Graduate Texts in Mathematics (GTM) is a series of graduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are small yellow books of a standard size. This particular series is easily identified by a white band at the top of the book.
In this page, i will upload some books in that series. Please don’t reply here, thanks!
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October 11, 2007 at 3:55 am
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The Arithmetic of Elliptic Curves by Joseph H. Silverman , GTM 106
Review
“This well-written book covers the basic facts about the geometry and arithmetic of elliptic curves, and is sure to become the standard reference in the subject. It meets the needs of at least three groups of people: students interested in doing research in Diophantine geometry, mathematicians needing a reference for standard facts about elliptic curves, and computer scientists interested in algorithms and needing an introduction to elliptic curves…”– MATHEMATICAL REVIEWS
Book Description
The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebro-geometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, elliptic curves over finite fields, the complex numbers, local fields, and global fields. The last two chapters deal with integral and rational points, including Siegel’s theorem and explicit computations for the curve Y^2 = X^3 + DX. The book contains three appendices: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and a third appendix giving an overview of more advanced topics.
Link download http://gtm.spve.googlepages.com/Thearithmeticofellipticcurvessilver.djvu
October 12, 2007 at 1:06 pm
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Elementary Methods in Number Theory
by Melvyn B. Nathanson
Editorial Reviews
Book Description
Elementary Methods in Number Theory begins with “a first course in number theory” for students with no previous knowledge of the subject. The main topics are divisibility, prime numbers, and congruences. There is also an introduction to Fourier analysis on finite abelian groups, and a discussion on the abc conjecture and its consequences in elementary number theory. In the second and third parts of the book, deep results in number theory are proved using only elementary methods. Part II is about multiplicative number theory, and includes two of the most famous results in mathematics: the Erdös-Selberg elementary proof of the prime number theorem, and Dirichlets theorem on primes in arithmetic progressions. Part III is an introduction to three classical topics in additive number theory: Warings problems for polynomials, Liouvilles method to determine the number of representations of an integer as the sum of an even number of squares, and the asymptotics of partition functions. Melvyn B. Nathanson is Professor of Mathematics at the City University of New York (Lehman College and the Graduate Center). He is the author of the two other graduate texts: Additive Number Theory: The Classical Bases and Additive Number Theory: Inverse Problems and the Geometry of Sumsets.
Book Info
Discusses divisibility, prime numbers, and congruences and provides an introduction to Fourier analysis on finite abelian groups. Discusses the abc conjecture and its consequences in elementary number theory. DLC: Number theory.
Link download http://graduate.texts.googlepages.com/NathansonM.B.ElementaryMethodsinNumb.pdf
October 13, 2007 at 4:32 am
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A First Course in Modular Forms
by Fred Diamond (Author), Jerry Shurman (Author)
Editorial Reviews
Review
From the reviews:
“An essentially self-contained treatment that readers will find valuable both as a reference and a pedagogical text. … The authors of FCMF are to be commended for producing a valuable addition to the literature which belongs on the shelf of all scholars with an interest in modular forms, modular curves and their arithmetic applications.” (Henri Darmon, Mathematical Reviews, Issue 2006 f)
“The textbook under review provides a modern introduction to the theory of modular forms … . This ambitious program … is carried out in as down-to-earth a way as possible. … this is the first comprehensive introduction to the recent modularity theorem … . Written in a very comprehensible, detailed, lucid and instructive manner, this unique textbook is widely self-contained and perfectly suitable for self-study by beginners. Moreover, this book is an excellent guide to the relevant research literature … .” (Werner Kleinert, Zentralblatt MATH, Vol. 1062 (13), 2005)
“It has always been difficult to start learning about modular forms. … we were still lacking a textbook that could be honestly described as both comprehensive and accessible. Diamond and Shurman’s First Course is a largely successful attempt to provide just such a book. … A First Course in Modular Forms is a success. … a course taught from this text would be a very good way to lead students into the area. … I expect that Diamond and Shurman’s book would serve very well.” (Fernando Q. Gouvêa, MathDL, February, 2007)
“While there are many books on modular forms and elliptic curves, and some of them discuss the Eicheler-Shimura theory, most that describe it do not go deeply into the proofs. … The book of Diamond and Shurman addresses this need. … it is clearly directed to the serious student and it will unquestionably be a useful book even to experts. … this is a very unique and valuable book, and one that I would recommend to anyone wishing to learn about modular forms … .” (Daniel Bump, SIAM Review, Vol. 47 (4), 2005)
“The … goal of Diamond (Brandeis Univ.) and Shurman (Reed College) is … to state the modularity conjecture in some of its many forms. … readers wishing eventually to read Wiles could hardly find a better place to start than this. … Summing Up: Highly recommended. General readers; upper-division undergraduates through professionals.” (D. V. Feldman, CHOICE, Vol. 43 (1), September, 2005)
“This introduction to modular forms is aimed at students with only a basic knowledge of complex function theory. … A useful and up-to-date exposition of topics scattered throughout the literature, aided by exercises with answers.” (Mathematika, Vol. 52, 2005)
“The aim of this book is to introduce the reader to the modularity theorem. … This book can be recommended to everyone wishing to learn about modular forms and their connections to number theory.” (J. Mahnkopf, Monatshefte für Mathematik, Vol. 146 (4), 2006)
Book Description
This book introduces the theory of modular forms with an eye toward the Modularity Theorem. All rational elliptic curves arise from modular forms. The topics covered include: elliptic curves as complex tori and as algebraic curves, modular curves as Riemann surfaces and as algebraic curves, Hecke operators and Atkin-Lehner theory, Hecke eigenforms and their arithmetic properties, the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms, elliptic and modular curves modulo p and the Eichler-Shimura Relation, the Galois representations associated to elliptic curves and to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. A First Course in Modular Forms is written for beginning graduate students and advanced undergraduates. It does not require background in algebraic number theory or algebraic geometry, and it contains exercises throughout.
Link download
http://graduate.texts.googlepages.com/gtm228Modularforms.djvu
October 18, 2007 at 10:20 am
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[1] Lectures in Abstract Algebra III: Theory of Fields and Galois Theory (Graduate Texts in Mathematics).
[2] Lectures in Abstract Algebra II: Linear Algebra (Graduate Texts in Mathematics)
[3] Lectures in Abstract Algebra I: Basic Concepts (Graduate Texts in Mathematics) by N. Jacobson
Links download
http://graduate.texts.googlepages.com/JacobsonN.Lecturesinabstractalgebra.djvu
http://graduate.texts.googlepages.com/lectures_in_abstract_algebra_2_-_lin.rar
http://graduate.texts.googlepages.com/FieldsandGaloisGTM32Springer1975KT2.djvu
October 27, 2007 at 4:58 pm
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Lam T Y. A First Course in Noncommutative Rings
Editorial Reviews
Review
From the reviews of the second edition:
MATHEMATICAL REVIEWS
“This is a textbook for graduate students who have had an introduction to abstract algebra and now wish to study noncummutative rig theory…there is a feeling that each topic is presented with specific goals in mind and that the most efficient path is taken to achieve these goals. The author received the Steele prize for mathematical exposition in 1982; the exposition of this text is also award-wining caliber. Although there are many books in print that deal with various aspects of ring theory, this book is distinguished by its quality and level of presentation and by its selection of material….This book will surely be the standard textbook for many years to come. The reviewer eagerly awaits a promised follow-up volume for a second course in noncummutative ring theory.”
“Ten years ago, the first edition … of this book appeared. It is quite rare that a book can become a classic in such a short time, but this did happen for this excellent book. Of course minor changes were made for the second edition; new exercises and an appendix on uniserial modules were added. Every part of the text was written with love and care. The explanations are very well done, useful examples help to understand the material … .” (G. Pilz, Internationale Mathematische Nachrichten, Issue 196, 2004)
“The present book is a radical update. For the second edition the text was retyped, some proofs were rewritten and improvements in exposition have also taken place. … It is well-written and consists of eight chapters. … There is a very good reference section for further study and a name index consisting of four pages of closely-packed names. … As always the standard of print and presentation by Springer is exemplary.” (Brian Denton, The Mathematical Gazette, Vol. 86 (505), 2002)
Book Description
This book, an outgrowth of the author¿s lectures at the University of California at Berkeley, is intended as a textbook for a one-semester course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semisimple rings, Jacobson¿s theory of the radical, representation theory of groups and algebras, prime and semiprime rings, local and semilocal rings, perfect and semiperfect rings, etc. By aiming the level of writing at the novice rather than the connoisseur and by stressing the role of examples and motivation, the author has produced a text that is suitable not only for use in a graduate course, but also for self-study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition.
Link download
http://graduate.texts.googlepages.com/LamT.Y.Afirstcourseinnoncommutative.djvu
October 29, 2008 at 3:51 pm
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An Introduction to the Theory of Groups
by Joseph J. Rotman
Product Description
Anyone who has studied “abstract algebra” and linear algebra as an undergraduate can understand this book. This edition has been completely revised and reorganized, without however losing any of the clarity of presentation that was the hallmark of the previous editions.
The first six chapters provide ample material for a first course: beginning with the basic properties of groups and homomorphisms, topics covered include Lagrange’s theorem, the Noether isomorphism theorems, symmetric groups, G-sets, the Sylow theorems, finite Abelian groups, the Krull-Schmidt theorem, solvable and nilpotent groups, and the Jordan-Holder theorem.
The middle portion of the book uses the Jordan-Holder theorem to organize the discussion of extensions (automorphism groups, semidirect products, the Schur-Zassenhaus lemma, Schur multipliers) and simple groups (simplicity of projective unimodular groups and, after a return to G-sets, a construction of the sporadic Mathieu groups).
Link Download http://ifile.it/1lmis9c/rotman_j.j._an_introduction_to_the_theory_of_groups__4ed__springer__1995__gtm148__268s_.djvu
September 3, 2009 at 11:04 am
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GTM 59 ,Cyclotomic Fields (Graduate Texts in Mathematics)
by Serge Lang (Author)
Link download http://s20.ifile.it/kbocvut/yjuc/3909799/GTM%2059%2C%20lang_cyclotomic_fields.djvu
October 7, 2009 at 1:05 pm
Toán Lý
3 cuốn Đại số đại cương trên kia đọc có hay không anh ? Trong máy em có,em xem qua qua thấy trình bày không hay lắm nên không đọc kỹ.
October 8, 2009 at 12:31 am
trungtuan
Em đọc Lang hay Dummit cũng được.