Park City Mathematics Institute
Exploring Discrete Mathematics
Drafts of Project Files (password required)
- Vicki Clancy, Brian Hamel, Armando Madrigal, Brian Hopkins*
- This three day project uses operations on polynomials to answer a question from basic probability about dice. The motivating question asks whether there are two six-sided dice with non-standard labels whose sum data match the results of two standard dice. Students address the problem first in an ad hoc way using logic and reasoning. For the second part of the project, a polynomial representation is introduced which allows students to solve similar problems more easily and prove the uniqueness of their solutions using factoring, multiplication, and synthetic division.
- Catalan Numbers Unit
- Allen Jacobson, Ted Linnenbringer, Breedeen Murray, Andrew Richardson, Brian Hopkins*
- The Catalan numbers play an important role in combinatorics and count a variety of objects accessible to students. We revised the Catalan Numbers Project written by the 2004 working group, incorporating reviewer suggestions and our own ideas. The current project is a unit where students explore five objects counted by Catalan numbers, develop four bijections connecting the various objects, and derive a formula using binomial coefficieints.
Back to Exploring Discrete Mathematics Index
PCMI@MathForum Home || IAS/PCMI Home
© 2001 - 2013 Park City Mathematics Institute
IAS/Park City Mathematics Institute is an outreach program of the School of Mathematics
at the Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540
Send questions or comments to: Suzanne Alejandre and Jim King
With program support provided by Math for America
This material is based upon work supported by the National Science Foundation under Grant No. 0314808.
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.