Mathematics Projects

Dr. Maureen Rush

Explore the World of Chaos & Fractals

Learn the tools that scientists use to uncover the seemingly chaotic behavior found in weather patterns, the spread of disease, or the creation of art. From the pure mathematics of a simple iterative system emerges dynamics so rich that very small changes – the slightest errors – can lead to unpredictable changes. We will learn these tools, show the emergence of chaos, and attempt to control these chaotic changes.

Dr. David Gove

Combinatorics is the mathematics of methodically counting. This includes basics such as permutations and combination and inclusion-exclusion. A typical (and now classic) geometric question is “how many ways can non-intersecting diagonals be drawn into a decagon so that all the resulting regions are triangular?” Some of the combinatorial principles we investigate will be illustrated with card tricks. Despite the whimsical-sounding nature of some of the problems, combinatorics has important applications in computer science and other fields. Some numerical investigations will be done with a computer – students will learn how to use SAGE, a computer algebra system that uses the Python language syntax. Students will choose their main research projects from several topics presented during our early sessions. Past projects have included Triangulations of Non-convex Polygons, How Many Guards Are Needed To Guard A Museum? Toroidal Arrays.