Concrete Mathematics: A Foundation for Computer Science eBook, 2nd Edition

Ronald L. Graham all

Concrete Mathematics: A Foundation for Computer Science eBook, 2nd Edition

By Ronald L. Graham, Donald E. Knuth, Oren Patashnik
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Ronald L. Graham all
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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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Table of contents
  • 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.