Lectures on Discrete Geometry

Jiri Matousek - Collection Graduate Texts in Mathematics

484 pages, parution le 30/03/2004

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Résumé

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.

Written for:
Graduate mathematics students, mathematicians, undergraduate mathematics students

L'auteur - Jiri Matousek

Charles University, Prague, Czechoslovakia

Sommaire

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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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Jiri Matousek
Collection	Graduate Texts in Mathematics
Parution	30/03/2004
Nb. de pages	484
Format	16 x 24
Couverture	Relié
Poids	810g
Intérieur	Noir et Blanc
EAN13	9780387953731
ISBN13	978-0-387-95373-1