Lectures on Polytopes

Author: Günter M. Ziegler

Publisher: Springer Science & Business Media

ISBN: 9780387943657

Category: Mathematics

Page: 370

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Based on a graduate course at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students.
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Lectures in Geometric Combinatorics

Author: Rekha R. Thomas

Publisher: American Mathematical Soc.

ISBN: 9780821841402

Category: Mathematics

Page: 143

View: 3867

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This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the state polytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics.The connections rely on Grobner bases of toric ideals and other methods from commutative algebra. The book is self-contained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational aspects of the theory of polytopes.
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Advances in Discrete Differential Geometry

Author: Alexander I. Bobenko

Publisher: Springer

ISBN: 3662504472

Category: Mathematics

Page: 439

View: 7395

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This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, and on pure mathematics and its practical applications. The interaction of these facets is demonstrated by concrete examples, including discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, conformal texture mappings in computer graphics, and free-form architecture. This richly illustrated book will convince readers that this new branch of mathematics is both beautiful and useful. It will appeal to graduate students and researchers in differential geometry, complex analysis, mathematical physics, numerical methods, discrete geometry, as well as computer graphics and geometry processing.
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Using the Mathematics Literature

Author: Kristine K. Fowler

Publisher: CRC Press

ISBN: 1482276445

Category: Language Arts & Disciplines

Page: 475

View: 1044

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This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathemati
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Lectures on Discrete Geometry

Author: Ji?í Matoušek

Publisher: Springer Science & Business Media

ISBN: 1461300398

Category: Mathematics

Page: 486

View: 9239

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The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.
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Novel Approaches to Hard Discrete Optimization

Author: Panos M. Pardalos,Henry Wolkowicz

Publisher: American Mathematical Soc.

ISBN: 9780821885918

Category: Mathematics

Page: 181

View: 5468

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During the last decade, many novel approaches have been considered for dealing with computationally difficult discrete optimization problems. Such approaches include interior point methods, semidefinite programming techniques, and global optimization. More efficient computational algorithms have been developed and larger problem instances of hard discrete problems have been solved. This progress is due in part to these novel approaches, but also to new computing facilities and massive parallelism. This volume contains the papers presented at the workshop on ''Novel Approaches to Hard Discrete Optimization''. The articles cover a spectrum of issues regarding computationally hard discrete problems.
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RAIRO.

Operations research

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Operations research

Page: N.A

View: 939

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International journal devoted to pure and applied research on the use of scientific methods and information processing in business and industry. Articles may be in English or French.
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Realization Spaces of Polytopes

Author: Jürgen Richter-Gebert

Publisher: Springer

ISBN: 9783540620846

Category: Mathematics

Page: 188

View: 5886

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The book collects results about realization spaces of polytopes. It gives a presentation of the author's "Universality Theorem for 4-polytopes". It is a comprehensive survey of the important results that have been obtained in that direction. The approaches chosen are direct and very geometric in nature. The book is addressed to researchers and to graduate students. The former will find a comprehensive source for the above mentioned results. The latter will find a readable introduction to the field. The reader is assumed to be familiar with basic concepts of linear algebra.
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Surveys in Combinatorics

Invited Papers for the ... British Combinatorial Conference

Author: Christopher D. Wensley

Publisher: N.A

ISBN: N.A

Category: Combinatorial analysis

Page: N.A

View: 5951

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