Lectures on Polytopes

Author: Günter M. Ziegler

Publisher: Springer Science & Business Media

ISBN: 9780387943657

Category: Mathematics

Page: 370

View: 2447

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.
Posted in Mathematics

VDI-Lexikon Informatik und Kommunikationstechnik

Author: Manfred Broy,Otto Spaniol

Publisher: Springer-Verlag

ISBN: 3642468454

Category: Technology & Engineering

Page: 863

View: 2374

Das erfolgreiche Lexikon ist wieder auf dem aktuellen Stand. Von den führenden Wissenschaftlern der Informatik bearbeitet, bietet es anschauliche und verständliche Informationen zur Informatik und Kommunikationstechnik.
Posted in Technology & Engineering

Using the Mathematics Literature

Author: Kristine K. Fowler

Publisher: CRC Press

ISBN: 9780824750350

Category: Language Arts & Disciplines

Page: 475

View: 1769

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 mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.
Posted in Language Arts & Disciplines

Lectures in Geometric Combinatorics

Author: Rekha R. Thomas

Publisher: American Mathematical Soc.

ISBN: 9780821841402

Category: Mathematics

Page: 143

View: 1744

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.
Posted in Mathematics

Topics in Algebraic Geometry and Geometric Modeling

Workshop on Algebraic Geometry and Geometric Modeling, July 29-August 2, 2002, Vilnius University, Lithuania

Author: Ron Goldman,Rimvydas Krasauskas

Publisher: American Mathematical Soc.

ISBN: 0821834207

Category: Mathematics

Page: 366

View: 4800

Algebraic geometry and geometric modeling both deal with curves and surfaces generated by polynomial equations. Algebraic geometry investigates the theoretical properties of polynomial curves and surfaces; geometric modeling uses polynomial, piecewise polynomial, and rational curves and surfaces to build computer models of mechanical components and assemblies for industrial design and manufacture. The NSF sponsored the four-day ``Vilnius Workshop on Algebraic Geometry and Geometric Modeling'', which brought together some of the top experts in the two research communities to examine a wide range of topics of interest to both fields. This volume is an outgrowth of that workshop. Included are surveys, tutorials, and research papers. In addition, the editors have included a translation of Minding's 1841 paper, ``On the determination of the degree of an equation obtained by elimination'', which foreshadows the modern application of mixed volumes in algebraic geometry. The volume is suitable for mathematicians, computer scientists, and engineers interested in applications of algebraic geometry to geometric modeling.
Posted in Mathematics

Advances in Discrete Differential Geometry

Author: Alexander I. Bobenko

Publisher: Springer

ISBN: 3662504472

Category: Mathematics

Page: 439

View: 9689

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.
Posted in Mathematics

Novel Approaches to Hard Discrete Optimization

Author: Panos M. Pardalos,Henry Wolkowicz

Publisher: American Mathematical Soc.

ISBN: 9780821885918

Category: Mathematics

Page: 181

View: 964

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.
Posted in Mathematics

Das BUCH der Beweise

Author: Martin Aigner,Günter M. Ziegler

Publisher: Springer-Verlag

ISBN: 3642022596

Category: Mathematics

Page: 312

View: 3978

Die Sammlung eleganter mathematischer Beweise wurde für die 3. Auflage deutlich erweitert: In fünf neuen Kapiteln präsentieren die Autoren Klassiker wie den Fundamentalsatz der Algebra, kombinatorisch-geometrische Zerlegungsprobleme, aber auch Beweise aus jüngster Zeit, etwa den für die Kneser-Vermutung in der Graphentheorie. Die Neuausgabe wartet noch mit weiteren Verbesserungen und Überraschungen auf - darunter einem neuen Beweis für Hilberts Drittes Problem.
Posted in Mathematics

Vorlesungen über die Theorie der Polyeder

unter Einschluß der Elemente der Topologie

Author: Ernst Steinitz

Publisher: Springer-Verlag

ISBN: 3642656099

Category: Mathematics

Page: 352

View: 6430

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
Posted in Mathematics

PAMQ

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 1428

Posted in Mathematics

Realization Spaces of Polytopes

Author: Jürgen Richter-Gebert

Publisher: Springer

ISBN: 9783540620846

Category: Mathematics

Page: 188

View: 1583

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.
Posted in Mathematics

RAIRO.

Operations research

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Operations research

Page: N.A

View: 7961

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.
Posted in Operations research