Book Description
The leading reference on probabilistic methods in combinatorics-now expanded and updated

When it was first published in 1991, The Probabilistic Method became instantly the standard reference on one of the most powerful and widely used tools in combinatorics. Still without competition nearly a decade later, this new edition brings you up to speed on recent developments, while adding useful exercises and over 30ew material. It continues to emphasize the basic elements of the methodology, discussing in a remarkably clear and informal style both algorithmic and classical methods as well as modern applications.

The Probabilistic Method, Second Edition begins with basic techniques that use expectation and variance, as well as the more recent martingales and correlation inequalities, then explores areas where probabilistic techniques proved successful, including discrepancy and random graphs as well as cutting-edge topics in theoretical computer science. A series of proofs, or "probabilistic lenses," are interspersed throughout the book, offering added insight into the application of the probabilistic approach. New and revised coverage includes:
* Several improved as well as new results
* A continuous approach to discrete probabilistic problems
* Talagrand's Inequality and other novel concentration results
* A discussion of the connection between discrepancy and VC-dimension
* Several combinatorial applications of the entropy function and its properties
* A new section on the life and work of Paul Erdös-the developer of the probabilistic methodDownload Description
The leading reference on probabilistic methods in combinatorics-now expanded and updated

When it was first published in 1991, The Probabilistic Method became instantly the standard reference on one of the most powerful and widely used tools in combinatorics. Still without competition nearly a decade later, this new edition brings you up to speed on recent developments, while adding useful exercises and over 30% new material. It continues to emphasize the basic elements of the methodology, discussing in a remarkably clear and informal style both algorithmic and classical methods as well as modern applications.

The Probabilistic Method, Second Edition begins with basic techniques that use expectation and variance, as well as the more recent martingales and correlation inequalities, then explores areas where probabilistic techniques proved successful, including discrepancy and random graphs as well as cutting-edge topics in theoretical computer science. A series of proofs, or "probabilistic lenses," are interspersed throughout the book, offering added insight into the application of the probabilistic approach. New and revised coverage includes:

• Several improved as well as new results
• A continuous approach to discrete probabilistic problems
• Talagrand's Inequality and other novel concentration results
• A discussion of the connection between discrepancy and VC-dimension
• Several combinatorial applications of the entropy function and its properties
• A new section on the life and work of Paul Erd��he developer of the probabilistic method

Customer Reviews (3)

Love, love, love this book...
I happen to love studying probability theory and the probabilistic method and this is the book I come to time and time again. It is well organized and provides great, straightforward, insightful explanations. However, its main strength is its wealth of beautiful (fairly recently) results (in varied fields) which show the method coming to life. Can't recommend this enough...

Learn from the masters
This book shows you how to approach problems in discrete mathematics that don't seem to be probabilistic at all, and nonetheless to apply probabilistic methods to find extremely sharp results. The book is full of beautifully chosen examples worked out by the authors, who are world class researchers in this subject area. Should be on the bookshelf of everyone who uses discrete mathematics.

A very interesting book
I found this book very enjoyable to read. Although theunderlying themeof the book is to demonstrate examples of proofs of existence of a propertyof a finite structure by showing the structure must have the property withpositive probabiltiy, the book goes beyond this to cover areas such ascircuit complexity and discrepancy theory that rely heavily onprobabilistic arguments. A must read for anyone who wants to addprobablistic tools to their toolbox for proving things about discretestructures. ... Read more