I am an associate professor in the department of mathematics and computer science, Muhlenberg College. I received Ph.D. in 2003 from Johns Hopkins University, specializing in number theory. After teaching at Hendrix College for three years, I came to Muhlenberg College in 2007.
I teach a variety of math courses at Muhlenberg, ranging from introductory-level statistics and calculus to elective math courses such as number theory.
My research interests lie in number theory and I currently study topics related to distribution of prime numbers in the context of function fields. I enjoy working on cool math problems with undergraduates.CV Schedule 2018 Spring
Jointly with Dr. Will Gryc, I was awarded a minigrant from the Center for Undergraduate Research in Mathematics, or, CURM for the academic year of 2015-2016. This grant supported two undergraduate research teams at Muhlenberg, one of which was supervised by myself. My team consisted of two bright and talented Muhlenberg students, Emily Nguyen ('16) and Brandon Tauber ('16).
We focused on generating integer triples satisfying ternary quadratic forms. The prototypical model is so-called Pythagorean triples, which satisfies the celebrated Pythagorean equation. It is known that all such integer triples that are positive and without common factor can be put into a tree-like structure by matrix multiplication. We generalized this structure to produce such trees for other quadratic forms. Emily and Brandon reported our progress in the 2016 MAA/CURM spring conference at Loyola Marymount University. Our paper, entitled "Quadratic forms and their Berggren trees", is published in Journal of Number Theory (see below the Research section of this page for the link.)
In ongoing collaboration with Dong Han Kim at Dongguk University in South Korea, we are now focusing our attention on dynamical systems, called "Romik systems", that arise from the Berggren trees.
Especially exciting is the fact this research project is accessible to undergraduates. In addition to Emily and Brandon, I have worked with Grace Ohanian ('18), Eric Jovinelly ('18), Gianna Barres ('18), Justin Greenbaum ('19) and Dan DeRemigi ('19).
Emily Nguyen graduated from Muhlenberg College in 2016 with majors in Mathematics and English. She is currently spending a year with an organization called City Year, an education-focused nonprofit funded by AmeriCorps. In her free time, she enjoys reading (and re-reading) books and doing CrossFit.
Brandon Tauber also graduated from Muhlenberg College in the same year. He majored in mathematics and minored in computer science. He was a captain on the track and field team at Muhlenberg. He enjoys playing games and making art.
All of my papers can be downloaded or are linked below. If you'd like a copy of my research presentation, please feel free to contact me. You can look up my CV for more information.