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Discrete Mathematics with Ducks

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MAA Review

There are many textbooks that can be used in discrete mathematics classes; this one has some unique features, of which one is the many references to ducks. As I looked through the book and approached new topics, my mind drifted to wondering whether the author would use another play on words involved web-footed fowl. For example, when the topic of induction began, my mind wandered to the word “inducktion”, wondering if it would be used. Images of ducks with pencils on their shoulders are used throughout to label positions where there are exercises to work through.

Some of the worked examples and exercises contain a reference to ducks, for example, “How many ways can you select 2 ducks from a flock of 9?” Through the references to ducks, serious and effective mathematical instruction is achieved. The coverage is pretty standard for discrete mathematics courses; the only unusual addition was the section on transfinite numbers. It was presented as a play featuring a set of duck droppings and a modified Hilbert Hotel, which is quite a combination.

There are three sections, each labeled with a theme. They are:

• The basics
• Combinatorics
• Graph theory
• Other material: probability and cardinality.

Graph theory is strongly emphasized; it is the primary topic of 5 of the fifteen chapters. The sections on the basics of set theory and logic are brief, a total of 30 pages. It includes the amusing and quite “natural” use of ducks that only tell the truth and others that only lie. There are some proofs, but probably not enough to satisfy the instructor that wants to emphasize the mathematics.

This book can certainly be used to teach the standard course in discrete mathematics designed for computer science majors. The lighter touch of duck references does amuse you and does not ever overshadow or disguise the mathematical concepts.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.

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