Applied Mathematics Research Experience (AMRE) (Link)

Pocket U-LAM, PeRT, and Self-Study Site

College of Wooster | May 2005 - July 2005

Three subprojects were developed during this AMRE project. I added functionality to the Self-Study Site which was designed for the AAC (Augmentative and Alternative Communication) Institute so speech language pathologists, family members, and others who wanted to learn about AAC devices and practices could do so in their own time. This required that I learn PHP, SQL, and CSS.

Research Experience for Undergraduates (REU) (Link)

Self-Similar Tilings of Nilpotent Lie Groups

University of Akron | June 2006 - July 2006

A paper published by Robert Strichartz dealing with fractals over nilpotent Lie groups motivated this REU project. Christoph Bandt developed the sufficient conditions for convergence of an IFS to a self-affine tile in n-dimensional Euclidean space. In a collaborative effort, our REU group proved a theorem similar to Bandt's for nilpotent Lie groups. It was natural to consider nilpotent Lie groups because they are a class of groups that have a metric, an automorphic dilation structure, discrete cocompact subgroups (lattices), and a measure. Our group was able to classify all automorphisms of the Heisenberg group. This allowed us to generate images of fractal tilings over the three-dimensional Heisenberg group using an OpenGL implementation.

Independent Study (IS) (Link)

SIAM 0 Dollar 100 Digit Challenge

College of Wooster | August 2006 - March 2007

The IS program gives me the opportunity to engage in meaningful research appropriate for an undergraduate seeking graduate level experience. My senior advisor Dr. Charles Hampton and I are studying the results of the SIAM 100-Digit Challenge. The method to find solutions to these problems is by devising numerical routines to run in Mathematica and Matlab. The problems were devised to make it very difficult to solve any through symbolic computations, therefore high precision arithmetic is necessary. I have been investigating the implementation of high precision arithmetic in Mathematica and why such an implementation facilitates the use of the algorithms I devise to solve the problems at hand.

Joint Mathematics Meetings (Link)

Self-Similar Tilings of Nilpotent Lie Groups

New Orleans, LA | January 2007

I gave a poster presentation during the Undergraduate Student Poster Session and a talk during the AMS-MAA-SIAM Special Session on Research in Mathematics by Undergraduates (This file is big!).