The Probabilistic Method 3rd Edition by Noga Alon, Joel H Spencer ISBN 1118210441 9781118210444

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Product details:

ISBN 10: 1118210441 
ISBN 13: 9781118210444
Author: Noga Alon, Joel H Spencer

Praise for the Second Edition:

“Serious researchers in combinatorics or algorithm design will wish to read the book in its entirety…the book may also be enjoyed on a lighter level since the different chapters are largely independent and so it is possible to pick out gems in one’s own area…”
—Formal Aspects of Computing

This Third Edition of The Probabilistic Method reflects the most recent developments in the field while maintaining the standard of excellence that established this book as the leading reference on probabilistic methods in combinatorics. Maintaining its clear writing style, illustrative examples, and practical exercises, this new edition emphasizes methodology, enabling readers to use probabilistic techniques for solving problems in such fields as theoretical computer science, mathematics, and statistical physics.

The book begins with a description of tools applied in probabilistic arguments, including basic techniques that use expectation and variance as well as the more recent applications of martingales and correlation inequalities. Next, the authors examine where probabilistic techniques have been applied successfully, exploring such topics as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Sections labeled “The Probabilistic Lens” offer additional insights into the application of the probabilistic approach, and the appendix has been updated to include methodologies for finding lower bounds for Large Deviations.

The Third Edition also features:

• A new chapter on graph property testing, which is a current topic that incorporates combinatorial, probabilistic, and algorithmic techniques

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

• New sections devoted to percolation and liar games

• A new chapter that provides a modern treatment of the Erdös-Rényi phase transition in the Random Graph Process

Written by two leading authorities in the field, The Probabilistic Method, Third Edition is an ideal reference for researchers in combinatorics and algorithm design who would like to better understand the use of probabilistic methods. The book’s numerous exercises and examples also make it an excellent textbook for graduate-level courses in mathematics and computer science.

The Probabilistic Method 3rd Table of contents:

Part I: Methods

1. The Basic Method

   • The Probabilistic Method
   • Graph Theory
   • Combinatorics
   • Combinatorial Number Theory
   • Disjoint Pairs
   • Exercises
   • The Probabilistic Lens: The Erdős–Ko–Rado Theorem

2. Linearity of Expectation

   • Basics
   • Splitting Graphs
   • Two Quickies
   • Balancing Vectors
   • Unbalancing Lights
   • Without Coin Flips
   • Exercises
   • The Probabilistic Lens: High Girth and High Chromatic Number

3. Alterations

   • Ramsey Numbers
   • Independent Sets
   • Combinatorial Geometry
   • Packing
   • Recoloring
   • Continuous Time
   • Exercises
   • The Probabilistic Lens: Hamiltonian Paths

4. The Second Moment

   • Basics
   • Number Theory
   • More Basics
   • Random Graphs
   • Clique Number
   • Distinct Sums
   • The Rödl–Niblack Theorem
   • Exercises
   • The Probabilistic Lens: Directed Cycles

5. The Local Lemma

   • The Lemma
   • Property B and Multicolored Sets of Real Numbers
   • Lower Bounds for Ramsey Numbers
   • A Geometric Result
   • Exercises
   • The Probabilistic Lens: The Erdős–Ko–Rado Theorem

6. Correlation Inequalities

   • The Four Functions Theorem of Ahlswede and Daykin
   • The FKG Inequality
   • Monotone Properties
   • Linear Extensions of Partially Ordered Sets
   • Exercises

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Noga Alon,Joel H Spencer,Probabilistic Method