Concrete mathematics : a foundation for computer science

Ronald L. Graham, Donald E. Knuth, Oren Patashnik

This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories.Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: *Sums *Recurrences *Integer functions *Elementary number theory *Binomial coefficients *Generating functions *Discrete probability *Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them. 0201558025B04062001

「Nielsen BookData」より

[目次]

  • (Most chapters contain Exercises.) 1. Recurrent Problems. The Tower of Hanoi. Lines in the Plane. The Josephus Problem. Exercises. 2. Sums. Notation. Sums and Recurrences. Manipulation of Sums. Multiple Sums. General Methods. Finite and Infinite Calculus. Infinite Sums. Exercises. 3. Integer Functions. Floors and Ceilings. Floor/Ceiling Applications. Floor/Ceiling Recurrences. 'mod': The Binary Operation. Floor/Ceiling Sums. Exercises. 4. Number Theory. Divisibility. Factorial Factors. Relative Primality. 'mod': The Congruence Relation. Independent Residues. Additional Applications. Phi and Mu. Exercises. 5. Binomial Coefficients. Basic Identities. Basic Practice. Tricks of the Trade. Generating Functions. Hypergeometric Functions. Hypergeometric Transformations. Partial Hypergeometric Sums. Mechanical Summation. Exercises. 6. Special Numbers. Stirling Numbers. Eulerian Numbers. Harmonic Numbers. Harmonic Summation. Bernoulli Numbers. Fibonacci Numbers. Continuants. Exercises. 7. Generating Functions. Domino Theory and Change. Basic Maneuvers. Solving Recurrences. Special Generating Functions. Convolutions. Exponential Generating Functions. Dirichlet Generating Functions. Exercises. 8. Discrete Probability. Definitions. Mean and Variance. Probability Generating Functions. Flipping Coins. Hashing. Exercises. 9. Asymptotics. A Hierarchy. O Notation. O Manipulation. Two Asymptotic Tricks. Euler's Summation Formula. Final Summations. Exercises. A. Answers to Exercises. B. Bibliography. C. Credits for Exercises. Index. List of Tables. 0201558025T04062001

「Nielsen BookData」より

この本の情報

書名 Concrete mathematics : a foundation for computer science
著作者等 Knuth, Donald Ervin
Graham, Ronald L
Patashnik, Oren
Knuth Donald E.
出版元 Addison-Wesley
刊行年月 c1994
版表示 2nd ed
ページ数 xiii, 657 p.
大きさ 24 cm
ISBN 9780201558029
NCID BA22647938
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国
この本を: 
このエントリーをはてなブックマークに追加

このページを印刷

外部サイトで検索

この本と繋がる本を検索

ウィキペディアから連想