Download e-book for iPad: Additive Combinatorics (Cambridge Studies in Advanced by Terence Tao,Van H. Vu

By Terence Tao,Van H. Vu

Additive combinatorics is the speculation of counting additive buildings in units. This concept has visible intriguing advancements and dramatic alterations in course in recent times because of its connections with components similar to quantity idea, ergodic conception 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 assemble in a self-contained and systematic demeanour the numerous diverse instruments and concepts which are utilized in the trendy idea, providing them in an available, coherent, and intuitively transparent demeanour, and delivering rapid purposes to difficulties in additive combinatorics. the facility of those instruments is definitely tested within the presentation of contemporary advances reminiscent of 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 by means of lots of workouts and new results.

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Additive Combinatorics (Cambridge Studies in Advanced Mathematics) by Terence Tao,Van H. Vu

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