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The Nature of Computation [Englisch] [Gebundene Ausgabe]

Cristopher Moore , Stephan Mertens

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Kurzbeschreibung

11. August 2011
Computational complexity is one of the most beautiful fields of modern mathematics, and it is increasingly relevant to other sciences ranging from physics to biology. But this beauty is often buried underneath layers of unnecessary formalism, and exciting recent results like interactive proofs, phase transitions, and quantum computing are usually considered too advanced for the typical student. This book bridges these gaps by explaining the deep ideas of theoretical computer science in a clear and enjoyable fashion, making them accessible to non-computer scientists and to computer scientists who finally want to appreciate their field from a new point of view. The authors start with a lucid and playful explanation of the P vs. NP problem, explaining why it is so fundamental, and so hard to resolve. They then lead the reader through the complexity of mazes and games; optimization in theory and practice; randomized algorithms, interactive proofs, and pseudorandomness; Markov chains and phase transitions; and the outer reaches of quantum computing. At every turn, they use a minimum of formalism, providing explanations that are both deep and accessible. The book is intended for graduate and undergraduate students, scientists from other areas who have long wanted to understand this subject, and experts who want to fall in love with this field all over again.

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A creative, insightful, and accessible introduction to the theory of computing, written with a keen eye toward the frontiers of the field and a vivid enthusiasm for the subject matter. Jon Kleinberg, Cornell University To put it bluntly: this book rocks! It's 900+ pages of awesome. It somehow manages to combine the fun of a popular book with the intellectual heft of a textbook, so much so that I don't know what to call it (but whatever the genre is, there needs to be more of it!). Scott Aaronson, Massachusetts Institute of Technology Moore and Mertens guide the reader through the interesting field of computational complexity in a clear, broadly accessible and informal manner, while systematically explaining the main concepts and approaches in this area and the existing links to other disciplines. The book is comprehensive and can be easily used as a textbook, at both advanced undergraduate and postgraduate levels, but is equally useful for researchers in neighbouring disciplines, such as statistical physics [...]. Some of the material covered, such as approximability issues and Probabilistically Checkable Proofs is typically not presented in books of this type, and the authors do an excellent job in presenting them very clearly and convincingly. David Saad, Aston University, Birmingham A treasure trove of ideas, concepts and information on algorithms and complexity theory. Serious material presented in the most delightful manner! Vijay Vazirani, Georgia Instituute of Technology In a class by itself - in The Nature of Computation, Cristopher Moore and Stephan Mertens have produced one of the most successful attempts to capture the broad scope and intellectual depth of theoretical computer science as it is practiced today. The Nature of Computation is one of those books you can open to a random page and find something amazing, surprising and, often, very funny. American Scientist

Synopsis

In the last decade, the boundary between physics and computer science has become a hotbed of interdisciplinary collaboration. Every passing year shows that physicists and computer scientists have a great deal to say to each other, sharing metaphors, intuitions, and mathematical techniques. In this book, two leading researchers in this area introduce the reader to the fundamental concepts of computational complexity. They go beyond the usual discussion of P, NP and NP-completeness to explain the deep meaning of the P vs. NP question, and explain many recent results which have not yet appeared in any textbook. They then give in-depth explorations of the major interfaces between computer science and physics: phase transitions in NP-complete problems, Monte Carlo algorithms, and quantum computing. The entire book is written in an informal style that gives depth with a minimum of mathematical formalism, exposing the heart of the matter without belabouring technical details. The only mathematical prerequisites are linear algebra, complex numbers, and Fourier analysis (and most chapters can be understood without even these).It can be used as a textbook for graduate students or advanced undergraduates, and will be enjoyed by anyone who is interested in understanding the rapidly changing field of theoretical computer science and its relationship with other sciences.

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Amazon.com: 5.0 von 5 Sternen  6 Rezensionen
11 von 13 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Beautiful encyclopedic book 22. Januar 2012
Von Josep Diaz - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe
This is a beautiful encyclopedic book, which covers a large range of topics from Theoretical Computer Science. The style favors intuition and clarity over technical details. Chapters 4 to 8 can be used as a textbook for an undergraduate complexity course. For computer science and mathematics students the book has the great advantage of examples from the physics world... the more advanced material can be easily used for graduate courses or seminars. For example, Chapters 12, 13 and 14 by themselves could be a perfect basic text for an advanced course in probabilistic methods in computer science and discrete mathematics. I hope future readers enjoy the book as much as I did.
(See longer review at Computer Science Reviews 5 (2011) 341.)
6 von 8 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Best theory of computation book ever! 23. März 2012
Von M. Villagra - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe
There are fantastic books all over theoretical computer science on the same subjects. But this one, I find it simply the best of all of them. Why? Because it explains what really computer science is about, which is computation as the object of study, and it does so in such a friendly manner and accessible to mathematicians, physicists and (of course) computer scientists of all levels. In the preface of the book explicitly says so, the objective of this book is to show why computational complexity is such a beautiful field with beautiful mathematics, without going too much deeper into the technicalities. Even though they omit the gruesome details, I felt that the understanding gained from reading the book was enough to look at the references and go directly to the papers. Thus, at the same time, this book presents a full review of all computational complexity theory. Also, the problems at the end of each chapter are very fun, and they make the reader gain a deeper understanding of the chapter and other subjects that were not covered. The notes section after each problem set are full of anecdotes and historical remarks that makes the reading experience even more wonderful.
6 von 9 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Fantastic introduction to computational complexity 20. Januar 2013
Von Brian Malley - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe|Von Amazon bestätigter Kauf
This book did not prove to be quite what I had expected when I purchased it, but I have greatly enjoyed it anyway. This book is not really about the *nature* of computation, or even about computation at all, but rather about the structure of the problem-space encountered by computational systems. It is about the different kinds of computational problems. I have found it very interesting, and this book is written in such a way that even a newbie with limited mathematics can understand the key ideas. I highly recommend this introduction to anyone interested in natural science or technology.
2 von 3 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen The best book on computational theory 10. Januar 2013
Von Parisa - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe|Von Amazon bestätigter Kauf
I have read several books on computational theory. The majority of these books make this amazing topic look agonizingly boring and difficult. This book on the other hand, makes you fall in love with the subject. If you want to have an intuitive while profound understanding of the field, this is the book, don't look any further.
3 von 5 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Headmelting 23. August 2012
Von Dan MacKinlay - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe|Von Amazon bestätigter Kauf
This book starts with high-school mathematics and takes you all the way through the amazing architecture of mathematical problems themselves. It's encyclopaedia-length, but light and readable in style all the way through, sprinkled with liberal references to Lewis Carroll, Douglas Hofstadter and various other cult favourites of the literate mathnerd. That is, this exemplifies everything good about mathematical texts. Amazing.

For background, I am a mathematics major, but I had almost no exposure to computational complexity theory before starting this book apart from, say, the awareness that matrix inversion is approximately O(n^3)
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