- Hardcover: 328 pages
- Publisher: Wiley-Interscience; 2 edition (Aug 10 2000)
- Language: English
- ISBN-10: 0471370460
- ISBN-13: 978-0471370468
- Product Dimensions: 23.6 x 16.3 x 2 cm
- Shipping Weight: 590 g
- Average Customer Review: 4.7 out of 5 stars See all reviews (3 customer reviews)
- Amazon Bestsellers Rank: #1,293,785 in Books (See Top 100 in Books)
- See Complete Table of Contents
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There is a newer edition of this item:
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Product Details |
Product Description
Review
"...an exciting well-written book which will give much enjoyment to a reader..." (Mathematical Reviews, 2003f)
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 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 Erdös-the developer of the probabilistic method
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 Erdös-the developer of the probabilistic method
Inside This Book
(Learn More)
First Sentence
The probabilistic method is a powerful tool for tackling many problems in discrete mathematics. Read the first page Browse Sample Pages
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
The probabilistic method is a powerful tool for tackling many problems in discrete mathematics. Read the first page Browse Sample Pages
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews
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Most helpful customer reviews
4.0 out of 5 stars
Almost very good.,
By
This review is from: The Probabilistic Method (Hardcover)
This has become the bible of the subject, the authors are great mathematicians, etc, you can read that in the official recommendations, and I agree with them. Also, the new chapters, on the Erdős-Rényi phase transition and on Szemerédi's Regularity Lemma and graph property testing, cover important hot topics. But I have some complaints:The book focuses on techniques, which is great, but the examples that illustrate the techniques are less so. If you are a hard-core combinatorialist, you will find these examples natural, but if you don't have a few years of training and some research experience in combinatorics, you might get quickly lost. For self-study, there are too many technical calculus details that are left out. The number of mistakes is surprisingly large for a 3rd edition. Two examples from Chapter 4. On page 45, when deducing \sum_{p primes < n} 1/p = \ln\ln n +O(1), there is a reference to Stirling's formula which looks completely off to me. It probably wanted to be the Prime Number Theorem. On page 48, the definition of a "symmetric" set of random variables is much weaker than what is actually needed. The typographical look is a bit too dense for me. I preferred the 1st edition in this respect.
5.0 out of 5 stars
Learn from the masters,
By Wonk "yeager" (Philadelphia, PA USA) - See all my reviews
This review is from: The Probabilistic Method (Hardcover)
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.
5.0 out of 5 stars
A very interesting book,
By Todd Ebert (Long Beach California) - See all my reviews
This review is from: The Probabilistic Method (Hardcover)
I found this book very enjoyable to read. Although the underlying theme of the book is to demonstrate examples of proofs of existence of a property of a finite structure by showing the structure must have the property with positive probabiltiy, the book goes beyond this to cover areas such as circuit complexity and discrepancy theory that rely heavily on probabilistic arguments. A must read for anyone who wants to add probablistic tools to their toolbox for proving things about discrete structures.
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