Mumford, David 1937
Overview
Works:  119 works in 816 publications in 5 languages and 11,199 library holdings 

Genres:  History Essays 
Roles:  Author, Editor, Other, Author of introduction, Interviewee, Creator 
Classifications:  QA564, 516.35 
Publication Timeline
.
Most widely held works by
David Mumford
Indra's pearls : the vision of Felix Klein by
David Mumford(
)
28 editions published between 2000 and 2015 in English and held by 1,967 WorldCat member libraries worldwide
"Felix Klein, one of the great nineteenthcentury geometers, discovered in mathematics an idea prefigured in Buddhist mythology: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple coexisting symmetries, each simple in itself, but whose interactions produce fractals on the edge of chaos. For a century these images, which were practically impossible to draw by hand, barely existed outside the imagination of mathematicians. However in the 1980s the authors embarked on the first computer exploration of Klein's vision, and in so doing found further extraordinary images of their own. Join the authors on the path from some basic mathemathical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can learn to understand what the images mean and follow the stepbystep instructions for writing computer programs that generate them. More advanced readers can see how the images relate to ideas that take them to the forefront of research."Jacket
28 editions published between 2000 and 2015 in English and held by 1,967 WorldCat member libraries worldwide
"Felix Klein, one of the great nineteenthcentury geometers, discovered in mathematics an idea prefigured in Buddhist mythology: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple coexisting symmetries, each simple in itself, but whose interactions produce fractals on the edge of chaos. For a century these images, which were practically impossible to draw by hand, barely existed outside the imagination of mathematicians. However in the 1980s the authors embarked on the first computer exploration of Klein's vision, and in so doing found further extraordinary images of their own. Join the authors on the path from some basic mathemathical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can learn to understand what the images mean and follow the stepbystep instructions for writing computer programs that generate them. More advanced readers can see how the images relate to ideas that take them to the forefront of research."Jacket
Geometric invariant theory by
David Mumford(
Book
)
55 editions published between 1965 and 2012 in 4 languages and held by 1,160 WorldCat member libraries worldwide
55 editions published between 1965 and 2012 in 4 languages and held by 1,160 WorldCat member libraries worldwide
The best writing on mathematics, 2012 by
Mircea Pitici(
)
11 editions published between 2011 and 2013 in English and held by 1,056 WorldCat member libraries worldwide
This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field. The Best Writing on Mathematics 2012 makes available to a wide audience many articles not easily found anywhere elseand you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Robert Lang explains mathematical aspects of origami foldings; Terence Tao discusses the frequency and distribution of the prime numbers; Timothy Gowers and Mario Livio ponder whether mathematics is invented or discovered; Brian Hayes describes what is special about a ball in five dimensions; Mark Colyvan glosses on the mathematics of dating; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this musthave anthology includes a foreword by esteemed mathematician David Mumford and an introduction by the editor Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken usand where it is headed
11 editions published between 2011 and 2013 in English and held by 1,056 WorldCat member libraries worldwide
This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field. The Best Writing on Mathematics 2012 makes available to a wide audience many articles not easily found anywhere elseand you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Robert Lang explains mathematical aspects of origami foldings; Terence Tao discusses the frequency and distribution of the prime numbers; Timothy Gowers and Mario Livio ponder whether mathematics is invented or discovered; Brian Hayes describes what is special about a ball in five dimensions; Mark Colyvan glosses on the mathematics of dating; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this musthave anthology includes a foreword by esteemed mathematician David Mumford and an introduction by the editor Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken usand where it is headed
Tata lectures on theta by
David Mumford(
)
79 editions published between 1982 and 2007 in English and Undetermined and held by 1,030 WorldCat member libraries worldwide
The first of a series of three volumes surveying the theory of theta functions and its significance in the fields of representation theory and algebraic geometry, this volume deals with the basic theory of theta functions in one and several variables, and some of its number theoretic applications. Requiring no background in advanced algebraic geometry, the text serves as a modern introduction to the subject
79 editions published between 1982 and 2007 in English and Undetermined and held by 1,030 WorldCat member libraries worldwide
The first of a series of three volumes surveying the theory of theta functions and its significance in the fields of representation theory and algebraic geometry, this volume deals with the basic theory of theta functions in one and several variables, and some of its number theoretic applications. Requiring no background in advanced algebraic geometry, the text serves as a modern introduction to the subject
The red book of varieties and schemes by
David Mumford(
Book
)
61 editions published between 1988 and 2004 in English and German and held by 1,022 WorldCat member libraries worldwide
Mumford's famous Red Book gives a simple readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduate students or mathematicians in other fields wishing to learn quickly what algebraic geometry is all about. This new edition also includes an overview of the theory of curves, their moduli spaces and their Jacobians, one of the most exciting fields within algebraic geometry. The book is aimed at graduate students and professors seeking to learn i) the concept of "scheme" as part of their study of algebraic geometry and ii) an overview of moduli problems for curves and of the use of theta functions to study these
61 editions published between 1988 and 2004 in English and German and held by 1,022 WorldCat member libraries worldwide
Mumford's famous Red Book gives a simple readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduate students or mathematicians in other fields wishing to learn quickly what algebraic geometry is all about. This new edition also includes an overview of the theory of curves, their moduli spaces and their Jacobians, one of the most exciting fields within algebraic geometry. The book is aimed at graduate students and professors seeking to learn i) the concept of "scheme" as part of their study of algebraic geometry and ii) an overview of moduli problems for curves and of the use of theta functions to study these
Lectures on curves on an algebraic surface by
David Mumford(
Book
)
35 editions published between 1964 and 2016 in 4 languages and held by 736 WorldCat member libraries worldwide
These lectures, delivered by Professor Mumford at Harvard in 19631964, are devoted to a study of properties of families of algebraic curves, on a nonsingular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint
35 editions published between 1964 and 2016 in 4 languages and held by 736 WorldCat member libraries worldwide
These lectures, delivered by Professor Mumford at Harvard in 19631964, are devoted to a study of properties of families of algebraic curves, on a nonsingular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint
Algebraic geometry I : complex projective varieties by
David Mumford(
Book
)
53 editions published between 1976 and 1995 in 3 languages and held by 701 WorldCat member libraries worldwide
53 editions published between 1976 and 1995 in 3 languages and held by 701 WorldCat member libraries worldwide
Abelian varieties by
David Mumford(
Book
)
62 editions published between 1970 and 2014 in 3 languages and held by 580 WorldCat member libraries worldwide
62 editions published between 1970 and 2014 in 3 languages and held by 580 WorldCat member libraries worldwide
Filtering, segmentation, and depth by
M Nitzberg(
Book
)
17 editions published in 1993 in English and Undetermined and held by 497 WorldCat member libraries worldwide
"Computer vision seeks a process that starts with a noisy, ambiguous signal from a TV camera and ends with a highlevel description of discrete objects located in 3dimensional space and identified in a human classification. This book addresses the process at several levels. First to be treated are the lowlevel imageprocessing issues of noise removaland smoothing while preserving important lines and singularities in an image. At a slightly higher level, a robust contour tracing algorithm is described that produces a cartoon of the important lines in the image. Thirdis the highlevel task of reconstructing the geometry of objects in the scene. The book has two aims: to give the computer vision community a new approach to early visual processing, in the form of image segmentation that incorporates occlusion at a low level, and to introduce real computer algorithms that do a better job than what most vision programmers use currently. The algorithms are:  a nonlinear filter that reduces noise and enhances edges,  an edge detector that also finds corners and produces smoothed contours rather than bitmaps,  an algorithm for filling gaps in contours."PUBLISHER'S WEBSITE
17 editions published in 1993 in English and Undetermined and held by 497 WorldCat member libraries worldwide
"Computer vision seeks a process that starts with a noisy, ambiguous signal from a TV camera and ends with a highlevel description of discrete objects located in 3dimensional space and identified in a human classification. This book addresses the process at several levels. First to be treated are the lowlevel imageprocessing issues of noise removaland smoothing while preserving important lines and singularities in an image. At a slightly higher level, a robust contour tracing algorithm is described that produces a cartoon of the important lines in the image. Thirdis the highlevel task of reconstructing the geometry of objects in the scene. The book has two aims: to give the computer vision community a new approach to early visual processing, in the form of image segmentation that incorporates occlusion at a low level, and to introduce real computer algorithms that do a better job than what most vision programmers use currently. The algorithms are:  a nonlinear filter that reduces noise and enhances edges,  an edge detector that also finds corners and produces smoothed contours rather than bitmaps,  an algorithm for filling gaps in contours."PUBLISHER'S WEBSITE
Curves and their Jacobians by
David Mumford(
Book
)
26 editions published between 1975 and 1980 in English and held by 336 WorldCat member libraries worldwide
26 editions published between 1975 and 1980 in English and held by 336 WorldCat member libraries worldwide
Pattern theory : the stochastic analysis of realworld signals by
David Mumford(
Book
)
16 editions published between 2010 and 2018 in English and held by 264 WorldCat member libraries worldwide
"Pattern Theory covers six classic attempts at modeling signals from the human and natural world: natural language (written), music, character recognition, texture modeling, face recognition, and natural scenes. These applications, appealing to students and researchers alike, include fourteen "crash courses" giving all the needed basics, exercises, and numerical simulations. Thus, it is a complete pedagogic tool at master or firstyear graduate level. I endorse the publication of Pattern Theory, and will actually use it and recommend it to other researchers."JeanMichel Morel, CMLA
16 editions published between 2010 and 2018 in English and held by 264 WorldCat member libraries worldwide
"Pattern Theory covers six classic attempts at modeling signals from the human and natural world: natural language (written), music, character recognition, texture modeling, face recognition, and natural scenes. These applications, appealing to students and researchers alike, include fourteen "crash courses" giving all the needed basics, exercises, and numerical simulations. Thus, it is a complete pedagogic tool at master or firstyear graduate level. I endorse the publication of Pattern Theory, and will actually use it and recommend it to other researchers."JeanMichel Morel, CMLA
Selected papers on the classification of varieties and moduli spaces by
David Mumford(
Book
)
12 editions published between 2004 and 2010 in English and held by 201 WorldCat member libraries worldwide
12 editions published between 2004 and 2010 in English and held by 201 WorldCat member libraries worldwide
Tata lectures on theta by
David Mumford(
Book
)
32 editions published between 1984 and 2012 in English and Italian and held by 146 WorldCat member libraries worldwide
The second in a series of three volumes surveying the theory of theta functions, this volume gives emphasis to the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the KortewegdeVries equations as well as other nonlinear differential equations of mathematical physics. This book presents an explicit elementary construction of hyperelliptic Jacobian varieties and is a selfcontained introduction to the theory of the Jacobians. It also ties together nineteenthcentury discoveries due to Jacobi, Neumann, and Frobenius with recent discoveries of Gelfand, McKean, Moser, John Fay, and others. A definitive body of information and research on the subject of theta functions, this volume will be a useful addition to individual and mathematics research libraries
32 editions published between 1984 and 2012 in English and Italian and held by 146 WorldCat member libraries worldwide
The second in a series of three volumes surveying the theory of theta functions, this volume gives emphasis to the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the KortewegdeVries equations as well as other nonlinear differential equations of mathematical physics. This book presents an explicit elementary construction of hyperelliptic Jacobian varieties and is a selfcontained introduction to the theory of the Jacobians. It also ties together nineteenthcentury discoveries due to Jacobi, Neumann, and Frobenius with recent discoveries of Gelfand, McKean, Moser, John Fay, and others. A definitive body of information and research on the subject of theta functions, this volume will be a useful addition to individual and mathematics research libraries
Tata lectures on theta III by
David Mumford(
Book
)
23 editions published between 1991 and 2010 in 3 languages and held by 145 WorldCat member libraries worldwide
This volume is the third of three in a series surveying the theory of theta functions which play a central role in the fields of complex analysis, algebraic geometry, number theory and most recently particle physics. Based on lectures given by the author at the Tata Institute of Fundamental Research in Bombay, these volumes constitute a systematic exposition of theta functions, beginning with their historical roots as analytic functions in one variable (Volume I), touching on some of the beautiful ways they can be used to describe moduli spaces (Volume II), and culminating in a methodical comp
23 editions published between 1991 and 2010 in 3 languages and held by 145 WorldCat member libraries worldwide
This volume is the third of three in a series surveying the theory of theta functions which play a central role in the fields of complex analysis, algebraic geometry, number theory and most recently particle physics. Based on lectures given by the author at the Tata Institute of Fundamental Research in Bombay, these volumes constitute a systematic exposition of theta functions, beginning with their historical roots as analytic functions in one variable (Volume I), touching on some of the beautiful ways they can be used to describe moduli spaces (Volume II), and culminating in a methodical comp
Stability of projective varieties : lectures ... by
David Mumford(
Book
)
21 editions published in 1977 in English and French and held by 133 WorldCat member libraries worldwide
21 editions published in 1977 in English and French and held by 133 WorldCat member libraries worldwide
Introduction to algebraic geometry; preliminary version of first 3 chapters by
David Mumford(
Book
)
20 editions published between 1966 and 1976 in English and held by 119 WorldCat member libraries worldwide
20 editions published between 1966 and 1976 in English and held by 119 WorldCat member libraries worldwide
Contributions to algebraic geometry in honor of Oscar Zariski by
Michael Artin(
Book
)
9 editions published in 1979 in English and held by 118 WorldCat member libraries worldwide
9 editions published in 1979 in English and held by 118 WorldCat member libraries worldwide
Toroidal embeddings by
George Kempf(
Book
)
12 editions published between 1973 and 2008 in 3 languages and held by 95 WorldCat member libraries worldwide
12 editions published between 1973 and 2008 in 3 languages and held by 95 WorldCat member libraries worldwide
A stochastic grammar of images by
Song Chun Zhu(
)
8 editions published between 2006 and 2007 in English and held by 92 WorldCat member libraries worldwide
This exploratory paper quests for a stochastic and context sensitive grammar of images. The grammar should achieve the following four objectives and thus serves as a unified framework of representation, learning, and recognition for a large number of object categories. (i) The grammar represents both the hierarchical decompositions from scenes, to objects, parts, primitives and pixels by terminal and nonterminal nodes and the contexts for spatial and functional relations by horizontal links between the nodes. It formulates each object category as the set of all possible valid configurations produced by the grammar. (ii) The grammar is embodied in a simple AndOr graph representation where each Ornode points to alternative subconfigurations and an Andnode is decomposed into a number of components. This representation supports recursive topdown/bottomup procedures for image parsing under the Bayesian framework and make it convenient to scale up in complexity. Given an input image, the image parsing task constructs a most probable parse graph onthefly as the output interpretation and this parse graph is a subgraph of the AndOr graph after making choice on the Ornodes. (iii) A probabilistic model is defined on this AndOr graph representation to account for the natural occurrence frequency of objects and parts as well as their relations. This model is learned from a relatively small training set per category and then sampled to synthesize a large number of configurations to cover novel object instances in the test set. This generalization capability is mostly missing in discriminative machine learning methods and can largely improve recognition performance in experiments. (iv) To fill the wellknown semantic gap between symbols and raw signals, the grammar includes a series of visual dictionaries and organizes them through graph composition. At the bottomlevel the dictionary is a set of image primitives each having a number of anchor points with open bonds to link with other primitives. These primitives can be combined to form larger and larger graph structures for parts and objects. The ambiguities in inferring local primitives shall be resolved through topdown computation using larger structures. Finally these primitives forms a primal sketch representation which will generate the input image with every pixels explained. The proposal grammar integrates three prominent representations in the literature: stochastic grammars for composition, Markov (or graphical) models for contexts, and sparse coding with primitives (wavelets). It also combines the structurebased and appearance based methods in the vision literature. Finally the paper presents three case studies to illustrate the proposed grammar
8 editions published between 2006 and 2007 in English and held by 92 WorldCat member libraries worldwide
This exploratory paper quests for a stochastic and context sensitive grammar of images. The grammar should achieve the following four objectives and thus serves as a unified framework of representation, learning, and recognition for a large number of object categories. (i) The grammar represents both the hierarchical decompositions from scenes, to objects, parts, primitives and pixels by terminal and nonterminal nodes and the contexts for spatial and functional relations by horizontal links between the nodes. It formulates each object category as the set of all possible valid configurations produced by the grammar. (ii) The grammar is embodied in a simple AndOr graph representation where each Ornode points to alternative subconfigurations and an Andnode is decomposed into a number of components. This representation supports recursive topdown/bottomup procedures for image parsing under the Bayesian framework and make it convenient to scale up in complexity. Given an input image, the image parsing task constructs a most probable parse graph onthefly as the output interpretation and this parse graph is a subgraph of the AndOr graph after making choice on the Ornodes. (iii) A probabilistic model is defined on this AndOr graph representation to account for the natural occurrence frequency of objects and parts as well as their relations. This model is learned from a relatively small training set per category and then sampled to synthesize a large number of configurations to cover novel object instances in the test set. This generalization capability is mostly missing in discriminative machine learning methods and can largely improve recognition performance in experiments. (iv) To fill the wellknown semantic gap between symbols and raw signals, the grammar includes a series of visual dictionaries and organizes them through graph composition. At the bottomlevel the dictionary is a set of image primitives each having a number of anchor points with open bonds to link with other primitives. These primitives can be combined to form larger and larger graph structures for parts and objects. The ambiguities in inferring local primitives shall be resolved through topdown computation using larger structures. Finally these primitives forms a primal sketch representation which will generate the input image with every pixels explained. The proposal grammar integrates three prominent representations in the literature: stochastic grammars for composition, Markov (or graphical) models for contexts, and sparse coding with primitives (wavelets). It also combines the structurebased and appearance based methods in the vision literature. Finally the paper presents three case studies to illustrate the proposed grammar
Algebraic geometry II by
David Mumford(
Book
)
10 editions published between 2015 and 2016 in English and held by 77 WorldCat member libraries worldwide
10 editions published between 2015 and 2016 in English and held by 77 WorldCat member libraries worldwide
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Audience Level
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Related Identities
 Series, Caroline Other
 Wright, David James
 Klein, Felix 18491925
 Indra (Hindu deity)
 Gonick, Larry Illustrator
 Pitici, Mircea 1965 Author Editor
 Fogarty, John 1934
 Musili, C. Other Contributor
 Shiota, Takahiro Editor
 Nitzberg, M. (Mark) 1961 Author
Useful Links
Associated Subjects
Abelian varieties Algebraic varieties Algebraic varietiesClassification theory Artificial intelligence AstronomyAwards Australia Cell aggregationMathematics China Combinatorial analysis Computer science Computer vision Curves, Algebraic Digital filters (Mathematics) Direct marketing Embeddings (Mathematics) Fractals Functional analysis Functions, Special Functions, Theta Functions of complex variables Geometry Geometry, Algebraic Graph grammars Image processingDigital techniques Image processingStatistical methods Indra (Hindu deity) Invariants Jacobians Klein, Felix, Linear algebraic groups Mathematicians Mathematics MathematicsAwards Moduli theory Mumford, David, Number theory Parsing (Computer grammar) Pattern perception Pattern recognition systems Perlmutter, Saul Schemes (Algebraic geometry) Schmidt, Brian, Scientists Software engineering Surfaces, Algebraic Symmetry Topological imbeddings Torus (Geometry) United States Zariski, Oscar,
Covers
Alternative Names
David Bryant Mumford englischer Mathematiker
David Mumford Amerikaans wiskundige
David Mumford amerikansk matematiker
David Mumford matemàtic estatunidenc
David Mumford matemático estadounidense
David Mumford matematico statunitense
David Mumford mathématicien américain
Mamford, D.
Mamford, D. 1937
Mumford, D.
Mumford, D. 1937
Mumford, D. (David)
Mumford, D. (David), 1937
Mumford, David
Mumford, David Bryant
Mumford, David Bryant 1937
Девід Мамфорд
Дэвид Мамфорд американский математик
Мамфорд Д.
Мамфорд, Д 1937
Мамфорд, Д. (Дэйвид), 1937
דייוויד ממפורד מתמטיקאי אמריקני
ديفيد مومفورد
ديفيد مومفورد رياضياتي أمريكي
دیوید ممفورد ریاضیدان آمریکایی
ڈیوڈ ممفورڈ
ডেভিড মামফোর্ড
ডেভিড মামফোর্ড মার্কিন গণিতবিদ
ဒေးဗစ် မန်းဖို့ဒ်
데이비드 멈퍼드
デヴィッド・マンフォード
マンフォード, D
戴维·芒福德
Languages