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Mathematics of Choice: Or, How to Count Without Counting

Ivan Morton Niven
Mathematical Association of America
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The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Tom Schulte
, on

This text is an engaging, even addictive, introduction to basic combinatorics. Written in a fun and inviting manner, reader interest is amplified by the author’s infectious enthusiasm. This is an excellent introduce to combinations and permutations. First published in 1975, before computers and calculators were assumed to be at hand, the exercises in this book can all be done by hand on paper. Students finishing high school or in their first year of college will find this work an excellent adjunct to textbooks and lectures.

The work is arranged in a logical progression beginning with the definitions and motivations for factorials, combinations, and permutations. From there the reader moves to binomial coefficients, power sets, and Fibonacci numbers. The effect of repetitions on combinations makes a natural prelude in Chapter Four to the Inclusion-Exclusion Principle and the groundwork for basic probability. From partitions of integers the author moves into a brief and basic, yet cogent and enlightening, explanation of generating functions and some applications for them. The book also includes the Pigeonhole Principle, induction, recursion, and allied topics.

Tom Schulte teaches mathematics at Oakland Community College in Michigan.

The table of contents is not available.