Additive Combinatorics by Terence Tao (English) Hardcover Book

Description: Additive Combinatorics by Terence Tao, Van Vu 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 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. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher 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 Szemeredis 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. Author Biography Terence Tao is a Professor in the Department of Mathematics, University of California, Los Angeles. Van Vu is a Professor in the Mathematics Department at Rutgers University, New Jersey. Table of Contents 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. Szemeredis theorem for k = 3; 11. Szemeredis theorem for k > 3; 12. Long arithmetic progressions in sum sets; Bibliography; Index. 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 "... 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. I have three copies myself: one at home, one in the office, and a spare in case either of those should become damaged." Bulletin of the AMS Review Quote 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 Promotional "Headline" A graduate-level 2006 text bringing together the tools from different fields used in additive combinatorics. Description for Bookstore 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. Description for Library 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. Details ISBN0521853869 Author Van Vu Short Title ADDITIVE COMBINATORICS Pages 512 Publisher Cambridge University Press Series Cambridge Studies in Advanced Mathematics (Hardcover) Language English ISBN-10 0521853869 ISBN-13 9780521853866 Media Book Format Hardcover DEWEY 511.6 Series Number 105 Year 2006 Publication Date 2006-09-30 Imprint Cambridge University Press Place of Publication Cambridge Country of Publication United Kingdom Edition 1st Birth 1975 Affiliation University of California, Los Angeles Illustrations Worked examples or Exercises Replaced by 9780521136563 DOI 10.1604/9780521853866 Audience Professional and Scholarly UK Release Date 2006-09-14 AU Release Date 2006-09-14 NZ Release Date 2006-09-14 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:91363223;

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