Lang, Serge 19272005
Overview
Works:  395 works in 2,970 publications in 11 languages and 44,988 library holdings 

Genres:  Textbooks Records and correspondence 
Roles:  Author, Editor, Honoree, Other, Creator, Dedicatee 
Classifications:  QA303, 515 
Publication Timeline
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Most widely held works about
Serge Lang
 Number theory, analysis and geometry : in memory of Serge Lang by D Goldfeld( Book )
 The Huntington file by Serge Lang( Book )
 John McCarthy papers by John McCarthy( )
 On Lang's diophantine conjecture for surfaces of general type by Cong Xuan Kang( Book )
 The T & L File (Teaching and Learning) by Serge Lang( Book )
 Math files by Serge Lang( Book )
 The Zinsser File and the Grading File by Serge Lang( Book )
 The fire without, the fire within by Serge Lang( Book )
 Two sons of the file : the Publication File the ScienceLipset File by Serge Lang( Book )
 Case study in correction by Serge Lang( Book )
 A trilogy by Serge Lang( Book )
 University Protest and Activism Collection by Columbia University( )
 by John McCarthy( )
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Most widely held works by
Serge Lang
Algebra by
Serge Lang(
Book
)
175 editions published between 1955 and 2012 in 8 languages and held by 2,362 WorldCat member libraries worldwide
Algebraic equations, Linear Algebra and Representations, Homological Algebra
175 editions published between 1955 and 2012 in 8 languages and held by 2,362 WorldCat member libraries worldwide
Algebraic equations, Linear Algebra and Representations, Homological Algebra
Linear algebra by
Serge Lang(
Book
)
144 editions published between 1966 and 2011 in 6 languages and held by 1,721 WorldCat member libraries worldwide
"Linear Algebra" is intended for a oneterm 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 finitedimensional KreinMilman 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 selfcontained. In this new edition, many parts of the book have been rewritten and reorganized, and new exercises have been added
144 editions published between 1966 and 2011 in 6 languages and held by 1,721 WorldCat member libraries worldwide
"Linear Algebra" is intended for a oneterm 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 finitedimensional KreinMilman 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 selfcontained. In this new edition, many parts of the book have been rewritten and reorganized, and new exercises have been added
A first course in calculus by
Serge Lang(
Book
)
155 editions published between 1964 and 2012 in 5 languages and held by 1,589 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
155 editions published between 1964 and 2012 in 5 languages and held by 1,589 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
)
59 editions published between 1987 and 2010 in 4 languages and held by 1,466 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 MasonStothers polynomial abc theorem."BOOK JACKET
59 editions published between 1987 and 2010 in 4 languages and held by 1,466 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 MasonStothers polynomial abc theorem."BOOK JACKET
Complex analysis by
Serge Lang(
Book
)
68 editions published between 1985 and 2010 in 3 languages and held by 1,416 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
68 editions published between 1985 and 2010 in 3 languages and held by 1,416 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
Introduction to differentiable manifolds by
Serge Lang(
Book
)
73 editions published between 1962 and 2010 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
73 editions published between 1962 and 2010 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
Real and functional analysis by
Serge Lang(
Book
)
54 editions published between 1969 and 2013 in 5 languages and held by 1,120 WorldCat member libraries worldwide
The second edition was published as Real Analysis, AddisonWesley, 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 onesemester course
54 editions published between 1969 and 2013 in 5 languages and held by 1,120 WorldCat member libraries worldwide
The second edition was published as Real Analysis, AddisonWesley, 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 onesemester course
Undergraduate analysis by
Serge Lang(
Book
)
56 editions published between 1983 and 2010 in 3 languages and held by 1,020 WorldCat member libraries worldwide
"This is a logically selfcontained 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
56 editions published between 1983 and 2010 in 3 languages and held by 1,020 WorldCat member libraries worldwide
"This is a logically selfcontained 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
Calculus of several variables by
Serge Lang(
Book
)
76 editions published between 1971 and 2012 in English and Spanish and held by 1,019 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 selfcontained, assuming only a knowledge of basic calculus in one variable. Many completely workedout problems have been included."Back cover
76 editions published between 1971 and 2012 in English and Spanish and held by 1,019 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 selfcontained, assuming only a knowledge of basic calculus in one variable. Many completely workedout problems have been included."Back cover
Topics in cohomology of groups by
Serge Lang(
Book
)
44 editions published between 1966 and 1996 in 3 languages and held by 974 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 ArtinTate 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
44 editions published between 1966 and 1996 in 3 languages and held by 974 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 ArtinTate 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
)
38 editions published between 1965 and 1979 in 5 languages and held by 913 WorldCat member libraries worldwide
38 editions published between 1965 and 1979 in 5 languages and held by 913 WorldCat member libraries worldwide
Introduction to algebraic and abelian functions by
Serge Lang(
Book
)
41 editions published between 1972 and 2009 in English and German and held by 882 WorldCat member libraries worldwide
Introduction to Algebraic and Abelian Functions is a selfcontained 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 secondyear graduate course, but it leads naturally to the study of more advanced books listed in the bibliography
41 editions published between 1972 and 2009 in English and German and held by 882 WorldCat member libraries worldwide
Introduction to Algebraic and Abelian Functions is a selfcontained 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 secondyear graduate course, but it leads naturally to the study of more advanced books listed in the bibliography
Algebraic number theory by
Serge Lang(
Book
)
34 editions published between 1986 and 2013 in English and Undetermined and held by 874 WorldCat member libraries worldwide
Publisher Description (unedited publisher data) This is a corrected printing of the second edition of Lang's wellknown 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 RiemannRoch 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 BrauerSiegel 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
34 editions published between 1986 and 2013 in English and Undetermined and held by 874 WorldCat member libraries worldwide
Publisher Description (unedited publisher data) This is a corrected printing of the second edition of Lang's wellknown 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 RiemannRoch 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 BrauerSiegel 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
Introduction to linear algebra by
Serge Lang(
Book
)
68 editions published between 1970 and 2014 in 3 languages and held by 833 WorldCat member libraries worldwide
A text in linear algebra which is intended for a oneterm 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
68 editions published between 1970 and 2014 in 3 languages and held by 833 WorldCat member libraries worldwide
A text in linear algebra which is intended for a oneterm 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
Introduction to algebraic geometry by
Serge Lang(
Book
)
52 editions published between 1957 and 2019 in English and held by 828 WorldCat member libraries worldwide
52 editions published between 1957 and 2019 in English and held by 828 WorldCat member libraries worldwide
The beauty of doing mathematics : three public dialogues by
Serge Lang(
Book
)
16 editions published in 1985 in English and held by 795 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
16 editions published in 1985 in English and held by 795 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 793 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
63 editions published between 1974 and 2009 in 4 languages and held by 793 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
)
32 editions published between 1959 and 2019 in 3 languages and held by 740 WorldCat member libraries worldwide
32 editions published between 1959 and 2019 in 3 languages and held by 740 WorldCat member libraries worldwide
Differential manifolds by
Serge Lang(
Book
)
39 editions published between 1972 and 1988 in 3 languages and held by 721 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 noman'sland 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])
39 editions published between 1972 and 1988 in 3 languages and held by 721 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 noman'sland 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
)
29 editions published between 1966 and 2012 in English and held by 720 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
29 editions published between 1966 and 2012 in English and held by 720 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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Related Identities
 Jorgenson, Jay Other Author Creator
 Murrow, Gene
 Artin, Emil 18981962 Author
 Tate, John Torrence 1925 Other Author Editor
 Trotter, Hale F. Author
 Cherry, William 1966
 Fulton, William 1939 Author
 Goldfeld, D. (Dorian) Other Author Editor Creator
 Kubert, Daniel S. Author
 Braemer, Jean Marc 1938 Other Translator
Useful Links
Associated Subjects
Abelian groups Abelian varieties Algebra Algebra, Abstract Algebra, Homological Algebraic functions Algebraic number theory Algebras, Linear Artificial intelligence Baskett, Forest Calculus Class field theory College teachers Computer programming Differentiable manifolds Differential topology Diophantine analysis Diophantine approximation Education, HigherAims and objectives Elections Field theory (Physics) Functions, Abelian Functions of complex variables Functions of several real variables Geometry Geometry, Algebraic Geometry, Differential Global analysis (Mathematics) Group theory Homology theory Knuth, Donald Ervin, Lang, Serge, Lederberg, Joshua Lie groups LISP (Computer program language) Manna, Zohar Mathematical analysis Mathematicians Mathematics Michie, Donald Moravec, Hans P National Academy of Sciences (U.S.) Number theory Representations of groups Sato, Masahiko, Semisimple Lie groups Stanford University.Computer Science Department Topology United States Universities and collegesFaculty
Covers
Alternative Names
Lang, S.
Lang, S 19272005
Lang, S. 1927 (Serge)
Lang, S. (Serge)
Lang, S. (Serge), 19272005
Lang, Serge
Lang, Serge 1927
Lang, Serge A.
Lang, Serzh.
Lang, Serzh, 1927
Lang, Serzh 19272005
LangTrotter, .. 19272005
Leng, S.
Leng, S. 19272005
Leng, Serž.
Leng, Serž 19272005
Serge Lang Frans wiskundige (19272005)
Serge Lang matematico francese
Serge Lang mathematician
Serge Lang mathématicien francoaméricain
Serge Lang USamerikanischer Mathematiker
Ленг, С..
Ленг, С 1927
Ленг, С. (Серж), 1927
Серж Ленг математик
سيرج لانغ
랑, 세르지 19272005
랭, 서지 19272005
랭, 써지 19272005
서지 랭
サージ・ラング
ラング, S.
ラング, サージ
塞尔日·兰
Languages