I do math at Muhlenberg!

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 Fall

REU at Muhlenberg (Updated: Aug 2018)

The 2018 summer REU program has recently completed. More information can be found at the REU at Muhlenberg College site.

Berggren Trees and Romik system

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.


  1. (with E. Nguyen '16 and B. Tauber '16) Quadratic Forms and Their Berggren Trees, Journal of Number Theory 185 (2018) 218-256.
  2. The summatory function of the Moebius function in function fields, Acta Arithmetica 179 (2017) no. 4, 375-395.
  3. (with D. Fiorilli and F. Jouve) Independence of the zeros of elliptic curve L-functions over function fields, International Mathematics Research Notices (2016) doi: 10.1093/imrn/rnw087.
  4. (with D. Fiorilli and F. Jouve) Prime number races for elliptic curves over function fields, Annales scientifiques de l'École normale supérieure, 49 fascicule 5 (2016).
  5. (with S. Bae and H. Jung) Moebius function in short intervals for function fields, Finite Fields and Their Applications 34 (2015) 235--249.
  6. (with B.-H. Im) Chebyshev's Bias in Galois Extensions of Global Function Fields, Journal of Number Theory 131 (2011) 1875--1886.
  7. (with S. Kim) Biases in the prime number race of function fields , Journal of Number Theory 130 (2010) 1048--1055.
  8. Chebyshev's Bias in Function Fields, Compositio Mathematica 144 (2008) 1351--1374.
  9. Special Units and Ideal Class Groups of Extensions of Imaginary Quadratic Fields, Mathematical Proceedings of the Cambridge Philosophical Society, 143 (2007) 265--270.
  10. (pedagogy article) Transcendental Functions, Initial Value Problems and a Different Approach to Calculus II, College Math Journal, September (2007) 288--296.
  11. Vanishing of Some Cohomology Groups and Bounds for the Order of Shafarevich-Tate Groups of Elliptic Curves, Journal of Number Theory, 111 (2005) 154--178.

Contact me!


Trumbower 13


  • Muhlenberg College
  • 2400 Chew st.
  • Allentown
  • PA, 18104