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

By Terence Tao,Van H. Vu

Additive combinatorics is the speculation of counting additive buildings in units. This concept has obvious interesting advancements and dramatic adjustments in path lately because of its connections with parts equivalent to quantity thought, ergodic idea and graph idea. 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 various diversified instruments and ideas which are utilized in the fashionable idea, proposing them in an available, coherent, and intuitively transparent demeanour, and supplying quick functions to difficulties in additive combinatorics. the ability of those instruments is definitely proven 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 loads of workouts and new results.

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