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Concrete Mathematics: A Foundation for Computer Science, 2nd edition

Published by Pearson (February 28, 1994) © 1994

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

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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

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  • 1. Recurrent Problems.
  • 2. Sums.
  • 3. Integer Functions.
  • 4. Number Theory.
  • 5. Binomial Coefficients.
  • 6. Special Numbers.
  • 7. Generating Functions.
  • 8. Discrete Probability.
  • 9. Asymptotics.
  • A. Answers to Exercises.
  • B. Bibliography.
  • C. Credits for Exercises.
  • Index.
Ronald L. Graham (1935–2020) was for many years the Chief Scientist at AT&T Labs Research. He was also a Professor of Computer and Information Science at the University of California, San Diego, and a former President of the American Mathematical Society and the Mathematical Association of America. He was the coauthor of seven other mathematics books.
Donald E. Knuth is Professor Emeritus of The Art of Computer Programming at Stanford University. His prolific writings include four volumes on The Art of Computer Programming, and five books related to his TEX and METAFONT typesetting systems.
Oren Patashnik is a member of the research staff at the Center for Communications Research, La Jolla, California. He is also the author of BibTEX, a widely used bibliography processor.

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