Graduate Texts in Mathematics

Lectures on Discrete Geometry

Authors: Matoušek, Ji?í

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About this Textbook

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.

Reviews

From the reviews:

"Discrete geometry is not quite a newcomer on the stage of mathematics. … The book under review covers … a gap in the pedagogical literature, providing an expository treatment of a wide range of topics in discrete geometry, without assuming too many prerequisites from the reader. … it will be ideal to be used both as a textbook and for self-study. … In fact … this book can be used as a ‘mathematical companion’ to a textbook on computational geometry … ." (Paul A. Blaga, Studia Universitatis Babes-Bolyai Mathematica, Vol. XLVIII (1), March, 2004)

"Matoušek’s excellent new book concerns discrete geometry. … The style is clear and pleasant; things are streamlined and collected in one place, and are explained on simple, concrete examples. … a final chapter on ‘What was it about? An informal summary’ was an innovation that I found to be an excellent idea. Lectures on discrete geometry is a splendid book. I recommend it both to students and researchers in the field, as well as to those who like mathematics for its own inherent beauty." (Imre Bárány, Bulletin of the London Mathematical Society, Issue 35, 2003)

"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." (L’ENSEIGNEMENT MATHEMATIQUE, Vol. 48 (3-4), 2002)

"This is an introduction to the field of discrete geometry understood as the investigation of combinatorial properties of configurations of (usually finitely many) geometric objects … . The book is written in a lively and stimulating but very precise style and contains many figures. It gives a good impression of the richness and the relevance of the field." (Johann Linhart, Zentralblatt Math, Vol. 999 (24), 2002)


Table of contents (16 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-1-4613-0039-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-0-387-95373-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $69.99
price for USA
  • ISBN 978-0-387-95374-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Lectures on Discrete Geometry
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
212
Copyright
2002
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-1-4613-0039-7
DOI
10.1007/978-1-4613-0039-7
Hardcover ISBN
978-0-387-95373-1
Softcover ISBN
978-0-387-95374-8
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XVI, 486
Topics