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Mumford is a well-known mathematician and winner of the Fields Medal, the highest honor available in mathematics.

Many of these papers are currently unavailable, and the commentaries by Gieseker, Lange, Viehweg and Kempf are being published here for the first time.

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This book is an introduction to pattern theory, the theory behind the task of analyzing types of signals that the real world presents to us. It deals with generating mathematical models of the patterns in those signals and algorithms for analyzing the data based on these models. It exemplifies the view of applied mathematics as starting with a collection of problems from some area of science and then seeking the appropriate mathematics for clarifying the experimental data and the underlying processes of producing these data. An emphasis is placed on finding the mathematical and, where needed, computational tools needed to reach those goals, actively involving the reader in this process. Among other examples and problems, the following areas are treated: music as a realvalued function of continuous time, character recognition, the decomposition of an image into regions with distinct colors and textures, facial recognition, and scaling effects present in natural images caused by their statistical selfsimilarity. ... Read more

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Deals with modern algebraic geometry. ... Read more

Customer Reviews (1)

a classic in mathematics
Such a nice book and the price wasn't so hight! I'd buy again with confidence. ... Read more

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Felix Klein, a great geometer of the nineteenth century, rediscovered an idea from Hindu mythology in mathematics: the heaven of Indra in which the whole Universe was mirrored in each pearl in a net of pearls. Practically impossible to represent by hand, this idea barely existed outside the imagination, until the 1980s when the authors embarked on the first computer investigation of Klein's vision.In this extraordinary book they explore the path from some basic mathematical ideas to the simple algorithms that create delicate fractal filigrees, most appearing in print for the first time.Step-by-step instructions for writing computer programs allow beginners to generate the images. ... Read more

Customer Reviews (4)

Great mathematics and graphics
The mathematician Felix Klein(1849-1925) made some great discoveries that can now be well understood by using computer graphics.Felix Klein is known for his work in non-euclidean geometry and for his work on the connections between geometry and group theory.

Some fairly simple mathematical ideas and algorithms reveal an endless universe of fractals. The book includes step-by-step instructions for writing computer programs allowing readers to perform further explorations.

How mathematics can be used to create physical beauty
As a long-time reviewer of mathematics books, there was a time when I grew very bored with books written for the general mathematical audience. For years, it seemed mandatory that all contain a section on basic fractals and the Mandelbrot and Julia sets. It was not that the topics were not interesting, I found them fascinating, it was just that the explanations were all so similar that it became tedious to read them. Therefore, when I looked at the coverage of this book, I felt a pang of negative nostalgia, thinking that what I would find would be a repeat of what I had read so many times.
Well, I am happy to report that my pang was unfounded. The first chapter covers the language of symmetry, and some of the enormous number of forms in which it appears, which sets the stage for the fractal operations. A large part of the book is devoted to the patterns that are simultaneously symmetrical under two Mobius maps, which makes the analysis of fractals in this book different from what I have seen in others. Indra's necklace is a limit set formed by a chain of tangent circles, and is quite beautiful.
Very high quality figures are heavily used throughout the book to demonstrate the results of the operations. They are also beautiful, and in my opinion, some are works of art. Other mathematical operations that are used in the generation of the results are: matrix operations, group theory, non-Euclidean geometry, continued fractions, formal language theory, tiling of surfaces and function theory. The incorporation of so many different areas of mathematics really spices up the book, and makes it more enjoyable for a wider audience of mathematicians. It cannot be said that it is written for a general audience, the level of mathematics is beyond the non-mathematician, and one probably has to have the skill set of a junior or senior undergraduate math major in order to understand the explanations.
Mathematical results are very beautiful in their internal consistency and the power of the ideas. In this book, you also see some of the physical beauty that can be created by applying mathematics in the appropriate way

Discrete groups made easy
[this review shall replace the already existing one]

Indras pearls provides a very well-made introduction to the basics of the theory of discrete groups acting on the complex plane. The whole discussion on the related limit sets had been accomplished in such a hand-by-hand method.
The reader starts from complex numbers and after he is led into the deepest concepts: Möbius trasformations, limit sets of discrete groups (Schottky, Fuchsian, ...).
These limit sets are related to another interesting topic in today maths: complex dynamics on the Riemann sphere (Julia sets, ...).
As known, computer experiments had been fundamental for supporting complex dynamics and the successive success of thislatter topic helped to promote and increase the interests for discrete groups too: in fact this book evinces already strong interest in the visualization and in the study of the properties of such limit sets since '80s, due to the efforts of the same authors.
One of the major points of attraction in Indra pearls is that all the theory had been helped by displaying a lot of detailed and colorful pictures which, aside the historical biography of the mathematicians that contributed to this theory, set this book as one of the masterpieces in this topic, for his lucid
and fresh approach to basic concepts.
In addition, the presence of amusing comic-strips, explaining some topological concepts on manifolds (for example), guarantees the easy-learning for the reader and also the approach, as imaginaed and completely accomplished by the authors. In this direction, it is clear how passion had been squandered by authors.
The goal has been reached: finding an easy way to introduce the harsch theory of discrete groups.
Interested readers will be rewarded and also excited.
No doubts: this book strikes and it will be a corner-stone for present and future.

Discontinuous Groups now made easy !
Indras pearls provides a very well-made introduction to the basics of the theory of discontinuous groups acting on the complex plane. The whole discussion about limit sets had been accomplished in such a hand-by-hand method.
That is, the reader starts from complex numbers and, after, he is taken into deepest concepts as Möbius trasformations and so to discontinuous groups (Schottky, Fuchsian, ...).
Limit sets of kleinian groups are related to another interesting topic in today maths: complex dynamics on the Riemann sphere (Julia sets, ...). The success of this latter topic helped to increase the interests for discontinuous groups too. Indra pearls also witnesses and resumes the last twenty years of efforts spent for studying the properties of the limit sets.
One of the major points of attraction in Indra pearls is that all the theory had been helped by displaying a lot of detailed and colorful pictures which, aside the historical biography of the mathematicians that contributed to this theory, set this book as one of the masterpieces in this topic, for his lucid
and fresh approach to basic concepts.
In addition, the presence of amusing comic-strips, explaining some topological concepts on manifolds, guarantees the easy-learning of the approach, achieved by the authors. In this direction, it could be evinced that authors were really enjoyed while writing.
The goal has been reached: finding an easy way to introduce the harsch theory of discontinuous groups.
Interested readers will be rewarded about their choice and also excited. ... Read more

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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.

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Mumford is a well-known mathematician and winner of the Fields Medal, the highest honor available in mathematics

Many of these papers are currently unavailable, and the correspondence with Grothendieck has never before been published

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Now back in print, the revised edition of this popular study gives a systematic account of the basic results about abelian varieties.Mumford describes the analytic methods and results applicable when the ground field k is the complex field C and discusses the scheme-theoretic methods and results used to deal with inseparable isogenies when the ground field k has characteristic p.The author also provides a self-contained proof of the existence of a dual abeilan variety, reviews the structure of the ring of endormorphisms, and includes in appendices "The Theorem of Tate" and the "Mordell-Weil Thorem."This is an established work by an eminent mathematician and the only book on this subject. ... Read more

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“Geometric Invariant Theory” by Mumford/Fogarty (the first edition was published in 1965, a second, enlarged edition appeared in 1982) is the standard reference on applications of invariant theory to the construction of moduli spaces. This third, revised edition has been long awaited for by the mathematical community. It is now appearing in a completely updated and enlarged version with an additional chapter on the moment map by Prof. Frances Kirwan (Oxford) and a fully updated bibliography of work in this area. The book deals firstly with actions of algebraic groups on algebraic varieties, separating orbits by invariants and construction quotient spaces; and secondly with applications of this theory to the construction of moduli spaces. It is a systematic exposition of the geometric aspects of the classical theory of polynomial invariants.

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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.

Product Description
Ties together applied mathematics, applied statistics, and engineering by applying general theories and concepts to the specific and familiar example of the human face.Includes fully worked out examples of two approaches to face recognition, demonstrating the power of pattern theory and suggesting interesting new mathematics. DLC: Human face recognition (Computer science). ... Read more

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In celebration of the 10th Anniversary of the RymanProgram for Young Artists, The Ryman-Carroll Foundation is proud topresent a book of extraordinary insight into the magical worlds ofDisney and its quintessential artist Herbert Dickens Ryman.

A Brush with Disney is the story in 252 pages of color illustrationsof artist Herbert Ryman's personal journeys around the world andthrough the "world of Walt".

Told through the marvelous illustrations of the artist and his ownpersonal notes and thoughts on a 50-year journey, this rarecompilation (many never-before-seen works) is edited by Bruce Gordonand David Mumford, with research by Irene Naoum. ... Read more

Customer Reviews (10)

A brush with Disney
And that is what this book really is. It's cover, depicting the famous Disney castle sketch had promised a wallow in Herb's creations for his boss, Walt Disney. It actually turns out to be a walk through Herb's life of sketching and interesting though this is, there is one meagre chapter devoted to his concepts for the Disney parks. I would have liked more. The other sections are more sketchy illustrations and whilst it shows how Herb's talents developed I would have liked more devoted to the House of Mouse.I've given it 4 out 5 because of my admiration for the artist rather than the content I was expecting. The title is exactly what it says: A BRUSH with Disney. Shame it wasn't the whole artist's palette.

A Wonderful Look at an Amazing Artist
This is an amazing and difficult book to review; not for any reason you would expect. The text is compelling and you learn about the man and the artist. The reproductions of Ryman's art is outstanding. You understand the gift the man possessed. What makes the book so difficult to review is also what makes it so amazing--there is no eloquent way for me to describe the artwork found in this book. You have to see it to enjoy the amazing pieces of art.

The book was put together by Bruce Gordon, David Mumford and the Ryman-Carroll Foundation. Bruce and David also did The Nickel Tour and Walt's Time. Bruce co-edited The Art of Disneyland and Disneyland: Now, Then and Forever. This work is a love letter from Mr. Ryman's closest friends, co-workers and family to the legendary artist.

There are four major sections of the book: Odysseys (journeys he took throughout his life), Hollywood (working for major studios), Fantasy Lands & Disney Worlds (Disneyland through Disneyland Paris) and Legacy (The Ryman Foundation). Most Disney enthusiasts will undoubtedly focus on the concept artwork for the theme parks. It is very impressive to see the artwork in one place and realize how much Mr. Ryman was responsible for developing the overall feel for the lands and attractions.

Each land in Disneyland is covered (except Mickey's Toontown) and we see the progressions that Mr. Ryman makes in his own artwork for the company. The early work for Disneyland is a little more focused on specific areas whereas the latter works seem to be more sweeping and carry more emotional weight.

The other section of the book refer to Mr. Ryman's non-Disney career. He spent a few years travelling Europe and Asia before doing studio work and he even spent a few years painting portraits of the performers and clowns for the Ringling Brother's Circus. After his Disneyland and early Magic Kingdom work, he travelled through Europe and Asia again. He never really left Disney; they called him back to work on concepts for Epcot, Tokyo Disneyland and Disneyland (The Indiana Jones Adventure).


There is so much more fantastic art throughout the whole book. The few pieces I have shared are just a few of the Disney-related works. So much of his life's work is more about emotions and feelings than realistic portrayal. In the book, his most powerful statements are from the time he spent painting the Pacific Coast near his home. He effectively captured the mood and feel of the rocky shores. I have read a few criticisms about the book--namely that there is too much sub par art and not enough Disney-focused art. Personally, I was fascinated with all of Mr. Ryman's art. Not only did it tell of his life, but it shed some light on the influences that were present in his work. Whether it was mood, shadows or vistas; you could immediately sense that you were viewing an artist that was meant to do his work.

Bottom Line: I thoroughly enjoyed this dedication to Herb Ryman. This book isn't for every Disney Geek, but those enthusiasts with an interest in concept art and a look at the development of a Disney artist will treasure it. The artwork is astounding and there were some surprises within the pages. As is, the book is out of print and you should expect to pay street prices well above the release price. Although it isn't as spectacular as The Nickel Tour or as comprehensive as The Art of Disneyland, you do see where Mr. Ryman excelled and where his influence was most prominent. If you can snag a copy of it, you will not be disappointed.

Originally posted at www.imaginerding.comA Brush with Disney : An Artist's Journey, Told through the words and works of Herbert Dickens Ryman

Good, but misleading
I found A Brush With Disney to be an overall good book. It looks great on the coffee table and shelf, has a beautiful cover, and clear, quality illustrations. That being said, if you think this is a book full of Disney concept art (as I did) you'll be disappointed. The book is not about Disney, but about the artist and his life and work. His work at Disney takes up only about a fourth of the book. I also thought it would feature concept work for different rides, parks, etc. In actuality it only had concept work for the parks and a few of the "lands" in Disneyland (Frontierland, New Orleans Square, Sleeping Beauty's Castle, etc.) I felt a bit cheated after paying $65 because it's as if the artist is selling himself under the Disney name for publicity and name recognition. Anyone heard of Herbert Dickens Ryman before? I sure haven't. I didn't give it a one star rating simply because the content is good, it's just not about what is advertised and promoted on cover.

Not much concept art of early golden Disney animation period
It is a great book when you want to learn about collors and style in Disney park design, but not much on the period of Dumbo animation and other early disney design and concept art for animation in the golden period of disney animation. Still great paintings and Aquarels (study the techniques) from traveling and the design paintings, for the disney world themeparks. It gave me the Idear of buying a sketchbook for my world traveling.
Jan Reijmerink Drontywood ART

Not enough Disney
I hate to sound like an ingrate writing this review:Herb Ryman has done some great illustrations.Unfortunately, this book spends too much time showcasing Herb Ryman's non-Disney art--which is pretty mediocre--and not enough space showcasing his Disney work.The highlight of the book--Ryman's first illustration of the soon-to-be-built Disneyland--is spread across two pages, but the page break makes it nearly impossible to decipher what's in the middle of the drawing.(It should have perhaps been on a fold-out, or at least on a single, uninterrupted page.)Other great illustrations, especially early renderings of Tomorrowland, are printed in extremely small 3" images, making them very hard to read.All in all, I'd say don't bother with this book.Ryman's best drawings are already showcased in many other books. ... Read more

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Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2004.

This book studies regularity properties of Mumford-Shah minimizers. The Mumford-Shah functional was introduced in the 1980s as a tool for automatic image segmentation, but its study gave rise to many interesting questions of analysis and geometric measure theory. The main object under scrutiny is a free boundary K where the minimizer may have jumps. The book presents an extensive description of the known regularity properties of the singular sets K, and the techniques to get them. Some time is spent on the C^1 regularity theorem (with an essentially unpublished proof in dimension 2), but a good part of the book is devoted to applications of A. Bonnet's monotonicity and blow-up techniques. In particular, global minimizers in the plane are studied in full detail.
The book is largely self-contained and should be accessible to graduate students in analysis.The core of the book is composed of regularity results that were proved in the last ten years and which are presented in a more detailed and unified way.

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The new edition of this celebrated and long-unavailable book preserves much of the content and structure of the original, which is still unrivaled in its presentation of a universal method for the resolution of a class of singularities in algebraic geometry.At the same time, the book has been completely retypeset, errors have been eliminated, proofs have been streamlined, the notation has been made consistent and uniform, an index has been added, and a guide to recent literature has been added. The authors begin by reviewing key results in the theory of toroidalembeddings and by explaining examples that illustrate the theory. Chapter II develops the theory of open self-adjoint homogeneous cones and their polyhedral reduction theory. Chapter III is devoted to basic facts on hermitian symmetric domains and culminates in the construction of toroidal compactifications of their quotients by an arithmetic group. The final chapter considers several applications of the general results. The book brings together ideas from algebraic geometry, differential geometry, representation theory and number theory, and will continue to prove of value for researchers and graduate students in these areas. ... Read more

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The Third Edition of CALCULUS reflects the strong consensus within the mathematics community for a new balance between the contemporary ideas of the original editions of this book and ideas and topics from earlier calculus books. Building on previous work, this Third Edition has the same philosophy as earlier editions but represents a new balance of topics. CALCULUS 3/e brings together the best of both new and traditional curricula in an effort to meet the needs of even more instructors teaching calculus. The author team's extensive experience teaching from both traditional and innovative books and their expertise in developing innovative problems put them in an unique position to make this new curriculum meaningful to students going into mathematics and those going into the sciences and engineering. The authors believe the new edition will work well for those departments who are looking for a calculus book that offers a middle ground for their calculus instructors.
CALCULUS 3/e exhibits the same strengths from earlier editions including the Rule of Four, an emphasis on modeling, exposition that students can read and understand and a flexible approach to technology. The conceptual and modeling problems, praised for their creativity and variety, continue to motivate and challenge students. ... Read more

Customer Reviews (1)

The life and works of Lewis Mumford
A well written, scholarly work with abundant references, including abiographical study of Mumford and his writings. Highly recommended. ... Read more

Product Description
Striking a balance between concepts, modeling, and skills, this highly acclaimed book arms readers with an accessible introduction to calculus. It builds on the strengths from previous editions, presenting key concepts graphically, numerically, symbolically, and verbally. Guided by this innovative Rule of Four approach, the fourth edition examines new topics while providing readers with a strong conceptual understanding of the material. ... Read more

Customer Reviews (1)

Excellent
The author of this book is well known in algebraic geometry, and, as of late in the field of computer graphics. In this book, he summarizes beautifully various results in algebraic geometry that were known at the time of publication. Most importantly, the author believes that in order to properly understand algebraic geometry, one must delve into the works of `Italian' algebraic geometry, as well as the works of Zariski, Weil, and Grothendieck. The former assists in building intuition, while the latter gives a unified algebraic framework in which to work in and relates the subject to number theory. Every student of algebraic geometry has perhaps been overwhelmed by the sheer volume of results in the subject, and the increasing level of abstraction in the form of the theory of schemes, that is encountered when learning algebraic geometry. This book introduces the `classical' point of view, with the modern scheme-theoretic approach left to a future work, says the author. Since its publication, many new interesting approaches have been taken toward algebraic geometry, one being that use is being made of the computer and various symbolic programming languages in order to deal with the geometric objects from a computational point of view. Another has been the role of physics, particularly that of `mirror symmetry' and superstring and M-theory. In fact, one might expand the words of the author in the introduction to this book, and now say that a proper understanding of algebraic geometry should also involve an understanding of quantum field theory, integrable systems, and superstring and membrane theory.

Some of the more interesting and well-motivated discussions in the book include:1. The author uses an `analytic' version of the implicit function theorem to show that the Zariski open set of smooth points on an affine variety has the structure of a complex manifold. The Zariski topology has been viewed as somewhat "mysterious" by some beginning students, so this characterization clears this up to some degree. 2. The need for the group of divisors and the resulting Picard group. This is done to make up for the fact that for a smooth variety X, the affine coordinate ring R(X) is not a unique factorization domain (UFD). The author describes this situation as being analogous to the one in algebraic number fields where the UFD property must be weakened to that of decomposing principal ideals into products of prime ideals. The Picard group is then the group of divisors modulo the principal divisors, and then R(X) is a UFD if and only if the Picard group is zero. 3. The discussion on Chow's theorem. The author motivates this famous result by asking to what extent the general theory of complex analytic spaces parallels the theory of algebraic varieties. The difficulty, he explains, is that in algebraic geometry one deals with rational functions, which do not have essential singularities like analytic functions do. The author discusses a case where no essential singularities occur, his example dealing with `analytic' and `*-analytic' subsets of complex n-space. Loosely speaking, analytic sets are essentially zero sets of analytic functions, whereas *-analytic sets can be represented as the union of complex submanifolds. He shows that a set is *-analytic if and only if it is analytic, and from this result follows Chow's theorem, which states that the only complex analytic subsets of n-dimensional projective space are algebraic varieties. Chow's theorem is a generalization of the result in complex variable theory that says that the only meromorphic functions on the extended complex plane are rational functions. 4. A natural question to ask when studying algebraic varieties is whether they have a "size", i.e. a volume or area of some sort. For r-dimensional subvarieties of n-dimensional projective space, the author proves that one can define the 2r-dimensional volume of the variety, and this is accomplished via a Riemannian metric on n-dimensional projective space. This metric only depends on r and the degree of the variety, and is in fact the famous Kahler metric. The author goes on to characterize algebraic varieties as minimal submanifolds of n-dimensional projective space, using the tools of DeRham cohomology. The volume result is then generalized to that of compact oriented submanifolds of n-dimensional projective space, with the first result holding when the submanifold is an algebraic subvariety. 5. The treatment of the Hilbert polynomial. The author motivates this in the context of the calculation of the dimension of the vector space of functions with poles at most a given divisor. He proves an explicit formula for the Hilbert polynomial for r-dimensional subvarieties of n-dimensional projective space. He also shows how the constant term of the Hilbert polynomial is related to the `arithmetic genus' of a projective variety. The arithmetic genus is then shown to be equal to the topological genus for smooth curves, this being the famous Hirzebruch-Riemann-Roch theorem in dimension one. His proof of this result is very detailed and actually quite fun to work through and read, as it does not depend on the theory of harmonic forms. 6. For those who are interested in the theory of elliptic curves, the author gives an elementary overview of their properties. ... Read more

Product Description
Striking a balance between concepts, modeling, and skills, this highly acclaimed book arms readers with an accessible introduction to calculus. It builds on the strengths from previous editions, presenting key concepts graphically, numerically, symbolically, and verbally. Guided by this innovative Rule of Four approach, the fourth edition examines new topics while providing readers with a strong conceptual understanding of the material. ... Read more