Additive Combinatorics

English

Series: Cambridge Studies in Advanced Mathematics Ser.

Volume: Vol. 105

ISBN: 0511243057

EAN: 9780511243059

Category: Mathematics / Graphic Methods/Mathematics / Set Theory/

Publisher: Cambridge University Press

Release Date: 10/16/2006

Synopsis: Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate level textbook will allow students and researchers easy entry into this fascinating field. Here, for the first time, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemer''di's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results.

Excerpt: Unknown Property Excerpt

Additive Combinatorics

Illustrated: No

Format: eBook - PDF

Pages: 530