Based on a graduate course at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes.

Author: Günter M. Ziegler

Publisher: Springer Science & Business Media

ISBN: 038794365X

Category: Mathematics

Page: 370

View: 938

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.

97 , American Mathematical Society , Providence , RI , 2002 . G . M . Ziegler , Lectures on Polytopes , Graduate Texts in Mathematics , vol . 152 , Springer -
Verlag , New York , 1995 . [ Stu02 ] [ Zie95 ] poset , 18 refinement , 70 prism , 13 ...

Author: Rekha R. Thomas

Publisher: American Mathematical Soc.

ISBN: 0821841408

Category: Mathematics

Page: 143

View: 193

This book presents a course in the geometry of convex polytopes in arbitrary dimension. It takes readers from the basics of polytope theory to recent developments around secondary and state polytopes arising from point configurations. The most needed concepts are developed from scratch. Text illustrates the interaction among discrete geometry, computational algebra and combinatorics. This book is published in cooperation with IAS/Park City Mathematics Institute.

Jiri Matousek is Professor of Computer Science at Charles University in Prague. His research has contributed to several of the considered areas and to their algorithmic applications. This is his third book.

Author: Ji?í Matoušek

Publisher: Springer Science & Business Media

ISBN: 9781461300397

Category: Mathematics

Page: 486

View: 310

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.

J. 37, pp 1–12, 1958 [13] B. GRÜNBAUM, Convex Polytopes, Interscience, New
York, 1967 [14] M. HENK, ... New York, 1975 [22] G.M. ZIEGLER, Lectures on Polytopes, Graduate Texts in Mathematics 152, Springer-Verlag, 1995; Revised ...

Author: Gil Kalai

Publisher: Birkhäuser

ISBN: 9783034884389

Category: Mathematics

Page: 225

View: 741

Questions that arose from linear programming and combinatorial optimization have been a driving force for modern polytope theory, such as the diameter questions motivated by the desire to understand the complexity of the simplex algorithm, or the need to study facets for use in cutting plane procedures. In addition, algorithms now provide the means to computationally study polytopes, to compute their parameters such as flag vectors, graphs and volumes, and to construct examples of large complexity. The papers of this volume thus display a wide panorama of connections of polytope theory with other fields. Areas such as discrete and computational geometry, linear and combinatorial optimization, and scientific computing have contributed a combination of questions, ideas, results, algorithms and, finally, computer programs.

[27] Hendrick W. Lenstra, Jr,, Factoring integers with elliptic curves, Annals of
Mathematics. Second Series 126 (19s7). no. 3. ... [40] Giinter M. Ziegler, Lectures on polytopes. Graduate Texts in Mathematics. voI. 152. Springer- Verlag, New
York ...

Author: Panos M. Pardalos

Publisher: American Mathematical Soc.

ISBN: 082188591X

Category: Mathematics

Page: 181

View: 146

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.

Math . Soc . , Providence , R . I . , 1991 , pp . 387 - 411 . [ 5 ] P . McMullen , The
maximum numbers of faces of a convez polytope , Mathematica 17 ( 1970 ) , 179
... [ 9 ] G . M . Ziegler , Lectures on Polytopes , Graduate Texts in Mathematics ,
Vol .

Ziegler , G. M .: Lectures on Polytopes . ( Graduate Texts in Mathematics 152. )
Springer - Verlag , New York / Berlin / Heidelberg / London / Paris / Tokyo / Hong
Kong / Barcelona / Budapest , 1995 , IX + 370 S. ISBN 3-540-94365 - X , ISBN ...

Author: Jurgen Richter-GebertPublish On: 1996-12-16

[ 53 ] P . SHOR , Stretchability of pseudolines is NP - hard , in : Applied Geometry
and Discrete Mathematics – The ... [ 65 ] G . M . ZIEGLER , Lectures on Polytopes
, Graduate Texts in Mathematics transformation groups , 18 translations , 18 ...

Author: Jurgen Richter-Gebert

Publisher: Springer Verlag

ISBN: STANFORD:36105017795068

Category: Mathematics

Page: 187

View: 998

Based on a course given to beginning physics, chemistry, and engineering students at the Winterthur Polytechnic Institute, this text approaches the fundamentals of thermodynamics from the view of continuum mechanics. By describing physical processes in terms of the flow and balance of physical quantities, this provides a unified approach to hydraulics, electricity, mechanics and thermodynamics. In this way it becomes clear that the entropy is the fundamental property that is transported in thermal process (what in lay terms would be called 'heat'), and that the temperature is the corresponding potential. The resulting theory of the creation, flow, and balance of entropy provides the foundation of a dynamical theory of heat. Previous knowledge of thermodynamics is not required, but the reader should be familiar with basic electricity, mechanics, and chemistry and should have some knowledge of elementary calculus.

[ 38 ] T. Zaslavsky , “ Facing up to arrangements : Face - count formulas for
partitions of space by hyperplanes , ” Memoirs of the American Mathematical
Society 1 ( 1975 ) . [ 39 ] G. Ziegler , Lectures on Polytopes , Graduate Texts in Mathematics ...

Author: Catherine Anne Stenson

Publisher:

ISBN: CORNELL:31924088881234

Category:

Page: 146

View: 708

First we present some of the history of this problem, along with the necessary mathematical background. We discuss several special classes of polytopes, including simplicials, simples, cubicals, and zonotopes, whose flag f-vectors satisfy inequalities not satisfied by all polytopes.

Author: Moʻatsah ha-leʼumit le-meḥḳar ule-fituaḥ (Israel)Publish On: 2005

References e [ 1 ] D. W. Barnette , A family of neighborly polytopes , Israel
Journal of Mathematics 39 ( 1981 ) , 127-140 . [ 2 ] F. Holt ... [ 9 ] G. M. Ziegler , Lectures on Polytopes , Graduate Texts in Mathematics 152 , Springer , New York
, 1995.

[ 12 ] E. Miller and B. Sturmfels , Combinatorial Commutative Algebra , Springer Graduate Texts in Mathematics , to appear . ( 13 ] W. D. ... [ 14 ] J. Richter - Gebert
, Realization Spaces of Polytopes , Springer Lecture Notes in Mathematics , no .

Author: Society for Industrial and Applied MathematicsPublish On: 2006

Society for Industrial and Applied Mathematics. ( 33 ) B . KUIJPERS AND ... ( 35 )
J . M . LEE , Introduction to Topological Manifolds , Graduate Texts in Math . ...
397 - 421 . ( 51 ) G . M . ZIEGLER , Lectures on Polytopes , Graduate Texts in Math .

Author: Society for Industrial and Applied Mathematics

Gröbner Bases and Conver Polytopes , University Lecture Series 8 , AMS ,
Providence , RI , 1996 . On the Newton polytope of the resultant , J. Algebraic
Combin . 3 ( 1994 ) , 207– ... G. Ziegler , Lectures on Polytopes , Graduate Texts in Math .

Author: János Kollár

Publisher: American Mathematical Soc.

ISBN: STANFORD:36105022859776

Category: Mathematics

Page: 896

View: 646

This volume contains many of the lectures delivered at the AMS Summer Research Institute on Algebraic Geometry held at the University of California, Santa Cruz in July 1995. The aim of the conference was to provide a comprehensive view of the development of algebraic geometry in the past decade and to lay special emphasis on emerging new directions. The focus of the papers in these volumes is on expository surveys of important areas rather than on technical presentations of new results. These proceedings will be an indispensable reference and guide for researchers in algebraic geometry or nearby fields. Features: Comprehensive coverage of developments over the past decade. Emphasis on new directions and future developments. Connections to related fields. Many expository survey papers.

( Fel01 ] Stefan Felsner , Convex drawings of planar graphs and the order
dimension of 3 - polytopes , Order 18 ( 2001 ) , no . 1 , 19 – 37 . ( Fel02 Stefan ... (
Zie95 ] Günter M . Ziegler , Lectures on polytopes , Graduate Texts in Mathematics , vol .