel
  • 101 Galois Theory, Harold M. Edwards
  • 102 Lie Groups, Lie Algebras, and Their Representations, V. S. Varadarajan
  • 103 Complex Analysis, Serge Lang
  • 104 Modern Geometry - Methods and Applications II, Dubrovin, Fomenko, Novikov et al.
  • 105 SL2(R), Serge Lang
  • 106 The Arithmetic of Elliptic Curves, Joseph H. Silverman
  • 107 Applications of Lie Groups to Differential Equations, Peter J. Olver
  • 108 Holomorphic Functions and Integral Representations in Several Complex Variables, R. Michael Range
  • 109 Univalent Functions and Teichmüller Spaces, O. Lehto
  • 110 Algebraic Number Theory, Serge Lang
  • 111 Elliptic Curves, Dale Husemoeller
  • 112 Elliptic Functions, Serge Lang
  • 113 Brownian Motion and Stochastic Calculus, Ioannis Karatzas, Steven Shreve
  • 114 A Course in Number Theory and Cryptography, Neal Koblitz
  • 115 Differential Geometry, Berger, Gostiaux, Levy
  • 116 Measure and Integral, John L. Kelley, Srinivasan
  • 117 Algebraic Groups and Class Fields, Jean-Pierre Serre
  • 118 Analysis Now, Gert K. Pedersen
  • 119 An Introduction to Algebraic Topology, Joseph J. Rotman
  • 120 Weakly Differentiable Functions, William P. Ziemer
  • 121 Cyclotomic Fields I-II, Serge Lang, Karl Rubin
  • 122 Theory of Complex Functions, Remmert, Burckel
  • 123 Numbers, Lamotke, Ewing, Ebbinghaus et al.
  • 124 Modern Geometry - Methods and Applications III, B. A. Dubrovin, Anatoly Timofeevich Fomenko, Sergei Petrovich Novikov et al. (1990, ISBN 978-0-387-97271-8)
  • 125 Complex Variables, Berenstein, Gay
  • 126 Linear Algebraic Groups, Armand Borel
  • 127 A Basic Course in Algebraic Topology, William S. Massey
  • 128 Partial Differential Equations, Jeffrey Rauch
  • 129 Representation Theory, Fulton, Harris
  • 130 Tensor Geometry, Dodson, Poston
  • 131 A First Course in Noncommutative Rings, Tsi-Yuen Lam
  • 132 Iteration of Rational Functions, Alan F. Beardon
  • 133 Algebraic Geometry, Joe Harris
  • 134 Coding and Information Theory, Steven Roman
  • 135 Advanced Linear Algebra, Steven Roman
  • 136 Algebra, Adkins, Weintraub
  • 137 Harmonic Function Theory, Axler, Bourdon, Ramey
  • 138 A Course in Computational Algebraic Number Theory, Henri Cohen (1996, ISBN 0-387-55640-0)
  • 139 Topology and Geometry, Glen E. Bredon
  • 140 Optima and Equilibria, Jean-Pierre Aubin
  • 141 Gröbner Bases, Becker, Weispfenning, Kredel
  • 142 Real and Functional Analysis, Serge Lang
  • 143 Measure Theory, J.L. Doob
  • 144 Noncommutative Algebra, Farb, Dennis
  • 145 Homology Theory, James W. Vick
  • 146 Computability, Douglas S. Bridges
  • 147 Algebraic K-Theory and Its Applications, Jonathan Rosenberg
  • 148 An Introduction to the Theory of Groups, Joseph J. Rotman
  • 149 Foundations of Hyperbolic Manifolds, John G. Ratcliffe
  • 150 Commutative Algebra with a View Toward Algebraic Geometry, David Eisenbud
  • 151 Advanced Topics in the Arithmetic of Elliptic Curves, Joseph H. Silverman
  • 152 Lectures on Polytopes, Guenter M. Ziegler
  • 153 Algebraic Topology, William Fulton
  • 154 An Introduction to Analysis, Brown, Pearcy
  • 155 Quantum Groups, Christian Kassel
  • 156 Classical Descriptive Set Theory, Alexander S. Kechris
  • 157 Integration and Probability, Malliavin, Airault, Kay et al.
  • 158 Field Theory, Steven Roman
  • 159 Functions of One Complex Variable II, John B. Conway
  • 160 Differential and Riemannian Manifolds, Serge Lang
  • 161 Polynomials and Polynomial Inequalities, Borwein, Erdelyi
  • 162 Groups and Representations, Alperin, Bell
  • 163 Permutation Groups, Dixon, Mortimer
  • 164 Additive Number Theory I, Melvyn B. Nathanson
  • 165 Additive Number Theory II, Melvyn B. Nathanson
  • 166 Differential Geometry, R.W. Sharpe, Shiing-Shen Chern
  • 167 Field and Galois Theory, Patrick Morandi
  • 168 Combinatorial Convexity and Algebraic Geometry, Guenter Ewald
  • 169 Matrix Analysis, Rajendra Bhatia
  • 170 Sheaf Theory, Glen E. Bredon
  • 171 Riemannian Geometry, Peter Petersen
  • 172 Classical Topics in Complex Function Theory, Remmert, Kay
  • 173 Graph Theory, Reinhard Diestel
  • 174 Foundations of Real and Abstract Analysis, Douglas S. Bridges
  • 175 An Introduction to Knot Theory, W. B. Raymond Lickorish
  • 176 Riemannian Manifolds, John M. Lee
  • 177 Analytic Number Theory ,Donald J. Newman
  • 178 Nonsmooth Analysis and Control Theory, Clarke, Ledyaev, Stern et. al
  • 179 Banach Algebra Techniques in Operator Theory, Ronald G. Douglas
  • 180 A Course on Borel Sets, S.M. Srivastava
  • 181 Numerical Analysis, Rainer Kress
  • 182 Ordinary Differential Equations, Walter, Thompson
  • 183 An Introduction to Banach Space Theory, Robert E. Megginson
  • 184 Modern Graph Theory, Bela Bollobas
  • 185 Using Algebraic Geometry, Cox, Little, O Shea
  • 186 Fourier Analysis on Number Fields, Ramakrishnan, Valenza
  • 187 Moduli of Curves, Harris, Morrison
  • 188 Lectures on the Hyperreals, Robert Goldblatt
  • 189 Lectures on Modules and Rings, Tsit-Yuen Lam
  • 190 Problems in Algebraic Number Theory, Esmonde, Murty
  • 191 Fundamentals of Differential Geometry, Serge Lang
  • 192 Elements of Functional Analysis Hirsch, Lacombe, Levy
  • 193 Advanced Topics in Computational Number Theory, Henri Cohen (2000, ISBN 0-387-98727-4)
  • 194 One-Parameter Semigroups for Linear Evolution Equations, Engel, Nagel
  • 195 Elementary Methods in Number Theory, Melvyn B. Nathanson
  • 196 Basic Homological Algebra, M. Scott Osborne
  • 197 The Geometry of Schemes, Eisenbud, Harris
  • 198 A Course in p-adic Analysis, Alain Robert
  • 199 Theory of Bergman Spaces, Hedenmalm, Korenblum, Zhu
  • 200 An Introduction to Riemann-Finsler Geometry, David Bao, Shiing-Shen Chern, Zhongmin Shen
  • 201 Diophantine Geometry, Hindry, Joseph H. Silverman (2000, ISBN 978-0-387-98975-4)
  • 202 Introduction to Topological Manifolds, John M. Lee
  • 203 The Symmetric Group, Bruce E. Sagan
  • 204 Galois Theory, Jean-Pierre Escofier
  • 205 Rational Homotopy Theory, Yves Félix, Stephen Halperin, Jean-Claude Thomas (2000, ISBN 978-0-387-95068-0 Parameter error in {{ISBN}}: checksum)
  • 206 Problems in Analytic Number Theory, M. Ram Murty (2001, ISBN 978-0-387-95143-0)
  • 207 Algebraic Graph Theory, Godsil, Royle (2001, ISBN 978-0-387-95241-3)
  • 208 Analysis for Applied Mathematics, Ward Cheney (2001, ISBN 978-0-387-95279-6)
  • 209 A Short Course on Spectral Theory, William Arveson (2002, ISBN 978-0-387-95300-7)
  • 210 Number Theory in Function Fields, Michael Rosen (2002, ISBN 978-0-387-95335-9)
  • 211 Algebra, Serge Lang
  • 212 Lectures on Discrete Geometry, Jiri Matousek
  • 213 From Holomorphic Functions to Complex Manifolds, Fritzsche, Grauert
  • 214 Partial Differential Equations, Juergen Jost
  • 215 Algebraic Functions and Projective Curves, David Goldschmidt
  • 216 Matrices, Denis Serre
  • 217 Model Theory: An Introduction, David Marker
  • 218 Introduction to Smooth Manifolds, John M. Lee (2003, ISBN 978-0-387-95448-6)
  • 219 The Arithmetic of Hyperbolic 3-Manifolds, Maclachlan, Reid
  • 220 Smooth Manifolds and Observables, Jet Nestruev
  • 221 Convex Polytopes, Branko Grünbaum (2003, ISBN 0-387-00424-6)
  • 222 Lie Groups, Lie Algebras, and Representations, Brian C. Hall
  • 223 Fourier Analysis and its Applications, Anders Vretblad
  • 224 Metric Structures in Differential Geometry, Walschap, G., (2004, ISBN 978-0-387-20430-7)
  • 225 Lie Groups, Bump, D., (2004, ISBN 978-0-387-21154-1)
  • 226 Spaces of Holomorphic Functions in the Unit Ball, Zhu, K., (2005, ISBN 978-0-387-22036-9)
  • 227 Combinatorial Commutative Algebra, Ezra Miller, Bernd Sturmfels, (2005, ISBN 978-0-387-22356-8)
  • 228 A First Course in Modular Forms, Fred Diamond, J. Shurman, (2006, ISBN 978-0-387-23229-4)
  • 229 The Geometry of Syzygies, David Eisenbud (2005, ISBN 978-0-387-22215-8)
  • 230 An Introduction to Markov Processes, Stroock, D.W., (2005, ISBN 978-3-540-23499-9)
  • 231 Combinatorics of Coxeter Groups, Anders Björner, Francisco Brenti, (2005, ISBN 978-3-540-44238-7)
  • 232 An Introduction to Number Theory, Everest, G., Ward, T., (2005, ISBN 978-1-85233-917-3)
  • 233 Topics in Banach Space Theory, Albiac, F., Kalton, N.J., (2006, ISBN 978-0-387-28141-4)
  • 234 Analysis and Probability · Wavelets, Signals, Fractals, Jorgensen, P.E.T., (2006, ISBN 978-0-387-29519-0)
  • 235 Compact Lie Groups, M. R. Sepanski, (2007, ISBN 978-0-387-30263-8)
  • 236 Bounded Analytic Functions, Garnett, J., (2007, ISBN 978-0-387-33621-3)
  • 237 An Introduction to Operators on the Hardy-Hilbert Space, Martinez-Avendano, R.A., Rosenthal, P., (2007, ISBN 978-0-387-35418-7)
  • 238 A Course in Enumeration, Aigner, M., (2007, ISBN 978-3-540-39032-9)
  • 239 Number Theory - Volume I: Elementary and Algebraic Methods for Diophantine Equations, Cohen, H., (2007, ISBN 978-0-387-49922-2)
  • 240 Number Theory - Volume II: Analytic and Modern Tools, Cohen, H., (2007, ISBN 978-0-387-49893-5)
  • 241 (unknown)
  • 242 Abstract Algebra, Grillet, Pierre Antoine, (2007, ISBN 978-0-387-71567-4)
[edit]

Logic and Foundations

[edit]
  • Foundations of Mathematics [156]
  • Axiom Systems [035]
  • Paradoxes [319]
  • Symbolic Logic [411]
  • Axiomatic Set Theory [033]
  • Model Theory [276]
  • Nonstandard Analysis [293]
  • Gödel Numbers [185]
  • Recursive Functions [356]
  • Decision Problem [097]
  • Constructive Ordinal Numbers [081]
  • Analytic Sets [022]

Sets, General Topology, and Categories

[edit]
  • Sets [381]
  • Relations [358]
  • Equivalence Relations [135]
  • Functions [165]
  • Axiom of Choice and Equivalents [034]
  • Cardinal Numbers [049]
  • Structures [409]
  • Permutations and Combinations [330]
  • Numbers [294]
  • Real Numbers [355]
  • Complex Numbers [074]
  • Ordering [311]
  • Ordinal Numbers [312]
  • Lattices [243]
  • Boolean Algebras [042]
  • Topological Spaces [425]
  • Metric Spaces [273]
  • Plane Domains [333]
  • Convergence [087]
  • Connectedness [079]
  • Dimension Theory [117]
  • Uniform Spaces [436]
  • Uniform Convergence [435]
  • Categories and Functors [052]
  • Inductive Limits and Projective Limits [210]
  • Sheaves [383]

Algebra

[edit]
  • Algebra [008]
  • Matrices [269]
  • Determinants [103]
  • Polynomials [337]
  • Algebraic Equations [010]
  • Fields [149]
  • Galois Theory [172]
  • Linear Spaces [256]
  • Rings [368]
  • Associative Algebras [029]
  • Commutative Rings [067]
  • Noetherian Rings [284]
  • Rings of Polynomials [369]
  • Rings of Power Series [370]
  • Quadratic Forms [348]
  • Clifford Algebras [061]
  • Differential Rings [113]
  • Witt Vectors [449]
  • Valuations [439]
  • Adèles and Idèles [006]
  • Cayley Algebras [054]
  • Jordan Algebras [231]
  • Modules [277]
  • Homological Algebra [200]
  • Hopf Algebras [203]

Group Theory

[edit]
  • Groups [190]
  • Abelian Groups [002]
  • Free Groups [161]
  • Finite Groups [151]
  • Classical Groups [060]
  • Topological Groups [423]
  • Topological Abelian Groups [422]
  • Compact Groups [069]
  • Lie Groups [249]
  • Lie Algebras [248]
  • Algebraics Groups [013]
  • Homogeneous Spaces [199]
  • Symmetric Riemannian Spaces and Real Forms [412]
  • Discontinuous Groups [122]
  • Crystallographic Groups [092]
  • Representations [362]
  • Unitary Representations [437]
  • Invariants and Covariants [226]

Number Theory

[edit]
  • Number Theory [296]
  • Number Theory, Elementary [297]
  • Continued Fractions [083]
  • Number-Theoretic Functions [295]
  • Additive Number Theory [004]
  • Partitions of Numbers [328]
  • Distributions of Prime Numbers [123]
  • Lattice-Point Problems [242]
  • Diophantine Equations [118]
  • Geometry of Numbers [182]
  • Transcendental Numbers [430]
  • Quadratic Fields [347]
  • Algebraic Number Fields [014]
  • Class Field Theory [059]
  • Complex Multiplication [073]
  • Fermat's Problem [145]
  • Local Fields [257]
  • Arithmetic of Associative Algebras [027]
  • Zeta Functions [450]

Euclidean and Projective Geometry

[edit]
  • Geometry [181]
  • Foundations of Geometry [155]
  • Euclidean Geometry [139]
  • Euclidean Spaces [140]
  • Geometric Constructions [179]
  • Regular Polyhedra [357]
  • Pi [332]
  • Trigonometry [432]
  • Conic Sections [078]
  • Quadric Surfaces [350]
  • Convex Sets [089]
  • Vectors [442]
  • Coordinates [090]
  • Projective Geometry [343]
  • Affine Geometry [007]
  • Non-Euclidean Geometry [285]
  • Conformal Geometry [076]
  • Erlangen Program [137]
  • Continuous Geometry [085]
  • Curves [093]
  • Surfaces [410]
  • Four-Color Problem [157]

Differential Geometry

[edit]
  • Differential Geometry [109]
  • Differentiable Manifolds [105]
  • Riemannian Manifolds [364]
  • Connections [080]
  • Tensor Calculus [417]
  • Geodesics [178]
  • Symmetric Spaces [413]
  • G-structures [191]
  • Complex Manifolds [072]
  • Kähler Manifolds [232]
  • Harmonic Integrals [194]
  • Differential Geometry of Curves and Surfaces [111]
  • Riemannian Submanifolds [365]
  • Minimal Submanifolds [275]
  • Harmonic Mappings [195]
  • Morse Theory [279]
  • Differential Geometry in Specific Spaces [110]
  • Finsler Spaces [152]
  • Integral Geometry [218]
  • Siegel Domains [384]
  • Pseudoconformal Geometry [344]
  • Spectral Geometry [391]
  • Global Analysis [183]

Algebraic Geometry

[edit]
  • Algebraic Geometry [012]
  • Algebraic Curves [009]
  • Algebraic Surfaces [015]
  • Algebraic Varieties [016]
  • Abelian Varieties [003]
  • Riemann-Roch Theorems [366]

Topology

[edit]
  • Topology [426]
  • Fundamental Groups [170]
  • Covering Spaces [091]
  • Degree of Mapping [099]
  • Complexes [070]
  • Homology Theory [201]
  • Fixed-Point Theorems [153]
  • Cohomology Operations [064]
  • Homotopy Theory [202]
  • Fiber Spaces [148]
  • Obstructions [305]
  • Topology of Lie Groups and Homogeneous Spaces [427]
  • Fiber Bundles [147]
  • Characteristic Classes [056]
  • K-Theory [237]
  • Knot Theory [235]
  • Combinatorial Manifolds [065]
  • Differential Topology [114]
  • Transformation Groups [431]
  • Theory of Singularities [418]
  • Foliations [154]
  • Dynamical Systems [126]
  • Shape Theory [382]
  • Catastrophe Theory [051]

Analysis

[edit]
  • Analysis [020]
  • Continuous Functions [084]
  • Inequalities [211]
  • Convex Analysis [088]
  • Functions of Bounded Variations [166]
  • Differential Calculus [106]
  • Implicit Functions [208]
  • Elementary Functions [131]
  • -Functions and Quasi-Analytic Functions [058]
  • Integral Calculus [216]
  • Curvilinear Integrals and Surface Integrals [094]
  • Measure Theory [270]
  • Integration Theory [221]
  • Invariant Measures [225]
  • Set Functions [380]
  • Length and Area [246]
  • Denjoy Integrals [100]
  • Series [379]
  • Asymptotic Series [030]
  • Polynomial Approximation [336]
  • Orthogonal Functions [317]
  • Fourier Series [159]
  • Fourier Transform [160]
  • Harmonic Analysis [192]
  • Almost Periodic Functions [018]
  • Laplace Transform [240]
  • Integral Transforms [220]
  • Potential Theory [338]
  • Harmonic Functions and Subharmonic Functions [193]
  • Dirichlet Problem [120]
  • Capacity [048]
  • Calculus of Variations [046]
  • Plateau's Problem [334]
  • Isoperimetric Problems [228]
  • Variational Inequalities [440]

Complex Analysis

[edit]
  • Holomorphic Functions [198]
  • Power Series [339]
  • Dirichlet Series [121]
  • Bounded Functions [043]
  • Univalent and Multivalent Functions [438]
  • Transcendental Entire Functions [429]
  • Meromorphic Functions [272]
  • Distributions of Values of Functions of a Complex Variable [124]
  • Cluster Sets [062]
  • Algebraic Functions [011]
  • Algebroidal Functions [017]
  • Riemann Surfaces [367]
  • Ideal Boundaries [207]
  • Conformal Mappings [077]
  • Quasiconformal Mappings [352]
  • Teichmüller Spaces [416]
  • Kleinian Groups [234]
  • Extremal Length [143]
  • Function-Theoretic Null Sets [169]
  • Analytic Functions of Several Complex Variables [021]
  • Analytic Spaces [023]
  • Automorphic Functions [032]

Functional Analysis

[edit]
  • Functional Analysis [162]
  • Hilbert Spaces [197]
  • Banach Spaces [037]
  • Ordered Linear Spaces [310]
  • Topological Linear Spaces [424]
  • Function Spaces [168]
  • Distributions and Hyperfunctions [125]
  • Vector-Valued Integrals [443]
  • Linear Operators [251]
  • Compact and Nuclear Operators [068]
  • Interpolation of Operators [224]
  • Spectral Analysis of Operators [390]
  • Perturbation of Linear Operators [331]
  • Semigroups of Operators and Evolution Equations [378]
  • Differential Operators [112]
  • Microlocal Analysis [274]
  • Banach Algebras [036]
  • Function Algebras [164]
  • Operator Algebras [308]
  • Operational Calculus [306]
  • Nonlinear Functional Analysis [286]

Differential, Integral, and Functional Equations

[edit]
  • Differential Equations [107]
  • Ordinary Differential Equations [313]
  • Ordinary Differential Equations (Initial Value Problems) [316]
  • Ordinary Differential Equations (Boundary Value Problems) [315]
  • Ordinary Differential Equations (Asymptotic Behaviour of Solutions) [315]
  • Linear Ordinary Differential Equations [252]
  • Linear Ordinary Differential Equations (Local Theory) [254]
  • Linear Ordinary Differential Equations (Global Theory) [253]
  • Nonlinear Ordinary Differential Equations (Local Theory) [289]
  • Nonlinear Ordinary Differential Equations (Global Theory) [288]
  • Nonlinear Oscillation [290]
  • Nonlinear Problems [291]
  • Stability [394]
  • Integral Invariants [219]
  • Difference Equations [104]
  • Functional-Differential Equations [163]
  • Total Differential Equations [428]
  • Contact Transformations [082]
  • Partial Differential Equations [320]
  • Partial Differential Equations (Methods of Integrations) [322]
  • Partial Differential Equations (Initial Value Problems) [321]
  • Partial Differential Equations of First Order [324]
  • Monge-Ampère Equations [278]
  • Partial Differential Equations of Elliptic Type [323]
  • Partial Differential Equations of Hyperbolic Type [325]
  • Partial Differential Equations of Parabolic Type [327]
  • Partial Differential Equations of Mixed Type [326]
  • Green's Functions [188]
  • Green's Operators [189]
  • Integral Equations [217]
  • Integrodifferential Equations [222]
  • Special Functional Equations [388]
  • Pseudodifferential Operators [345]

Special Functions

[edit]
  • Special Functions [389]
  • Generating Functions [177]
  • Elliptic Functions [134]
  • Gamma Function [174]
  • Hypergeometric Functions [206]
  • Spherical Functions [393]
  • Functions of Confluent Type [167]
  • Bessel Functions [039]
  • Ellipsoidal Harmonics [133]
  • Mathieu Functions [268]

Numerical Analysis

[edit]
  • Numerical Methods [300]
  • Interpolations [223]
  • Error Analysis [138]
  • Numerical Solutions of Linear Equations [302]
  • Numerical Solutions of Algebraic Equations [301]
  • Numerical Computations of Eigenvalues [298]
  • Numerical Integration [299]
  • Numerical Solutions of Ordinary Differential Equations [303]
  • Numerical Solutions of Partial Differential Equations [304]
  • Analog Computation [019]
  • Evaluation of Functions [142]

Computer Science and Combinatorics

[edit]
  • Automata [031]
  • Computers [075]
  • Coding Theory [063]
  • Cybernetics [095]
  • Random Numbers [354]
  • Simulations [385]
  • Data Processing [096]
  • Mathematical Models in Biology [263]
  • Complexity of Computations [071]
  • Combinatorics [066]
  • Latin Squares [241]
  • Graph Theory [186]

Probability Theory

[edit]
  • Probability Theory [342]
  • Probability Measures [341]
  • Limit Theorems in Probability Theory [250]
  • Stochastic Processes [407]
  • Markov Processes [261]
  • Markov Chains [260]
  • Brownian Motion [045]
  • Diffusion Processes [115]
  • Additive Processes [005]
  • Branching Processes [044]
  • Martingales [262]
  • Stationary Processes [395]
  • Gaussian Processes [176]
  • Stochastic Differential Equations [406]
  • Ergodic Theory [136]
  • Stochastic Control and Stochastic Filtering [405]
  • Probabilistic Methods in Statistical Mechanics [340]

Statistics

[edit]
  • Statistical Data Analysis [397]
  • Statistical Inference [401]
  • Statistic [396]
  • Sampling Distributions [374]
  • Statistical Models [403]
  • Statistical Decision Functions [398]
  • Statistical Estimation [399]
  • Statistical Hypothesis Testing [400]
  • Multivariable Analysis [280]
  • Robust and Nonparametric Methods [371]
  • Time Series Analysis [421]
  • Design of Experiments [102]
  • Sample Survey [373]
  • Statistical Quality Control [404]
  • Econometrics [128]
  • Biometrics [040]
  • Psychometrics [346]
  • Insurance Mathematics [214]

Mathematical Programming and Operations Research

[edit]
  • Mathematical Programming [264]
  • Linear Programming [255]
  • Quadratic Programming [349]
  • Nonlinear Programming [292]
  • Network Flow Problems [281]
  • Integer Programming [215]
  • Stochastic Programming [408]
  • Dynamic Programming [127]
  • Game Theory [173]
  • Differential Games [108]
  • Control Theory [086]
  • Information Theory [213]
  • Operations Research [307]
  • Inventory Control [227]
  • Scheduling and Production Planning [376]

Mechanics and Theoretical Physics

[edit]
  • Systems of Units [414]
  • Dimensional Analysis [116]
  • Variational Principles [441]
  • Mechanics [271]
  • Spherical Astronomy [392]
  • Celestial Mechanics [055]
  • Orbit Determination [309]
  • Three-Body Problem [420]
  • Hydrodynamics [205]
  • Hydrodynamical Equations [204]
  • Magnetohydrodynamics [259]
  • Turbulence and Chaos [433]
  • Wave Propagation [446]
  • Oscillations [318]
  • Geometric Optics [180]
  • Electromagnetism [130]
  • Networks [282]
  • Thermodynamics [419]
  • Statistical Mechanics [402]
  • Boltzman Equation [041]
  • Relativity [359]
  • Unified Field Theory [434]
  • Quantum Mechanics [351]
  • Lorentz Group [258]
  • Racah Algebra [353]
  • Scattering Theory [375]
  • Second Quantization [377]
  • Field Theory [150]
  • S-Matrices [386]
  • Feynman Integrals [146]
  • Elementary Particles [132]
  • Renormalization Group [361]
  • Nonlinear Lattice Dynamics [287]
  • Solitons [387]
  • Approximation Methods in Physics [025]
  • Inequalities in Physics [212]

History of Mathematics

[edit]
  • Ancient Mathematics [024]
  • Greek Mathematics [187]
  • Roman and Medieval Mathematics [372]
  • Arab Mathematics [026]
  • Indian Mathematics [209]
  • Chinese Mathematics [057]
  • Japanese Mathematics (Wasan) [230]
  • Renaissance Mathematics [360]
  • Mathematics in the 17th Century [265]
  • Mathematics in the 18th Century [266]
  • Mathematics in the 19th Century [267]
  • Abel, Niels Henrik [001]
  • Artin, Emil [028]
  • Bernoulli Family [038]
  • Cantor, Georg [047]
  • Cartan, Élie [050]
  • Cauchy, Augustin Louis [053]
  • Dedekind, Julius Wilhelm Richard [098]
  • Descartes, René [101]
  • Dirichlet, Peter Gustav Lejeune [119]
  • Einstein, Albert [129]
  • Euler, Leonhard [141]
  • Fermat, Pierre de [144]
  • Fourier, Jean Baptiste Joseph [158]
  • Galois, Évariste [171]
  • Gauss, Carl Friedrich [175]
  • Gödel, Kurt [184]
  • Hilbert, David [196]
  • Jacobi, Carl Gustav Jacob [229]
  • Klein, Felix [233]
  • Kronecker, Leopold [236]
  • Lagrange, Joseph Louis [238]
  • Laplace, Pierre Simon [239]
  • Lebesgue, Henri Leon [244]
  • Leibniz, Gottfried Wilhelm [245]
  • Lie, Marius Sophus [247]
  • Newton, Isaac [283]
  • Pascal, Blaise [329]
  • Poincaré, Henri [335]
  • Riemann, Georg Friedrich Bernhard [363]
  • Takagi, Teiji [415]
  • Viète, François [444]
  • Von Neumann, John [445]
  • Weierstrass, Karl [447]
  • Weyl, Hermann [448]

Appendices

[edit]
  • 03: Algebraic Equations, App. A-1
  • 04: Characters of Finite Groups and Crystallographic Groups, App. B-5
  • 04: Lie Algebras, Symmetric Riemannian Spaces, and Singularities, App. A-5
  • 05: Class Numbers of Algebraic Number Fields, App. B-4
  • 05: Indices Modulo p, App. B-2
  • 05: Prime Numbers and Primitive Roots, App. B-1
  • 06: Trigonometry, App. A-2
  • 06: Vector Analysis and Coordinate Systems, App. A-3
  • 07: Differential Geometry, App. A-4
  • 09: Knot Theory, App. A-7
  • 09: Lie Algebras, Symmetric Riemannian Spaces, and Singularities, App. A-5
  • 09: Topology, App. A-6
  • 10: Differential and Integral Calculus, App. A-9
  • 10: Fourier Analysis, App. A-11
  • 10: Inequalities, App. A-8
  • 10: Laplace Transforms and Operational Calculus, App. A-12
  • 10: Series, App. A-10
  • 10: Systems of Orthogonal Functions, App. A-20
  • 11: Conformal Mappings, App. A-13
  • 13: Ordinary Differential Equations, App. A-14
  • 13: Total and Partial Differential Equations, App. A-15
  • 14: Bernoulli Numbers and Euler Numbers, App. B-3
  • 14: Elliptic Integrals and Elliptic Functions, App. A-16
  • 14: Functions of Confluent Type and Bessel Functions, App. A-19
  • 14: Gamma Function and Related Functions, App. A-17
  • 14: Hypergeometric Functions and Spherical Functions, App. A-18
  • 15: Interpolation, App. A-21
  • 15: Miscellaneous Constants, App. B-6
  • 18: Distribution of Typical Random Variables, App. A-22
  • 18: Statistical Estimation and Statistical Hypothesis Testing, App. A-23