Complexity Theory: A Modern Approach
by Sanjeev Arora, Boaz Barak
Publisher: Cambridge University Press 2008
Number of pages: 489
This book aims to describe such recent achievements of complexity theory in the context of the classical results. It is intended to be a text and as well as a reference for self-study. This means it must simultaneously cater to many audiences, and it is carefully designed with that goal. The book will explain the context in which a certain notion is useful, and why things are defined in a certain way. Examples and solved exercises accompany key definitions. This book assumes essentially no computational background (though a slight exposure to computing may help) and very little mathematical background apart from the ability to understand proofs and some elementary probability on finite sample spaces. A typical undergraduate course on "Discrete Math" taught in many math and CS departments should suffice (together with the Appendix).
Home page url
Download or read it online for free here:
by Karl Petersen - University of North Carolina
These notes provide an introduction to the subject of measure-preserving dynamical systems, discussing the dynamical viewpoint; how and from where measure-preserving systems arise; the construction of measures and invariant measures; etc.
by Neil D. Jones - The MIT Press
The author builds a bridge between computability and complexity theory and other areas of computer science. Jones uses concepts familiar from programming languages to make computability and complexity more accessible to computer scientists.
by Alexander Shen - arXiv.org
Algorithmic information theory studies description complexity and randomness. This text covers the basic notions of algorithmic information theory: Kolmogorov complexity, Solomonoff universal a priori probability, effective Hausdorff dimension, etc.
by Tim Roughgarden - Stanford University
The two biggest goals of the course are: 1. Learn several canonical problems that have proved the most useful for proving lower bounds; 2. Learn how to reduce lower bounds for fundamental algorithmic problems to communication complexity lower bounds.