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This book constitutes the thoroughly refereed post-proceedings of the Indonesia-Japan Joint Conference on Combinatorial Geometry and Graph Theory, IJCCGGT 2003, held in Bandung, Indonesia in September 2003.

The 23 revised papers presented were carefully selected during two rounds of reviewing and improvement. Among the topics covered are coverings, convex polygons, convex polyhedra, matchings, graph colourings, crossing numbers, subdivision numbers, combinatorial optimization, combinatorics, spanning trees, various graph characteristica, convex bodies, labelling, Ramsey number estimation, etc.

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This book constitutes the thoroughly refereed post-proceedings of the 7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005, held in Tianjin, China, as well as in Xi'an, China, in November 2005.

The 30 revised full papers presented were carefully selected during two rounds of reviewing and improvement from over 60 talks at the conference. All current issues in discrete algorithmic geometry, combinatorics and graph theory are addressed.

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The book is devoted to the theory of pairs of compact convex sets and in particular to the problem of finding different types of minimal representants of a pair of nonempty compact convex subsets of a locally convex vector space in the sense of the Rådström-Hörmander Theory. Minimal pairs of compact convex sets arise naturally in different fields of mathematics, as for instance in non-smooth analysis, set-valued analysis and in the field of combinatorial convexity.
In the first three chapters of the book the basic facts about convexity, mixed volumes and the Rådström-Hörmander lattice are presented. Then, a comprehensive theory on inclusion-minimal representants of pairs of compact convex sets is given. Special attention is given to the two-dimensional case, where the minimal pairs are uniquely determined up to translations. This fact is not true in higher dimensional spaces and leads to a beautiful theory on the mutual interactions between minimality under constraints, separation and decomposition of convex sets, convexificators and invariants of minimal pairs. ... Read more

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This book constitutes the thoroughly refereed post-proceedings of the Japanese Conference on Discrete Computational Geometry, JCDCG 2002, held in Tokyo, Japan, in December 2002.

The 29 revised full papers presented were carefully selected during two rounds of reviewing and improvement. All current issues in discrete algorithmic geometry are addressed.

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Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book offers a comprehensive summary together with a global view, establishing both old and new links. Its treatment ranges from classical theorems of Menger and Schoenberg to recent developments such as approximation results for multicommodity flow and max-cut problems, metric aspects of Delaunay polytopes, isometric graph embeddings, and matrix completion problems. The discussion leads to many interesting subjects that cannot be found elsewhere, providing a unique and invaluable source for researchers and graduate students. ... Read more

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This book constitutes the thoroughly refereed post-proceedings of the Japanese Conference on Discrete Computational Geometry, JCDCG 2004, held in Tokyo, Japan in October 2004, to honor János Pach on his fiftieth year.

The 20 revised full papers presented were carefully selected during two rounds of reviewing and improvement from over 60 talks at the conference. All current issues in discrete algorithmic geometry are addressed.

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This book provides a comprehensive study of convex integration theory in immersion-theoretic topology. Convex integration theory, developed originally by M. Gromov, provides general topological methods for solving the h-principle for a wide variety of problems in differential geometry and topology, with applications also to PDE theory and to optimal control theory. Though topological in nature, the theory is based on a precise analytical approximation result for higher order derivatives of functions, proved by M. Gromov. This book is the first to present an exacting record and exposition of all of the basic concepts and technical results of convex integration theory in higher order jet spaces, including the theory of iterated convex hull extensions and the theory of relative h-principles. A second feature of the book is its detailed presentation of applications of the general theory to topics in symplectic topology, divergence free vector fields on 3-manifolds, isometric immersions, totally real embeddings, underdetermined non-linear systems of PDEs, the relaxation theorem in optimal control theory, as well as applications to the traditional immersion-theoretical topics such as immersions, submersions, k-mersions and free maps.

The book should prove useful to graduate students and to researchers in topology, PDE theory and optimal control theory who wish to understand the h-principle and how it can be applied to solve problems in their respective disciplines.

------  Reviews

The first eight chapters of Spring’s monograph contain a detailed exposition of convex integration theory for open and ample relations with detailed proofs that were often omitted in Gromov’s book. (…) Spring’s book makes no attempt to include all topics from convex integration theory or to uncover all of the gems in Gromov’s fundamental account, but it will nonetheless (or precisely for that reason) take its place as a standard reference for the theory next to Gromov’s towering monograph and should prove indispensable for anyone wishing to learn about the theory in a more systematic way.

- Mathematical Reviews

This volume provides a comprehensive study of convex integration theory. (…) We recommended the book warmly to all interested in differential topology, symplectic topology and optimal control theory.

- Matematica

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This classic geometry text explores the theory of 3-dimensional convex polyhedra in a unique fashion, with exceptional detail. Vital and clearly written, the book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method. This edition includes a comprehensive bibliography by V.A. Zalgaller, and related papers as supplements to the original text.

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Fundamentals of Convex Analysis offers an in-depth lookat some of the fundamental themes covered within an area ofmathematical analysis called convex analysis. In particular, itexplores the topics of duality, separation,representation, and resolution. The work is intended forstudents of economics, management science, engineering, andmathematics who need exposure to the mathematical foundations ofmatrix games, optimization, and general equilibrium analysis. It iswritten at the advanced undergraduate to beginning graduate level andthe only formal preparation required is some familiarity with setoperations and with linear algebra and matrix theory. Fundamentalsof Convex Analysis is self-contained in that a brief reviewof the essentials of these tool areas is provided in Chapter 1.Chapter exercises are also provided.
Topics covered include: convex sets and their properties; separationand support theorems; theorems of the alternative; convex cones; dualhomogeneous systems; basic solutions and complementary slackness;extreme points and directions; resolution and representation ofpolyhedra; simplicial topology; and fixed point theorems, amongothers. A strength of this work is how these topics are developed in afully integrated fashion.
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This book constitutes the refereed proceedings of the 11th International Conference on Discrete Geometry for Computer Imagery, DGCI 2003, held in Naples, Italy, in November 2003.

The 49 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 68 submissions. All current issues in discrete geometry for computer imagery are addressed including topology, surfaces and volumes, morphology, shape representation, and shape analysis. ... Read more

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Proceedings of the Japanese Conference, JCDCG, held in Tokyo, Japan, November 22-25, 2001. Thirty-five papers were presented. Revised papers. Softcover. ... Read more

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The appearance of Gruenbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the book's immense influence made them quickly obsolete. Some other chapters promise beautiful unexplored land for future research. The appearance of the new edition is going to be another moment of grace. Kaibel, Klee and Ziegler were able to update the convex polytope saga in a clear, accurate, lively, and inspired way. --Gil Kalai, The Hebrew University of Jerusalem The original book of Gruenbaum has provided the central reference for work in this active area of mathematics for the past 35 years...I first consulted this book as a graduate student in 1967; yet, even today, I am surprised again and again by what I find there. It is an amazingly complete reference for work on this subject up to that time and continues to be a major influence on research to this day. --Louis J. Billera, Cornell University The original edition of Convex Polytopes inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again. --Peter McMullen, University College London

The combinatorial study of convex polytopes is today an extremely active and healthy area of mathematical research, and the number and depth of its relationships to other parts of mathematics have grown astonishingly since Convex Polytopes was first published in 1966. The new edition contains the full text of the original and the addition of notes at the end of each chapter. The notes are intended to bridge the thirty five years of intensive research on polytopes that were to a large extent initiated, guided, motivated and fuelled by the first edition of Convex Polytopes. The new material provides a direct guide to more than 400 papers and books that have appeared since 1967. Branko Grünbaum is Professor of Mathematics at the University of Washington. ... Read more

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Flavors of Geometry is a collection of lectures on four geometrically-influenced fields of mathematics that have experienced great development in recent years. It presents chapters by masters in their fields on hyperbolic geometry, dynamics in several complex variables, convex geometry, and volume estimation.Each lecture begins with a discussion of elementary concepts, examines the highlights of the field, and concludes with a look at more advanced material. The style and presentation of the chapters are clear and accessible, and many of the lectures are richly illustrated. The book includes bibiliographies and indexes to encourage further reading. It will be an influential resource for graduate students and advanced undergraduates in mathematics. ... Read more

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Great book
Even when the book was used, it is entire. Pages are clean and the contents is awesome! ... Read more

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This book is the result of a 25-year-old project and comprises a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research.

Customer Reviews (1)

Excellent Reference
I've owned this book since last Summer.I find myself going to it first whenever I need more information on a topic. The book provides ample background information for almost any problem in either discrete or combinatorial geometry. Each section has an extensive bibliography.The authors also maintain a webpage for problems in the book which have been solved (or partially solved) since its printing.

A must-have for anyone doing research in this or a related area (e.g. computational geometry). ... Read more

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This is the first and only reference to provide a comprehensive treatment of the Lie theory of subsemigroups of Lie groups.The book is uniquely accessible and requires little specialized knowledge.It includes information on the infinitesimal theory of Lie subsemigroups, and a characterization of those cones in a Lie algebra which are invariant under the action of the group of inner automporphisms.It provides full treatment of the local Lie theory for semigroups, and finally, gives the reader a useful account of the global theory for the existence of subsemigroups with a given set of infinitesimal generators. ... Read more

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In this short book, the authors discuss three types of problems from combinatorial geometry: Borsuk's partition problem, covering convex bodies by smaller homothetic bodies, and the illumination problem. They show how closely related these problems are to each other. The presentation is elementary, with no more than high-school mathematics and an interest in geometry required to follow the arguments. Most of the discussion is restricted to two- and three-dimensional Euclidean space, though sometimes more general results and problems are given. Thus even the mathematically unsophisticated reader can grasp some of the results of a branch of twentieth-century mathematics that has applications in such disciplines as mathematical programming, operations research and theoretical computer science. At the end of the book the authors have collected together a set of unsolved and partially solved problems that a sixth-form student should be able to understand and even attempt to solve. ... Read more

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This volume contains a fairly complete picture of the geometry of numbers, including relations to other branches of mathematics such as analytic number theory, diophantine approximation, coding and numerical analysis. It deals with convex or non-convex bodies and lattices in euclidean space, etc.

This second edition was prepared jointly by P.M. Gruber and the author of the first edition. The authors have retained the existing text (with minor corrections) while adding to each chapter supplementary sections on the more recent developments. While this method may have drawbacks, it has the definite advantage of showing clearly where recent progress has taken place and in what areas interesting results may be expected in the future.

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Chapters: Convex Set, Minkowski's Theorem, Face, Convex Hull, Antimatroid, Convex Polytope, Radon's Theorem, Oriented Matroid, Convex Hull Algorithms, Minkowski Addition, Graham Scan, Helly's Theorem, Orthogonal Convex Hull, Rotating Calipers, Mahler Volume, Convex Metric Space, Carathéodory's Theorem, Separating Axis Theorem, Chan's Algorithm, Tangent Cone, Gift Wrapping Algorithm, Brunn-minkowski Theorem, Dual Cone and Polar Cone, Kirkpatrick-seidel Algorithm, Conical Combination, Krein-milman Theorem, Convex Combination, Convex and Concave Polygons, Supporting Hyperplane, Geodesic Convexity, Gilbert-johnson-keerthi Distance Algorithm, M. Riesz Extension Theorem, Tverberg's Theorem, B-Convex Space, Minkowski Portal Refinement, Absolutely Convex Set, List of Convexity Topics, Kakutani's Theorem, Concave Set. Source: Wikipedia. Pages: 144. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In mathematics, an antimatroid is a formal system that describes processes in which a set is built up by including elements one at a time, and in which an element, once available for inclusion, remains available until it is included. Antimatroids are commonly axiomatized in two equivalent ways, either as a set system modeling the possible states of such a process, or as a formal language modeling the different sequences in which elements may be included. Dilworth (1940) was the first to study antimatroids, using yet another axiomatization based on lattice theory, and they have been frequently rediscovered in other contexts; see Korte et al. (1991) for a comprehensive survey of antimatroid theory with many additional references. The axioms defining antimatroids as set systems have some similarity to those of matroids, but whereas matroids can be defined by an exchange axiom (e.g., the basis exchange, or inde...More: http://booksllc.net/?id=667063 ... Read more