Additive Combinatorics: 105 (Cambridge Studies in Advanced Mathematics, Series Number 105) - Softcover

Tao, Terence

Softcover

ISBN 10: 0521136563 ISBN 13: 9780521136563

Publisher: Cambridge University Press, 2005

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 text 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 Szemerédi'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.

About this title

Review

'The book under review is a vital contribution to the literature, and it has already become required reading for a new generation of students as well as for experts in adjacent areas looking to learn about additive combinatorics. ... This was very much a book that needed to be written at the time it was, and the authors are to be highly commended for having done so in such an effective way.' Bulletin of the American Mathematical Society

'The book gathers diverse important techniques used in additive combinatorics, and its main advantage is that it is written in a very readable and easy to understand style. The authors try very successfully to develop all the necessary background material ... [which] makes the book useful not only to graduate students, but also to researchers who are interested to learn more about the variety of diverse tools and ideas applied in this fascinating subject.' Zentralblatt MATH

Book Description

The many different tools from different fields that are used in additive combinatorics are brought together in a self-contained and systematic manner. This graduate-level 2006 text will quickly allow students and researchers easy entry into the fascinating field of additive combinatorics.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2005
• ISBN 10: 0521136563
• ISBN 13: 9780521136563
• Binding: Paperback
• Language: English
• Number of pages: 532