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＜電子ブック＞
Geometric Discrepancy : An Illustrated Guide / edited by Jiri Matousek
(Algorithms and Combinatorics. ISSN:21976783 ; 18)

版	1st ed. 1999.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1999
本文言語	英語
大きさ	XI, 289 p : online resource
著者標目	Matousek, Jiri editor SpringerLink (Online service)
件　名	LCSH:Geometry LCSH:Discrete mathematics FREE:Geometry FREE:Discrete Mathematics
一般注記	1. Introduction -- 2. Low-Discrepancy Sets for Axis-Parallel Boxes -- 3. Upper Bounds in the Lebesgue-Measure Setting -- 4. Combinatorial Discrepancy -- 5. VC-Dimension and Discrepancy -- 6. Lower Bounds -- 7. More Lower Bounds and the Fourier Transform -- A. Tables of Selected Discrepancy Bounds -- Hints 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) HTTP:URL=https://doi.org/10.1007/978-3-642-03942-3

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