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 yellow books of a standard size (with variable numbers of pages). The GTM series is easily identified by a white band at the top of the book.
The books in this series tend to be written at a more advanced level than the similar Undergraduate Texts in Mathematics series, although there is a fair amount of overlap between the two series in terms of material covered and difficulty level. Five of the volumes (122, 123, 129, 182, 206) are part of the subseries Readings in Mathematics.
The series was founded and edited by Paul Halmos, with the first voumes appearing in 1971. Halmos has said that it is the most successful series that he worked on. Early volumes in this series contained the following motivation for this book series
A student approaching mathematical research is often discouraged by the sheer volume of the literature and the long history of the subject, even when the actual problems are readily understandable. The new series, Graduate Texts in Mathematics, is intended to bridge the gap between passive study and creative understanding; it offers introductions on a suitably advanced level to areas of current research. These introductions are neither complete surveys nor brief accounts of the latest results only. They are textbooks carefully designed as teaching aids; the purpose of the authors is, in every case, to highlight the characteristic features of the theory. Graduate Texts in Mathematics can serve as the basis for advanced courses, they can be either the main or subsidiary sources for seminars, and they can be used for private study. Their guiding principle is to convince the student that mathematics is a living science.
List of books
Introduction to Axiomatic Set Theory, Gaisi Takeuti, Wilson M. Zaring (1971 1st ed. ; 1982, 2nd ed., ) Measure and Category – A Survey of the Analogies between Topological and Measure Spaces, John C. Oxtoby ( 1971 1st ed., ; 1980, 2nd ed., ) Topological Vector Spaces, H. H. Schaefer, M. P. Wolff (1971 1st ed. ; 1999, 2nd ed., )The first edition is a reprint, originally published by Macmillan in 1966 and was singly authored by Schaefer. A Course in Homological Algebra, Peter Hilton, Urs Stammbach ( 1971 1st ed. ; 1997, 2nd ed., ) Categories for the Working Mathematician, Saunders Mac Lane (1971 1st ed. ; 1998, 2nd ed., ) Projective Planes, Daniel R. Hughes, Fred C. Piper, (1973 ) This book is out of print. A Course in Arithmetic, Jean-Pierre Serre (1973 )This is a translation from the original French edition Cours d'Arithmetique, Presses Universitaires de France, Paris, 1970,. Axiomatic Set Theory, Gaisi Takeuti, Wilson M. Zaring, (1973, ) Introduction to Lie Algebras and Representation Theory, James E. Humphreys (1972 )
A Course in Simple-Homotopy Theory, Marshall. M. Cohen, (1973, ) Functions of One Complex Variable I, John B. Conway (1973 1st ed., ; 1978, 2nd ed., ) Advanced Mathematical Analysis, Richard Beals (1973, ) Rings and Categories of Modules, Frank W. Anderson, Kent R. Fuller (1974 1st ed, ; 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, )Originally published by Oxford University Press 1962. Measure Theory, Paul R. Halmos (1974, )Originally published by D. Van Nostrand, Company, Princeton New Jersey 1950 in the series The University Series in Higher Mathematics . A Hilbert Space Problem Book, Paul R. Halmos (1974, 1st ed., ; 1982, 2nd ed., ) Fibre Bundles, Dale Husemoller (1975, 2nd ed., ; 1994, 3rd ed., )Originally published by McGraw-Hill Book Company, New York, 1966 in the McGraw-Hill Series in Higher Mathematics .
Linear Algebraic Groups, James E. Humphreys (1975, ) An Algebraic Introduction to Mathematical Logic, Donald W. Barnes, John M. Mack (1975, ) Linear Algebra, Werner H. Greub (1975, 4th ed., )The 3rd edition was published as volume 97 of the series Grundlehren der mathematischen Wissenschaften in 1967 LCCN 67014017. Geometric Functional Analysis and Its Applications, Richard B. Holmes, (1975, ) Real and Abstract Analysis, Edwin Hewitt, Karl Stromberg (1975, )Originally published as a standalone book, before the establishment of the GTM series Springer-Verlag Berlin Heidelberg 1965 . Algebraic Theories, Ernest G. Manes, (1976, ) General Topology, John L. Kelley (1975, )Originally published by D. Van Nostrand, Company, Princeton New Jersey, The University Series in Higher Mathematics, 1955 . Commutative Algebra I, Oscar Zariski, Pierre Samuel (1975, )Originally published by D. Van Nostrand, Company, Princeton New Jersey, The University Series in Higher Mathematics, 1958, . Also reprinted by Dover, 2019 . Commutative Algebra II, Oscar Zariski, Pierre Samuel (1975, )Originally published by D. Van Nostrand, Company, Princeton New Jersey, The University Series in Higher Mathematics, 1960, . Also reprinted by Dover, 2019 .
Lectures in Abstract Algebra I: Basic Concepts, Nathan Jacobson (1976, )Originally published by D. Van Nostrand, Company, Princeton New Jersey, The University Series in Higher Mathematics 1951 . Lectures in Abstract Algebra II: Linear Algebra, Nathan Jacobson (1984, )Originally published by D. Van Nostrand, Company, Princeton New Jersey, The University Series in Higher Mathematics 1953 . Lectures in Abstract Algebra III: Theory of Fields and Galois Theory, Nathan Jacobson (1976, )Originally published by D. Van Nostrand, Company, Princeton New Jersey, The University Series in Higher Mathematics 1964 . Differential Topology, Morris W. Hirsch (1976, ) Principles of Random Walk, Frank Spitzer (1976, 2nd ed., )Originally published by D. Van Nostrand, Company, Princeton New Jersey, The University Series in Higher Mathematics 1964 . Several Complex Variables and Banach Algebras, Herbert Alexander, John Wermer (1976 1st edition ; 1998, 3rd ed., )Herbert Alexander was added as author in 3rd edition. Originally published by Markham Publishing, 1971 . 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, 2nd ed., )Originally published by Van Nostrand Publishing Company, 1966 . The 2nd edition was published by Springer, with an added chapter by David Griffeath. 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, ) Translation of Représentations linéaires des groupes finis (2nd edition), Hermann 1971 . Rings of Continuous Functions, Leonard Gillman, Meyer Jerison (1976, )Originally published by Van Nostrand, 1960 in The University Series in Higher Mathematics. There is also a republication by Dover, 2018 . Elementary Algebraic Geometry, Keith Kendig (1977, )Also published from Dover Publications as the second edition. (2015, ) Probability Theory I, M. Loève (1977, 4th ed., )The Springer 4th edition is two volumes, based on 3rd Edition which was a single volume published by Van Nostrand, 1963 in The University Series in Higher Mathematics. The third edition is still available from Dover, 2017 . 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 (1977, 2nd ed., )
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, )Translated by David Hoffman from Eine Vorlesung uber Differentialgeometrie, which was published by Springer as Band 107 of the series: Heidelberger Taschenbücher, 1973 . 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, )Originally published by Harcourt, Brace & World Inc., 1967, . Introduction to Knot Theory, Richard H. Crowell, Ralph H. Fox (1977, )Originally published Ginn and Company, 1963 in the series Introduction to Higher Mathematics, . Also published by Dover, 2008, 2008. p-adic Numbers, p-adic Analysis, and Zeta-Functions, Neal Koblitz (1984, 2nd ed., ) Cyclotomic Fields, Serge Lang (1978, )This volume of the series with volume 69 were combined as volume 121.
Mathematical Methods of Classical Mechanics, V. I. Arnold,(1989, 2nd ed., )Translated by K. Vogtmann and A. Weinstein. Title of the original Russian edition: Matematiceskie metody klassiceskoj mechaniki A Математические методы классической механики 1974 by Nauka . Elements of Homotopy Theory, George W. Whitehead (1978, ) Fundamentals of the Theory of Groups, M. I. Kargapolov, J. I. Merzljakov (1979, )Translated by Robert G. Burns from the 2nd Russian edition, Основы теории групп / Osnovy teorii grupp, Nauka, Moskva, 1977, . Graph Theory – An Introductory Course, Béla Bollobás (1979, ) Fourier Series – A Modern Introduction Volume 1, R. E. Edwards (1979, 2nd ed., )Originally published by Holt, Rinehart and Winston, 1967, . Differential Analysis on Complex Manifolds, Raymond O. Wells, Jr. (2008, 3rd ed., )Originally published by Prentice-Hall Inc., 1973, . Introduction to Affine Group Schemes, W. C. Waterhouse (1979, ) Local Fields, Jean-Pierre Serre (1979, )Translated by Marvin Jay Greenberg from Corps locaux, Hermann, Paris, 1968, Publications de l'Institut de mathématique de l'Université de Nancago, 8, Linear Operators in Hilbert Spaces, (1980, )Translated by Joseph Szücs from Lineare Operatoren in Hilberträumen, Teubner, Stuttgart, 1976 . 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, 2nd ed., 1993, ) Algebra, Thomas W. Hungerford (1974, )Originally published by Holt, Rinehart and Winston, Inc. 1974, . Multiplicative Number Theory, Harold Davenport, Hugh Montgomery (2000, 3rd ed., )First edition published by Markham Publishing Co., 1967 . 2nd Edition revised by Hugh L. Montgomery published by Springer in 1980 . 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, )Grew out of the author's book in Japanese published in 3 volumes by Iwanami, Tokyo in 1977, . Lectures on the Theory of Algebraic Numbers, E. T. Hecke (1981, )Translated by George U. Brauer and J. R. Goldman from Vorlesung Uber die Theorie der algebraischen Zahlen, Akademische Verlagsgesellschaft, Leipzig, 1923 . 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, Otto Forster (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., )Revised and expanded version of Elements of Number Theory, 1972, Bogden and Quigley, .