Exploring Discrete Mathematics Summary

Monday - Friday, June 28 - July 2, 2010

Brian, our faithful (or fateful) leader, has introduced the discrete group to Eduard Lucas' (1842-1891) Frogs & Toads problem and to M.C.K. Tweedie's "billiards" solution to the famous Water Jugs problems. These were chosen to "get our juices flowing."

After working on the problems for one day each, the group starting leaning towards the water jugs problems. The different variations of the Frogs & Toads problem have proven to be a notational nightmare, while the triangular grid billiards solution to the Water Jugs problem has been quite intriguing.

On our last two days, the group worked on solving additional variations of the Water Jugs problem, started looking through various related journal articles that Brian provided, and searched the web for additional resources, including any "competing" lessons plans and a movie clip ("Die Hard With a Vengeance"). The group is hoping to develop a multi-tiered approach for a product that will be useful for all of our various classrooms.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.