...i Computational Complexity: A Modern Approach Draft of a book: Dated January 2007 Comments welcome! Sanjeev Arora and Boaz Barak Princeton University complexitybook@gmail.com Not to be reproduced or distributed without the authors’ permission This is an Internet draft. Some chapters are more finished than others. References and attributions are very preliminary and we apologize in advance for any omissions (but hope you will nevertheless point them out to us). Please send us bugs, typos, missing references or general comments to complexitybook@gmail.com — Thank You!! DRAFT ii DRAFT About this book Computational complexity theory has developed rapidly in the past three decades. The list of surprising and fundamental results proved since 1990 alone could fill a book: these include new probabilistic definitions of classical complexity classes (IP = PSPACE and the PCP Theorems) and their implications for the field of approximation algorithms; Shor’s algorithm to factor integers using a quantum computer; an understanding of why current approaches to the famous P versus NP will not be successful; a theory of derandomization and pseudorandomness based upon computational hardness; and beautiful constructions of pseudorandom objects such as extractors and expanders. This book aims to describe such recent achievements of complexity theory in the context of the classical results. It is intended to both serve as a textbook as a reference for self-study. This means...
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...Problem Books in Mathematics Edited by P. Winkler Problem Books in Mathematics Series Editors: Peter Winkler Pell’s Equation by Edward J. Barbeau Polynomials by Edward J. Barbeau Problems in Geometry by Marcel Berger, Pierre Pansu, Jean-Pic Berry, and Xavier Saint-Raymond Problem Book for First Year Calculus by George W. Bluman Exercises in Probability by T. Cacoullos Probability Through Problems by Marek Capi´ski and Tomasz Zastawniak n An Introduction to Hilbert Space and Quantum Logic by David W. Cohen Unsolved Problems in Geometry by Hallard T. Croft, Kenneth J. Falconer, and Richard K. Guy Berkeley Problems in Mathematics (Third Edition) by Paulo Ney de Souza and Jorge-Nuno Silva The IMO Compendium: A Collection of Problems Suggested for the International Mathematical Olympiads: 1959–2004 by Duˇan Djuki´, Vladimir Z. Jankovi´, Ivan Mati´, and Nikola Petrovi´ s c c c c Problem-Solving Strategies by Arthur Engel Problems in Analysis by Bernard R. Gelbaum Problems in Real and Complex Analysis by Bernard R. Gelbaum (continued after subject index) Wolfgang Schwarz 40 Puzzles and Problems in Probability and Mathematical Statistics Wolfgang Schwarz Universit¨ t Potsdam a Humanwissenschaftliche Fakult¨ t a Karl-Liebknecht Strasse 24/25 D-14476 Potsdam-Golm Germany wschwarz@uni-potsdam.de Series Editor: Peter Winkler Department of Mathematics Dartmouth College Hanover, NH 03755 USA Peter.winkler@dartmouth.edu ISBN-13: 978-0-387-73511-5 e-ISBN-13: 978-0-387-73512-2 ...
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...User SONPR:Job EFF01417:6264_ch01:Pg 0:23907#/eps at 100% *23907* Fri, Nov 9, 2001 11:52 AM part I Introduction User SONPR:Job EFF01417:6264_ch01:Pg 1:21266#/eps at 100% *21266* Fri, Nov 9, 2001 11:52 AM C H A P T E R The Science of Macroeconomics The whole of science is nothing more than the refinement of everyday thinking. — Albert Einstein 1 O N E 1-1 What Macroeconomists Study Why have some countries experienced rapid growth in incomes over the past century while others stay mired in poverty? Why do some countries have high rates of inflation while others maintain stable prices? Why do all countries experience recessions and depressions—recurrent periods of falling incomes and rising unemployment—and how can government policy reduce the frequency and severity of these episodes? Macroeconomics, the study of the economy as a whole, attempts to answer these and many related questions. To appreciate the importance of macroeconomics, you need only read the newspaper or listen to the news. Every day you can see headlines such as INCOME GROWTH SLOWS, FED MOVES TO COMBAT INFLATION, or STOCKS FALL AMID RECESSION FEARS. Although these macroeconomic events may seem abstract, they touch all of our lives. Business executives forecasting the demand for their products must guess how fast consumers’ incomes will grow. Senior citizens living on fixed incomes wonder how fast prices will rise. Recent college graduates looking for jobs hope that the economy...
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...User SONPR:Job EFF01417:6264_ch01:Pg 0:23907#/eps at 100% *23907* Fri, Nov 9, 2001 11:52 AM part I Introduction User SONPR:Job EFF01417:6264_ch01:Pg 1:21266#/eps at 100% *21266* Fri, Nov 9, 2001 11:52 AM C H A P T E R The Science of Macroeconomics The whole of science is nothing more than the refinement of everyday thinking. — Albert Einstein 1 O N E 1-1 What Macroeconomists Study Why have some countries experienced rapid growth in incomes over the past century while others stay mired in poverty? Why do some countries have high rates of inflation while others maintain stable prices? Why do all countries experience recessions and depressions—recurrent periods of falling incomes and rising unemployment—and how can government policy reduce the frequency and severity of these episodes? Macroeconomics, the study of the economy as a whole, attempts to answer these and many related questions. To appreciate the importance of macroeconomics, you need only read the newspaper or listen to the news. Every day you can see headlines such as INCOME GROWTH SLOWS, FED MOVES TO COMBAT INFLATION, or STOCKS FALL AMID RECESSION FEARS. Although these macroeconomic events may seem abstract, they touch all of our lives. Business executives forecasting the demand for their products must guess how fast consumers’ incomes will grow. Senior citizens living on fixed incomes wonder how fast prices will rise. Recent college graduates looking for jobs hope that the economy...
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...Emory University | Internetworking Technology Handbook | [Type the document subtitle] | | SAVIOUR EMMANUEL UDOBONG | [Pick the date] | [Type the abstract of the document here. The abstract is typically a short summary of the contents of the document. Type the abstract of the document here. The abstract is typically a short summary of the contents of the document.] | Internetworking Basics An internetwork is a collection of individual networks, connected by intermediate networking devices, that functions as a single large network. Internetworking refers to the industry, products, and procedures that meet the challenge of creating and administering internetworks. The following articles provide information about internetworking basics: * Internetworking Basics * Introduction to LAN Protocols * Introduction to WAN Technologies * Bridging and Switching Basics * Routing Basics * Network Management Basics * Open System Interconnection Protocols LAN Technologies A LAN is a high-speed data network that covers a relatively small geographic area. It typically connects workstations, personal computers, printers, servers, and other devices. LANs offer computer users many advantages, including shared access to devices and applications, file exchange between connected users, and communication between users via electronic mail and other applications. The following articles provide information different LAN technologies: * Ethernet...
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