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

By Terence Tao,Van H. Vu

Additive combinatorics is the idea of counting additive buildings in units. This concept has noticeable interesting advancements and dramatic adjustments in course lately due to its connections with components resembling quantity conception, ergodic thought and graph concept. This graduate-level 2006 textual content will permit scholars and researchers effortless access into this interesting box. the following, the authors collect in a self-contained and systematic demeanour the various various instruments and ideas which are utilized in the fashionable conception, offering them in an obtainable, coherent, and intuitively transparent demeanour, and delivering rapid functions to difficulties in additive combinatorics. the ability of those instruments is easily proven within the presentation of modern 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 by way of quite a few workouts and new results.

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Additive Combinatorics (Cambridge Studies in Advanced Mathematics)

Additive combinatorics is the idea of counting additive constructions in units. This concept has visible fascinating advancements and dramatic adjustments in course in recent times because of its connections with components resembling quantity concept, ergodic conception and graph idea. This graduate-level 2006 textual content will enable scholars and researchers effortless access into this attention-grabbing box.

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