Mumford, David 1937
Overview
Works:  132 works in 710 publications in 5 languages and 9,466 library holdings 

Genres:  History 
Roles:  Author, Editor, Author of introduction, Creator, Interviewee, Director, Author of screenplay 
Classifications:  QA564, 516.5 
Publication Timeline
.
Most widely held works by
David Mumford
Geometric invariant theory by
David Mumford(
Book
)
51 editions published between 1965 and 2012 in 4 languages and held by 1,126 WorldCat member libraries worldwide
51 editions published between 1965 and 2012 in 4 languages and held by 1,126 WorldCat member libraries worldwide
Algebraic geometry I : complex projective varieties by
David Mumford(
Book
)
46 editions published between 1976 and 1995 in 4 languages and held by 669 WorldCat member libraries worldwide
46 editions published between 1976 and 1995 in 4 languages and held by 669 WorldCat member libraries worldwide
Abelian varieties by
David Mumford(
Book
)
56 editions published between 1970 and 2012 in 3 languages and held by 555 WorldCat member libraries worldwide
56 editions published between 1970 and 2012 in 3 languages and held by 555 WorldCat member libraries worldwide
Tata lectures on theta by
David Mumford(
Book
)
69 editions published between 1982 and 2007 in 4 languages and held by 521 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
69 editions published between 1982 and 2007 in 4 languages and held by 521 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
Lectures on curves on an algebraic surface by
David Mumford(
Book
)
28 editions published between 1964 and 2005 in 4 languages and held by 511 WorldCat member libraries worldwide
28 editions published between 1964 and 2005 in 4 languages and held by 511 WorldCat member libraries worldwide
Indra's pearls : the vision of Felix Klein by
David Mumford(
Book
)
24 editions published between 2000 and 2008 in English and Undetermined and held by 497 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
24 editions published between 2000 and 2008 in English and Undetermined and held by 497 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
The red book of varieties and schemes by
David Mumford(
Book
)
21 editions published between 1988 and 1999 in English and Undetermined and held by 451 WorldCat member libraries worldwide
"The book under review is a reprint of Mumford's famous Harvard lecture notes, widely used by the few past generations of algebraic geometers. SpringerVerlag has done the mathematical community a service by making these notes available once again.... The informal style and frequency of examples make the book an excellent text." (Mathematical Reviews)
21 editions published between 1988 and 1999 in English and Undetermined and held by 451 WorldCat member libraries worldwide
"The book under review is a reprint of Mumford's famous Harvard lecture notes, widely used by the few past generations of algebraic geometers. SpringerVerlag has done the mathematical community a service by making these notes available once again.... The informal style and frequency of examples make the book an excellent text." (Mathematical Reviews)
The red book of varieties and schemes : includes the Michigan Lectures (1974) on Curves and their Jacobinians by
David Mumford(
Book
)
34 editions published between 1988 and 2004 in 3 languages and held by 335 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
34 editions published between 1988 and 2004 in 3 languages and held by 335 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
Filtering, segmentation, and depth by
M Nitzberg(
Book
)
17 editions published in 1993 in English and Undetermined and held by 331 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 331 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
)
25 editions published between 1975 and 1980 in English and Undetermined and held by 325 WorldCat member libraries worldwide
25 editions published between 1975 and 1980 in English and Undetermined and held by 325 WorldCat member libraries worldwide
Selected papers on the classification of varieties and moduli spaces by
David Mumford(
Book
)
8 editions published in 2004 in English and held by 185 WorldCat member libraries worldwide
8 editions published in 2004 in English and held by 185 WorldCat member libraries worldwide
Pattern theory : the stochastic analysis of realworld signals by
David Mumford(
Book
)
11 editions published in 2010 in English and held by 161 WorldCat member libraries worldwide
Pattern Theory, pioneered by Ulf Grenander, is a distinctive approach to the analysis of all forms of realworld signals. At its core is the design of a large variety of probabilistic models whose samples reproduce the look and feel of the real signals, their patterns, and their variability. Bayesian statistical inference then allows you to apply these models in the analysis of new signals. This book treats the mathematical tools, the models themselves, and the computational algorithms for applying statistics to analyze six representative classes of signals of increasing complexity
11 editions published in 2010 in English and held by 161 WorldCat member libraries worldwide
Pattern Theory, pioneered by Ulf Grenander, is a distinctive approach to the analysis of all forms of realworld signals. At its core is the design of a large variety of probabilistic models whose samples reproduce the look and feel of the real signals, their patterns, and their variability. Bayesian statistical inference then allows you to apply these models in the analysis of new signals. This book treats the mathematical tools, the models themselves, and the computational algorithms for applying statistics to analyze six representative classes of signals of increasing complexity
Tata lectures on theta III by
David Mumford(
Book
)
22 editions published between 1983 and 2010 in 4 languages and held by 135 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
22 editions published between 1983 and 2010 in 4 languages and held by 135 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
)
20 editions published in 1977 in English and French and held by 124 WorldCat member libraries worldwide
20 editions published in 1977 in English and French and held by 124 WorldCat member libraries worldwide
Contributions to algebraic geometry in honor of Oscar Zariski by
Michael Artin(
Book
)
6 editions published in 1979 in English and held by 113 WorldCat member libraries worldwide
6 editions published in 1979 in English and held by 113 WorldCat member libraries worldwide
Introduction to algebraic geometry; preliminary version of first 3 chapters by
David Mumford(
Book
)
20 editions published between 1966 and 1971 in English and held by 112 WorldCat member libraries worldwide
20 editions published between 1966 and 1971 in English and held by 112 WorldCat member libraries worldwide
Tata lectures on theta by
David Mumford(
Book
)
23 editions published between 1984 and 2012 in English and Italian and held by 83 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
23 editions published between 1984 and 2012 in English and Italian and held by 83 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
Toroidal embeddings by
George Kempf(
Book
)
10 editions published in 1973 in 3 languages and held by 76 WorldCat member libraries worldwide
10 editions published in 1973 in 3 languages and held by 76 WorldCat member libraries worldwide
A stochastic grammar of images by
Song Chun Zhu(
Book
)
9 editions published between 2006 and 2007 in English and held by 13 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
9 editions published between 2006 and 2007 in English and held by 13 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
The best writing on mathematics, 2012 by
Mircea Pitici(
Book
)
7 editions published between 2011 and 2013 in English and held by 10 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
7 editions published between 2011 and 2013 in English and held by 10 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
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Related Identities
 Series, Caroline
 Wright, David James
 Klein, Felix 18491925
 Indra (Hindu deity)
 Fogarty, John 1934
 Musili, C. Other Contributor
 Pitici, Mircea 1965 Author Editor
 Shiota, Takahiro Editor
 Nitzberg, M. (Mark) 1961 Author
 Tata Institute of Fundamental Research
Useful Links
Associated Subjects
Abelian varieties Algebraic topology Algebraic varieties Algebraic varietiesClassification theory Artificial intelligence Cell aggregationMathematics China Combinatorial analysis Computer science Computer vision Curves, Algebraic Differential equations, Partial 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 Mathematical physics Mathematicians Mathematics MathematicsAwards Moduli theory Mumford, David, Number theory Parsing (Computer grammar) Pattern perception Pattern recognition systems Schemes (Algebraic geometry) Series, Theta Software engineering Surfaces, Algebraic Symmetry Topological imbeddings Torus (Geometry) United States Zariski, Oscar,
Alternative Names
David Bryant Mumford englischer Mathematiker
David Mumford Amerikaans wiskundige
David Mumford matematico statunitense
David Mumford mathématicien américain
Mamford, D.
Mamford, D. 1937
Mumford, D.
Mumford, D. 1937
Mumford, D. (David), 1937
Mumford, David
Mumford, David Bryant
Девід Мамфорд
Дэвид Мамфорд американский математик
Мамфорд, Д..
Мамфорд, Д 1937
Мамфорд, Д. (Дэйвид), 1937
דייוויד ממפורד מתמטיקאי אמריקני
ديفيد مومفورد
دیوید ممفورد ریاضیدان آمریکایی
ڈیوڈ ممفورڈ
ডেভিড মামফোর্ড
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
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