Download Additive Combinatorics (Cambridge Studies in Advanced by Terence Tao,Van H. Vu PDF

By Terence Tao,Van H. Vu

Additive combinatorics is the idea of counting additive constructions in units. This thought has noticeable interesting advancements and dramatic alterations in path lately due to its connections with parts corresponding to quantity conception, ergodic concept and graph thought. This graduate-level 2006 textual content will enable scholars and researchers effortless access into this interesting box. right here, the authors collect in a self-contained and systematic demeanour the numerous diversified instruments and concepts which are utilized in the trendy concept, proposing them in an obtainable, coherent, and intuitively transparent demeanour, and delivering instant functions to difficulties in additive combinatorics. the ability of those instruments is definitely verified within the presentation of modern advances akin to Szemerédi's theorem on mathematics progressions, the Kakeya conjecture and Erdos distance difficulties, and the constructing box of sum-product estimates. The textual content is supplemented through various workouts and new results.

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