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Probability and Computing: Randomized Algorithms and Probabilistic Analysis [Englisch] [Gebundene Ausgabe]

Michael Mitzenmacher , Eli Upfal

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31. Januar 2005
Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This 2005 textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, the probabilistic method and Markov chains. The second half covers more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool.

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Probability and Computing: Randomized Algorithms and Probabilistic Analysis + Randomized Algorithms (Cambridge International Series on Parallel Computation)
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'This text provides a solid background in probabilistic techniques, illustrating each with well-chosen examples. The explanations are clear, and convey the intuition behind the results and techniques, yet the coverage is rigorous. An excellent advanced undergraduate text.' Peter Bartlett, Professor of Computer Science, University of California, Berkeley

'This book is suitable as a text for upper division undergraduates and first year graduate students in computer science and related disciplines. It will also be useful as a reference for researchers who would like to incorporate these tools into their work. I enjoyed teaching from the book and highly recommend it.' Valerie King, Professor of Computer Science, University of Victoria, British Columbia

'Buy it, read it, enjoy it; profit from it. it feels as if it has been well tested out of students and will work straight away.' Colin Cooper, Department of computer Science, King's College, University of London

'An exciting new book on randomized algorithms. It nicely covers all the basics, and also has some interesting modern applications for the more advanced student.' Alan Frieze, professor of Mathematics, Carnegie-Mellon University

' … very well written and contains useful material on probability theory and its application in computer science.' Zentralblatt MATH

' … this book offers a very good introduction to randomised algorithms and probabilistic analysis, both for the lecturer and independent reader alike. it is also a good book for those wanting practical examples that can be applied to real world problems.' Mathematics Today

Über das Produkt

Assuming only an elementary background in discrete mathematics, this 2005 textbook is designed to accompany an introductory course on the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses, including random sampling, expectations, Markov's and Chevyshev's inequalities, Chernoff bounds, balls and bins models, the probabilistic method, Markov chains, MCMC, martingales and entropy.

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Die hilfreichsten Kundenrezensionen auf (beta) 3.9 von 5 Sternen  10 Rezensionen
26 von 27 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Advanced probability topics without measure theory 18. August 2007
Von Jung Dalg - Veröffentlicht auf
Format:Gebundene Ausgabe
This book is underestimated by two reviewers below. I totally do not agree with them. This book covers a wide range of topics in a very readable style. The contents in this book is complementary to the book of Motwani and Raghavan (but this book is much easier to digest).

It, without requiring any knowledge on measure theory, contains excellent introductions to many difficult topics in probability including

- concentration bounds (Chernoff, Azuma-Hoeffding, etc.)
- applications of stochastic processes such as queuing theory
- martingale (Wald's equation)
- coupling of Markov chains and their mixing times
- Shannon's source coding and noisy channel theorems
- Erdos' probabilistic method
- etc.

All of these topics are provided with excellent applications in computing.
The authors illustrate many clever tricks for proving theorems, and these tricks give insights to the readers as well.
4 von 4 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen An excellent book for computing students and professionals 17. Dezember 2010
Von Todd Ebert - Veröffentlicht auf
Format:Gebundene Ausgabe
I found this book to be one of the better mathematics texts that I've ever read.
The authors do an excellent job in combining mathematical rigor with
good intuitive explanations of why a given theorem ought to be true.

I felt very impressed with how the authors have included just about every important
area of probability that has relevance to computing, and helped make them all accessible.

A good example of this is the chapter on Information Theory. Rather than prove the more difficult
and time consuming general cases of Shannon's Coding and Channel-Coding Theorems, the authors
presented special cases of these results, without losing much of the flavor of how the more general
proofs proceed. For example, in the case of the Channel-Coding Theorem, the authors assume that the
channel independently changes a single bit of the codeword with probability p.

Now despite all the stated positives, I would not recommend this book to anyone with no prior knowledge of probability.
For such a reader, a good prerequisite read is "Probability Models" by Sheldon Ross, which provides an excellent
introduction to applied probability.
3 von 3 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Accessible, thorough, and reader-friendly 10. April 2011
Von no name - Veröffentlicht auf
Format:Gebundene Ausgabe
Far from being "unnecessary", this book does a wonderful job at making randomized algorithms accessible and fun. It is great for self-learners because it first motivates a concept, then states relevant theorems, then provides full proofs of these theorems, and then provides an example where the theorem is used. Rather than leaving the proofs of theorems as an "exercise for the reader", it fully proves the theorems stated in the text. Each chapter also includes a section with an interesting application of how the material in the chapter can be utilized. Although not as advanced as the Motwani Randomized Algorithms book, it provides an excellent introduction and is much more accessible.
26 von 36 Kunden fanden die folgende Rezension hilfreich
2.0 von 5 Sternen Just unnecessary 17. Mai 2007
Von anon - Veröffentlicht auf
Format:Gebundene Ausgabe
This book, while written by two renowned computer scientists, is truly disappointing. In trying to discuss randomness and computation, this book just does a mediocre job on discussing randomized computation and also an equally poor job discussing relevant aspects of probability theory. Their approach is not novel and many of their examples can be found in other texts. If you really want to learn randomized computation, get Motwani et al's book on Randomized Algorithms. If you want to learn probability theory, get any advanced probability theory book like Spencer and Alon on the probabilistic method, one of Sheldon Ross's books, or even Grimmett and Stirzaker. Whatever you do don't get this weak hybrid of a book that will require you to get another book at some point to supplement your understanding.
2 von 2 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen Great book for a clean introduction to (advanced) discrete probability 16. April 2013
Von MA - Veröffentlicht auf
Format:Gebundene Ausgabe|Verifizierter Kauf
This book is a really nice introduction to probability (graduate level).
The material is presented in a way appealing to an engineer; the authors
- describe concepts (and provide intuition) that are motivated (derived) by applications in computer science and electrical engineering,
- restrict themselves to the presentation of discrete problems (e.g. settings where there are finite/countable number of variables, and finite/countable domains etc) whose presentation is cleaner and easily digested by the reader who need not have an advanced math background.
- omit details (e.g. in definitions) that would probably be required to make a statement formally correct, but are meaningless in the problems encountered in real applications.

I definitely suggest the book as a starting point to any young graduate student who wants to quickly familiarize with a wide range of important concepts in (discrete) probability without having to worry about frustrating details, extreme cases and notation.
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