Lectures on Discrete Geometry - Matousek, Jiri

Lectures on Discrete Geometry

Jiri Matousek

Yayınevi: Springer

Yayın tarihi: 05/2002

ISBN: 9780387953748

İngilizce | 481 Sayfa | 155 mm x 235 mm; 206 illustrations

Tür: Matematik-İstatistik

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A text to discrete geometry. It contains topics that 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.

Contents:
- 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

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