WorldCat Identities

Lang, Serge 1927-2005

Works: 393 works in 2,935 publications in 10 languages and 44,760 library holdings
Genres: Textbooks  Records and correspondence 
Roles: Author, Editor, Honoree, Other, Creator, Dedicatee
Classifications: QA247, 515
Publication Timeline
Most widely held works about Serge Lang
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Most widely held works by Serge Lang
Algebra by Serge Lang( Book )

167 editions published between 1955 and 2008 in 8 languages and held by 2,306 WorldCat member libraries worldwide

This book is intended as a basic text for a one-year course in Algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higher-level algebra. It successfully addresses the basic concepts of algebra. For the revised third edition, the author has added exercises and made numerous corrections to the text. Comments on Serge Lang's Algebra: Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books. April 1999 Notices of the AMS, announcing that the author was awarded the Leroy P. Steele Prize for Mathematical Exposition for his many mathematics books. The author has an impressive knack for presenting the important and interesting ideas of algebra in just the "right" way, and he never gets bogged down in the dry formalism which pervades some parts of algebra. MathSciNet's review of the first edition
Linear algebra by Serge Lang( Book )

137 editions published between 1966 and 2011 in 5 languages and held by 1,653 WorldCat member libraries worldwide

"Linear Algebra" is intended for a one-term course at the junior or senior level. It begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorem for linear maps, including eigenvectors and eigenvalues, quadratic and hermitian forms, diagnolization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. The book also includes a useful chapter on convex sets and the finite-dimensional Krein-Milman theorem. The presentation is aimed at the student who has already had some exposure to the elementary theory of matrices, determinants and linear maps. However the book is logically self-contained. In this new edition, many parts of the book have been rewritten and reorganized, and new exercises have been added
Complex analysis by Serge Lang( Book )

81 editions published between 1977 and 2010 in 4 languages and held by 1,566 WorldCat member libraries worldwide

The first part of the book covers the basic material of complex analysis, and the second covers many special topics, such as the Riemann Mapping Theorem, the gamma function, and analytic continuation. Power series methods are used more systematically than in other texts, and the proofs using these methods often shed more light on the results than the standard proofs do. The first part of Complex Analysis is suitable for an introductory course on the undergraduate level, and the additional topics covered in the second part give the instructor of a graduate course a great deal of flexibility in structuring a more advanced course
A first course in calculus by Serge Lang( Book )

140 editions published between 1964 and 2012 in 5 languages and held by 1,505 WorldCat member libraries worldwide

Intended to teach the student the basic notions of derivative and integral, and the basic techniques and applications that accompany them
Algebraic number theory by Serge Lang( Book )

49 editions published between 1968 and 2014 in English and Undetermined and held by 1,247 WorldCat member libraries worldwide

Publisher Description (unedited publisher data) This is a corrected printing of the second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms. Part I introduces some of the basic ideas of the theory: number fields, ideal classes, ideles and adeles, and zeta functions. It also contains a version of a Riemann-Roch theorem in number fields, proved by Lang in the very first version of the book in the sixties. This version can now be seen as a precursor of Arakelov theory. Part II covers class field theory, and Part III is devoted to analytic methods, including an exposition of Tate's thesis, the Brauer-Siegel theorem, and Weil's explicit formulas. The second edition contains corrections, as well as several additions to the previous edition, and the last chapter on explicit formulas has been rewritten
Real and functional analysis by Serge Lang( Book )

58 editions published between 1969 and 2013 in 5 languages and held by 1,159 WorldCat member libraries worldwide

The second edition was published as Real Analysis, Addison-Wesley, 1983. The third edition has been reorganized. After a brief introduction to point set topology, some basic theorems on continuous functions, and the introduction of Banach and Hilbert spaces, integration theory is covered so it can fit in a one-semester course
Cyclotomic fields I and II by Serge Lang( Book )

59 editions published between 1978 and 2011 in English and Undetermined and held by 1,139 WorldCat member libraries worldwide

This second volume incorporates a number of results which were discovered and/or systematized since the first volume was being written. Again, I limit myself to the cyclotomic fields proper without introducing modular func tions. As in the first volume, the main concern is with class number formulas, Gauss sums, and the like. We begin with the Ferrero-Washington theorems, proving Iwasawa's conjecture that the p-primary part of the ideal class group in the cyclotomic Zp-extension of a cyclotomic field grows linearly rather than exponentially. This is first done for the minus part (the minus referring, as usual, to the eigenspace for complex conjugation), and then it follows for the plus part because of results bounding the plus part in terms of the minus part. Kummer had already proved such results (e.g. if p, (h; then p, (h;). These are now formulated in ways applicable to the Iwasawa invariants, following Iwasawa himself. After that we do what amounts to " Dwork theory," to derive the Gross Koblitz formula expressing Gauss sums in terms of the p-adic gamma function. This lifts Stickel berger's theorem p-adically. Half of the proof relies on a course of Katz, who had first obtained Gauss sums as limits of certain factorials, and thought of using Washnitzer-Monsky cohomology to prove the Gross-Koblitz formula
Undergraduate algebra by Serge Lang( Book )

58 editions published between 1987 and 2010 in 4 languages and held by 998 WorldCat member libraries worldwide

"Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theory, and other topics. The author has also included a chapter on groups of matrices which is unique in a book at this level. Throughout the book, the author strikes a balance between abstraction and concrete results, which enhance each other. Illustrative examples accompany the general theory. Numerous exercises range from the computational to the theoretical, complementing results from the main text." "For the Third Edition, the author has included new material on product structure for matrices (e.g. the Iwasawa and polar decompositions), as well as a description of the conjugation representation of the diagonal group. He has also added material on polynomials, culminating in Noah Snyder's proof of the Mason-Stothers polynomial abc theorem."--Résumé de l'éditeur
Calculus of several variables by Serge Lang( Book )

73 editions published between 1971 and 2012 in 3 languages and held by 969 WorldCat member libraries worldwide

"This is a new, revised, edition of this widely known text. All of the basic topics in calculus of several variables are covered, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green's theorem, multiple integrals, surface integrals, Stokes' theorem, and the inverse mapping theorem and its consequences. The presentation is self-contained, assuming only a knowledge of basic calculus in one variable. Many completely worked-out problems have been included."--Back cover
Introduction to differentiable manifolds by Serge Lang( Book )

72 editions published between 1962 and 2010 in 4 languages and held by 902 WorldCat member libraries worldwide

This work gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. The author has made numerous corrections to this new edition, and he has also added a chapter on applications of Stokes' Theorem
Undergraduate analysis by Serge Lang( Book )

53 editions published between 1983 and 2010 in 3 languages and held by 897 WorldCat member libraries worldwide

"This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. Topics discussed include the classical test for convergence of series, Fourier series, polynomial approximation, the Poisson kernel, the construction of harmonic functions on the disk, ordinary differential equations, curve integrals, derivatives in vector spaces, multiple integrals, and others. One of the author's main concerns is to achieve a balance between concrete examples and general theorems, augmented by a variety of interesting exercises." "Some new material has been added in this second edition, for example: a new chapter on the global version of integration of locally integrable vector fields; a brief discussion of [actual symbol not reproducible]-Cauchy sequences, introducing students to the Lebesgue integral; more material on Dirac sequences and families, including a section on the heat kernel; a more systematic discussion of orders of magnitude; and a number of new exercises."--Jacket
Algebraic structures by Serge Lang( Book )

37 editions published between 1965 and 1979 in 5 languages and held by 897 WorldCat member libraries worldwide

Elliptic functions by Serge Lang( Book )

36 editions published between 1971 and 2012 in 3 languages and held by 896 WorldCat member libraries worldwide

Elliptic functions parametrize elliptic curves, and the intermingling of the analytic and algebraic-arithmetic theory has been at the center of mathematics since the early part of the nineteenth century. The book is divided into four parts. In the first, Lang presents the general analytic theory starting from scratch. Most of this can be read by a student with a basic knowledge of complex analysis. The next part treats complex multiplication, including a discussion of Deuring's theory of l-adic and p-adic representations, and elliptic curves with singular invariants. Part three covers curves with non-integral invariants, and applies the Tate parametrization to give Serre's results on division points. The last part covers theta functions and the Kronecker Limit Formula. Also included is an appendix by Tate on algebraic formulas in arbitrary charactistic
Introduction to algebraic geometry by Serge Lang( Book )

50 editions published between 1955 and 2014 in English and held by 828 WorldCat member libraries worldwide

Introduction to algebraic and abelian functions by Serge Lang( Book )

40 editions published between 1972 and 2009 in 3 languages and held by 813 WorldCat member libraries worldwide

Introduction to Algebraic and Abelian Functions is a self-contained presentation of a fundamental subject in algebraic geometry and number theory. For this revised edition, the material on theta functions has been expanded, and the example of the Fermat curves is carried throughout the text. This volume is geared toward a second-year graduate course, but it leads naturally to the study of more advanced books listed in the bibliography
Topics in cohomology of groups by Serge Lang( Book )

46 editions published between 1956 and 1996 in 4 languages and held by 790 WorldCat member libraries worldwide

The book is a mostly translated reprint of a report on cohomology of groups from the 1950s and 1960s, originally written as background for the Artin-Tate notes on class field theory, following the cohomological approach. This report was first published (in French) by Benjamin. For this new English edition, the author added Tate's local duality, written up from letters which John Tate sent to Lang in 1958 - 1959. Except for this last item, which requires more substantial background in algebraic geometry and especially abelian varieties, the rest of the book is basically elementary, depending only on standard homological algebra at the level of first year graduate students
Introduction to linear algebra by Serge Lang( Book )

66 editions published between 1970 and 2014 in 4 languages and held by 781 WorldCat member libraries worldwide

A text in linear algebra which is intended for a one-term course. It examines the relation between the geometry and the algebra underlying the subject. It features sections on linear equations, matrices and Gaussian elimination, vector spaces, linear maps, scalar products, determinants, and eigenvalues
The beauty of doing mathematics : three public dialogues by Serge Lang( Book )

16 editions published in 1985 in English and held by 745 WorldCat member libraries worldwide

Enthält: What does a mathematician do and why? - Prime numbers - To do mathematics, a lively activity - diophantine equations - Great problems of geometry and space
SL₂(R) by Serge Lang( Book )

63 editions published between 1974 and 2009 in 4 languages and held by 730 WorldCat member libraries worldwide

SL2(R) gives the student an introduction to the infinite dimensional representation theory of semisimple Lie groups by concentrating on one example - SL2(R). This field is of interest not only for its own sake, but for its connections with other areas such as number theory, as brought out, for example, in the work of Langlands. The rapid development of representation theory over the past 40 years has made it increasingly difficult for a student to enter the field. This book makes the theory accessible to a wide audience, its only prerequisites being a knowledge of real analysis, and some differential equations
Abelian varieties by Serge Lang( Book )

30 editions published between 1959 and 1983 in 3 languages and held by 675 WorldCat member libraries worldwide

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The beauty of doing mathematics : three public dialogues
Alternative Names
Lang, S.

Lang, S 1927-2005

Lang, S. 1927- (Serge)

Lang, S. (Serge)

Lang, S. (Serge), 1927-2005

Lang, Serge

Lang, Serge 1927-

Lang, Serge A.

Lang, Serzh.

Lang, Serzh, 1927-

Lang, Serzh 1927-2005

Lang-Trotter, .. 1927-2005

Leng, S.

Leng, S. 1927-2005

Leng, Serž.

Leng, Serž 1927-2005

Serge Lang Frans wiskundige (1927-2005)

Serge Lang matematico francese

Serge Lang mathematician

Serge Lang mathématicien franco-américain

Serge Lang US-amerikanischer Mathematiker

Ленг, С..

Ленг, С 1927-

Ленг, С. (Серж), 1927-

Серж Ленг математик

سيرج لانغ

랑, 세르지 1927-2005

랭, 서지 1927-2005

랭, 써지 1927-2005

서지 랭


ラング, S.

ラング, サージ


Linear algebraComplex analysisA first course in calculusAlgebraic number theoryReal and functional analysisCyclotomic fields I and IIUndergraduate algebraCalculus of several variables