Analysis of Boolean Functions by Ryan O'Donnell

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By Ryan O'Donnell

Boolean features are might be the main simple gadgets of research in theoretical laptop technological know-how. additionally they come up in different components of arithmetic, together with combinatorics, statistical physics, and mathematical social selection. the sphere of research of Boolean capabilities seeks to appreciate them through their Fourier rework and different analytic equipment. this article supplies a radical review of the sphere, starting with the main simple definitions and continuing to complex subject matters resembling hypercontractivity and isoperimetry. every one bankruptcy features a 'highlight program' resembling Arrow's theorem from economics, the Goldreich–Levin set of rules from cryptography/learning conception, Håstad's NP-hardness of approximation effects, and 'sharp threshold' theorems for random graph houses. The ebook comprises approximately 450 routines and will be used because the foundation of a one-semester graduate path. it's going to entice complicated undergraduates, graduate scholars and researchers in machine technology conception and comparable mathematical fields.

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