New PDF release: Analysis of Boolean Functions

By Ryan O'Donnell

Boolean capabilities are maybe the main simple gadgets of analysis in theoretical computing device technology. in addition they come up in different components of arithmetic, together with combinatorics, statistical physics, and mathematical social selection. the sphere of research of Boolean features seeks to appreciate them through their Fourier rework and different analytic equipment. this article offers an intensive assessment of the sphere, starting with the main simple definitions and continuing to complex issues comparable to hypercontractivity and isoperimetry. each one bankruptcy incorporates a 'highlight software' equivalent to Arrow's theorem from economics, the Goldreich–Levin set of rules from cryptography/learning thought, Håstad's NP-hardness of approximation effects, and 'sharp threshold' theorems for random graph houses. The booklet contains approximately 450 workouts and will be used because the foundation of a one-semester graduate direction. it's going to entice complicated undergraduates, graduate scholars and researchers in laptop technology conception and similar mathematical fields.

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Analysis of Boolean Functions by Ryan O'Donnell

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