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Download The Probabilistic Method (Wiley Series in Discrete Mathematics and Optimization) fb2, epub

by Joel H. Spencer,Noga Alon

Download The Probabilistic Method (Wiley Series in Discrete Mathematics and Optimization) fb2, epub

ISBN: 0471370460
Author: Joel H. Spencer,Noga Alon
Language: English
Publisher: Wiley-Interscience; 2 edition (August 24, 2000)
Pages: 328
Category: Mathematics
Subcategory: Science
Rating: 4.1
Votes: 626
Size Fb2: 1780 kb
Size ePub: 1155 kb
Size Djvu: 1985 kb
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The Probabilistic Method (Wiley Series in Discrete Mathematics and Optimization)Hardcover.

The Probabilistic Method (Wiley Series in Discrete Mathematics and Optimization)Hardcover. This text is the gold standard in the field; one of those texts that every practitioner reads.

by Noga Alon (Author), Joel H. Spencer (Author).

Series: Wiley Series in Discrete Mathematics and Optimization.

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.

The Probabilistic Method (Wiley-Interscience Series in Discrete Mathematics and Optimization). To ask other readers questions about Probabilistic Method, The. Wiley-Interscience Series in Discrete Mathematics and Optimization

The Probabilistic Method (Wiley-Interscience Series in Discrete Mathematics and Optimization). 1281766615 (ISBN13: 9781281766618). Wiley-Interscience Series in Discrete Mathematics and Optimization. Lists with This Book. This book is not yet featured on Listopia.

In book: Cellular Automata: A Discrete View of the World, p. 53-254. Cite this publication. University of Auckland.

Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. The Probabilistic Method Wiley Series in Discrete Mathematics and Optimization. Noga Alon, Joel H. Spencer. Noga Alon and Joel H.

Noga Alon, Joel H. Spencer

Noga Alon, Joel H. John Wiley & Sons, 0. 4. The leading reference on probabilistic methods in combinatorics-now expanded and updated.

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

Comments:

Hallolan
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.
LadyShlak
This is a very nice book.

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.
Beardana
The book describes the application of probabilistic methods to deterministic 'countable' problems.
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.
Cesar
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.
DarK-LiGht
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...
Pumpit
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.
Dranar
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.

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