The Probabilistic Method (Wiley Series in Discrete Mathematics and Optimization) - Hardcover

Alon, Noga; Spencer, Joel H.

Hardcover

ISBN 10: 0470170204 ISBN 13: 9780470170205

Publisher: Wiley–Blackwell, 2008

Synopsis

Praise for the Second Edition:

"Serious researchers in combinatorics or algorithm design willwish to read the book in its entirety...the book may also beenjoyed on a lighter level since the different chapters are largelyindependent and so it is possible to pick out gems in one′s ownarea..."
Formal Aspects of Computing

This Third Edition of The Probabilistic Method reflectsthe most recent developments in the field while maintaining thestandard of excellence that established this book as the leadingreference on probabilistic methods in combinatorics. Maintainingits clear writing style, illustrative examples, and practicalexercises, this new edition emphasizes methodology, enablingreaders to use probabilistic techniques for solving problems insuch fields as theoretical computer science, mathematics, andstatistical physics.

The book begins with a description of tools applied inprobabilistic arguments, including basic techniques that useexpectation and variance as well as the more recent applications ofmartingales and correlation inequalities. Next, the authors examinewhere probabilistic techniques have been applied successfully,exploring such topics as discrepancy and random graphs, circuitcomplexity, computational geometry, and derandomization ofrandomized algorithms. Sections labeled "The Probabilistic Lens"offer additional insights into the application of the probabilisticapproach, and the appendix has been updated to includemethodologies for finding lower bounds for Large Deviations.

The Third Edition also features:

• A new chapter on graph property testing, which is a currenttopic that incorporates combinatorial, probabilistic, andalgorithmic techniques

• An elementary approach using probabilistic techniques to thepowerful Szemerédi Regularity Lemma and its applications

• New sections devoted to percolation and liar games

• A new chapter that provides a modern treatment of theErdös–Rényi phase transition in the Random GraphProcess

Written by two leading authorities in the field, TheProbabilistic Method, Third Edition is an ideal reference forresearchers in combinatorics and algorithm design who would like tobetter understand the use of probabilistic methods. The book′snumerous exercises and examples also make it an excellent textbookfor graduate–level courses in mathematics and computer science.

About this title

About the Author

NOGA ALON, PhD, is Baumritter Professor of Mathematics andComputer Science at Tel Aviv University, Israel. A member of theIsrael National Academy of Sciences, Dr. Alon has written over 400published papers, mostly in the areas of combinatorics andtheoretical computer science. He is the recipient of numeroushonors in the field, including the Erdös Prize (1989), thePólya Prize (2000), the Landau Prize (2005), and theGödel Prize (2005).

JOEL H. SPENCER, PhD, is Professor of Mathematics andComputer Science at the Courant Institute of Mathematical Sciencesat New York University and is the cofounder and coeditor of thejournal Random Structures and Algorithms. Dr. Spencer has writtenover 150 published articles and is the coauthor of RamseyTheory, Second Edition, also published by Wiley.

"Serious researchers in combinatorics or algorithm design willwish to read the book in its entirety...the book may also beenjoyed on a lighter level since the different chapters are largelyindependent and so it is possible to pick out gems in one′s ownarea..."
Formal Aspects of Computing

This Third Edition of The Probabilistic Method reflectsthe most recent developments in the field while maintaining thestandard of excellence that established this book as the leadingreference on probabilistic methods in combinatorics. Maintainingits clear writing style, illustrative examples, and practicalexercises, this new edition emphasizes methodology, enablingreaders to use probabilistic techniques for solving problems insuch fields as theoretical computer science, mathematics, andstatistical physics.

The book begins with a description of tools applied inprobabilistic arguments, including basic techniques that useexpectation and variance as well as the more recent applications ofmartingales and correlation inequalities. Next, the authors examinewhere probabilistic techniques have been applied successfully,exploring such topics as discrepancy and random graphs, circuitcomplexity, computational geometry, and derandomization ofrandomized algorithms. Sections labeled "The Probabilistic Lens"offer additional insights into the application of the probabilisticapproach, and the appendix has been updated to includemethodologies for finding lower bounds for Large Deviations.

The Third Edition also features:

• A new chapter on graph property testing, which is a currenttopic that incorporates combinatorial, probabilistic, andalgorithmic techniques

• An elementary approach using probabilistic techniques to thepowerful Szemerédi Regularity Lemma and its applications

• New sections devoted to percolation and liar games

• A new chapter that provides a modern treatment of theErdös–Rényi phase transition in the Random GraphProcess

Written by two leading authorities in the field, TheProbabilistic Method, Third Edition is an ideal reference forresearchers in combinatorics and algorithm design who would like tobetter understand the use of probabilistic methods. The book′snumerous exercises and examples also make it an excellent textbookfor graduate–level courses in mathematics and computer science.

Edition details

• Publisher: Wiley–Blackwell
• Publication date: 2008
• Language: English
• ISBN 10: 0470170204
• ISBN 13: 9780470170205
• Binding: Hardcover
• Edition number: 3
• Number of pages: 376