Overview

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.).

Full Product Details

Author:   Jiri Matousek
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1999 ed.
Volume:   18
Dimensions:   Width: 15.50cm , Height: 1.90cm , Length: 23.50cm
Weight:   1.340kg
ISBN:  

9783540655282

ISBN 10:   354065528
Pages:   289
Publication Date:   19 May 1999
Audience:   College/higher education ,  General/trade ,  Postgraduate, Research & Scholarly ,  General
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

Table of Contents

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.

Reviews

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)

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)

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)

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