Get Additive Combinatorics (Cambridge Studies in Advanced PDF

By Terence Tao,Van H. Vu

Additive combinatorics is the idea of counting additive buildings in units. This idea has noticeable fascinating advancements and dramatic alterations in path lately because of its connections with components similar to quantity thought, ergodic idea and graph concept. This graduate-level 2006 textual content will permit scholars and researchers effortless access into this attention-grabbing box. the following, the authors compile in a self-contained and systematic demeanour the various diverse instruments and ideas which are utilized in the fashionable idea, proposing them in an obtainable, coherent, and intuitively transparent demeanour, and offering instant purposes to difficulties in additive combinatorics. the facility of those instruments is definitely confirmed within the presentation of contemporary advances comparable 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 via plenty of workouts and new results.

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