By Ryan O'Donnell

Boolean features are maybe the main uncomplicated gadgets of analysis in theoretical laptop technology. additionally they come up in different parts of arithmetic, together with combinatorics, statistical physics, and mathematical social selection. the sector of research of Boolean capabilities seeks to appreciate them through their Fourier remodel and different analytic tools. this article supplies an intensive assessment of the sphere, starting with the main easy definitions and continuing to complicated subject matters reminiscent of hypercontractivity and isoperimetry. each one bankruptcy features a 'highlight software' corresponding to Arrow's theorem from economics, the Goldreich–Levin set of rules from cryptography/learning concept, Håstad's NP-hardness of approximation effects, and 'sharp threshold' theorems for random graph houses. The booklet comprises approximately 450 workouts and will be used because the foundation of a one-semester graduate direction. it may attract complex undergraduates, graduate scholars and researchers in desktop technological know-how idea and similar mathematical fields.

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Analysis of Boolean Functions by Ryan O'Donnell

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