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Geometric Discrepancy

An Illustrated Guide

  • Jiří Matoušek

Part of the Algorithms and Combinatorics book series (AC, volume 18)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Jiří Matoušek
    Pages 1-35
  3. Jiří Matoušek
    Pages 37-81
  4. Jiří Matoušek
    Pages 83-99
  5. Jiří Matoušek
    Pages 101-135
  6. Jiří Matoušek
    Pages 137-169
  7. Jiří Matoušek
    Pages 171-211
  8. Jiří Matoušek
    Pages 213-240
  9. Back Matter
    Pages 241-289

About this book

Introduction

What is the "most uniform" way of distributing n points in the unit square? How big is the "irregularity" necessarily present in any such distribution? Such questions are treated in geometric discrepancy theory. The book is an accessible and lively introduction to this area, with numerous exercises and illustrations. In separate, more specialized parts, it also provides a comprehensive guide to recent research. Including a wide variety of mathematical techniques (from harmonic analysis, combinatorics, algebra etc.) in action on non-trivial examples, the book is suitable for a "special topic" course for early graduates in mathematics and computer science. Besides professional mathematicians, it will be of interest to specialists in fields where a large collection of objects should be "uniformly" represented by a smaller sample (such as high-dimensional numerical integration in computational physics or financial mathematics, efficient divide-and-conquer algorithms in computer science, etc.).

From the reviews: "...The numerous illustrations are well placed and instructive. The clear and elegant exposition conveys a wealth of intuitive insights into the techniques utilized. Each section usually consists of text, historical remarks and references for the specialist, and exercises. Hints are provided for the more difficult exercises, with the exercise-hint format permitting inclusion of more results than otherwise would be possible in a book of this size..."

Allen D. Rogers, Mathematical Reviews Clippings (2001)

 

Keywords

Combinatorics Dimension Diskrepanz Gleichverteilung Grad Kombinatorik Lattice Matching Ramsey theory Stichproben algorithms discrepancy sampling uniform distribution

Authors and affiliations

  • Jiří Matoušek
    • 1
  1. 1.Department of Applied MathematicsCharles UniversityPrahaCzech Republic

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-03942-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-03941-6
  • Online ISBN 978-3-642-03942-3
  • Series Print ISSN 0937-5511
  • Buy this book on publisher's site
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