Written by: Herbert S. Wilf (University of Pennsylvania)

The name of this free online discrete mathematics textbook is generatingfunctionology. The topic is generating functions, a “bridge between discrete mathematics and continuous analysis.” There are three editions of this text – the second edition from 1994 is the one which the publishers and the author have made available on the University of Pennsylvania website.

The author, Herbert S. Wilf, is most remembered for his work in combinatorics and graph theory. He was a pioneer in the mathematical programming of early computers. He taught from 1962 until he retired in 2008.

His textbook is about generating functions and some of their uses in discrete mathematics. This textbook was designed to convey some of the main ideas rather than be a comprehensive discussion of the topic. It has been used for a senior course in discrete mathematics at Penn. According to their course catalog, students should have two semesters of calculus prior to taking that course.

Chapter Titles for generatingfunctionology

  1. Introductory Ideas and Examples
  2. Series
  3. Cards, Decks, and Hands: The Exponential Formula
  4. Applications of generating functions
  5. Analytic and asymptotic methods

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