數學研究生教材

數學研究生教材（，簡稱GTM）是由施普林格出版的一系統研究所程度之數學教科書。這一系列的書與施普林格其他數學系列的書一樣，都是具相同尺寸（但有不同頁數）的黃色封面書籍。GTM系列的書在封面上端都會有一段白底黃字的字樣，標示著「Graduate Texts in Mathematics」。

這一系列的書會偏向於寫成較性質相似的數學大學生教材（）系列還要困難，雖然這兩個系列有許多部分重疊，不論是在其所涉及之材料，或是在其難易程度。

书目列表

Introduction to Axiomatic Set Theory, Gaisi Takeuti, Wilson M. Zaring (1982, 2nd ed., )
Measure and Category - A Survey of the Analogies between Topological and Measure Spaces, John C. Oxtoby (1980, 2nd ed., )
Topological Vector Spaces, H. H. Schaefer, M. P. Wolff (1999, 2nd ed., )
A Course in Homological Algebra, Peter Hilton, Urs Stammbach (1997, 2nd ed., )
Categories for the Working Mathematician, Saunders Mac Lane (1998, 2nd ed., )
Projective Planes, Daniel R. Hughes, Fred C. Piper, (1982, )
A Course in Arithmetic, Jean-Pierre Serre (1996, )
Axiomatic Set Theory, Gaisi Takeuti, Wilson M. Zaring, (1973, )
Introduction to Lie Algebras and Representation Theory, James E. Humphreys (1997, )
A Course in Simple-Homotopy Theory, Marshall. M. Cohen, (1973, )
Functions of One Complex Variable I, John B. Conway (1978, 2nd ed., )
Advanced Mathematical Analysis, Richard Beals  (1973, )
Rings and Categories of Modules, Frank W. Anderson, Kent R. Fuller  (1992, 2nd ed., )
Stable Mappings and Their Singularities, Martin Golubitsky, Victor Guillemin, (1974, )
Lectures in Functional Analysis and Operator Theory, Sterling K. Berberian, (1974, )
The Structure of Fields, David J. Winter, (1974, )
Random Processes, Murray Rosenblatt, (1974, )
Measure Theory, Paul R. Halmos (1974, )
A Hilbert Space Problem Book, Paul R. Halmos (1982, 2nd ed., )
Fibre Bundles, Dale Husemoller (1994, 3rd ed., )
Linear Algebraic Groups, James E. Humphreys  (1998, )
An Algebraic Introduction to Mathematical Logic, Donald W. Barnes, John M. Mack (1975, )
Linear Algebra, Werner H. Greub (1981, )
Geometric Functional Analysis and Its Applications, Richard B. Holmes, (1975, )
Real and Abstract Analysis, Edwin Hewitt, Karl Stromberg (1975, )
Algebraic Theories, Ernest G. Manes, (1976, )
General Topology, John L. Kelley (1975, )
Commutative Algebra I, Oscar Zariski, Pierre Samuel, Cohen (1975, )
Commutative Algebra II, Oscar Zariski, Pierre Samuel (1975, )
Lectures in Abstract Algebra I: Basic Concepts, Nathan Jacobson (1976, )
Lectures in Abstract Algebra II: Linear Algebra, Nathan Jacobson (1984, )
Lectures in Abstract Algebra III: Theory of Fields and Galois Theory, Nathan Jacobson (1976, )
Differential Topology, Morris W. Hirsch (1976, )
Principles of Random Walk, Frank Spitzer (2001, )
Several Complex Variables and Banach Algebras, Herbert Alexander, John Wermer (1998, 3rd ed., )
Linear Topological Spaces, John L. Kelley, Isaac Namioka (1982, )
Mathematical Logic, J. Donald Monk (1976, )
Several Complex Variables, H. Grauert, K. Fritzsche (1976, )
An Invitation to -Algebras, William Arveson (1976, )
Denumerable Markov Chains, John G. Kemeny, J. Laurie Snell, Anthony W. Knapp, D.S. Griffeath (1976, )
Modular Functions and Dirichlet Series in Number Theory, Tom M. Apostol (1989, 2nd ed., )
Linear Representations of Finite Groups, Jean-Pierre Serre, Leonhard L. Scott (1977, )
Rings of Continuous Functions, Leonard Gillman, Meyer Jerison (1976, )
Elementary Algebraic Geometry, Keith Kendig (1977, )
Probability Theory I, M. Loève (1977, 4th ed, )
Probability Theory II, M. Loève (1978, 4th ed, )
Geometric Topology in Dimensions 2 and 3, Edwin E. Moise (1977, )
General Relativity for Mathematicians, R. K. Sachs, H. Wu (1983, )
Linear Geometry, K. W. Gruenberg, A. J. Weir (2010, )
Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory, Harold M. Edwards (2000, )
A Course in Differential Geometry, William Klingenberg, D. Hoffman (1983, )
Algebraic Geometry, Robin Hartshorne (2010, )
A Course in Mathematical Logic for Mathematicians,  Yu. I. Manin, Boris Zilber  (2009, 2nd ed., )
Combinatorics with Emphasis on the Theory of Graphs, Mark E. Watkins, Jack E. Graver (1977, )
Introduction to Operator Theory I: Elements of Functional Analysis, Arlen Brown, Carl Pearcy (1977, )
Algebraic Topology: An Introduction, William S. Massey (1977, )
Introduction to Knot Theory, Richard H. Crowell, Ralph H. Fox (1977, )
p-adic Numbers, p-adic Analysis, and Zeta-Functions, Neal Koblitz (1984, 2nd ed., )
Cyclotomic Fields, Serge Lang (1978, )
Mathematical Methods of Classical Mechanics, V. I. Arnold, A. Weinstein, K. Vogtmann (1989, 2nd ed., )
Elements of Homotopy Theory, George W. Whitehead (1978, )
Fundamentals of the Theory of Groups, M. I. Kargapolov, J. I. Merzljakov (1979, )
Graph Theory - An Introductory Course, Béla Bollobás (1979, )
Fourier Series - A Modern Introduction Volume 1, R. E. Edwards (1979, 2nd ed., )
Differential Analysis on Complex Manifolds, Raymond O. Wells, Jr. (2008, 3rd ed., )
Introduction to Affine Group Schemes, W. C. Waterhouse (1979, )
Local Fields, Jean-Pierre Serre (1979, )
Linear Operators in Hilbert Spaces,  (1980, )
Cyclotomic Fields II, Serge Lang (1980, )
Singular Homology Theory, William S. Massey (1980, )
Riemann Surfaces, , Irwin Kra (1992, 2nd ed., )
Classical Topology and Combinatorial Group Theory, John Stillwell (1980, 2ed 1993, )
Algebra, Thomas W. Hungerford (1974, )
Multiplicative Number Theory, Harold Davenport, Hugh Montgomery (2000, 3rd ed., )
Basic Theory of Algebraic Groups and Lie Algebras, G. P. Hochschild (1981, )
Algebraic Geometry - An Introduction to Birational Geometry of Algebraic Varieties, Shigeru Iitaka (1982, )
Lectures on the Theory of Algebraic Numbers, E. T. Hecke (1981, )
A Course in Universal Algebra, Burris, Stanley and  Sankappanavar, H. P. (Online ) (1981 )
An Introduction to Ergodic Theory, Peter Walters (1982, )
A Course in the Theory of Groups,  (1996, 2nd ed., )
Lectures on Riemann Surfaces,  (1981, )
Differential Forms in Algebraic Topology, Raoul Bott, Loring W. Tu (1982, )
Introduction to Cyclotomic Fields, Lawrence C. Washington (1997, 2nd ed., )
A Classical Introduction to Modern Number Theory, Kenneth Ireland, Michael Rosen (1990, 2nd ed., )
Fourier Series - A Modern Introduction Volume 2, R. E. Edwards (1982, 2nd ed., )
Introduction to Coding Theory, J. H. van Lint (3rd ed 1998, )
Cohomology of Groups, Kenneth S. Brown (1982, )
Associative Algebras, R. S. Pierce (1982, )
Introduction to Algebraic and Abelian Functions, Serge Lang (1982, 2nd ed., )
An Introduction to Convex Polytopes, Arne Brondsted (1983, )
The Geometry of Discrete Groups,  (1983, 2nd print 1995, )
Sequences and Series in Banach Spaces, J. Diestel (1984, )
Modern Geometry — Methods and Applications Part I: The Geometry of Surfaces, Transformation Groups, and Fields, B. A. Dubrovin, Anatoly Timofeevich Fomenko, Sergei Novikov (1992, 2nd ed., )
Foundations of Differentiable Manifolds and Lie Groups,  (1983, )
Probability-1, Albert N. Shiryaev (2016, 3rd ed., )
A Course in Functional Analysis, John B. Conway (2007, 2nd ed., )
Introduction to Elliptic Curves and Modular Forms, Neal I. Koblitz (1993, 2nd ed., )
Representations of Compact Lie Groups, ,  (1985, )
Finite Reflection Groups, L.C. Grove, C.T. Benson (1985, 2nd ed., )
Harmonic Analysis on Semigroups - Theory of Positive Definite and Related Functions, Christian Berg, Jens Peter Reus Christensen, Paul Ressel (1984, )
Galois Theory, Harold M. Edwards (1984, )
Lie Groups, Lie Algebras, and Their Representations, V. S. Varadarajan (1984, )
Complex Analysis, Serge Lang (1999, 4th ed., )
Modern Geometry — Methods and Applications Part II: The Geometry and Topology of Manifolds, B. A. Dubrovin, Anatoly Timofeevich Fomenko, Sergei Novikov (1985, )
SL2(R), Serge Lang (1985, )
The Arithmetic of Elliptic Curves, Joseph H. Silverman (2009, 2nd ed., )
Applications of Lie Groups to Differential Equations, Peter J. Olver (2ed 1993, )
Holomorphic Functions and Integral Representations in Several Complex Variables, R. Michael Range (1986, )
Univalent Functions and Teichmüller Spaces, O. Lehto (1987, )
Algebraic Number Theory, Serge Lang (1994, 2nd ed., )
Elliptic Curves,  (2004, 2nd ed., )
Elliptic Functions, Serge Lang (1987, 2nd ed., )
Brownian Motion and Stochastic Calculus, Ioannis Karatzas, Steven Shreve (2ed 2000, )
A Course in Number Theory and Cryptography, Neal Koblitz (2ed 1994, )
Differential Geometry: Manifolds, Curves and Surfaces, Marcel Berger, Bernard Gostiaux (1988, )
Measure and Integral — Volume 1, John L. Kelley, T.P. Srinivasan (1988, )
Algebraic Groups and Class Fields, Jean-Pierre Serre (1988, )
Analysis Now, Gert K. Pedersen (1989, )
An Introduction to Algebraic Topology, Joseph J. Rotman, (1988, )
Weakly Differentiable Functions — Sobolev Spaces and Functions of Bounded Variation, William P. Ziemer (1989, )
Cyclotomic Fields I and II, Serge Lang (1990, Combined 2nd ed. )
Theory of Complex Functions, Reinhold Remmert (1991, )
Numbers, Heinz-Dieter Ebbinghaus et al. (1990, )
Modern Geometry — Methods and Applications Part III: Introduction to Homology Theory, B. A. Dubrovin, Anatoly Timofeevich Fomenko, Sergei Novikov (1990, )
Complex Variables — An Introduction, Carlos A. Berenstein, Roger Gay (1991, )
Linear Algebraic Groups, Armand Borel (1991, )
A Basic Course in Algebraic Topology, William S. Massey (1991,  )
Partial Differential Equations, Jeffrey Rauch (1991, )
Representation Theory, William Fulton, Joe Harris (1991, )
Tensor Geometry — The Geometric Viewpoint and its Uses, Christopher T. J. Dodson, Timothy Poston (1991, 2nd ed., )
A First Course in Noncommutative Rings, T. Y. Lam (2001, 2nd ed., )
Iteration of Rational Functions — Complex Analytic Dynamical Systems, Alan F. Beardon (1991, )
Algebraic Geometry, Joe Harris (1992, )
Coding and Information Theory, Steven Roman (1992, )
Advanced Linear Algebra, Steven Roman (2008, 3rd ed., )
Algebra — An Approach via Module Theory, William Adkins, Steven Weintraub (1992, )
Harmonic Function Theory, Sheldon Axler, Paul Bourdon, Wade Ramey (2001, 2nd ed., )
A Course in Computational Algebraic Number Theory, Henri Cohen (1996, )
Topology and Geometry, Glen E. Bredon (1993, )
Optima and Equilibria, Jean-Pierre Aubin (1998, )
Gröbner Bases — A Computational Approach to Commutative Algebra, Thomas Becker, Volker Weispfenning (1993, )
Real and Functional Analysis, Serge Lang (1993, 3rd ed., )
Measure Theory, J. L. Doob (1994, )
Noncommutative Algebra, Benson Farb, R. Keith Dennis (1993, )
Homology Theory — An Introduction to Algebraic Topology, James W. Vick (1994, 2nd ed., )
Computability — A Mathematical Sketchbook, Douglas S. Bridges (1994, )
Algebraic K-Theory and Its Applications, Jonathan Rosenberg (1994, )
An Introduction to the Theory of Groups, Joseph J. Rotman (1995, 4th ed., )
Foundations of Hyperbolic Manifolds, John G. Ratcliffe (2006, 2nd ed., )
Commutative Algebra — with a View Toward Algebraic Geometry, David Eisenbud (1995, )
Advanced Topics in the Arithmetic of Elliptic Curves, Joseph H. Silverman (1994, )
Lectures on Polytopes, Günter M. Ziegler (1995, )
Algebraic Topology — A First Course, William Fulton (1995, )
An Introduction to Analysis, Arlen Brown, Carl Pearcy (1995, )
Quantum Groups, Christian Kassel (1995, )
Classical Descriptive Set Theory, Alexander S. Kechris (1995, )
Integration and Probability, Paul Malliavin (1995, )
Field Theory, Steven Roman (2006, 2nd ed., )
Functions of One Complex Variable II, John B. Conway (1995, )
Differential and Riemannian Manifolds, Serge Lang (1995, )
Polynomials and Polynomial Inequalities, Peter Borwein, Tamas Erdelyi (1995, )
Groups and Representations, J. L. Alperin, Rowen B. Bell (1995, )
Permutation Groups, John D. Dixon, Brian Mortimer (1996, )
Additive Number Theory The Classical Bases, Melvyn B. Nathanson (1996, )
Additive Number Theory: Inverse Problems and the Geometry of Sumsets, Melvyn B. Nathanson (1996, )
Differential Geometry — Cartan's Generalization of Klein's Erlangen Program, R. W. Sharpe (1997, )
Field and Galois Theory, Patrick Morandi (1996, )
Combinatorial Convexity and Algebraic Geometry, Guenter Ewald (1996, )
Matrix Analysis, Rajendra Bhatia (1997, )
Sheaf Theory, Glen E. Bredon (1997, 2nd ed., )
Riemannian Geometry, Peter Petersen (2016, 3rd ed., )
Classical Topics in Complex Function Theory, Reinhold Remmert (1998, )
Graph Theory,  (2017, 5th ed., )
Foundations of Real and Abstract Analysis, Douglas S. Bridges (1998, )
An Introduction to Knot Theory, W. B. Raymond Lickorish (1997, )
Introduction to Riemannian Manifolds, John M. Lee (2018, 2nd ed., )
Analytic Number Theory , Donald J. Newman (1998, )
Nonsmooth Analysis and Control Theory, Francis H. Clarke, Yuri S. Ledyaev, Ronald J. Stern, Peter R. Wolenski (1998, )
Banach Algebra Techniques in Operator Theory, Ronald G. Douglas (1998, 2nd ed., )
A Course on Borel Sets, S. M. Srivastava (1998, )
Numerical Analysis, Rainer Kress (1998, )
Ordinary Differential Equations, Wolfgang Walter (1998, )
An Introduction to Banach Space Theory, Robert E. Megginson (1998, )
Modern Graph Theory, Béla Bollobás (1998, )
Using Algebraic Geometry, David A. Cox, John Little, Donal O'Shea (2005, 2nd ed., )
Fourier Analysis on Number Fields, Dinakar Ramakrishnan, Robert J. Valenza (1999, )
Moduli of Curves, Joe Harris, Ian Morrison (1998, )
Lectures on the Hyperreals, Robert Goldblatt (1998, )
Lectures on Modules and Rings, Tsit-Yuen Lam (1999, )
Problems in Algebraic Number Theory, M. Ram Murty, Jody Indigo Esmonde (2005, 2nd ed., )
Fundamentals of Differential Geometry, Serge Lang (1999, )
Elements of Functional Analysis, Francis Hirsch, Gilles Lacombe (1999, )
Advanced Topics in Computational Number Theory, Henri Cohen (2000, )
One-Parameter Semigroups for Linear Evolution Equations, Engel, Nagel (2000, )
Elementary Methods in Number Theory, Melvyn B. Nathanson (2000, )
Basic Homological Algebra, M. Scott Osborne (2000, )
The Geometry of Schemes, Eisenbud, Joe Harris (2000, )
A Course in p-adic Analysis, Alain M. Robert (2000, )
Theory of Bergman Spaces, Hakan Hedenmalm, Boris Korenblum, Kehe Zhu (2000, )
An Introduction to Riemann-Finsler Geometry, David Bao, Shiing-Shen Chern, Zhongmin Shen (2000, )
Diophantine Geometry, Marc Hindry, Joseph H. Silverman (2000, )
Introduction to Topological Manifolds, John M. Lee (2011, 2nd ed., )
The Symmetric Group — Representations, Combinatorial Algorithms, and Symmetric Functions, Bruce E. Sagan (2001, 2nd ed., )
Galois Theory, Jean-Pierre Escofier (2001, )
Rational Homotopy Theory, Yves Félix, Stephen Halperin, Jean-Claude Thomas (2000, )
Problems in Analytic Number Theory, M. Ram Murty (2007, 2nd ed., )
Algebraic Graph Theory, Chris Godsil, Gordon Royle (2001, )
Analysis for Applied Mathematics, Ward Cheney (2001, )
A Short Course on Spectral Theory, William Arveson (2002, )
Number Theory in Function Fields, Michael Rosen (2002, )
Algebra, Serge Lang (2002, Revised 3rd ed, )
Lectures on Discrete Geometry, Jiří Matoušek (2002, )
From Holomorphic Functions to Complex Manifolds, , Hans Grauert (2002, )
Partial Differential Equations, Jürgen Jost, (2013, 3rd ed., )
Algebraic Functions and Projective Curves, David M. Goldschmidt, (2003, )
Matrices — Theory and Applications, Denis Serre, (2010, 2nd ed., )
Model Theory: An Introduction, David Marker, (2002, )
Introduction to Smooth Manifolds, John M. Lee (2012, 2nd ed., )
The Arithmetic of Hyperbolic 3-Manifolds, Colin Maclachlan, Alan W. Reid, (2003, )
Smooth Manifolds and Observables, Jet Nestruev, (2003,  )
Convex Polytopes, Branko Grünbaum (2003, )
Lie Groups, Lie Algebras, and Representations - An Elementary Introduction, Brian C. Hall, (2015, 2nd ed., )
Fourier Analysis and its Applications, Anders Vretblad, (2003, )
Metric Structures in Differential Geometry, Walschap, G., (2004, )
Lie Groups, Daniel Bump, (2013, 2nd ed., )
Spaces of Holomorphic Functions in the Unit Ball, Kehe Zhu, (2005, )
Combinatorial Commutative Algebra, Ezra Miller, Bernd Sturmfels, (2005, )
A First Course in Modular Forms, Fred Diamond, J. Shurman,  (2006, )
The Geometry of Syzygies, David Eisenbud (2005, )
An Introduction to Markov Processes, Daniel W. Stroock, (2014, 2nd ed., )
Combinatorics of Coxeter Groups, Anders Björner, Francisco Brenti, (2005, )
An Introduction to Number Theory, Everest, G., Ward, T., (2005, )
Topics in Banach Space Theory, Albiac, F., Kalton, N. J., (2016, 2nd ed., )
Analysis and Probability — Wavelets, Signals, Fractals, Jorgensen, P. E. T., (2006, )
Compact Lie Groups, M. R. Sepanski, (2007, )
Bounded Analytic Functions, Garnett, J., (2007, )
An Introduction to Operators on the Hardy-Hilbert Space, Ruben A. Martinez-Avendano, Peter Rosenthal, (2007, )
A Course in Enumeration, Aigner, M., (2007, )
Number Theory — Volume I: Tools and Diophantine Equations, Cohen, H., (2007, )
Number Theory — Volume II: Analytic and Modern Tools, Cohen, H., (2007, )
The Arithmetic of Dynamical Systems, Joseph H. Silverman, (2007, )
Abstract Algebra, Grillet, Pierre Antoine, (2007, )
Topological Methods in Group Theory, Geoghegan, Ross, (2007, )
Graph Theory, Adrian Bondy, U.S.R. Murty, (2008, )
Complex Analysis: Introduced in the Spirit of Lipman Bers, Gilman, Jane P., Kra, Irwin, Rodriguez, Rubi E. (2007, )
A Course in Commutative Banach Algebras, Kaniuth, Eberhard,  (2008, )
Braid Groups, Kassel, Christian, Turaev, Vladimir, (2008, )
Buildings Theory and Applications, Abramenko, Peter, Brown, Ken (2008, )
Classical Fourier Analysis, Loukas Grafakos (2014, 3rd ed., )
Modern Fourier Analysis, Loukas Grafakos (2014, 3rd ed., )
The Finite Simple Groups, Robert A. Wilson (2009, )
Distributions and Operators, Gerd Grubb, (2009, )
Elementary Functional Analysis, MacCluer, Barbara D., (2009, )
Algebraic Function Fields and Codes, , (2009, )
Symmetry, Representations, and Invariants, Goodman, Roe, Wallach, Nolan R., (2009, )
A Course in Commutative Algebra, Kemper, Gregor, (2010, )
Deformation Theory, Robin Hartshorne, (2010, )
Foundations of Optimization in Finite Dimensions, Osman Guler, (2010, )
Ergodic Theory - with a view towards Number Theory, Thomas Ward, Manfred Einsiedler, (2011, )
Monomial Ideals, Jürgen Herzog, Hibi Takayuki(2010, )
Probability and Stochastics, Erhan Cinlar, (2011, )
Essentials of Integration Theory for Analysis, Daniel W. Stroock, (2012, )
Analysis on Fock Spaces, Kehe Zhu, (2012, )
Functional Analysis, Calculus of Variations and Optimal Control, Francis H. Clarke, (2013, )
Unbounded Self-adjoint Operators on Hilbert Space, Konrad Schmüdgen, (2012, )
Calculus Without Derivatives, Jean-Paul Penot, (2012, )
Quantum Theory for Mathematicians, Brian C. Hall, (2013, )
Geometric Analysis of the Bergman Kernel and Metric, Krantz, Steven G., (2013, )
Locally Convex Spaces, M Scott Osborne, (2014, )
Fundamentals of Algebraic Topology, Steven Weintraub, (2014, )
Integer Programming, Michelangelo Conforti, Gérard P. Cornuéjols, Giacomo Zambelli, (2014, )
Operator Theoretic Aspects of Ergodic Theory, Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel, (2015, )
Homotopical Topology, Anatoly Fomenko, Dmitry Fuchs, (2016, 2nd ed., )
Brownian Motion, Martingales, and Stochastic Calculus, Jean-François Le Gall, (2016, )
Differential Geometry - Connections, Curvature, and Characteristic Classes, Loring W. Tu (2017, )
Functional Analysis, Spectral Theory, and Applications, Manfred Einsiedler, Thomas Ward (2017, )
The Moment Problem, Konrad Schmüdgen (2017, )
Modern Real Analysis, William P. Ziemer (2017, 2nd ed., )
Binomial Ideals, Jürgen Herzog, Takayuki Hibi, Hidefumi Ohsugi (2018, )
Introduction to Real Analysis, Christopher Heil (2019, )
Intersection Homology & Perverse Sheaves with Applications to Singularities, Laurenţiu G. Maxim (2019, )
Measure, Integration & Real Analysis, Sheldon Axler (2020, )
Basic Representation Theory of Algebras, Ibrahim Assem, Flávio U Coelho (2020, )
Spectral Theory, David Borthwick (2020, )

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