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

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Additive combinatorics is the idea of counting additive buildings in units. This idea has visible fascinating advancements and dramatic alterations in path in recent times because of its connections with components equivalent to quantity idea, ergodic conception and graph conception. This graduate-level 2006 textual content will let scholars and researchers effortless access into this attention-grabbing box. right here, the authors assemble in a self-contained and systematic demeanour the various varied instruments and ideas which are utilized in the trendy thought, proposing them in an obtainable, coherent, and intuitively transparent demeanour, and offering speedy purposes to difficulties in additive combinatorics. the facility of those instruments is easily verified within the presentation of modern 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 via quite a few routines and new results.

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


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