By Terence Tao,Van H. Vu

Additive combinatorics is the idea of counting additive buildings in units. This concept has visible intriguing advancements and dramatic adjustments in course in recent times because of its connections with components resembling quantity thought, ergodic idea and graph idea. This graduate-level 2006 textual content will let scholars and researchers effortless access into this interesting box. right here, the authors assemble in a self-contained and systematic demeanour the various various instruments and ideas which are utilized in the fashionable idea, offering them in an obtainable, coherent, and intuitively transparent demeanour, and supplying speedy functions to difficulties in additive combinatorics. the ability of those instruments is definitely verified within the presentation of contemporary advances akin 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 numerous routines and new results.

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Additive combinatorics is the idea of counting additive constructions in units. This thought has obvious interesting advancements and dramatic adjustments in path lately due to its connections with components resembling quantity idea, ergodic thought and graph concept. This graduate-level 2006 textual content will permit scholars and researchers effortless access into this attention-grabbing box.

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