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The Probabilistic Method (Wiley-Interscience Series in Discrete Mathematics and Optimization) (Englisch) Gebundene Ausgabe – 22. August 2008

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  • Gebundene Ausgabe: 376 Seiten
  • Verlag: John Wiley & Sons; Auflage: 3. Auflage (22. August 2008)
  • Sprache: Englisch
  • ISBN-10: 0470170204
  • ISBN-13: 978-0470170205
  • Größe und/oder Gewicht: 16,3 x 2,7 x 24,4 cm
  • Durchschnittliche Kundenbewertung: 5.0 von 5 Sternen  Alle Rezensionen anzeigen (1 Kundenrezension)
  • Amazon Bestseller-Rang: Nr. 183.905 in Fremdsprachige Bücher (Siehe Top 100 in Fremdsprachige Bücher)
  • Komplettes Inhaltsverzeichnis ansehen

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" exciting well--written book which will give much enjoyment to a reader..." (Mathematical Reviews, 2003f) -- Dieser Text bezieht sich auf eine vergriffene oder nicht verfügbare Ausgabe dieses Titels.


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. This 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 Szemeredi Regularity Lemma and its applications; new sections devoted to percolation and liar games; and, a new chapter that provides a modern treatment of the Erdos-Renyi 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.

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1 von 1 Kunden fanden die folgende Rezension hilfreich Von Hans Simon am 17. Januar 2011
Format: Gebundene Ausgabe
The book offers very powerful tools for proving the existence of combinatorial objects
that are hard to find constructively. Great book !
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Die hilfreichsten Kundenrezensionen auf (beta) 6 Rezensionen
33 von 37 Kunden fanden die folgende Rezension hilfreich
Learn from the masters 3. Juli 2001
Von Wonk - Veröffentlicht auf
Format: Gebundene Ausgabe
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.
19 von 22 Kunden fanden die folgende Rezension hilfreich
A very interesting book 14. September 2000
Von Todd Ebert - Veröffentlicht auf
Format: Gebundene Ausgabe
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.
14 von 17 Kunden fanden die folgende Rezension hilfreich
Love, love, love this book... 8. September 2005
Von anon - Veröffentlicht auf
Format: Gebundene Ausgabe
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...
8 von 12 Kunden fanden die folgende Rezension hilfreich
DO NOT buy Kindle version 8. November 2013
Von jkl - Veröffentlicht auf
Format: Kindle Edition
This is a great book, indeed, but DO NOT buy a kindle version.

The Kindle version is a trash. Since Amazon transfered many formulas by plane alphabets in a hapharzard manner , I can find at least one typo in each page. The authors could feel insulted by this.
5 von 8 Kunden fanden die folgende Rezension hilfreich
Great Text by Authoritative Experts 31. März 2013
Von Jeremy Kun - Veröffentlicht auf
Format: Gebundene Ausgabe Verifizierter Kauf
Alon & Spencer are some of the leading researchers in their field, and you'll find yourself jumping right into their research papers after having covered the broad overview in this volume. They write concisely and appropriately to the intended audience (graduate students in mathematics, and researchers in other fields of mathematics looking to apply the probabilistic method to their work). This text is the gold standard in the field; one of those texts that every practitioner reads.

The introduction and breadth of examples and applied topics are wonderful. I particularly enjoyed their treatments of the local lemma, circuit complexity, and graph property testing. In addition, between each chapter there is an example of an elegant use of the probabilistic method (usually the techniques displayed from the previous chapter) which they collectively call "The probabilistic Lens." These proofs are definitely worth reading, but not necessary to understand the rest of the text.

That being said, there were some parts of this book that I thought fell short. In particular, many of the applications in the topics chapters begin with the most complicated examples, and either omit or downplay the historically first and technically simpler results. For instance, in the chapter on graph property testing they discuss colorability and not connectivity. In their treatment on the ER-phase transition for random graphs, they jump immediately into "fine parameterizations" of the model, and it comes together in a kludgy way, making the analysis much more detailed and complicated than it needs to be. The connection between the big picture and these details was too tenuous for comfort. Instead of this book, I would recommend referring to Bela Bollobas's Random Graphs (Cambridge Studies in Advanced Mathematics), which gives a much more fluid treatment of these topics.

My last objection is the authors' dismissive use of the Chernoff bounds. I understand that a serious reader of this text should be well versed in Chernoff bounds, but their treatment (and somewhat messy appendix covering the basics) does not explain clearly enough how to apply these crucial bounds to problems when it's not obvious they apply. Considering how frequently the Chernoff bounds are used in practice, considering how they introduce other elementary topics like the second moment, and considering that this book is about applications (and uses Chernoff heavily), I would have liked to see an entire chapter dedicated to its use, perhaps between the second moment and the Local Lemma chapters.
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