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Concrete Mathematics: A Foundation for Computer Science

by Ronald Graham

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A problem-solving bridge between discrete and continuous mathematics

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Hardcover New English

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AlbakiReads Editorial

A problem-solving bridge between discrete and continuous mathematics

Designed around the mathematics used in advanced programming and algorithm analysis, this substantial reference develops techniques for manipulating formulas and extracting patterns from complex calculations. Its coverage moves through sums, recurrences, integer functions, elementary number theory, binomial coefficients, generating functions, discrete probability, and asymptotic methods, with added material on mechanical summation in this second edition. The book expands on the mathematical preliminaries associated with *The Art of Computer Programming*, treating individual subjects in greater depth and tracing major ideas to historical sources. More than 500 exercises, organized into six categories, make practice central; answers are supplied for every exercise except the research problems. An expanded bibliography and index also support its use as a long-term desk reference.

Good fit for readers who enjoy

  • Computer science students studying algorithms and their mathematical foundations
  • Independent learners who want worked practice in discrete and continuous methods
  • Mathematics users needing reference coverage of sums, recurrences, and generating functions

Themes

Discrete mathematicsAlgorithm analysisMathematical problem-solvingCombinatorics and number theoryAsymptotic methods

Based on publisher information and book metadata.

Book overview

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.
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