Mathematics Projects 2013

Investigations in Combinatorics

Faculty Mentor - Dr. David Gove

Combinatorics is the theory and methodology of counting described sets. We will begin with the counting principles of list multiplication,permutations, combinations, and inclusion-exclusion. Typical questions include 1) how many poker hands are there and how many of each type? 2) how many 10-person committees could be made in the U.S. senate, assuming each committee member has to be from a different state? 3) how many ways could a secretary accidently stuff 20 envelopes with 20 letters so that no letter was in the correct envelope? We will move on the more powerful methods of generating functions and compare algebraic and combinatorial methods of proof. These will lead us to partition problems and Fibonacci numbers. Many open problems will be discussed and investigated.

Explore the World of Chaos

Faculty Mentor - Dr. Maureen Rush

This workshop is for high school students who want to explore the mathematical phenomenon known as chaos. Chaos is what results when very small changes in the initial conditions of a system lead to very large discrepancies over time. This phenomenon can account for our inability to predict weather, spread of disease, among other things.

You will learn the basics of mathematical iteration, both linear and nonlinear, with only an algebra background. Much of our work will utilize graphing calculators and software spreadsheets. We'll create wonderful graphs and create animations!