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Algorithms, Theory, and Discrete Mathematics
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- Michael Mitzenmacher, Eli Upfal
"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, UC Berkley
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- Sriram Pemmaraju, Steven Skiena
With examples of all 450 functions in action plus tutorial text on the mathematics, this book is the definitive guide to Experimenting with Combinatorica, a widely used software package for teaching and research in discrete mathematics. Three interesting classes of exercises are provided--theorem/proof, programming exercises, and experimental explorations--ensuring great flexibility in teaching and learning the material. The Combinatorica user community ranges from students to engineers, researchers in mathematics, computer science, physics, economics, and the humanities. Recipient of the EDUCOM Higher Education Software Award, Combinatorica is included with every copy of the popular computer algebra system Mathematica.
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- Joachim von zur Gathen, Jürgen Gerhard
Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students, this text's comprehensiveness and reliability also make it an essential reference for professionals. Errors have been corrected and new sections on greatest common divisors and symbolic integration have been added to this updated edition.
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- Rajeev Motwani, Prabhakar Raghavan
"The techniques described by Rajeev Motwani and Prabhaker Raghavan are wide-ranging and powerful, so this book is an important one...We are particularly lucky, therefore, that this excellent volume does us so proud!...clearly written and well thought out, with an interesting collection of exercises and applications, and shows the comprehensive breadth and valuable insights of a mature text...I would recommend the book both to newcomers to the field and to more seasoned practitioners...It is a pleasure to read."
John H. Halton, American Scientist
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"...an important summary of the state of the art in pattern matching and an indicator of the importance biological problems have assumed among many researchers. It will hopefully encourage them to question the importance of the problems they endeavor to solve."
SIGACT News
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"This is an applied approach to fundamental concepts in computational geometry and should be read by every serious practitioner....From a pedagogical point of view, this book is an excellent choice for both undergraduate classes (perhaps with more emphasis on the implementations) and graduate classes (considering a number of the exercises) because of the extensive exercises that review, explore details, and encourage further reading."
Computing Reviews
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"This book presents most of the topics usually found in a full-year sequence on probability and mathematical statistics."
The American Statistician
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- J. H. van Lint, R. M. Wilson
"...their choice of subject matter is superb...would indeed make an excellent text for a full-year introduction to combinatorics."
Mathematical Reviews
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Concerned with successfully transmitting data through a noisy channel, coding theory can be applied to electronic engineering and communications. Based on the authors' extensive teaching experience, this text provides a completely modern and accessible course on the subject. It includes sections on linear programming and decoding methods essential for contemporary mathematics. Numerous examples and exercises make the volume ideal for students and instructors.
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- Michael A. Nielsen, Isaac L. Chuang
"Quantum Computation and Quantum Information is a challenging text that offers a thorough discussion of the relevant physics and a reference book that guides readers to the original literature...Perhaps the best way to use the book, though, is to ask questions and then search within it for answers. Such a self-guided tour can keep one from getting lost in details and can provide a rewarding journey...Nielsen and Chuang have set a high standard."
Science
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Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The mathematical prerequisites are minimal: nothing beyond material in a typical undergraduate course in calculus is presumed, other than some experience in doing proofs - everything else is developed from scratch. Thus the book can serve several purposes. It can be used as a reference and for self-study by readers who want to learn the mathematical foundations of modern cryptography. It is also ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students.
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"[Foundations of Cryptography: Basic Tools] presents complexity research which gives the mathematical underpinnings for cryptography; this includes one-way functions, pseudorandom generators, and zero-knowledge proofs...if a reader wants to learn about foundational work, Goldreich's books are the place to go."
Bulletin of the American Mathematical Society
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Cryptography is concerned with the conceptualization, definition and construction of computing systems that address security concerns. The design of cryptographic systems must be based on firm foundations. Building on the basic tools presented in the first volume, this second volume of Foundations of Cryptography contains a rigorous and systematic treatment of three basic applications: Encryption, Signatures, and General Cryptographic Protocols. It is suitable for use in a graduate course on cryptography and as a reference book for experts. The author assumes basic familiarity with the design and analysis of algorithms; some knowledge of complexity theory and probability is also useful.
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