Milnor, John W. (John Willard) 1931
Overview
Works:  160 works in 720 publications in 5 languages and 10,100 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Speaker, Honoree, Dedicatee, Author of introduction, Other 
Classifications:  QA612, 513.83 
Publication Timeline
.
Most widely held works about
John W Milnor
 Topological methods in modern mathematics : a symposium in honor of John Milnor's sixtieth birthday by Symposium in Honor of John Milnor's Sixtieth Birthday( Book )
 Milnor, John( )
 Frontiers in complex dynamics : in celebration of John Milnor's 80th birthday by Scott Sutherland( Book )
 Collected papers by John W Milnor( Book )
Most widely held works by
John W Milnor
Topology from the differentiable viewpoint by
John W Milnor(
Book
)
78 editions published between 1965 and 2012 in 3 languages and held by 1,014 WorldCat member libraries worldwide
78 editions published between 1965 and 2012 in 3 languages and held by 1,014 WorldCat member libraries worldwide
Morse theory by
John W Milnor(
Book
)
69 editions published between 1960 and 2013 in 4 languages and held by 842 WorldCat member libraries worldwide
One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse. (Morse was on the faculty of the Institute for Advanced Study, and Princeton published his Topological Methods in the Theory of Functions of a Complex Variable in the Annals of Mathematics Studies series in 1947.) One classical application of Morse theory includes the attempt to understand, with only limited information, the largescale structure of an object. This kind of problem occurs in mathematical physics, dynamic systems, and mechanical engineering. Morse theory has received much attention in the last two decades as a result of a famous paper in which theoretical physicist Edward Witten relates Morse theory to quantum field theory. Milnor was awarded the Fields Medal (the mathematical equivalent of a Nobel Prize) in 1962 for his work in differential topology. He has since received the National Medal of Science (1967) and the Steele Prize from the American Mathematical Society twice (1982 and 2004) in recognition of his explanations of mathematical concepts across a wide range of scienti.c disciplines. The citation reads, "The phrase sublime elegance is rarely associated with mathematical exposition, but it applies to all of Milnor's writings. Reading his books, one is struck with the ease with which the subject is unfolding and it only becomes apparent after re.ection that this ease is the mark of a master." Milnor has published five books with Princeton University Press
69 editions published between 1960 and 2013 in 4 languages and held by 842 WorldCat member libraries worldwide
One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse. (Morse was on the faculty of the Institute for Advanced Study, and Princeton published his Topological Methods in the Theory of Functions of a Complex Variable in the Annals of Mathematics Studies series in 1947.) One classical application of Morse theory includes the attempt to understand, with only limited information, the largescale structure of an object. This kind of problem occurs in mathematical physics, dynamic systems, and mechanical engineering. Morse theory has received much attention in the last two decades as a result of a famous paper in which theoretical physicist Edward Witten relates Morse theory to quantum field theory. Milnor was awarded the Fields Medal (the mathematical equivalent of a Nobel Prize) in 1962 for his work in differential topology. He has since received the National Medal of Science (1967) and the Steele Prize from the American Mathematical Society twice (1982 and 2004) in recognition of his explanations of mathematical concepts across a wide range of scienti.c disciplines. The citation reads, "The phrase sublime elegance is rarely associated with mathematical exposition, but it applies to all of Milnor's writings. Reading his books, one is struck with the ease with which the subject is unfolding and it only becomes apparent after re.ection that this ease is the mark of a master." Milnor has published five books with Princeton University Press
Characteristic classes by
John W Milnor(
Book
)
38 editions published between 1962 and 2016 in 5 languages and held by 657 WorldCat member libraries worldwide
38 editions published between 1962 and 2016 in 5 languages and held by 657 WorldCat member libraries worldwide
Introduction to algebraic Ktheory by
John W Milnor(
Book
)
21 editions published between 1971 and 1974 in English and Russian and held by 576 WorldCat member libraries worldwide
21 editions published between 1971 and 1974 in English and Russian and held by 576 WorldCat member libraries worldwide
Singular points of complex hypersurfaces by
John W Milnor(
Book
)
34 editions published between 1968 and 2003 in 3 languages and held by 554 WorldCat member libraries worldwide
34 editions published between 1968 and 2003 in 3 languages and held by 554 WorldCat member libraries worldwide
Symmetric bilinear forms by
John W Milnor(
Book
)
23 editions published between 1970 and 1986 in 5 languages and held by 518 WorldCat member libraries worldwide
The theory cf quadratic forms and the intimately related theory of sym metrie bilinear forms have a lang and rich his tory, highlighted by the work of Legendre, Gauss, Minkowski, and Hasse. (Compare [Dickson] and [Bourbaki, 24, p. 185].) Our exposition will concentrate on the rela tively recent developments which begin with and are inspired by Witt's 1937 paper "Theorie der quadratischen Formen in beliebigen Körpern." We will be particularly interested in the work of A. Pfister and M. Knebusch. However, some older material will be described, particularly in Chapter II. The presentation is based on lectures by Milnor at the Institute for Ad vanced Study, and at Haverford College under the Phillips Lecture Pro gram, during the Fall of 1970, as weIl as Iectures at Princeton University il1 1966. We want to thank J. Cunningham, M. Knebusch, M. Kneser, A. Rosenberg, W. Scharlau and J.P. Serre for helpful suggestions and corrections. Prerequisites. The reader should be familiar with the rudiments of algebra., incJuding for example the concept of tensor product for mo dules over a commutative ring. A few individual sections will require quite a bit more. The logical relationship between the various chapters can be roughly described by the diagram below. There are also five appendices, largely selfcontained, which treat special topics. I. Arbitrary commutative rings I H. The ring of V. Miscellaneous IIl. Fields integers examples IV. Dedekind domains Contents Chapter r. Basie Coneepts
23 editions published between 1970 and 1986 in 5 languages and held by 518 WorldCat member libraries worldwide
The theory cf quadratic forms and the intimately related theory of sym metrie bilinear forms have a lang and rich his tory, highlighted by the work of Legendre, Gauss, Minkowski, and Hasse. (Compare [Dickson] and [Bourbaki, 24, p. 185].) Our exposition will concentrate on the rela tively recent developments which begin with and are inspired by Witt's 1937 paper "Theorie der quadratischen Formen in beliebigen Körpern." We will be particularly interested in the work of A. Pfister and M. Knebusch. However, some older material will be described, particularly in Chapter II. The presentation is based on lectures by Milnor at the Institute for Ad vanced Study, and at Haverford College under the Phillips Lecture Pro gram, during the Fall of 1970, as weIl as Iectures at Princeton University il1 1966. We want to thank J. Cunningham, M. Knebusch, M. Kneser, A. Rosenberg, W. Scharlau and J.P. Serre for helpful suggestions and corrections. Prerequisites. The reader should be familiar with the rudiments of algebra., incJuding for example the concept of tensor product for mo dules over a commutative ring. A few individual sections will require quite a bit more. The logical relationship between the various chapters can be roughly described by the diagram below. There are also five appendices, largely selfcontained, which treat special topics. I. Arbitrary commutative rings I H. The ring of V. Miscellaneous IIl. Fields integers examples IV. Dedekind domains Contents Chapter r. Basie Coneepts
Lectures on the hcobordism theorem by
John W Milnor(
Book
)
26 editions published between 1965 and 2016 in 3 languages and held by 436 WorldCat member libraries worldwide
These lectures provide students and specialists with preliminary and valuable information from university courses and seminars in mathematics. This set gives new proof of the hcobordism theorem that is different from the original proof presented by S. Smale. Originally published in 1965. The Princeton Legacy Library uses the latest printondemand technology to again make available previously outofprint books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905
26 editions published between 1965 and 2016 in 3 languages and held by 436 WorldCat member libraries worldwide
These lectures provide students and specialists with preliminary and valuable information from university courses and seminars in mathematics. This set gives new proof of the hcobordism theorem that is different from the original proof presented by S. Smale. Originally published in 1965. The Princeton Legacy Library uses the latest printondemand technology to again make available previously outofprint books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905
Dynamics in one complex variable by
John W Milnor(
Book
)
19 editions published between 2006 and 2013 in English and held by 396 WorldCat member libraries worldwide
This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of twodimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattés map has been made more inclusive, and the écalleVoronin theory of parabolic points is described. The résidu itératif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated. Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field
19 editions published between 2006 and 2013 in English and held by 396 WorldCat member libraries worldwide
This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of twodimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattés map has been made more inclusive, and the écalleVoronin theory of parabolic points is described. The résidu itératif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated. Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field
Dynamics in one complex variable : introductory lectures by
John W Milnor(
Book
)
27 editions published between 1990 and 2000 in English and held by 323 WorldCat member libraries worldwide
This text studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. It is based on introductory lectures given by the author at Stony Brook, NY, in the past ten years. The subject is large and rapidly growing. These notes are intended to introduce the reader to some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of twodimensional differential geometry, as well as some basic topics from topology. The exposition is clear and enriched by many beautiful illustrations
27 editions published between 1990 and 2000 in English and held by 323 WorldCat member libraries worldwide
This text studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. It is based on introductory lectures given by the author at Stony Brook, NY, in the past ten years. The subject is large and rapidly growing. These notes are intended to introduce the reader to some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of twodimensional differential geometry, as well as some basic topics from topology. The exposition is clear and enriched by many beautiful illustrations
Laminations and foliations in dynamics, geometry and topology : proceedings of the conference on laminations and foliations
in dynamics, geometry and topology, May 1824, 1998, SUNY at Stony Brook by
Mikhail Lyubich(
Book
)
11 editions published between 2000 and 2001 in English and held by 230 WorldCat member libraries worldwide
11 editions published between 2000 and 2001 in English and held by 230 WorldCat member libraries worldwide
Differential topology by
John W Milnor(
Book
)
20 editions published between 1958 and 2007 in English and Russian and held by 182 WorldCat member libraries worldwide
20 editions published between 1958 and 2007 in English and Russian and held by 182 WorldCat member libraries worldwide
Frontiers in complex dynamics : in celebration of John Milnor's 80th birthday by
Scott Sutherland(
Book
)
7 editions published in 2014 in English and held by 163 WorldCat member libraries worldwide
John Milnor, best known for his work in differential topology, Ktheory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing. This collection will be useful to students and researchers for decades to come. The contributors are Marco Abate, Marco Arizzi, Alexander Blokh, Thierry Bousch, Xavier Buff, Serge Cantat, Tao Chen, Robert Devaney, Alexandre Dezotti, TienCuong Dinh, Romain Dujardin, Hugo GarcíaCompeán, William Goldman, Rotislav Grigorchuk, John Hubbard, Yunping Jiang, Linda Keen, Jan Kiwi, Genadi Levin, Daniel Meyer, John Milnor, Carlos Moreira, Vincente Muñoz, VietAnh Nguyên, Lex Oversteegen, Ricardo PérezMarco, Ross Ptacek, Jasmin Raissy, Pascale Roesch, Roberto SantosSilva, Dierk Schleicher, Nessim Sibony, Daniel Smania, Tan Lei, William Thurston, Vladlen Timorin, Sebastian van Strien, and Alberto Verjovsky
7 editions published in 2014 in English and held by 163 WorldCat member libraries worldwide
John Milnor, best known for his work in differential topology, Ktheory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing. This collection will be useful to students and researchers for decades to come. The contributors are Marco Abate, Marco Arizzi, Alexander Blokh, Thierry Bousch, Xavier Buff, Serge Cantat, Tao Chen, Robert Devaney, Alexandre Dezotti, TienCuong Dinh, Romain Dujardin, Hugo GarcíaCompeán, William Goldman, Rotislav Grigorchuk, John Hubbard, Yunping Jiang, Linda Keen, Jan Kiwi, Genadi Levin, Daniel Meyer, John Milnor, Carlos Moreira, Vincente Muñoz, VietAnh Nguyên, Lex Oversteegen, Ricardo PérezMarco, Ross Ptacek, Jasmin Raissy, Pascale Roesch, Roberto SantosSilva, Dierk Schleicher, Nessim Sibony, Daniel Smania, Tan Lei, William Thurston, Vladlen Timorin, Sebastian van Strien, and Alberto Verjovsky
Topological methods in modern mathematics : a symposium in honor of John Milnor's sixtieth birthday by Symposium in Honor of John Milnor's Sixtieth Birthday(
Book
)
9 editions published in 1993 in English and held by 147 WorldCat member libraries worldwide
9 editions published in 1993 in English and held by 147 WorldCat member libraries worldwide
Geometry by
John W Milnor(
Book
)
19 editions published between 1993 and 1994 in English and held by 130 WorldCat member libraries worldwide
19 editions published between 1993 and 1994 in English and held by 130 WorldCat member libraries worldwide
Collected papers by
John W Milnor(
Book
)
in English and held by 105 WorldCat member libraries worldwide
in English and held by 105 WorldCat member libraries worldwide
Algebra by
John W Milnor(
Book
)
6 editions published between 2010 and 2011 in English and held by 98 WorldCat member libraries worldwide
6 editions published between 2010 and 2011 in English and held by 98 WorldCat member libraries worldwide
Holomorphic dynamics and renormalization : a volume in honour of John Milnor's 75th birthday(
Book
)
5 editions published in 2008 in English and held by 93 WorldCat member libraries worldwide
The papers collected in this volume reflect some of the directions of research in two closely related fields: Complex Dynamics and Renormalization in Dynamical Systems. While dynamics of polynomial mappings, particularly quadratics, has by now reached a mature state of development, much less is known about nonpolynomial rational maps. The reader will be introduced into this fascinating world and a related area of transcendental dynamics by the papers in this volume. A graduate student will find an area rich with open problems and beautiful computer simulations. A survey by V. Nekrashevych int
5 editions published in 2008 in English and held by 93 WorldCat member libraries worldwide
The papers collected in this volume reflect some of the directions of research in two closely related fields: Complex Dynamics and Renormalization in Dynamical Systems. While dynamics of polynomial mappings, particularly quadratics, has by now reached a mature state of development, much less is known about nonpolynomial rational maps. The reader will be introduced into this fascinating world and a related area of transcendental dynamics by the papers in this volume. A graduate student will find an area rich with open problems and beautiful computer simulations. A survey by V. Nekrashevych int
Homotopy, homology, and manifolds by
John W Milnor(
Book
)
6 editions published in 2009 in English and held by 87 WorldCat member libraries worldwide
6 editions published in 2009 in English and held by 87 WorldCat member libraries worldwide
Lectures on characteristic classes by
John W Milnor(
Book
)
24 editions published between 1957 and 1992 in English and Undetermined and held by 84 WorldCat member libraries worldwide
24 editions published between 1957 and 1992 in English and Undetermined and held by 84 WorldCat member libraries worldwide
Collected papers by
John W Milnor(
Book
)
4 editions published in 1994 in English and held by 4 WorldCat member libraries worldwide
4 editions published in 1994 in English and held by 4 WorldCat member libraries worldwide
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Related Identities
 Lyubich, Mikhail 1959 Other Author Editor
 Bonifant, Araceli 1963 Editor
 Stasheff, James D.
 Husemöller, Dale
 Sutherland, Scott Editor
 Minsky, Yair Nathan Other Editor
 Sutherland, Scott 1959 Editor
 Bass, Hyman 1932 Author Editor
 Goldberg, Lisa R. Editor
 Phillips, Anthony V. (Anthony Valiant) 1938
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Associated Subjects
Abelian groups Associative rings Bilinear forms Characteristic classes Cobordism theory Differentiable dynamical systems Differentiable manifolds Differential topology Fiber bundles (Mathematics) Foliations (Mathematics) Forms, Quadratic Functions of complex variables Functor theory Geometry Geometry, Algebraic Geometry, Differential Hamiltonian systems Holomorphic functions Holomorphic mappings Homology theory Homotopy theory Ktheory Linear algebraic groups Manifolds (Mathematics) Mappings (Mathematics) Mathematicians Mathematics Milnor, John W.(John Willard), Modules (Algebra) Morse, Marston, Morse theory Renormalization group Riemann surfaces Siegel domains Topological manifolds Topology United States
Alternative Names
Con Milnor
Džons Milnors
John Milnor Amerikaans wiskundige
John Milnor amerikansk matematikar
John Milnor amerikansk matematiker
John Milnor matematico statunitense
John Milnor mathématicien américain
John Willard Milnor USamerikanischer Mathematiker, Professor für Mathematik
Milnor, Dž.
Milnor, Dž. 1931
Milnor, Dzh.
Milnor, Dzh 1931
Milnor, Dzhon 1931
Milnor, J.
Milnor J. 1931
Milnor, J. (John), 1931
Milnor, J. W.
Milnor, John.
Milnor John 1931....
Milnor, John W.
Milnor, John W. 1931
Milnor, John W. (John Willard)
Milnor, John Willard
Milnor, John Willard 1931
Willard Milnor, John 1931
Джон Мілнор
Милнор, Дж..
Милнор, Дж 1931
Милнор, Джон.
Милнор, Джон Уиллард
ג'ון מלינור
جان ملنار
جان میلنور ریاضیدان آمریکایی
جون ملنور
ဂျွန် မီလ်နော
존 밀너
ジョン・ウィラード・ミルナー
ミルナー
ミルナー, J
ミルナー, J. W
约翰·米尔诺
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