WorldCat Identities

Mumford, David 1937-

Works: 124 works in 622 publications in 6 languages and 10,055 library holdings
Genres: History 
Roles: Author, Editor, Other, Author of introduction, Creator
Classifications: QA564, 516.5
Publication Timeline
Most widely held works about David Mumford
Most widely held works by David Mumford
Geometric invariant theory by David Mumford( Book )

44 editions published between 1965 and 2012 in 4 languages and held by 862 WorldCat member libraries worldwide

The red book of varieties and schemes by David Mumford( Book )

47 editions published between 1988 and 2006 in 4 languages and held by 783 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
Abelian varieties by David Mumford( Book )

60 editions published between 1970 and 2014 in 3 languages and held by 575 WorldCat member libraries worldwide

Algebraic geometry I : complex projective varieties by David Mumford( Book )

23 editions published between 1976 and 1995 in English and Russian and held by 571 WorldCat member libraries worldwide

Indra's pearls : the vision of Felix Klein by David Mumford( Book )

27 editions published between 2000 and 2015 in English and held by 533 WorldCat member libraries worldwide

"Felix Klein, one of the great nineteenth-century 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 co-existing 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 step-by-step 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
Lectures on curves on an algebraic surface by David Mumford( Book )

29 editions published between 1964 and 2016 in 3 languages and held by 519 WorldCat member libraries worldwide

These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular 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
Tata lectures on theta by David Mumford( Book )

45 editions published between 1982 and 2007 in 4 languages and held by 471 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 Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics. This book presents an explicit elementary construction of hyperelliptic Jacobian varieties and is a self-contained introduction to the theory of the Jacobians. It also ties together nineteenth-century 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
Filtering, segmentation, and depth by M Nitzberg( Book )

17 editions published in 1993 in English and Undetermined and held by 330 WorldCat member libraries worldwide

"Computer vision seeks a process that starts with a noisy, ambiguous signal from a TV camera and ends with a high-level description of discrete objects located in 3-dimensional space and identified in a human classification. This book addresses the process at several levels. First to be treated are the low-level image-processing 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 high-level 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 )

20 editions published between 1975 and 1980 in English and held by 327 WorldCat member libraries worldwide

Geometric invariant theory by David Mumford( Book )

3 editions published between 1994 and 2002 in English and held by 240 WorldCat member libraries worldwide

Pattern theory : the stochastic analysis of real-world signals by David Mumford( Book )

9 editions published in 2010 in English and held by 171 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 first-year graduate level. I endorse the publication of Pattern Theory, and will actually use it and recommend it to other researchers."--Jean-Michel Morel, CMLA
Selected papers on the classification of varieties and moduli spaces by David Mumford( Book )

in English and held by 149 WorldCat member libraries worldwide

Tata lectures on theta III by David Mumford( Book )

17 editions published between 1991 and 2010 in 3 languages and held by 123 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 )

15 editions published in 1977 in English and French and held by 116 WorldCat member libraries worldwide

Contributions to algebraic geometry in honor of Oscar Zariski by Michael Artin( Book )

7 editions published in 1979 in English and held by 116 WorldCat member libraries worldwide

Introduction to algebraic geometry; preliminary version of first 3 chapters by David Mumford( Book )

21 editions published between 1966 and 1976 in English and held by 116 WorldCat member libraries worldwide

Toroidal embeddings by George Kempf( Book )

11 editions published in 1973 in English and Undetermined and held by 79 WorldCat member libraries worldwide

The topology of normal singularities of an algebraic surface and a criterion for simplicity by David Mumford( Book )

8 editions published in 1961 in English and held by 60 WorldCat member libraries worldwide

The best writing on mathematics, 2012 by Mircea Pitici( Book )

10 editions published between 2011 and 2013 in English and Undetermined and held by 15 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 else--and 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 must-have 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 us--and where it is headed
A stochastic grammar of images by Song Chun Zhu( Book )

8 editions published between 2006 and 2007 in English and held by 15 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 non-terminal 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 And-Or graph representation where each Or-node points to alternative sub-configurations and an And-node is decomposed into a number of components. This representation supports recursive top-down/bottom-up 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 on-the-fly as the output interpretation and this parse graph is a subgraph of the And-Or graph after making choice on the Or-nodes. (iii) A probabilistic model is defined on this And-Or 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 well-known semantic gap between symbols and raw signals, the grammar includes a series of visual dictionaries and organizes them through graph composition. At the bottom-level 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 top-down 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 structure-based and appearance based methods in the vision literature. Finally the paper presents three case studies to illustrate the proposed grammar
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Indra's pearls : the vision of Felix Klein
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)

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

دیوید ممفورد ریاضی‌دان آمریکایی

ڈیوڈ ممفورڈ

ডেভিড মামফোর্ড

데이비드 멈퍼드


マンフォード, D


The red book of varieties and schemesAbelian varietiesAlgebraic geometry I : complex projective varietiesIndra's pearls : the vision of Felix KleinLectures on curves on an algebraic surfaceTata lectures on thetaFiltering, segmentation, and depthGeometric invariant theory