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Analysis of Boolean Functions
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Table of Contents

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.

Promotional Information

This graduate-level text gives a thorough overview of the analysis of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics.

About the Author

Ryan O'Donnell is an Associate Professor in the Computer Science Department at Carnegie Mellon University.

Reviews

'The applications of the ideas in this book are plentiful and diverse, and O'Donnell does an excellent job of leading the reader from one viewpoint to the next. I found it especially enjoyable to see theorems that I'm personally familiar with as a cryptographer, such as the Goldreich-Levin theorem, placed alongside other things I didn't know as well, like Arrow's theorem from social choice - with everything woven into a single, consistent story. I suspect other 'fresh readers' will similarly find parts of this book that they recognize, and others they don't. The relationships exposed between these ideas should be of interest to everyone. Altogether, I highly recommend that you take a glance at Analysis of Boolean Functions.' Daniel Apon, SIGACT News
'This 423-page book is a rich source of material presented in an attractive form. Each chapter highlights one main result which provides a focus and incentive for the reader to go to the end of the chapter.' Martin C. Cooper, MathSciNet
'The applications of the ideas in this book are plentiful and diverse, and O'Donnell does an excellent job of leading the reader from one viewpoint to the next. I found it especially enjoyable to see theorems that I'm personally familiar with as a cryptographer, such as the Goldreich-Levin theorem, placed alongside other things I didn't know as well, like Arrow's theorem from social choice - with everything woven into a single, consistent story. I suspect other `fresh readers' will similarly find parts of this book that they recognize, and others they don't. The relationships exposed between these ideas should be of interest to everyone. Altogether, I highly recommend that you take a glance at Analysis of Boolean Functions.' Daniel Apon, SIGACT News
'This 423-page book is a rich source of material presented in an attractive form. Each chapter highlights one main result which provides a focus and incentive for the reader to go to the end of the chapter.' Martin C. Cooper, MathSciNet

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