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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)
Links
[edit]- Springer-Verlag's Summary of Graduate Texts in Mathematics
- The Springer GTM test - An online quiz
- Undergraduate Texts in Mathematics
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