Park City Mathematics Institute
Exploring Discrete Mathematics
Project Abstract

Drafts of Project Files (password required)

A Reservoir of Counting Problems
Calvin Armstrong* (Group Coordinator), Sandra Corbacioglu, Debra Gamson, Teri Hulbert, Andy Katz, Ekaterina Orfanova, Andrew Richardson (Assistant)
Of the many popular topics offered in Discrete Mathematics courses, our working group chose to focus on the study of counting techniques, in part because of our high level of interest in the subject and in part because of its practical use in other areas of mathematics, such as probability. We have developed a reservoir of counting problems categorized, primarily, by method of solution. Our goal in this project is to assist readers in interpreting the question and in choosing a technique for solving, and then we offered full, worked solutions with explanations. Within categories, we tried to make connections between problems in order to demonstrate how similar techniques can be employed in seemingly different circumstances to solve increasingly complex problems.
What Goes Up... An Introduction to Counting Methods
Andrew Richardson*
The purpose of this activity is to introduce, through a series of questions, the basic principles of counting. The focus of the problem is to determine the number of ways that 7 people can exit an elevator which stops on 5 floors. Students will be lead through a series of activities which require them to investigate combinations with and without repetition, events that occur together, cases of occurrences, and the use of lattices to visualize the outcomes.

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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.