| Additive Combinatorics Contributor(s): Tao, Terence (Author), Vu, Van (Author) |
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ISBN: 0521853869 ISBN-13: 9780521853866 Publisher: Cambridge University Press OUR PRICE: $162.45 Product Type: Hardcover - Other Formats Published: September 2006 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Combinatorics - Mathematics | Mathematical Analysis |
| Dewey: 511.6 |
| LCCN: 2006299772 |
| Series: Cambridge Studies in Advanced Mathematics (Hardcover) |
| Physical Information: 1.22" H x 6.37" W x 9.16" (1.83 lbs) 532 pages |
| Descriptions, Reviews, Etc. |
| 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 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. |
Contributor Bio(s): Tao, Terence: - 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. |