Graduate Texts in Mathematics

Graduate Texts in Mathematics   は、Springer-Verlag により出版されている数学の graduate-levelのテキストのシリーズである。

1. 概要
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いくつかは和訳され丸善出版より出版されている。このシリーズの本は、 Springer-Verlag の他の数学のシリーズと同様、標準的なサイズの黄色い本である。GTM シリーズは本の上部が白くなっており容易に識別できる。

このシリーズの本は類似の Undergraduate Texts in Mathematics  シリーズよりも進んだ内容が書かれる傾向にあるが、この2つのシリーズは内容や難易度についてかなりかぶる部分もあり、GTMは一概に大学院生向けとは言えない側面もある。大学院を目指す人向けの内容でもありうる。

2. 一覧
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//Introduction to Axiomatic Set Theory//, Gaisi Takeuti, Wilson M. Zaring 
//Measure and Category   - A Survey of the Analogies between Topological and Measure Spaces//, John C. Oxtoby 
//Topological Vector Spaces//, H. H. Schaefer, M. P. Wolff 
//A Course in Homological Algebra//, Peter Hilton, Urs Stammbach 
//Categories for the Working Mathematician//, Saunders Mac Lane 
//Projective Planes//, Daniel R. Hughes, Fred C. Piper, 
//A Course in Arithmetic//, Jean-Pierre Serre 
//Axiomatic Set Theory//, Gaisi Takeuti, Wilson M. Zaring, 
//Introduction to Lie Algebras and Representation Theory//, James E. Humphreys 
//A Course in Simple-Homotopy Theory//, Marshall. M. Cohen, 
//Functions of One Complex Variable I//, John B. Conway 
//Advanced Mathematical Analysis//, Richard Beals 
//Rings and Categories of Modules//, Frank W. Anderson, Kent R. Fuller 
//Stable Mappings and Their Singularities//, Martin Golubitsky, Victor Guillemin, 
//Lectures in Functional Analysis and Operator Theory//, Sterling K. Berberian, 
//The Structure of Fields//, David J. Winter, 
//Random Processes//, Murray Rosenblatt, 
//Measure Theory//, Paul R. Halmos 
//A Hilbert Space Problem Book//, Paul R. Halmos 
//Fibre Bundles//, Dale Husemoller 
//Linear Algebraic Groups//, James E. Humphreys 
//An Algebraic Introduction to Mathematical Logic//, Donald W. Barnes, John M. Mack 
//Linear Algebra//, Werner H. Greub 
//Geometric Functional Analysis and Its Applications//, Richard B. Holmes, 
//Real and Abstract Analysis//, Edwin Hewitt, Karl Stromberg 
//Algebraic Theories//, Ernest G. Manes, 
//General Topology//, John L. Kelley 
//Commutative Algebra I//, Oscar Zariski, Pierre Samuel 
//Commutative Algebra II//, Oscar Zariski, Pierre Samuel 
//Lectures in Abstract Algebra I: Basic Concepts//, Nathan Jacobson 
//Lectures in Abstract Algebra II: Linear Algebra//, Nathan Jacobson 
//Lectures in Abstract Algebra III: Theory of Fields and Galois Theory//, Nathan Jacobson 
//Differential Topology//, Morris W. Hirsch 
//Principles of Random Walk//, Frank Spitzer 
//Several Complex Variables and Banach Algebras//, Herbert Alexander, John Wermer 
//Linear Topological Spaces//, John L. Kelley, Isaac Namioka 
//Mathematical Logic//, J. Donald Monk 
//Several Complex Variables//, H. Grauert, K. Fritzsche 
//An Invitation to -Algebras//, William Arveson 
//Denumerable Markov Chains//, John G. Kemeny, J. Laurie Snell, Anthony W. Knapp, D.S. Griffeath 
//Modular Functions and Dirichlet Series in Number Theory//, Tom M. Apostol 
//Linear Representations of Finite Groups//, Jean-Pierre Serre, Leonhard L. Scott 
//Rings of Continuous Functions//, Leonard Gillman, Meyer Jerison 
//Elementary Algebraic Geometry//, Keith Kendig 
//Probability Theory I//, M. Loève 
//Probability Theory II//, M. Loève 
//Geometric Topology in Dimensions 2 and 3//, Edwin E. Moise 
//General Relativity for Mathematicians//, R. K. Sachs, H. Wu 
//Linear Geometry//, K. W. Gruenberg, A. J. Weir 
//Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory//, Harold M. Edwards 
//A Course in Differential Geometry//, William Klingenberg, D. Hoffman 
//Algebraic Geometry//, Robin Hartshorne 
//A Course in Mathematical Logic for Mathematicians//, Yu. I. Manin, Boris Zilber 
//Combinatorics with Emphasis on the Theory of Graphs//, Mark E. Watkins, Jack E. Graver 
//Introduction to Operator Theory I: Elements of Functional Analysis//, Arlen Brown, Carl Pearcy 
//Algebraic Topology: An Introduction//, William S. Massey 
//Introduction to Knot Theory//, Richard H. Crowell, Ralph H. Fox 
//p-adic Numbers, p-adic Analysis, and Zeta-Functions//, Neal Koblitz 
//Cyclotomic Fields//, Serge Lang 
//Mathematical Methods of Classical Mechanics//, V. I. Arnold, A. Weinstein, K. Vogtmann 
//Elements of Homotopy Theory//, George W. Whitehead 
//Fundamentals of the Theory of Groups//, M. I. Kargapolov, J. I. Merzljakov 
//Graph Theory   - An Introductory Course//, Béla Bollobás 
//Fourier Series   - A Modern Introduction Volume 1//, R. E. Edwards 
//Differential Analysis on Complex Manifolds//, Raymond O. Wells, Jr. 
//Introduction to Affine Group Schemes//, W. C. Waterhouse 
//Local Fields//, Jean-Pierre Serre 
//Linear Operators in Hilbert Spaces//, Joachim Weidmann 
//Cyclotomic Fields II//, Serge Lang 
//Singular Homology Theory//, William S. Massey 
//Riemann Surfaces//, Herschel Farkas, Irwin Kra 
//Classical Topology and Combinatorial Group Theory//, John Stillwell 
//Algebra//, Thomas W. Hungerford 
//Multiplicative Number Theory//, Harold Davenport, Hugh Montgomery 
//Basic Theory of Algebraic Groups and Lie Algebras//, G. P. Hochschild 
//Algebraic Geometry   - An Introduction to Birational Geometry of Algebraic Varieties//, Shigeru Iitaka 
//Lectures on the Theory of Algebraic Numbers//, E. T. Hecke 
//A Course in Universal Algebra//, Burris, Stanley and Sankappanavar, H. P.  
//An Introduction to Ergodic Theory//, Peter Walters 
//A Course in the Theory of Groups//, Derek J.S. Robinson 
//Lectures on Riemann Surfaces//, Otto Forster 
//Differential Forms in Algebraic Topology//, Raoul Bott, Loring W. Tu 
//Introduction to Cyclotomic Fields//, Lawrence C. Washington 
//A Classical Introduction to Modern Number Theory//, Kenneth Ireland, Michael Rosen 
//Fourier Series   - A Modern Introduction Volume 2//, R. E. Edwards 
//Introduction to Coding Theory//, J. H. van Lint 
//Cohomology of Groups//, Kenneth S. Brown 
//Associative Algebras//, R. S. Pierce 
//Introduction to Algebraic and Abelian Functions//, Serge Lang 
//An Introduction to Convex Polytopes//, Arne Brondsted 
//The Geometry of Discrete Groups//, Alan F. Beardon 
//Sequences and Series in Banach Spaces//, J. Diestel 
//Modern Geometry   — Methods and Applications Part I: The Geometry of Surfaces, Transformation Groups, and Fields//, B. A. Dubrovin, Anatoly Timofeevich Fomenko, Sergei Novikov 
//Foundations of Differentiable Manifolds and Lie Groups//, Frank W. Warner  
//Probability-1//, Albert N. Shiryaev 
//A Course in Functional Analysis//, John B. Conway 
//Introduction to Elliptic Curves and Modular Forms//, Neal I. Koblitz 
//Representations of Compact Lie Groups//, Theodor Bröcker, Tammo tom Dieck 
//Finite Reflection Groups//, L.C. Grove, C.T. Benson 
//Harmonic Analysis on Semigroups   - Theory of Positive Definite and Related Functions//, Christian Berg, Jens Peter Reus Christensen, Paul Ressel 
//Galois Theory//, Harold M. Edwards 
//Lie Groups, Lie Algebras, and Their Representations//, V. S. Varadarajan 
//Complex Analysis//, Serge Lang 
//Modern Geometry   — Methods and Applications Part II: The Geometry and Topology of Manifolds//, B. A. Dubrovin, Anatoly Timofeevich Fomenko, Sergei Novikov 
//SL//2, Serge Lang 
//The Arithmetic of Elliptic Curves//, Joseph H. Silverman 
//Applications of Lie Groups to Differential Equations//, Peter J. Olver 
//Holomorphic Functions and Integral Representations in Several Complex Variables//, R. Michael Range 
//Univalent Functions and Teichmüller Spaces//, O. Lehto 
//Algebraic Number Theory//, Serge Lang 
//Elliptic Curves//, Dale Husemöller 
//Elliptic Functions//, Serge Lang 
//Brownian Motion and Stochastic Calculus//, Ioannis Karatzas, Steven Shreve 
//A Course in Number Theory and Cryptography//, Neal Koblitz 
//Differential Geometry: Manifolds, Curves and Surfaces//, Marcel Berger, Bernard Gostiaux 
//Measure and Integral   — Volume 1//, John L. Kelley, T.P. Srinivasan 
//Algebraic Groups and Class Fields//, Jean-Pierre Serre 
//Analysis Now//, Gert K. Pedersen 
//An Introduction to Algebraic Topology//, Joseph J. Rotman, 
//Weakly Differentiable Functions   — Sobolev Spaces and Functions of Bounded Variation//, William P. Ziemer 
//Cyclotomic Fields I and II//, Serge Lang 
//Theory of Complex Functions//, Reinhold Remmert 
//Numbers//, Heinz-Dieter Ebbinghaus //et al.// 
//Modern Geometry   — Methods and Applications Part III: Introduction to Homology Theory//, B. A. Dubrovin, Anatoly Timofeevich Fomenko, Sergei Novikov 
//Complex Variables   — An Introduction//, Carlos A. Berenstein, Roger Gay 
//Linear Algebraic Groups//, Armand Borel 
//A Basic Course in Algebraic Topology//, William S. Massey 
//Partial Differential Equations//, Jeffrey Rauch 
//Representation Theory//, William Fulton, Joe Harris 
//Tensor Geometry   — The Geometric Viewpoint and its Uses//, Christopher T. J. Dodson, Timothy Poston 
//A First Course in Noncommutative Rings//, T. Y. Lam 
//Iteration of Rational Functions   — Complex Analytic Dynamical Systems//, Alan F. Beardon 
//Algebraic Geometry//, Joe Harris 
//Coding and Information Theory//, Steven Roman 
//Advanced Linear Algebra//, Steven Roman 
//Algebra   — An Approach via Module Theory//, William Adkins, Steven Weintraub 
//Harmonic Function Theory//, Sheldon Axler, Paul Bourdon, Wade Ramey 
//A Course in Computational Algebraic Number Theory//, Henri Cohen 
//Topology and Geometry//, Glen E. Bredon 
//Optima and Equilibria//, Jean-Pierre Aubin 
//Gröbner Bases   — A Computational Approach to Commutative Algebra//, Thomas Becker, Volker Weispfenning 
//Real and Functional Analysis//, Serge Lang 
//Measure Theory//, J. L. Doob 
//Noncommutative Algebra//, Benson Farb, R. Keith Dennis 
//Homology Theory   — An Introduction to Algebraic Topology//, James W. Vick 
//Computability   — A Mathematical Sketchbook//, Douglas S. Bridges 
//Algebraic K-Theory and Its Applications//, Jonathan Rosenberg 
//An Introduction to the Theory of Groups//, Joseph J. Rotman 
//Foundations of Hyperbolic Manifolds//, John G. Ratcliffe 
//Commutative Algebra   — with a View Toward Algebraic Geometry//, David Eisenbud 
//Advanced Topics in the Arithmetic of Elliptic Curves//, Joseph H. Silverman 
//Lectures on Polytopes//, Günter M. Ziegler 
//Algebraic Topology   — A First Course//, William Fulton 
//An Introduction to Analysis//, Arlen Brown, Carl Pearcy 
//Quantum Groups//, Christian Kassel 
//Classical Descriptive Set Theory//, Alexander S. Kechris 
//Integration and Probability//, Paul Malliavin 
//Field Theory//, Steven Roman 
//Functions of One Complex Variable II//, John B. Conway 
//Differential and Riemannian Manifolds//, Serge Lang 
//Polynomials and Polynomial Inequalities//, Peter Borwein, Tamas Erdelyi 
//Groups and Representations//, J. L. Alperin, Rowen B. Bell 
//Permutation Groups//, John D. Dixon, Brian Mortimer 
//Additive Number Theory The Classical Bases//, Melvyn B. Nathanson 
//Additive Number Theory: Inverse Problems and the Geometry of Sumsets//, Melvyn B. Nathanson 
//Differential Geometry   — Cartan's Generalization of Klein's Erlangen Program//, R. W. Sharpe 
//Field and Galois Theory//, Patrick Morandi 
//Combinatorial Convexity and Algebraic Geometry//, Guenter Ewald 
//Matrix Analysis//, Rajendra Bhatia 
//Sheaf Theory//, Glen E. Bredon 
//Riemannian Geometry//, Peter Petersen 
//Classical Topics in Complex Function Theory//, Reinhold Remmert 
//Graph Theory//, Reinhard Diestel 
//Foundations of Real and Abstract Analysis//, Douglas S. Bridges 
//An Introduction to Knot Theory//, W. B. Raymond Lickorish 
//Introduction to Riemannian Manifolds//, John M. Lee 
//Analytic Number Theory //, Donald J. Newman 
//Nonsmooth Analysis and Control Theory//, Francis H. Clarke, Yuri S. Ledyaev, Ronald J. Stern, Peter R. Wolenski 
//Banach Algebra Techniques in Operator Theory//, Ronald G. Douglas 
//A Course on Borel Sets//, S. M. Srivastava 
//Numerical Analysis//, Rainer Kress 
//Ordinary Differential Equations//, Wolfgang Walter 
//An Introduction to Banach Space Theory//, Robert E. Megginson 
//Modern Graph Theory//, Béla Bollobás 
//Using Algebraic Geometry//, David A. Cox, John Little, Donal O'Shea 
//Fourier Analysis on Number Fields//, Dinakar Ramakrishnan, Robert J. Valenza 
//Moduli of Curves//, Joe Harris, Ian Morrison 
//Lectures on the Hyperreals//, Robert Goldblatt 
//Lectures on Modules and Rings//, Tsit-Yuen Lam 
//Problems in Algebraic Number Theory//, M. Ram Murty, Jody Indigo Esmonde 
//Fundamentals of Differential Geometry//, Serge Lang 
//Elements of Functional Analysis//, Francis Hirsch, Gilles Lacombe 
//Advanced Topics in Computational Number Theory//, Henri Cohen 
//One-Parameter Semigroups for Linear Evolution Equations//, Engel, Nagel 
//Elementary Methods in Number Theory//, Melvyn B. Nathanson 
//Basic Homological Algebra//, M. Scott Osborne 
//The Geometry of Schemes//, Eisenbud, Joe Harris 
//A Course in p-adic Analysis//, Alain M. Robert 
//Theory of Bergman Spaces//, Hakan Hedenmalm, Boris Korenblum, Kehe Zhu 
//An Introduction to Riemann-Finsler Geometry//, David Bao, Shiing-Shen Chern, Zhongmin Shen 
//Diophantine Geometry//, Marc Hindry, Joseph H. Silverman 
//Introduction to Topological Manifolds//, John M. Lee 
//The Symmetric Group   — Representations, Combinatorial Algorithms, and Symmetric Functions//, Bruce E. Sagan 
//Galois Theory//, Jean-Pierre Escofier 
//Rational Homotopy Theory//, Yves Félix, Stephen Halperin, Jean-Claude Thomas 
//Problems in Analytic Number Theory//, M. Ram Murty 
//Algebraic Graph Theory//, Chris Godsil, Gordon Royle 
//Analysis for Applied Mathematics//, Ward Cheney 
//A Short Course on Spectral Theory//, William Arveson 
//Number Theory in Function Fields//, Michael Rosen 
//Algebra//, Serge Lang 
//Lectures on Discrete Geometry//, Jiří Matoušek 
//From Holomorphic Functions to Complex Manifolds//, Klaus Fritzsche, Hans Grauert 
//Partial Differential Equations//, Jürgen Jost, 
//Algebraic Functions and Projective Curves//, David M. Goldschmidt, 
//Matrices   — Theory and Applications//, Denis Serre, 
//Model Theory: An Introduction//, David Marker, 
//Introduction to Smooth Manifolds//, John M. Lee 
//The Arithmetic of Hyperbolic 3-Manifolds//, Colin Maclachlan, Alan W. Reid, 
//Smooth Manifolds and Observables//, Jet Nestruev, 
//Convex Polytopes//, Branko Grünbaum 
//Lie Groups, Lie Algebras, and Representations   - An Elementary Introduction//, Brian C. Hall, 
//Fourier Analysis and its Applications//, Anders Vretblad, 
//Metric Structures in Differential Geometry//, Walschap, G., 
//Lie Groups//, Daniel Bump, 
//Spaces of Holomorphic Functions in the Unit Ball//, Kehe Zhu, 
//Combinatorial Commutative Algebra//, Ezra Miller, Bernd Sturmfels, 
//A First Course in Modular Forms//, Fred Diamond, J. Shurman, 
//The Geometry of Syzygies//, David Eisenbud 
//An Introduction to Markov Processes//, Daniel W. Stroock, 
//Combinatorics of Coxeter Groups//, Anders Björner, Francisco Brenti, 
//An Introduction to Number Theory//, Everest, Graham., Ward, T., 
//Topics in Banach Space Theory//, Albiac, F., Kalton, N. J., 
//Analysis and Probability   — Wavelets, Signals, Fractals//, Jorgensen, P. E. T., 
//Compact Lie Groups//, M. R. Sepanski, 
//Bounded Analytic Functions//, Garnett, J., 
//An Introduction to Operators on the Hardy-Hilbert Space//, Ruben A. Martinez-Avendano, Peter Rosenthal, 
//A Course in Enumeration//, Aigner, M., 
//Number Theory   — Volume I: Tools and Diophantine Equations//, Cohen, H., 
//Number Theory   — Volume II: Analytic and Modern Tools//, Cohen, H., 
//The Arithmetic of Dynamical Systems//, Joseph H. Silverman, 
//Abstract Algebra//, Grillet, Pierre Antoine, 
//Topological Methods in Group Theory//, Geoghegan, Ross, 
//Graph Theory//, Adrian Bondy, U.S.R. Murty, 
//Complex Analysis: Introduced in the Spirit of Lipman Bers//, Gilman, Jane P., Kra, Irwin, Rodriguez, Rubi E. 
//A Course in Commutative Banach Algebras//, Kaniuth, Eberhard, 
//Braid Groups//, Kassel, Christian, Turaev, Vladimir, 
//Buildings Theory and Applications//, Abramenko, Peter, Brown, Ken 
//Classical Fourier Analysis//, Loukas Grafakos 
//Modern Fourier Analysis//, Loukas Grafakos 
//The Finite Simple Groups//, Robert A. Wilson 
//Distributions and Operators//, Gerd Grubb, 
//Elementary Functional Analysis//, MacCluer, Barbara D., 
//Algebraic Function Fields and Codes//, Henning Stichtenoth, 
//Symmetry, Representations, and Invariants//, Goodman, Roe, Wallach, Nolan R., 
//A Course in Commutative Algebra//, Kemper, Gregor, 
//Deformation Theory//, Robin Hartshorne, 
//Foundations of Optimization in Finite Dimensions//, Osman Guler, 
//Ergodic Theory   - with a view towards Number Theory//, Thomas Ward, Manfred Einsiedler, 
//Monomial Ideals//, Jürgen Herzog, Hibi Takayuki
//Probability and Stochastics//, Erhan Cinlar, 
//Essentials of Integration Theory for Analysis//, Daniel W. Stroock, 
//Analysis on Fock Spaces//, Kehe Zhu, 
//Functional Analysis, Calculus of Variations and Optimal Control//, Francis H. Clarke, 
//Unbounded Self-adjoint Operators on Hilbert Space//, Konrad Schmüdgen, 
//Calculus Without Derivatives//, Jean-Paul Penot, 
//Quantum Theory for Mathematicians//, Brian C. Hall, 
//Geometric Analysis of the Bergman Kernel and Metric//, Krantz, Steven G., 
//Locally Convex Spaces//, M Scott Osborne, 
//Fundamentals of Algebraic Topology//, Steven Weintraub, 
//Integer Programming//, Michelangelo Conforti, Gérard P. Cornuéjols, Giacomo Zambelli, 
//Operator Theoretic Aspects of Ergodic Theory//, Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel, 
//Homotopical Topology//, Anatoly Fomenko, Dmitry Fuchs, 
//Brownian Motion, Martingales, and Stochastic Calculus//, Jean-François Le Gall, 
//Differential Geometry   - Connections, Curvature, and Characteristic Classes//, Loring W. Tu 
//Functional Analysis, Spectral Theory, and Applications//, Manfred Einsiedler, Thomas Ward 
//The Moment Problem//, Konrad Schmüdgen 
//Modern Real Analysis//, William P. Ziemer 
//Binomial Ideals//, Jürgen Herzog, Takayuki Hibi, Hidefumi Ohsugi 
//Introduction to Real Analysis//, Christopher Heil 
//Intersection Homology & Perverse Sheaves with Applications to Singularities//, Laurenţiu G. Maxim 
//Measure, Integration & Real Analysis//, Sheldon Axler 
//Basic Representation Theory of Algebras, Ibrahim Assem//, Flávio U Coelho 
//Spectral Theory - Basic Concepts and Applications//, David Borthwick 
//An Invitation to Unbounded Representations of Algebras on Hilbert Space//, Konrad Schmüdgen 
//Lectures on Convex Geometry, Daniel Hug//, Wolfgang Weilt 
//Explorations in Complex Functions//, Richard Beals, Roderick S. C. Wong 
//Quaternion Algebras//, John Voight 
//Ergodic Dynamics - From Basic Theory to Applications//, Jane M. Hawkins 
//Lessons in Enumerative Combinatorics//, Omer Egecioglu , Adriano Garsia 
//Mathematical Logic//, Heinz-Dieter Ebbinghaus, Jörg Flum, Wolfgang Thomas 
//Random Walk, Brownian Motion and Martingales//, Rabi Bhattacharya, Edward C. Waymire 
//Quaternion Algebras//
//Stationary Processes and Discrete Parameter Markov Processes//
//Measure Theory, Probability, and Stochastic Processes//
//Partial Differential Equations//
//Drinfeld Modules//

3. 脚注
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3.1. 注釈
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3.2. 出典
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4. 外部リンク
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