MATHEMATICS - Example Student Summer Positions

Ben Dill
REU: Groups, Graphs, and Geometry at University of North Carolina at Asheville
"An Investigation of Two-Dimensional Coxeter Groups"

In my summer research, we sought to understand a generalization of Coxeter groups, which we called two-dimensional Coxeter groups. To analyze these groups, we used van Kampen diagrams and a technique in which we added new relators to a Coxeter group's representation by group actions on a fundamental domain. Specifically, we defined a condition for a two-dimensional Coxeter group to be finite and found the order of all two-dimensional Coxeter groups with a certain basic presentation.

Amber Nuxoll
Statistics Intern, University of North Carolina at Greensboro
"Wilcoxon Rank-Sum Procedure for Multiple Comparisons Using Permutations Tests"

During my summer internship at UNCG in Greensboro, North Carolina, I explored the use of nonparametric statistical methods. After learning about a few of the most popular nonparametric methods, I then developed a nonparametric statistical procedure for making multiple comparisons using the Wilcoxon Rank-Sum procedure using restricted randomization within permutation tests. I compared the accuracy of this new procedure to existing ones and began creating a simulation in SAS to further explore the power of this new procedure. After graduation I plan to pursue a PhD in Operations Research.

Nathan Woods
REU: Computer Vision and Multi-Agent Systems at Utah State University, Logan, Utah , "License Plate Localization using Concurrent Columns"

The research I was working on was based off of the localization of license plates in a static or motion image. The particular process I was attempting to improve involved the use of a computation learning algorithm which was used for a cascading rejecter in a feature extraction method. The training and test data was gathered from upright Haar-like features.

Jessica Forbes
AMGEN Scholars Program, Kristin Swanson's Lab, University of Washington
"Glioma Segmentation on Magnetic Resonance Imaging: Assessing the Spatial Variability of a Semi-Automated Method"

This summer I worked with the Kristin Swanson lab at the University of Washington in the AMGEN Scholars Program. Utilizing MatLab, I assessed the spatial variability of a semi-automated method for segmenting brain tumors from MRI scans. The segmentations are then used to calculate the growth rate of glioma brain tumors in actual patients. The data from segmentations will be used to design treatment plans for patients to help treat this uniformly fatal disease. My work from this summer is to be submitted for publishing in one of the lab's papers.

Brittany Harris
Cornell Summer Mathematics Institute, Cornell University, Ithaca, NY

I participated in Cornell University's 8-week Summer Math Institute. The purpose of the program was to prepare for graduate-level studies in mathematics. I spent 20-30 hours per week doing coursework in mathematical analysis (a rigorous, proof-based course), and 15-20 hours per week conducting research. The program also afforded me the opportunity to meet professors and professionals in my field to prepare for the next step of my education.

Jeff Allen
Borealis Project, Montana State University, Bozeman
"The Ozonesonde"

Borealis is a ballooning program that designed to test atmospheric conditions. A large weather balloon is sent into the upper stratosphere with a string of various experiments attached. One of the experiments was the ozonesonde, which is a small device that records ozone levels using an electrolytic cell that reacts in the presents of O3. This device was used to create an ozone profile for the surrounding areas of Bozeman, MT.

Scott Harmon
NIST SURF Boulder, Colorado
"High-performance carbon nanotube coatings for high-energy laser measurement"

The aim of the project is to generate a suitable coating for laser measurement devices for kilowatt-range lasers. Over the course of the summer, I generated a stockpile of the ceramic-composite nanotube coating, optimized the production of said material, and conducted research in order to improve coating techniques.

Sam Schaefer
Intern, Montana State Auditor's Office, Helena

Throughout the summer I worked alongside two actuaries at the State Auditor's Office here in Helena. The majority of my work revolved around rate filing, reviewing benchmark calculations for insurance companies, learning some of the basic rate-making techniques used by actuaries, analyzing companies' non-forfeiture and forfeiture filings for errors, and incorporating rate-making techniques into various spreadsheets. Almost all of my work was done in front of a computer and the majority of it was done using Excel.