Additive Combinatorics

Additive Combinatorics

by Terence Tao, Van H. Vu
     
 

ISBN-10: 0521136563

ISBN-13: 9780521136563

Pub. Date: 12/31/2009

Publisher: Cambridge University Press

Additive combinatorics is the theory of counting additive structures in sets. While this theory has been developing for many decades, the field has seen exciting advances and dramatic changes in direction in recent years thanks to its connections with other areas of mathematics, such as number theory, ergodic theory, and graph theory.

Now in paperback, this

Overview

Additive combinatorics is the theory of counting additive structures in sets. While this theory has been developing for many decades, the field has seen exciting advances and dramatic changes in direction in recent years thanks to its connections with other areas of mathematics, such as number theory, ergodic theory, and graph theory.

Now in paperback, this graduate-level textbook will quickly 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 way, 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 the Green-Tao theorem on arithmetic progressions; Erdos distance problems; and the newly developing field of sum-product estimates. The text is supplemented by a large number of exercises and other material that has not previously appeared elsewhere.

Product Details

ISBN-13:
9780521136563
Publisher:
Cambridge University Press
Publication date:
12/31/2009
Series:
Cambridge Studies in Advanced Mathematics Series, #105
Edition description:
New Edition
Pages:
532
Product dimensions:
6.00(w) x 8.90(h) x 1.00(d)

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. Szemerédi's theorem for k = 3; 11. Szemerédi's theorem for k > 3; 12. Long arithmetic progressions in sum sets; Bibliography; Index.

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