Additive Combinatorics
1st Edition
Published on 5. November 2006
978-0-511-24305-9 (ISBN)
Description
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 2006 text will allow students and researchers easy entry into this fascinating field. Here, 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 Szemeredi'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.
Reviews / Votes
'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 MATHMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
File size
3,04 MB
ISBN-13
978-0-511-24305-9 (9780511243059)
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Schweitzer Classification
Other editions
Additional editions
Terence Tao | Van H. Vu
Additive Combinatorics
Book
11/2009
Cambridge University Press
€80.00
Shipment within 15-20 days
Terence Tao | Van H. Vu
Additive Combinatorics
Book
09/2006
Cambridge University Press
€185.00
Shipment within 15-20 days
Persons
Terence Tao is a Professor in the Department of Mathematics at the University of California, Los Angeles. He was awarded the Fields Medal in 2006 for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory. Van H. Vu is a Professor in the Department of Mathematics at Rutgers University, New Jersey.
Content
Prologue; 1. The probabilistic method; 2. Sum set estimates; 3. Additive geometry; 4. Fourier-analytic methods; 5. Inverse sum set theorems; 6. Graph-theoretic methods; 7. The Littlewood-Offord problem; 8. Incidence geometry; 9. Algebraic methods; 10. Szemeredi's theorem for k = 3; 11. Szemeredi's theorem for k > 3; 12. Long arithmetic progressions in sum sets; Bibliography; Index.
