Boolean functions are perhaps the most basic objects of study in theoretical computer science. They also arise in other areas of mathematics, including combinatorics, statistical physics, and mathematical social choice. The field of analysis of Boolean functions seeks to understand them via their Fourier transform and other analytic methods. This text gives a thorough overview of the field, beginning with the most basic definitions and proceeding to advanced topics such as hypercontractivity and isoperimetry. Each chapter includes a 'highlight application' such as Arrow's theorem from economics, the Goldreich-Levin algorithm from cryptography/learning theory, Hastad's NP-hardness of approximation results, and 'sharp threshold' theorems for random graph properties. The book includes roughly 450 exercises and can be used as the basis of a one-semester graduate course. It should appeal to advanced undergraduates, graduate students and researchers in computer science theory and related mathematical fields.
Ryan O'Donnell is an Associate Professor in the Computer Science Department at Carnegie Mellon University.
1. Boolean functions and the Fourier expansion; 2. Basic concepts and social choice; 3. Spectral structure and learning; 4. DNF formulas and small-depth circuits; 5. Majority and threshold functions; 6. Pseudorandomness and F2-polynomials; 7. Property testing, PCPPs, and CSPs; 8. Generalized domains; 9. Basics of hypercontractivity; 10. Advanced hypercontractivity; 11. Gaussian space and invariance principles.
Number Of Pages:
- ID: 9781107038325
- Saver Delivery: Yes
- 1st Class Delivery: Yes
- Courier Delivery: Yes
- Store Delivery: Yes
Prices are for internet purchases only. Prices and availability in WHSmith Stores may vary significantly
© Copyright 2013 - 2016 WHSmith and its suppliers.
WHSmith High Street Limited Greenbridge Road, Swindon, Wiltshire, United Kingdom, SN3 3LD, VAT GB238 5548 36