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? This book is an accessible and lively introduction to the area of geometric discrepancy theory.

The book is a monograph in an important area of discrete mathematics and geometry. It is bound to become a standard reference.

Only up-to-date comprehensive guide to the subject Includes supplementary material: sn.pub/extras

Zusammenfassung

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)

Inhalt

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.