The Nature of Computation: Hardback: Cristopher Moore
- Oxford University Press

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Covers deep and recent results in theoretical computer science

Authors are leaders in interdisciplinary work at the boundary between computer science and physics.

Many non-standard examples given

Several structured problems (with solutions manual for teachers)

Includes interdisciplinary topics like quantum computing, Monte Carlo algorithms and phase transitions

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.

Readership: First-year graduate students in computer science; instructors in theoretical computer science; graduate students in mathematics, physics, engineering, and theoretical biology.
Statistical and quantum physicists interested in the interdisciplinary boundary between physics and computer science; scientists from mathematics, physics, engineering, and theoretical biology who are interested in computational complexity; motivated undergraduates in computer science and the above fields.

Cristopher Moore, Santa Fe Institute, and Stephan Mertens, Institute of Theoretical Physics, Otto-von-Guericke University, Magdeburg, and External Professor, Santa Fe Institute

Cristopher Moore graduated from Northwestern University with honors in 1986, at the age of 18, with a B.A. in Mathematics, Physics, and Integrated Science. He received his Ph.D. in Physics from Cornell University at the age of 23. After a postdoc at the Santa Fe Institute, he joined the faculty of the University of New Mexico, where he holds joint appointments in Computer Science and Physics and Astronomy. He
has written over 90 papers, on topics ranging from undecidability in dynamical systems, to quantum computing, to phase transitions in NP-complete problems, to the analysis of social and biological networks.

Stephan Mertens got his Diploma in Physics in 1989, and his Ph.D. in Physics in 1991, both from Georg-August University Göttingen. He holds scholarships from the "Studienstiftung des Deutschen Volkes", Germany's most prestigious organisation sponsoring the academically gifted. After his Ph.D. he worked for three years in the software industry before he joined the faculty of Otto-von-Guericke University Magdeburg as a theoretical physicist. His research focuses on disordered systems in statistical mechanics, average case complexity of algorithms, and parallel computing.

"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

1: Prologue
2: The Basics
3: Insights and Algorithms
4: Needles in a Haystack: The class NP
5: Who is the Hardest One of All: NP-Completeness
6: The Deep Question: P vs. NP
7: Memory, Paths and games
8: Grand Unified Theory of Computation
9: Simply the Best: Optimization
10: The Power of Randomness
11: Random Walks and Rapid Mixing
12: Counting, Sampling, and Statistical Physics
13: When Formulas Freeze: Phase Transitions in Computation
14: Quantum Computing
15: Epilogue
16: Appendix: Mathematical Tools

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