Lang, Serge 19272005
Overview
Works:  280 works in 2,452 publications in 10 languages and 41,811 library holdings 

Genres:  Textbooks Records and correspondence 
Roles:  Author, Editor, Honoree, Creator, Commentator for written text 
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 )
 Case study in correction by Serge Lang( Book )
 On Lang's diophantine conjecture for surfaces of general type by Cong Xuan Kang( Book )
 The Huntington file by Serge Lang( Book )
 John McCarthy papers by John McCarthy( )
 The T & L File (Teaching and Learning) by Serge Lang( Book )
 University Protest and Activism Collection by Columbia University( )
 The fire without, the fire within by Serge Lang( Book )
 A trilogy by Serge Lang( Book )
 The Zinsser file and the Grading file by Serge Lang( Book )
 Math files by Serge Lang( Book )
 Two sons of the file : the Publication File the ScienceLipset File by Serge Lang( Book )
 by John McCarthy( )
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Most widely held works by
Serge Lang
Algebra by
Serge Lang(
Book
)
156 editions published between 1955 and 2014 in 8 languages and held by 2,215 WorldCat member libraries worldwide
This book is intended as a basic text for a oneyear course in Algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higherlevel 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 graduatelevel 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
156 editions published between 1955 and 2014 in 8 languages and held by 2,215 WorldCat member libraries worldwide
This book is intended as a basic text for a oneyear course in Algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higherlevel 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 graduatelevel 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
A first course in calculus by
Serge Lang(
Book
)
150 editions published between 1964 and 2012 in 6 languages and held by 1,536 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
150 editions published between 1964 and 2012 in 6 languages and held by 1,536 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
Complex analysis by
Serge Lang(
Book
)
71 editions published between 1977 and 2010 in 4 languages and held by 1,506 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
71 editions published between 1977 and 2010 in 4 languages and held by 1,506 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
Algebraic number theory by
Serge Lang(
Book
)
42 editions published between 1968 and 2014 in English and Undetermined and held by 1,219 WorldCat member libraries worldwide
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
42 editions published between 1968 and 2014 in English and Undetermined and held by 1,219 WorldCat member libraries worldwide
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
Differential manifolds by
Serge Lang(
Book
)
59 editions published between 1972 and 1996 in 3 languages and held by 1,057 WorldCat member libraries worldwide
This text provides an introduction to basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas: for instance, the existence, uniqueness, and smoothness theorems for differential equations and the flow of a vector field; the basic theory of vector bundles including the existence of tubular neighborhoods for a submanifold; the calculus of differential forms; basic notions of symplectic manifolds, including the canonical 2form; sprays and covariant derivatives for Riemannian and pseudoRiemannian manifolds; applications to the exponential map, including the CartanHadamard theorem, and the first basic theorem of calculus of variations. These are all covered for infinitedimensional manifolds, modeled on Banach and Hilbert spaces, at no cost in complications, and some gain in the elegance of the proofs
59 editions published between 1972 and 1996 in 3 languages and held by 1,057 WorldCat member libraries worldwide
This text provides an introduction to basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas: for instance, the existence, uniqueness, and smoothness theorems for differential equations and the flow of a vector field; the basic theory of vector bundles including the existence of tubular neighborhoods for a submanifold; the calculus of differential forms; basic notions of symplectic manifolds, including the canonical 2form; sprays and covariant derivatives for Riemannian and pseudoRiemannian manifolds; applications to the exponential map, including the CartanHadamard theorem, and the first basic theorem of calculus of variations. These are all covered for infinitedimensional manifolds, modeled on Banach and Hilbert spaces, at no cost in complications, and some gain in the elegance of the proofs
Undergraduate algebra by
Serge Lang(
Book
)
55 editions published between 1987 and 2010 in 4 languages and held by 949 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."Jacket
55 editions published between 1987 and 2010 in 4 languages and held by 949 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."Jacket
Calculus of several variables by
Serge Lang(
Book
)
79 editions published between 1971 and 2012 in 3 languages and held by 945 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
79 editions published between 1971 and 2012 in 3 languages and held by 945 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
Undergraduate analysis by
Serge Lang(
Book
)
50 editions published between 1983 and 2010 in 4 languages and held by 891 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
50 editions published between 1983 and 2010 in 4 languages and held by 891 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
Algebraic structures by
Serge Lang(
Book
)
35 editions published between 1965 and 1979 in 5 languages and held by 882 WorldCat member libraries worldwide
35 editions published between 1965 and 1979 in 5 languages and held by 882 WorldCat member libraries worldwide
Elliptic functions by
Serge Lang(
Book
)
40 editions published between 1971 and 2003 in 4 languages and held by 872 WorldCat member libraries worldwide
Elliptic functions parametrize elliptic curves, and the intermingling of the analytic and algebraicarithmetic 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 ladic and padic representations, and elliptic curves with singular invariants. Part three covers curves with nonintegral 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
40 editions published between 1971 and 2003 in 4 languages and held by 872 WorldCat member libraries worldwide
Elliptic functions parametrize elliptic curves, and the intermingling of the analytic and algebraicarithmetic 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 ladic and padic representations, and elliptic curves with singular invariants. Part three covers curves with nonintegral 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 differentiable manifolds by
Serge Lang(
Book
)
65 editions published between 1962 and 2010 in 4 languages and held by 837 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
65 editions published between 1962 and 2010 in 4 languages and held by 837 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
Introduction to algebraic geometry by
Serge Lang(
Book
)
42 editions published between 1955 and 1973 in English and Undetermined and held by 835 WorldCat member libraries worldwide
42 editions published between 1955 and 1973 in English and Undetermined and held by 835 WorldCat member libraries worldwide
Introduction to algebraic and abelian functions by
Serge Lang(
Book
)
38 editions published between 1972 and 2009 in 4 languages and held by 798 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
38 editions published between 1972 and 2009 in 4 languages and held by 798 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
Topics in cohomology of groups by
Serge Lang(
Book
)
41 editions published between 1966 and 1996 in 3 languages and held by 769 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
41 editions published between 1966 and 1996 in 3 languages and held by 769 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
Introduction to linear algebra by
Serge Lang(
Book
)
58 editions published between 1970 and 2014 in 4 languages and held by 739 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
58 editions published between 1970 and 2014 in 4 languages and held by 739 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
The beauty of doing mathematics : three public dialogues by
Serge Lang(
Book
)
13 editions published in 1985 in English and held by 734 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
13 editions published in 1985 in English and held by 734 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
)
48 editions published between 1975 and 2009 in 3 languages and held by 716 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
48 editions published between 1975 and 2009 in 3 languages and held by 716 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
Analysis I by
Serge Lang(
Book
)
75 editions published between 1968 and 1978 in 5 languages and held by 710 WorldCat member libraries worldwide
75 editions published between 1968 and 1978 in 5 languages and held by 710 WorldCat member libraries worldwide
Introduction to diophantine approximations by
Serge Lang(
Book
)
27 editions published between 1966 and 2012 in 3 languages and held by 661 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
27 editions published between 1966 and 2012 in 3 languages and held by 661 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
Abelian varieties by
Serge Lang(
Book
)
28 editions published between 1959 and 1983 in 3 languages and held by 656 WorldCat member libraries worldwide
28 editions published between 1959 and 1983 in 3 languages and held by 656 WorldCat member libraries worldwide
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Related Identities
 Jorgenson, Jay Author Editor Creator
 Artin, Emil 18981962 Author
 Murrow, Gene
 Tate, John Torrence 1925 Author Editor
 Trotter, Hale F.
 Cherry, William 1966
 Fulton, William 1939 Author
 Goldfeld, D. (Dorian) Author Editor Creator
 Kubert, Daniel S. Author
 Rosenberg, Alfred 18931946 Author
Useful Links
Associated Subjects
Abelian groups Abelian varieties Algebra Algebra, Abstract Algebra, Homological Algebraic functions Algebraic number theory Algebras, Linear Calculus Class field theory College teachers College teachersProfessional ethics College teaching Cordier, Andrew W.(Andrew Wellington), Differentiable manifolds Differential topology Diophantine analysis Diophantine approximation Education, HigherAims and objectives Elections Elliptic functions English language 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 Huntington, Samuel P Lang, Serge, Lie groups Mail surveys Mathematical analysis Mathematicians Mathematics National Academy of Sciences (U.S.) Number theory Peace movements Representations of groups Riemannian manifolds Rings (Algebra) Students Topology United States Universities and collegesFaculty Vietnam War
Alternative Names
Lang, S.
Lang, S 19272005
Lang, S. (Serge), 19272005.
Lang, Serge
Lang, Serge 1927
Lang, Serge A.
Lang, Serzh.
Lang, Serzh 19272005
LangTrotter, .. 19272005
Leng, S.
Leng, S. 19272005
Leng, Serž.
Leng, Serž 19272005
Serge Lang matematico francese
Serge Lang mathematician
Serge Lang USamerikanischer Mathematiker
Ленг, С..
Ленг, С 1927
Ленг, С. (Серж), 1927
Серж Ленг математик
서지 랭
サージ・ラング
ラング, S
ラング, サージ
塞尔日兰
Languages
English
(980)
Spanish (48)
French (44)
Russian (30)
German (24)
Italian (9)
Portuguese (8)
Polish (4)
Chinese (3)
Japanese (2)
Spanish (48)
French (44)
Russian (30)
German (24)
Italian (9)
Portuguese (8)
Polish (4)
Chinese (3)
Japanese (2)
Covers