WorldCat Identities

Lang, Serge 1927-2005

Works: 684 works in 3,449 publications in 10 languages and 47,429 library holdings
Genres: Textbooks  Personal correspondence 
Roles: Author, Editor, Contributor, Other, htt, Creator, Collector
Classifications: QA303, 515
Publication Timeline
Most widely held works about Serge Lang
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Most widely held works by Serge Lang
Linear algebra by Serge Lang( Book )

154 editions published between 1966 and 2011 in 6 languages and held by 1,785 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
Algebra by Serge Lang( Book )

93 editions published between 1955 and 2000 in 6 languages and held by 1,617 WorldCat member libraries worldwide

A first course in calculus by Serge Lang( Book )

155 editions published between 1964 and 2012 in 4 languages and held by 1,595 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
Undergraduate algebra by Serge Lang( Book )

64 editions published between 1900 and 2010 in 3 languages and held by 1,488 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 goups, rings, modules, fields, finite fields, Galois theory, and other topics
Complex analysis by Serge Lang( Book )

65 editions published between 1977 and 2010 in 3 languages and held by 1,451 WorldCat member libraries worldwide

"This is the fourth edition of Serge Lang's Complex Analysis. 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."--BOOK JACKET
Introduction to differentiable manifolds by Serge Lang( Book )

72 editions published between 1962 and 2011 in 4 languages and held by 1,383 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
Algebraic number theory by Serge Lang( Book )

55 editions published between 1968 and 2014 in 3 languages and held by 1,362 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 1,179 WorldCat member libraries worldwide

This book is meant as a text for a first year graduate course in analysis. Any standard course in undergraduate analysis will constitute sufficient preparation for its understanding, for instance, my Undergraduate Anal­ ysis. I assume that the reader is acquainted with notions of uniform con­ vergence and the like. In this third edition, I have reorganized the book by covering inte­ gration before functional analysis. Such a rearrangement fits the way courses are taught in all the places I know of. I have added a number of examples and exercises, as well as some material about integration on the real line (e.g. on Dirac sequence approximation and on Fourier analysis), and some material on functional analysis (e.g. the theory of the Gelfand transform in Chapter XVI). These upgrade previous exercises to sections in the text. In a sense, the subject matter covers the same topics as elementary calculus, viz. linear algebra, differentiation and integration. This time, however, these subjects are treated in a manner suitable for the training of professionals, i.e. people who will use the tools in further investiga­ tions, be it in mathematics, or physics, or what have you. In the first part, we begin with point set topology, essential for all analysis, and we cover the most important results
Calculus of several variables by Serge Lang( Book )

85 editions published between 1971 and 2012 in 4 languages and held by 1,077 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
Topics in cohomology of groups by Serge Lang( Book )

50 editions published between 1966 and 2006 in 3 languages and held by 1,010 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
Algebraic structures by Serge Lang( Book )

41 editions published between 1496 and 1979 in 5 languages and held by 921 WorldCat member libraries worldwide

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

43 editions published between 1972 and 2009 in 4 languages and held by 899 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
Undergraduate analysis by Serge Lang( Book )

33 editions published between 1983 and 2011 in English and German and held by 886 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
Introduction to algebraic geometry by Serge Lang( Book )

47 editions published between 1955 and 2019 in English and held by 883 WorldCat member libraries worldwide

"Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory. Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured."--
Introduction to linear algebra by Serge Lang( Book )

73 editions published between 1970 and 2014 in 4 languages and held by 881 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
SL₂(R) by Serge Lang( Book )

68 editions published between 1972 and 2009 in 5 languages and held by 837 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
The beauty of doing mathematics : three public dialogues by Serge Lang( Book )

20 editions published in 1985 in 3 languages and held by 798 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
Abelian varieties by Serge Lang( Book )

36 editions published between 1959 and 2019 in 4 languages and held by 783 WorldCat member libraries worldwide

"Based on the work in algebraic geometry by Norwegian mathematician Niels Henrik Abel (1802–29), this monograph was originally published in 1959 and reprinted later in author Serge Lang's career without revision. The treatment remains a basic advanced text in its field, suitable for advanced undergraduates and graduate students in mathematics. Prerequisites include some background in elementary qualitative algebraic geometry and the elementary theory of algebraic groups. The book focuses exclusively on Abelian varieties rather than the broader field of algebraic groups; therefore, the first chapter presents all the general results on algebraic groups relevant to this treatment. Each chapter begins with a brief introduction and concludes with a historical and bibliographical note. Topics include general theorems on Abelian varieties, the theorem of the square, divisor classes on an Abelian variety, functorial formulas, the Picard variety of an arbitrary variety, the I-adic representations, and algebraic systems of Abelian varieties. The text concludes with a helpful Appendix covering the composition of correspondences."
Differential manifolds by Serge Lang( Book )

43 editions published between 1972 and 1988 in 3 languages and held by 768 WorldCat member libraries worldwide

The present volume supersedes my Introduction to Differentiable Manifolds written a few years back. I have expanded the book considerably, including things like the Lie derivative, and especially the basic integration theory of differential forms, with Stokes' theorem and its various special formulations in different contexts. The foreword which I wrote in the earlier book is still quite valid and needs only slight extension here. Between advanced calculus and the three great differential theories (differential topology, differential geometry, ordinary differential equations), there lies a no-man's-land for which there exists no systematic exposition in the literature. It is the purpose of this book to fill the gap. The three differential theories are by no means independent of each other, but proceed according to their own flavor. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differentiable maps in them (immersions, embeddings, isomorphisms, etc.). One may also use differentiable structures on topological manifolds to determine the topological structure of the manifold (e.g. it la Smale [26])
Introduction to diophantine approximations by Serge Lang( Book )

36 editions published between 1966 and 2012 in 3 languages and held by 753 WorldCat member libraries worldwide

The aim of this book is to illustrate by significant special examples three aspects of the theory of Diophantine approximations: the formal relationships that exist between counting processes and the functions entering the theory; the determination of these functions for numbers given as classical numbers; and certain asymptotic estimates holding almost everywhere. Each chapter works out a special case of a much broader general theory, as yet unknown. Indications for this are given throughout the book, together with reference to current publications. The book may be used in a course in number theory, whose students will thus be put in contact with interesting but accessible problems on the ground floor of mathematics
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Audience level: 0.59 (from 0.40 for The beauty ... to 1.00 for Papers, 19 ...)

WorldCat IdentitiesRelated Identities
The beauty of doing mathematics : three public dialogues
AlgebraA first course in calculusUndergraduate algebraComplex analysisIntroduction to differentiable manifoldsAlgebraic number theoryReal and functional analysisCalculus of several variables
Alternative Names
Lang, S.

Lang, S 1927-2005

Lang, S. 1927- (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 matemáticu francés (1927–2005)

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

Սերժ Լենգ մաթեմատիկոս

سيرج لانج

سيرج لانغ

랭, 서지 1927-2005

랭, 써지 1927-2005

서지 랭


ラング, S

ラング, サージ