Lectures on Discrete Geometry / Edition 1

Lectures on Discrete Geometry / Edition 1

by Ji?i Matousek, J. Matousek
     
 

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ISBN-10: 0387953744

ISBN-13: 9780387953748

Pub. Date: 05/02/2002

Publisher: Springer New York

Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization.

This book is primarily a textbook introduction to various

Overview

Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization.

This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics 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; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces.

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.

Product Details

ISBN-13:
9780387953748
Publisher:
Springer New York
Publication date:
05/02/2002
Series:
Graduate Texts in Mathematics Series, #212
Edition description:
Softcover reprint of the original 1st ed. 2002
Pages:
486
Product dimensions:
1.01(w) x 9.21(h) x 6.14(d)

Table of Contents

* Preface
• Notation and Terminology
• Convexity
• Lattices and Minkowski's Theorem
• Convex Independent Subsets
• Incidence Problems
• Convex Polytopes
• Number of Faces in Arrangements
• Lower Envelopes
• More Theorems in Convexity
• Geometric Selection Theorems
• Transversals and Epsilon-Nets
• Attempts to Count k-sets
• Two Applications of High-Dimensional Polytopes
• Volumes in High Dimension
• Measure Concentration and Almost Spherical Sections
• Embedding Finite Metric Spaces into Normed Spaces
• What Was It About: An Informal Summary
• Bibliography
• Index

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