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Concrete mathematics. A foundation for computer science. (English) Zbl 0668.00003
Reading, MA: Addison-Wesley Publishing Company. xiii, 625 p. (1989).
In the continuing debate on what should constitute an undergraduate background in mathematics for the mathematician or the computer scientist, this book is destined for a major role. It is not a traditional course in discrete mathematics, though it does overlap some of the material taught there. Rather it is a compendium of some of the basic techniques for solving the very specific problems that arise in all branches of the mathematical sciences. The heart of the book presents elementary number theory, binomial coefficient identities, topics from combinatorics and probability, and a primer on how to use and find asymptotic arguments.
The style is extremely informal, often irreverent. But it also conveys the joy and exuberance of the craftsman who is only too pleased to share his lore by shaping a well-turned example before your eyes.
My only reservation concerns the chapter on binomial coefficient identities, by far the longest in the book. While the authors do introduce hypergeometric functions, a standardized notation for binomial coefficient identities that quickly enables you to identify when the summation you are pondering is equivalent to one that has been previously studied, they wait until they are more than fifty pages into the subject before letting the reader in on the existence of this notation. They could have brought it in earlier.

MSC:
00A05 Mathematics in general
68-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science
11B65 Binomial coefficients; factorials; \(q\)-identities
11Axx Elementary number theory
05A10 Factorials, binomial coefficients, combinatorial functions
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