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By Terence Tao,Van H. Vu

Additive combinatorics is the speculation of counting additive constructions in units. This thought has noticeable intriguing advancements and dramatic alterations in path in recent times due to its connections with components equivalent to quantity concept, ergodic conception and graph concept. This graduate-level 2006 textual content will let scholars and researchers effortless access into this attention-grabbing box. the following, the authors compile in a self-contained and systematic demeanour the various various instruments and ideas which are utilized in the fashionable conception, proposing them in an obtainable, coherent, and intuitively transparent demeanour, and delivering fast functions to difficulties in additive combinatorics. the ability of those instruments is definitely confirmed within the presentation of modern advances corresponding 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 by way of various 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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