Download e-book for kindle: Analysis of Boolean Functions by Ryan O'Donnell

By Ryan O'Donnell

Boolean capabilities are maybe the main easy items of analysis in theoretical laptop technology. in addition 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 rework and different analytic equipment. this article offers an intensive assessment of the sphere, starting with the main uncomplicated definitions and continuing to complicated themes equivalent to hypercontractivity and isoperimetry. every one bankruptcy encompasses a 'highlight software' similar to Arrow's theorem from economics, the Goldreich–Levin set of rules from cryptography/learning idea, Håstad's NP-hardness of approximation effects, and 'sharp threshold' theorems for random graph homes. The publication contains approximately 450 routines and will be used because the foundation of a one-semester graduate direction. it may attract complicated undergraduates, graduate scholars and researchers in machine technological know-how thought and similar mathematical fields.

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Analysis of Boolean Functions by Ryan O'Donnell


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