Undergraduate Research

Since Spring 2017, I have been advising Danielle Wood, an undergraduate at the University of South Carolina, on a project focused on implementing flipped-classroom instruction in middle schools, which will continue through Spring 2018. We were awarded a Magellan Explorer grant for this project. Our first goal was to create and maintain a website with information and data about flipped learning together with resources and tools that can be utilized by middle-school educators to quickly and easily implement this alternative approach to instruction. Our long-term goal is to begin implementing this instructional method in Richland County schools and measure its effect on students, especially in regards to their perception of mathematical thinking as a practical life skill.


UGA MathCamp

Over the last few years, Angela Gibney and Danny Krashen have organized week long summer math camps for middle and high school students in the Athens area. These students participate in exploratory projects with mathematics faculty, graduate and undergraduate students. Topics have included graph theory, elementary number theory, cryptography, epidemiology, and algebraic topology. I have had the opportunity to participate as a graduate helper in two of these groups.

In June, 2016, I worked with Ester Dalvit and Justin Johnson having students explore the action of the braid group on the fundamental group of the (thrice) punctured disk. The students were first presented with the challenge of putting a closed rope around the strands at the top of a braid so that it would have a specific shape when it falls to the bottom. They were able to solve this problem by using metal braids and strands of yarn to explicitly determine the group action.

Cryptography and Cryptology
In July, 2014, I worked with Joe Vandehey and Juan Vargas in teaching our students about cryptography and cryptology, ultimately having them understand the RSA cryptosystem. We began by introducing substitution ciphers, including Caesar and pigpen ciphers. We then covered the basics on divisibility and modular arithmetic in order to explain the Diffie-Hellman algorithm for sharing information. This naturally led to an explanation of RSA and other public key cryptosystems.


During Fall 2015 and Spring 2016, I had the opportunity to volunteer at Burney-Harris-Lyons Middle School in Athens, GA through the Project REFOCUS 21st Century Skills Program. The purpose of this program is to emphasize interest and aptitude in STEM fields by bringing faculty and graduate students in STEM disciplines into the classroom. I had the pleasure of working with various groups of students over a full academic year, helping them prepare for the Future Cities competition, science olympiad, quiz bowl, and video game coding.