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.
"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.
