Resources for Teaching Discrete Mathematics: Classroom Projects, History Modules, and Articles

MAA Notes

by Brian Hopkins, Mathematical Association of America

A resource for discrete mathematics teachers at all levels.

Resources for Teaching Discrete Mathematics presents nineteen classroom tested projects complete with student handouts, solutions, and notes to the instructor. Topics range from a first day activity that motivates proofs to applications of discrete mathematics to chemistry, biology, and data storage. Other projects provide: supplementary material on classic topics such as the towers of Hanoi and the Josephus problem, how to use a calculator to explore various course topics, how to employ Cuisenaire rods to examine the Fibonacci numbers and other sequences, and how you can use plastic pipes to create a geodesic dome.

The book contains eleven history modules that allow students to explore topics in their original context. Sources range from eleventh century Chinese figures that prompted Leibniz to write on binary arithmetic, to a 1959 article on automata theory. Excerpts include: Pascal's "Treatise on the Arithmetical Triangle," Hamilton's "Account of the Icosian Game," and Cantor's (translated) "Contributions to the Founding of the Theory of Transfinite Numbers."

Five articles complete the book. Three address extensions of standard discrete mathematics content: an exploration of historical counting problems with attention to discovering formulas, a discussion of how computers store graphs, and a survey connecting the principle of inclusion-exclusion to Möbius inversion. Finally, there are two articles on pedagogy specifically related to discrete mathematics courses: a summary of adapting a group discovery method to larger classes, and a discussion of using logic in encouraging students toconstruct proofs.

323 pages, Paperback

First published December 15, 2008

Reviews

[Charles · Rating 5 out of 5]

Great breadth of resources for a course where there is great breadth in the viable options

Being somewhat of a hybrid (some would say mongrel) course, there has been a great deal of discussion about the content and role of discrete mathematics since it first emerged as a math course for computer science majors decades ago. Major math conferences have regularly contained sessions on the structure and content of discrete math courses. One of the points of consensus was that the range of material that could legitimately be included was too broad to ever be contained in a single course.
This book provides significant breadth of coverage so that every teacher of the course will find something that deals with what they want to include in their class. Topics from staples such as the Tower of Hanoi, basic games and binary arithmetic to more unusual and entertaining ways to present such material are included. Examples of the more unusual are “Using Trains to Model Recurrence Relations,” using benzene rings as a tool in counting and “Calculator Activities for a Discrete Mathematics Course.”
More advanced topics such as predicate logic, the topology of partially ordered sets and Turing Machines are also included. If you are looking for a new angle on the presentation of material in your discrete mathematics course, you will find this book to be a valuable resource.

This review also appears on Amazon