Mathematics for the Analysis of Algorithms

  • Daniel H. Greene
  • Donald E. Knuth

Part of the Progress in Computer Science and Applied Logic (PCS) book series (volume 1)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Pages 1-10
  3. Pages 11-30
  4. Pages 31-41
  5. Pages 42-76
  6. Back Matter
    Pages 77-132

About this book


A quantitative study of the efficiency of computer methods requires an in-depth understanding of both mathematics and computer science. This monograph, derived from an advanced computer science course at Stanford University, builds on the fundamentals of combinatorial analysis and complex variable theory to present many of the major paradigms used in the precise analysis of algorithms, emphasizing the more difficult notions. The authors cover recurrence relations, operator methods, and asymptotic analysis in a format that is terse enough for easy reference yet detailed enough for those with little background. Approximately half the book is devoted to original problems and solutions from examinations given at Stanford.


"...a very valuable collection of mathematical techniques for the analysis of algorithms..."   — Mathematical Reviews

"The book covers the important mathematical tools used in computer science, especially in the exact analysis of algorithms. A wide range of topics are covered, from the binomial theorem to the saddle point method and Laplace’s techniques for asymptotic analysis...The book is very well written. The style and the mathematical exposition make the book pleasant to read...It covers many of the major paradigms used in the analysis of algorithms in its one hundred plus pages."   SIAM Review

"The book presents a welcome selection a

nd careful exposition of material that can be (and is) covered in a single course...In this reviewer’s opinion, this would be an interesting text to use with a group of advanced students well-grounded in undergraduate mathematics and computer science, and would produce a valuable course for the participating students."   Computing Reviews


algorithmic analysis algorithms asymptotic analysis binomial identities combinatorial analysis complex variable theory operator methods recurrence relations saddle point method calculus computer science Hashing Mathematica mathematics Variable

Authors and affiliations

  • Daniel H. Greene
    • 1
  • Donald E. Knuth
    • 2
  1. 1.Computer Science LaboratoryXerox Palo Alto Research CenterStanfordUSA
  2. 2.Department of Computer ScienceStanford UniversityStanfordUSA

Bibliographic information