Graduate Texts in Mathematics (GTM) (

ISSN An International Standard Serial Number (ISSN) is an eight-digit serial number used to uniquely identify a serial publication, such as a magazine. The ISSN is especially helpful in distinguishing between serials with the same title. ISSNs ...

0072-5285) is a series of

graduate-level Postgraduate or graduate education refers to academic or professional degrees, certificates, diplomas, or other qualifications pursued by post-secondary students who have earned an undergraduate ( bachelor's) degree. The organization and stru ...

textbooks A textbook is a book containing a comprehensive compilation of content in a branch of study with the intention of explaining it. Textbooks are produced to meet the needs of educators, usually at educational institutions. Schoolbooks are textbook ...

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

published by

Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

. 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.

List of books

#''Introduction to Axiomatic Set Theory'',

Gaisi Takeuti was a Japanese mathematician, known for his work in proof theory. After graduating from Tokyo University, he went to Princeton to study under Kurt Gödel. He later became a professor at the University of Illinois at Urbana–Champaign. Takeu ...

, 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 Peter John Hilton (7 April 1923Peter Hilton, "On all Sorts of Automorphisms", '' The American Mathematical Monthly'', 92(9), November 1985, p. 6506 November 2010) was a British mathematician, noted for his contributions to homotopy theory and ...

, Urs Stammbach (1997, 2nd ed., ) #''

Categories for the Working Mathematician ''Categories for the Working Mathematician'' (''CWM'') is a textbook in category theory written by American mathematician Saunders Mac Lane, who cofounded the subject together with Samuel Eilenberg. It was first published in 1971, and is based on ...

'',

Saunders Mac Lane Saunders Mac Lane (4 August 1909 – 14 April 2005) was an American mathematician who co-founded category theory with Samuel Eilenberg. Early life and education Mac Lane was born in Norwich, Connecticut, near where his family lived in Taftville ...

(1998, 2nd ed., ) #''Projective Planes'', Daniel R. Hughes, Fred C. Piper, (1982, ) #''A Course in Arithmetic'',

Jean-Pierre Serre Jean-Pierre Serre (; born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the ina ...

(1996, ) #''Axiomatic Set Theory'',

, 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 John Bligh Conway (born September 22, 1939) is an American mathematician. He is currently a professor emeritus at the George Washington University. His specialty is functional analysis, particularly bounded operators on a Hilbert space. Conw ...

(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 Martin Aaron Golubitsky is an American Distinguished professor of mathematics at Ohio State University and the former director of the Mathematical Biosciences Institute. Biography Education Marty Golubitsky was born on April 5, 1945 in Philadelp ...

Victor Guillemin Victor William Guillemin (born 1937 in Boston) is an American mathematician working in the field of symplectic geometry, who has also made contributions to the fields of microlocal analysis, spectral theory, and mathematical physics. He is a te ...

, (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 Dale Husemöller (also spelled Husemoller) is an American mathematician specializing in algebraic topology and homological algebra who is known for his books on fibre bundles, elliptic curves, and, in collaboration with John Milnor, symmetric bil ...

(1994, 3rd ed., ) #''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, ) #''Geometric Functional Analysis and Its Applications'', Richard B. Holmes, (1975, ) #''Real and Abstract Analysis'',

Edwin Hewitt Edwin Hewitt (January 20, 1920, Everett, Washington – June 21, 1999) was an American mathematician known for his work in abstract harmonic analysis and for his discovery, in collaboration with Leonard Jimmie Savage, of the Hewitt–Savage z ...

, Karl Stromberg (1975, ) #''Algebraic Theories'', Ernest G. Manes, (1976, ) #''General Topology'', John L. Kelley (1975, ) #''Commutative Algebra I'',

Oscar Zariski , birth_date = , birth_place = Kobrin, Russian Empire , death_date = , death_place = Brookline, Massachusetts, United States , nationality = American , field = Mathematics , work_institutions = ...

Pierre Samuel Pierre Samuel (12 September 1921 – 23 August 2009) was a French mathematician, known for his work in commutative algebra and its applications to algebraic geometry. The two-volume work ''Commutative Algebra'' that he wrote with Oscar Zariski ...

(1975, ) #''Commutative Algebra II'',

(1975, ) #''Lectures in Abstract Algebra I: Basic Concepts'',

Nathan Jacobson Nathan Jacobson (October 5, 1910 – December 5, 1999) was an American mathematician. Biography Born Nachman Arbiser in Warsaw, Jacobson emigrated to America with his family in 1918. He graduated from the University of Alabama in 1930 and was awar ...

(1976, ) #''Lectures in Abstract Algebra II: Linear Algebra'',

(1984, ) #''Lectures in Abstract Algebra III: Theory of Fields and Galois Theory'',

(1976, ) #''Differential Topology'', Morris W. Hirsch (1976, ) #''Principles of Random Walk'',

Frank Spitzer Frank Ludvig Spitzer (July 24, 1926 – February 1, 1992) was an Austrian-born American mathematician who made fundamental contributions to probability theory, including the theory of random walks, fluctuation theory, percolation theory, the W ...

(1964, 2nd ed., ) #''Several Complex Variables and Banach Algebras'', Herbert Alexander,

John Wermer John Wermer is a mathematician specializing in Complex analysis. Wermer received his Ph.D. from Harvard University in 1951 under the supervision of George Whitelaw Mackey. In 1962 Wermer was an invited speaker at the International Congress of Math ...

(1998, 3rd ed., ) #''Linear Topological Spaces'', John L. Kelley,

Isaac Namioka Isaac Namioka (April 25, 1928 - September 25, 2019) was a Japanese-American mathematician who worked in general topology and functional analysis. He was a professor emeritus of mathematics at the University of Washington. He died at home in Seatt ...

(1982, ) #''Mathematical Logic'', J. Donald Monk (1976, ) #''Several Complex Variables'', H. Grauert, K. Fritzsche (1976, ) #''An Invitation to

C^*

-Algebras'',

William Arveson William B. Arveson (22 November 1934 – 15 November 2011) was a mathematician specializing in operator algebras who worked as a professor of Mathematics at the University of California, Berkeley. Biography Arveson obtained his Ph.D. from UCLA i ...

(1976, ) #''Denumerable Markov Chains'', John G. Kemeny, J. Laurie Snell,

Anthony W. Knapp Anthony W. Knapp (born 2 December 1941, Morristown, New Jersey) is an American mathematician at the State University of New York, Stony Brook working on representation theory, who classified the tempered representations of a semisimple Lie grou ...

, D.S. Griffeath (1976, ) #''Modular Functions and Dirichlet Series in Number Theory'',

Tom M. Apostol Tom Mike Apostol (August 20, 1923 – May 8, 2016) was an American analytic number theorist and professor at the California Institute of Technology, best known as the author of widely used mathematical textbooks. Life and career Apostol was bor ...

(1989, 2nd ed., ) #''Linear Representations of Finite Groups'',

, Leonhard L. Scott (1977, ) #''Rings of Continuous Functions'',

Leonard Gillman Leonard E. Gillman (January 8, 1917 – April 7, 2009) was an American mathematician, emeritus professor at the University of Texas at Austin. He was also an accomplished classical pianist. Biography Early life and education Gillman was born i ...

Meyer Jerison Meyer Jerison (November 28, 1922 – March 13, 1995) was an American mathematician known for his work in functional analysis and rings, and especially for collaborating with Leonard Gillman on one of the standard texts in the field: ''Rings of Co ...

(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 (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, ) #''

Algebraic Geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

'',

Robin Hartshorne __NOTOC__ Robin Cope Hartshorne ( ; born March 15, 1938) is an American mathematician who is known for his work in algebraic geometry. Career Hartshorne was a Putnam Fellow in Fall 1958 while he was an undergraduate at Harvard University (under ...

(2010, ) #''A Course in Mathematical Logic for Mathematicians'', Yu. I. Manin,

Boris Zilber Boris Zilber (russian: Борис Иосифович Зильбер, born 1949) is a Soviet-British mathematician who works in mathematical logic, specifically model theory. He is a professor of mathematical logic at the University of Oxford. H ...

(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 Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...

'', Arlen Brown, Carl Pearcy (1977, ) #''Algebraic Topology: An Introduction'',

William S. Massey William Schumacher Massey (August 23, 1920 – June 17, 2017) was an American mathematician, known for his work in algebraic topology. The Massey product is named for him. He worked also on the formulation of spectral sequences by means of exact ...

(1977, ) #''Introduction to Knot Theory'', Richard H. Crowell, Ralph H. Fox (1977, ) #''p-adic Numbers, p-adic Analysis, and Zeta-Functions'',

Neal Koblitz Neal I. Koblitz (born December 24, 1948) is a Professor of Mathematics at the University of Washington. He is also an adjunct professor with the Centre for Applied Cryptographic Research at the University of Waterloo. He is the creator of hyp ...

(1984, 2nd ed., ) #''Cyclotomic Fields'', Serge Lang (1978, ) #''

Mathematical Methods of Classical Mechanics Mathematical Methods of Classical Mechanics is a classic graduate textbook by the mathematician Vladimir I. Arnold. It was originally written in Russian, but was translated into English by A. Weinstein and K. Vogtmann. Contents * Part I: Ne ...

'', 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 Béla Bollobás FRS (born 3 August 1943) is a Hungarian-born British mathematician who has worked in various areas of mathematics, including functional analysis, combinatorics, graph theory, and percolation. He was strongly influenced by Pa ...

(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 ''Corps Locaux'' by Jean-Pierre Serre, originally published in 1962 and translated into English as ''Local Fields'' by Marvin Jay Greenberg in 1979, is a seminal graduate-level algebraic number theory text covering local fields, ramification, ...

'',

(1979, ) #''Linear Operators in Hilbert Spaces'', (1980, ) #''Cyclotomic Fields II'', Serge Lang (1980, ) #''Singular Homology Theory'',

(1980, ) #''Riemann Surfaces'', , Irwin Kra (1992, 2nd ed., ) #''Classical Topology and Combinatorial Group Theory'',

John Stillwell John Colin Stillwell (born 1942) is an Australian mathematician on the faculties of the University of San Francisco and Monash University. Biography He was born in Melbourne, Australia and lived there until he went to the Massachusetts Institu ...

(1980, 2ed 1993, ) #''Algebra'',

Thomas W. Hungerford Thomas William Hungerford (March 21, 1936 – November 28, 2014) was an American mathematician who worked in algebra and mathematics education. He is the author or coauthor of several widely used and widely cited textbooks covering high-school to ...

(1974, ) #''Multiplicative Number Theory'',

Harold Davenport Harold Davenport FRS (30 October 1907 – 9 June 1969) was an English mathematician, known for his extensive work in number theory. Early life Born on 30 October 1907 in Huncoat, Lancashire, Davenport was educated at Accrington Grammar Scho ...

, 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'', Otto Forster (1981, ) #''Differential Forms in Algebraic Topology'',

Raoul Bott Raoul Bott (September 24, 1923 – December 20, 2005) was a Hungarian-American mathematician known for numerous basic contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions whi ...

, Loring W. Tu (1982, ) #''Introduction to Cyclotomic Fields'',

Lawrence C. Washington Lawrence Clinton Washington (born 1951, Vermont) is an American mathematician at the University of Maryland who specializes in number theory. Biography Washington studied at Johns Hopkins University, where in 1971 he received his B.A. and master's ...

(1997, 2nd ed., ) #''A Classical Introduction to Modern Number Theory'', Kenneth Ireland,

Michael Rosen Michael Wayne Rosen (born 7 May 1946) is a British children's author, poet, presenter, political columnist, broadcaster and activist who has written 140 books. He served as Children's Laureate from 2007 to 2009. Early life Michael Wayne Ro ...

(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'',

Alan F. Beardon Alan Frank Beardon (April 16, 1940) is a British mathematician. Education and career Beardon obtained his doctorate at Imperial College London in 1964, supervised by Walter Hayman. In 1970 he was appointed as a lecturer in the Department of Pu ...

(1983, 2nd print 1995, ) #''Sequences and Series in

Banach Spaces In mathematics, more specifically in functional analysis, a Banach space (pronounced ) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vector ...

'', J. Diestel (1984, ) #''Modern Geometry — Methods and Applications Part I: The Geometry of Surfaces, Transformation Groups, and Fields'', B. A. Dubrovin,

Anatoly Timofeevich Fomenko Anatoly Timofeevich Fomenko (russian: Анато́лий Тимофе́евич Фоме́нко) (born 13 March 1945 in Stalino, USSR) is a Soviet and Russian conspiracy theorist, mathematician, professor at Moscow State University, well-known as ...

, Sergei Novikov (1992, 2nd ed., ) #''Foundations of Differentiable Manifolds and Lie Groups'', Frank W. Warner (1983, ) #''Probability-1'', ''Probability-2'', Albert N. Shiryaev (2016, 2019, 3rd ed., , ) #''A Course in Functional Analysis'',

(2007, 2nd ed., ) #''Introduction to Elliptic Curves and Modular Forms'', Neal I. Koblitz (1993, 2nd ed., ) #''Representations of Compact Lie Groups'', ,

Tammo tom Dieck Tammo tom Dieck (29 May 1938, São Paulo) is a German mathematician, specializing in algebraic topology. Tammo tom Dieck studied mathematics from 1957 at the University of Göttingen and at Saarland University, where he received his Promotion (Ge ...

(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,

, Sergei Novikov (1985, ) #''SL''₂(''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'',

(2ed 1994, ) #''Differential Geometry: Manifolds, Curves and Surfaces'',

Marcel Berger Marcel Berger (14 April 1927 – 15 October 2016) was a French mathematician, doyen of French differential geometry, and a former director of the Institut des Hautes Études Scientifiques (IHÉS), France. Formerly residing in Le Castera in Las ...

, Bernard Gostiaux (1988, ) #''Measure and Integral — Volume 1'', John L. Kelley, T.P. Srinivasan (1988, ) #''Algebraic Groups and Class Fields'',

(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 Reinhold Remmert (22 June 1930 – 9 March 2016) was a German mathematician. Born in Osnabrück, Lower Saxony, he studied mathematics, mathematical logic and physics in Münster. He established and developed the theory of complex-analytic spac ...

(1991, ) #''Numbers'', Heinz-Dieter Ebbinghaus ''et al.'' (1990, ) #''Modern Geometry — Methods and Applications Part III: Introduction to Homology Theory'', B. A. Dubrovin,

, Sergei Novikov (1990, ) #''Complex Variables — An Introduction'', Carlos A. Berenstein, Roger Gay (1991, ) #''Linear Algebraic Groups'',

Armand Borel Armand Borel (21 May 1923 – 11 August 2003) was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993. He worked in alg ...

(1991, ) #''A Basic Course in Algebraic Topology'',

(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 Henri Cohen may refer to: *Henri Cohen (composer) (1808–1880), French music theorist and composer *Henri Cohen (water polo) (died 1930), Belgian water polo athlete *Henri Cohen (number theorist) Henri Cohen (born 8 June 1947) is a number theor ...

(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 Joseph Leo Doob (February 27, 1910 – June 7, 2004) was an United States of America, American mathematician, specializing in Mathematical analysis, analysis and probability theory. The theory of Martingale (probability theory), martingales was ...

(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 (2019, 3rd 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 Günter Matthias Ziegler (born 19 May 1963) is a German mathematician who has been serving as president of the Free University of Berlin since 2018. Ziegler is known for his research in discrete mathematics and geometry, and particularly on the ...

(1995, ) #''Algebraic Topology — A First Course'', William Fulton (1995, ) #''An Introduction to Analysis'', Arlen Brown,

Carl Pearcy Carl Mark Pearcy, Jr. (born August 25, 1935) is an American mathematician whose research has been concentrated on operator theory and operator algebras. He has coauthored several books, including "Introduction to operator theory I", Introduction ...

(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'',

(1995, ) #''Differential and Riemannian Manifolds'', Serge Lang (1995, ) #''Polynomials and Polynomial Inequalities'',

Peter Borwein Peter Benjamin Borwein (born St. Andrews, Scotland, May 10, 1953 – 23 August 2020) was a Canadian mathematician and a professor at Simon Fraser University. He is known as a co-author of the paper which presented the Bailey–Borwein–Plo ...

, Tamas Erdelyi (1995, ) #''Groups and Representations'',

J. L. Alperin Jonathan Lazare Alperin (; born 1937) is an Americans, American mathematician specializing in the area of algebra known as group theory. He is notable for his work in group theory which has been cited over 500 times according to the Mathematical R ...

, 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

'', Guenter Ewald (1996, ) #''Matrix Analysis'',

Rajendra Bhatia Rajendra Bhatia (born 1952) is an Indian mathematician, author, and educator. He is currently a professor of mathematics at Ashoka University located in Sonipat, Haryana ,India. Education He studied at the University of Delhi, where he compl ...

(1997, ) #''Sheaf Theory'', Glen E. Bredon (1997, 2nd ed., ) #''Riemannian Geometry'', Peter Petersen (2016, 3rd ed., ) #''Classical Topics in Complex Function Theory'',

(1998, ) #''Graph Theory'', Reinhard Diestel (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., )The first edition is ''Riemannian Manifolds: An Introduction to Curvature''. #''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 Ronald George Douglas (December 10, 1938 – February 27, 2018) was an American mathematician, best known for his work on operator theory and operator algebras. Education and career Douglas was born in Osgood, Indiana. He was an undergraduate a ...

(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'',

(1998, ) #''Using Algebraic Geometry'',

David A. Cox David Archibald Cox (born September 23, 1948 in Washington, D.C.) is a retired American mathematician, working in algebraic geometry. Cox graduated from Rice University with a bachelor's degree in 1970 and his Ph.D. in 1975 at Princeton Universit ...

, 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 – An Introduction to Nonstandard Analysis'',

Robert Goldblatt __notoc__ Robert Ian Goldblatt (born 1949) is a mathematical logician who is Emeritus Professor in the School of Mathematics and Statistics at Victoria University, Wellington, New Zealand. His most popular books are ''Logics of Time and Computatio ...

(1998, ) #''Lectures on Modules and Rings'', Tsit-Yuen Lam (1999, ) #''Problems in Algebraic Number Theory'',

M. Ram Murty Maruti Ram Pedaprolu Murty, FRSC (born 16 October 1953 in Guntur, India) is an Indo-Canadian mathematician at Queen's University, where he holds a Queen's Research Chair in mathematics. Biography M. Ram Murty is the brother of mathematician ...

, 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'',

(2000, ) #''One-Parameter Semigroups for Linear Evolution Equations'', Klaus-Jochen Engel, Rainer 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 Shiing-Shen Chern (; , ; October 28, 1911 – December 3, 2004) was a Chinese-American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geome ...

, 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'',

(2007, 2nd ed., ) #''Algebraic Graph Theory'',

Chris Godsil Christopher David Godsil is a professor and the former Chair at the Department of Combinatorics and mathematical optimization, Optimization in the University of Waterloo Faculty of Mathematics, faculty of mathematics at the University of Waterloo. ...

Gordon Royle Gordon F. Royle is a professor at the School of Mathematics and Statistics at The University of Western Australia. Royle is the co-author (with Chris Godsil) of the book ''Algebraic Graph Theory'' (Springer Verlag, 2001, ). Royle is also known ...

(2001, ) #''Analysis for Applied Mathematics'',

Ward Cheney Ward may refer to: Division or unit * Hospital ward, a hospital division, floor, or room set aside for a particular class or group of patients, for example the psychiatric ward * Prison ward, a division of a penal institution such as a pris ...

(2001, ) #''A Short Course on Spectral Theory'',

(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 Hans Grauert (8 February 1930 in Haren, Emsland, Germany – 4 September 2011) was a German mathematician. He is known for major works on several complex variables, complex manifolds and the application of sheaf theory in this area, which i ...

(2002, ) #''Partial Differential Equations'',

Jürgen Jost Jürgen Jost (born 9 June 1956) is a German mathematician specializing in geometry. He has been a director of the Max Planck Institute for Mathematics in the Sciences in Leipzig since 1996. Life and work In 1975, he began studying mathematics, ...

, (2013, 3rd ed., ) #''Algebraic Functions and Projective Curves'', David M. Goldschmidt, (2003, ) #''Matrices — Theory and Applications'',

Denis Serre Denis Serre (born 1 November 1954) is a French mathematician who works as a professor at the École normale supérieure de Lyon, where he has chaired the mathematics department since 2012.

, (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 Alan may refer to: People *Alan (surname), an English and Turkish surname *Alan (given name), an English given name **List of people with given name Alan ''Following are people commonly referred to solely by "Alan" or by a homonymous name.'' *Al ...

, (2003, ) #''Smooth Manifolds and Observables'', Jet Nestruev, (2020, 2nd ed., ) #'' Convex Polytopes'',

Branko Grünbaum Branko Grünbaum ( he, ברנקו גרונבאום; 2 October 1929 – 14 September 2018) was a Croatian-born mathematician of Jewish descentDaniel Bump Daniel Willis Bump (born 13 May 1952) is a mathematician who is a professor at Stanford University. He is a fellow of the American Mathematical Society since 2015, for "contributions to number theory, representation theory, combinatorics, and ran ...

, (2013, 2nd ed., ) #''Spaces of Holomorphic Functions in the Unit Ball'', Kehe Zhu, (2005, ) #''Combinatorial Commutative Algebra'', Ezra Miller,

Bernd Sturmfels Bernd Sturmfels (born March 28, 1962 in Kassel, West Germany) is a Professor of Mathematics and Computer Science at the University of California, Berkeley and is a director of the Max Planck Institute for Mathematics in the Sciences in Leipzig si ...

, (2005, ) #''A First Course in Modular Forms'',

Fred Diamond Fred Irvin Diamond (born November 19, 1964) is a mathematician, known for his role in proving the modularity theorem for elliptic curves. His research interest is in modular forms and Galois representations. Diamond received his B.A. from the ...

, J. Shurman, (2006, ) #''The Geometry of Syzygies – A Second Course in Algebraic Geometry and Commutative Algebra'', David Eisenbud (2005, ) #''An Introduction to Markov Processes'',

Daniel W. Stroock Daniel Wyler Stroock (born March 20, 1940) is an United States, American mathematician, a probability theory, probabilist. He is regarded and revered as one of the fundamental contributors to Malliavin calculus with Shigeo Kusuoka and the theory ...

, (2014, 2nd ed., ) #''Combinatorics of Coxeter Groups'',

Anders Björner Anders Björner (born 17 December 1947) received his Ph.D. from Stockholm University in 1979, under Bernt Lindström. He is a Swedish professor of mathematics, in the Department of Mathematics at the Royal Institute of Technology, Stockholm, Swe ...

, Francisco Brenti, (2005, ) #''An Introduction to Number Theory'', Graham Everest., Thomas Ward., (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 Peter Michael Rosenthal (born June 1, 1941) is Canadian-American Professor Emeritus of Mathematics at the University of Toronto, an adjunct professor of Law at the University of Toronto, and a lawyer in private practice. Early life Rosenthal g ...

, (2007, ) #''A Course in Enumeration'',

Martin Aigner Martin Aigner (born February 28, 1942 in Linz) is an Austrian mathematician and professor at Freie Universität Berlin since 1974 with interests in combinatorial mathematics and graph theory. He received his Ph.D from the University of Vienna. Hi ...

, (2007, ) #''Number Theory — Volume I: Tools and Diophantine Equations'',

, (2007, ) #''Number Theory — Volume II: Analytic and Modern Tools'',

, (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 – In the Spirit of Lipman Bers'', Rubí E. Rodríguez, Irwin Kra, Jane P. Gilman (2013, 2nd ed., ) #''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, 2nd ed., ) #''Symmetry, Representations, and Invariants'', Goodman, Roe, Wallach, Nolan R., (2009, ) #''A Course in Commutative Algebra'', Kemper, Gregor, (2010, ) #''Deformation Theory'',

, (2010, ) #''Foundations of Optimization in Finite Dimensions'', Osman Guler, (2010, ) #''Ergodic Theory – with a view towards Number Theory'', Thomas Ward,

Manfred Einsiedler Manfred Leopold Einsiedler is an Austrian mathematician who studies ergodic theory. He was born in Scheibbs, Austria in 1973. Education and career Einsiedler studied mathematics at the University of Vienna, where he received his undergraduate d ...

, (2011, ) #''Monomial Ideals'', Jürgen Herzog, Hibi Takayuki(2010, ) #''Probability and Stochastics'', Erhan Cinlar, (2011, ) #''Essentials of Integration Theory for Analysis'',

, (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 Stephen or Steven is a common English first name. It is particularly significant to Christians, as it belonged to Saint Stephen ( grc-gre, Στέφανος ), an early disciple and deacon who, according to the Book of Acts, was stoned to death; ...

, (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 Anatoly Timofeevich Fomenko (russian: Анато́лий Тимофе́евич Фоме́нко) (born 13 March 1945 in Stalino, USSR) is a Soviet and Russian conspiracy theorist, mathematician, professor at Moscow State University, well-known as ...

, 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'',

, 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 – Basic Concepts and Applications'', David Borthwick (2020, ) #''An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space'', Konrad Schmüdgen (2020, ) #''Lectures on Convex Geometry'', Daniel Hug, Wolfgang Weilt (2020, ) #''Explorations in Complex Functions'', Richard Beals, Roderick S. C. Wong (2020, ) #''Quaternion Algebras'', John Voight (2020, ) #''Ergodic Dynamics – From Basic Theory to Applications'',

Jane M. Hawkins Jane Margaret Hawkins is an American mathematician who works as a professor of mathematics at University of North Carolina at Chapel Hill.Graduate Studies in Mathematics

Notes

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External links

Springer-Verlag's Summary of Graduate Texts in Mathematics
Series of mathematics books Mathematics textbooks Mathematics-related lists