Additive Combinatorics

Terence Tao, Van H. Vu - Collection Cambridge Studies in Advanced Mathematics

530 pages, parution le 22/11/2006

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Résumé

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 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.

Comprehensive graduate level textbook for a highly active current area of research
The authors bring together for the first time the many different tools and ideas that are used in the modern theory of additive combinatorics
The text is supplemented with a large number of exercises

L'auteur - Terence Tao

Terence Tao est professeur à l'université de Californie à Los Angeles et médaillé Fields.

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Sommaire

The probabilistic method
Sum set estimates
Additive geometry
Fourier analytic methods
Inverse sumset theorems
Graph theoretic methods
The Littlewood-Offord problem
Incidence geometry
Algebraic methods
Szemerédi's theorem for k = 3
Szemerédi's theorem for k > 3
Long arithmetic progressions in sumsets

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Terence Tao, Van H. Vu
Collection	Cambridge Studies in Advanced Mathematics
Parution	22/11/2006
Nb. de pages	530
Format	16 x 24
Couverture	Relié
Poids	850g
Intérieur	Noir et Blanc
EAN13	9780521853866
ISBN13	978-0-521-85386-6