Lectures on Discrete Geometry

  • Jiří Matoušek

Part of the Graduate Texts in Mathematics book series (GTM, volume 212)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Jiří Matoušek
    Pages 1-16
  3. Jiří Matoušek
    Pages 17-28
  4. Jiří Matoušek
    Pages 29-39
  5. Jiří Matoušek
    Pages 41-76
  6. Jiří Matoušek
    Pages 77-124
  7. Jiří Matoušek
    Pages 125-163
  8. Jiří Matoušek
    Pages 165-194
  9. Jiří Matoušek
    Pages 195-206
  10. Jiří Matoušek
    Pages 207-229
  11. Jiří Matoušek
    Pages 231-263
  12. Jiří Matoušek
    Pages 265-288
  13. Jiří Matoušek
    Pages 289-309
  14. Jiří Matoušek
    Pages 311-328
  15. Jiří Matoušek
    Pages 355-400
  16. Jiří Matoušek
    Pages 401-407
  17. Back Matter
    Pages 409-485

About this book

Introduction

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.

Keywords

Discrete Geometry Dimension discrete geometry geometry mathematics

Editors and affiliations

  • Jiří Matoušek
    • 1
  1. 1.Department of Applied MathematicsCharles UniversityPraha 1Czech Republic

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-0039-7
  • Copyright Information Springer-Verlag New York 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-95374-8
  • Online ISBN 978-1-4613-0039-7
  • Series Print ISSN 0072-5285
  • About this book