## Ryan O'Donnell ↠ 6 Summary

Analysis of Boolean Functions Characters ☆ PDF, eBook or Kindle ePUB õ [Reading] ➬ Analysis of Boolean Functions ➳ Ryan O'Donnell – Danpashley.co.uk Boolean functions are perhaps the most basic objects of study in theoretical computer science They also arise in other areas of mathematics incBoolean 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 book is mostly concerned with Fourier analysis of functions of the form f01^n 01 known as Boolean functions These functions play a very important role in theoretical computer science and combinatorics They are simple elegant and yet they're expressive enough to capture most problems encountered in these fieldsRyan O'Donnell a well known expert in this area gives a very accessible and highly motivated exposition of the topic Indeed some knowledge of probability theory and linear algebra is enough to get you started In particular no prior knowledge of Fourier analysis is assumed Each chapter ends with a highlight section which is an exposé of a usually important result using the techniues covered in that chapter Already by the end of the first chapter the reader can appreciate an application of simple Fourier analytic notions to the problem of function linearity testing In later chapters these highlight sections will consider constant depth circuits pseudorandomness PCPs the KLL theorem decision tree complexity and much Additionally in chapter 8 generalizations of Boolean functions to probability product spaces are considered Finally the last three chapters contain a wealth of information on hypercontractivityNeedless to say this book is highly recommended to students and researchers in theoretical computer science and mathematics Indeed there is no other book with a scope like thisAn online version of the book is available athttpwwwcontribandrewcmueduryanodNonetheless it's still a good idea to get the print version There are exercises for some chapters expanded notes in some cases plus a much needed symbol list and of course an index

### Summary Ç PDF, eBook or Kindle ePUB ↠ Ryan O'Donnell

This text gives a thorough overview of Analysis of Epubthe 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 cryptographylearning theory H?. An excellent clear and complete review of the area as of circa 2013 It is a great graduate text Perhaps a bit dry as the author was careful to provide very precise definitions and exact statements Superb exercises at the end of chapters provide a range of challenges from simple applications of definitions through straightforward exercises proving lemmas that are used in later chapters to nontrivial extensions The final chapters are cover advanced materials Very highly recommended For calibration I consider the Feynman Lectures a 5 star book

### Read Analysis of Boolean Functions

Analysis of Boolean Functions?stad's NP hardness of approximation results and 'sharp threshold' theorems for random graph properties The book includes roughly 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. Fantastic book The inkfont is not of as good uality as I expectedhoped but the contents very much make up for it