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The book is a collection of some of the research presented at the workshop of the same name held in May 2003 at Rutgers University. The workshop brought together researchers from two different communities: statisticians and specialists in computational geometry. The main idea unifying these two research areas turned out to be the notion of data depth, which is an important notion both in statistics and in the study of efficiency of algorithms used in computational geometry. Many of the articles in the book lay down the foundations for further collaboration and interdisciplinary research.Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM). ... Read more

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For courses that cover basic math, algebra, and geometry in career-oriented community college and technical school programs. This new text is adapted from the best-selling College Mathematics for Technology, 6/E. It features very practical coverage of basic math, algebra, and geometry concepts with applications to a broad range of career fields. Topics are introduced and reinforced using a step-by-step "spiral learning" approach and are supported by numerous examples. The approach to presenting concepts, examples, and applications supports the standards set by AMATYC, NCTM, and MAA. ... Read more

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StudentWorks^TM CD-ROM combines the complete interactive Student Edition with all of the associated student worksheets in one convenient place. ... Read more

Customer Reviews (1)

Good introduction to the subject
This is the only elementary, yet not too cursory, introduction to the subject that I have seen.It begins at the level of a lower-division college math student.It is too bad that the publisher let it go out of print.In view of the many other books on the subject of computer graphics and computer vision, there would be many needing this book.It treats more carefully the math that some other books gloss over.

My criticism so far is a minor one of style.The author writes things like, "The line l passing through the point A[4, 4, 1] and B[-2, 0, 2]."That is, he introduces a variable name (A or B) along with the value of the variable, by juxtapostion.This used to be done in high-school level books, but it conflicts with other uses of juxtaposition and so seems slightly nonsensical.I am used to the more accepted style using an equals sign: "The line l passing through the point A = [4, 4, 1] and B = [-2, 0, 2]."However, this is a minor criticism.

Postscript:Since I wrote this, I have become aware of other textbooks on the mathematics of computer graphics and computer vision, some recently published.I recommend _Applied Geometry for Computer Graphics and CAD_ by Duncan Marsh. ... Read more

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Volume 166 Lecture Notes in Pure and Applied Mathematics, explores current topics in projective geometry, revealing a locus of mathematical techniques and approaches. Paper. DLC: Geometry, Projective. ... Read more

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This book, the inaugural volume in the University Lecture Series, is based on lectures presented at Pennsylvania State University in February 1987. The lectures attempt to give a taste of the accomplishments of manifold topology over the last 30 years. By the late 1950s, algebra and topology had produced a successful and beautiful fusion. Geometric methods and insight, now vitally important in topology, encompass analytic objects such as instantons and minimal surfaces, as well as nondifferentiable constructions. Keeping technical details to a minimum, the authors lead the reader on a fascinating exploration of several developments in geometric topology. They begin with the notions of manifold and smooth structures and the Gauss-Bonnet theorem, and proceed to the topology and geometry of foliated 3-manifolds. They also explain, in terms of general position, why four-dimensional space has special attributes, and they examine the insight Donaldson theory brings. The book ends with a chapter on exotic structures on $\mathbf R^4$, with a discussion of the two competing theories of four-dimensional manifolds, one topological and one smooth. Background material was added to clarify the discussions in the lectures, and references for more detailed study are included. Suitable for graduate students and researchers in mathematics and the physical sciences, the book requires only background in undergraduate mathematics. It should prove valuable for those wishing a not-too-technical introduction to this vital area of current research. ... Read more

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This book is the first volume in a two-volume set, which will provide the complete proof of classification of two important classes of geometries, closely related to each other: Petersen and tilde geometries. There is an infinite family of tilde geometries associated with nonsplit extensions of symplectic groups over a field of two elements. Besides that there are twelve exceptional Petersen and tilde geometries. These exceptional geometries are related to sporadic simple groups, including the famous Monster group and this volume gives a construction for each of the Petersen and tilde geometries that provides an independent existence proof for the corresponding automorphism group. Important applications of Petersen and tilde geometries are considered, including the so-called Y-presentations for the Monster and related groups, and a complete identification of Y-groups is given. This is an essential purchase for researchers in finite group theory, finite geometries and algebraic combinatorics. ... Read more

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This is one of the first monographs to deal with the metrictheory of spatial mappings and incorporates results in the theory ofquasi-conformal, quasi-isometric and other mappings.
The main subject is the study of the stability problem in Liouville'stheorem on conformal mappings in space, which is representative of anumber of problems on stability for transformation classes. To enablethis investigation a wide range of mathematical tools has beendeveloped which incorporate the calculus of variation, estimates fordifferential operators like Korn inequalities, properties of functionswith bounded mean oscillation, etc.
Results obtained by others researching similar topics are mentioned,and a survey is given of publications treating relevant questions orinvolving the technique proposed.
This volume will be of great value to graduate students andresearchers interested in geometric function theory.
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This volume contains 18 papers from the Algebraic Geometry Conference, Yaroslavl, Russia, August 10-14, 1992. These conferences have a great tradition in Russia and have been held since 1979 in Yaroslavl every second year. This eighth conference is the first in which several foreign mathematicians participated. From the Russian side there was a large group of specialists in algebraic geometry and related fields - invariant theory, topology of manifolds, theory of categories and mathematical physics. Lectures on modern directions in modern algebraic geometry, such as the theory of exceptional bundles and helices on algebraic varieties, moduli of vector bundles on algebraic surfaces with applications to string theory, Hodge theory, problems of rationality in the invariant theory, topology of complex algebraic varieties and others are contained in this volume. ... Read more

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Algebraic Geometry and its Applications will be of interest not only to mathematicians but also to computer scientists working on visualization and related topics. The book is based on 32 invited papers presented at a conference in honor of Shreeram Abhyankar's 60th birthday, which was held in June 1990 at Purdue University and attended by many renowned mathematicians (field medalists), computer scientists and engineers. The keynote paper is by G. Birkhoff; other contributors include such leading names in algebraic geometry as R. Hartshorne, J. Heintz, J.I. Igusa, D. Lazard, D. Mumford, and J.-P. Serre. ... Read more

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The book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a new approach to differential geometry based on sheaf theoretic methods, without use of ordinary calculus. This point of view complies with the demand of contemporary physics to cope with non-smooth models of physical phenomena and spaces with singularities.

Starting with a brief survey of the required sheaf theory and cohomology, the exposition then moves on to differential triads (the abstraction of smooth manifolds) and Lie sheaves of groups (the abstraction of Lie groups). Having laid the groundwork, the main part of the book is devoted to the theory of connections on principal sheaves, incorporating connections on vector and associated sheaves. Topics such as the moduli sheaf of connections, classification of principal sheaves, curvature, flat connections and flat sheaves, Chern-Weil theory, are also treated.

The study brings to light fundamental notions and tools of the standard differential geometry which are susceptible of the present abstraction, and whose role remains unexploited in the classical context, because of the abundance of means therein. However, most of the latter are nonsensical in ADG.