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- About this book
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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)
- Reviews
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From the reviews:
“The book gives a very useful introduction to geometric discrepancy theory. The style is quite informal and lively which makes the book easily readable.” (Robert F. Tichy, Zentralblatt MATH, Vol. 1197, 2010)
- Table of contents (7 chapters)
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Introduction
Pages 1-35
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Low-Discrepancy Sets for Axis-Parallel Boxes
Pages 37-81
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Upper Bounds in the Lebesgue-Measure Setting
Pages 83-99
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Combinatorial Discrepancy
Pages 101-135
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VC-Dimension and Discrepancy
Pages 137-169
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Table of contents (7 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Geometric Discrepancy
- Book Subtitle
- An Illustrated Guide
- Editors
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- Jiri Matousek
- Series Title
- Algorithms and Combinatorics
- Series Volume
- 18
- Copyright
- 1999
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-642-03942-3
- DOI
- 10.1007/978-3-642-03942-3
- Hardcover ISBN
- 978-3-540-65528-2
- Softcover ISBN
- 978-3-642-03941-6
- Series ISSN
- 0937-5511
- Edition Number
- 1
- Number of Pages
- XI, 289
- Topics
