- Gebundene Ausgabe: 376 Seiten
- Verlag: John Wiley & Sons; Auflage: 3 (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: 1 Kundenrezension
- Amazon Bestseller-Rang: Nr. 162.940 in Fremdsprachige Bücher (Siehe Top 100 in Fremdsprachige Bücher)
- Komplettes Inhaltsverzeichnis ansehen
The Probabilistic Method (Wiley-Interscience Series in Discrete Mathematics and Optimization) (Englisch) Gebundene Ausgabe – 22. August 2008
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"...an 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. Alle Produktbeschreibungen
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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.
The content is well written and organized.
The proof detail of theorem is very reasonable. May omit something, but for the reader have some math background, it is quite easy to complete the proofs.
5 star without thinking.
The mathematical prerequisites are not very high, but some knowledge of probability theory ( not the measure - theoretic stuff, however, as virtually everything is countable.) and of graph theory (as many examples and trheorems refer to graphs and their properties), maybe at the level of Bolodas' Modern Graph Theory is definitely helpful.
The proofs are generally not too difficult ( I am only a "hobby mathematician", this may help to evaluate the statement), and very often they are truly "surprising"!
The book contains very few typos ( I counted around 20 only ), and most of them are harmless.
I recommend this book to anybody interested in discrete mathematics, or interested in beautiful proofs.
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