## Grad Student Spotlight: Lola Thompson

Lola Thompson: Teacher and Number Theorist

A fifth-year PhD candidate in the Math Department, Lola Thompson spends a large portion of her time at Dartmouth training for a career in teaching. In addition to completing the teacher-training program required by her department, Lola has taken a number of professional development courses at the Dartmouth Center for the Advancement of Learning (DCAL), and worked as an instructor at the Summer Institute for the Gifted (SIG)—a month-long educational program for children between the ages of 13-17 hosted by Dartmouth each summer.

“Dartmouth’s Arts and Science Graduate Programs are known for preparing students for careers in teaching, and that’s one of the main reasons I chose Dartmouth,” says Lola. “The math department’s doctoral curriculum allows students to engage in cutting-edge research while getting hands-on experience in the classroom. I think it’s a wonderful balance.”

Lola got her first taste of teaching as an undergraduate at the University of Chicago. During both her junior and senior summers, Lola taught at an intensive, eight-week math camp hosted by Ohio State University. It was at this summer program that Lola came across the mathematical problem that inspired her doctoral research.

“I usually tell people that the program at Ohio State was ‘math boot camp,’ and in retrospect, that’s really what it was. At the camp, things like playing cards, board games, the internet, and television were prohibited. As a result, our students were immersed in math for the duration of the summer,” explains Lola.

“Anyways, I was reviewing a problem set with one of my students when I came across an interesting question. It was in the true or false section of the problem set, and askedFor every positive integer n, the cyclotomic polynomial фn(x) [the unique irreducible polynomial that divides xn-1 but does not divide xk-1 for any k < n] has only +1 or -1 as its coefficients. True or False?’ At first, I thought that the answer was ‘true’ but I couldn’t think of a way to prove it, so I tried to find a counterexample. As it turns out, when n = 105, the statement is false; ф105(x) has 2 as a coefficient. This made me wonder `How large can the coefficients get?’”

When applying to doctoral programs, Lola learned that Professor Carl Pomerance had published a paper related to the problem she came across at the Ohio State summer program. After enrolling at Dartmouth, Lola selected Prof. Pomerance as her advisor, and began her research in Number Theory.

“Most of my doctoral research builds on the counterexample that I discovered with my students at Ohio State, and examines statistical questions related to both the degrees and coefficients of polynomials,” says Lola. “The most practical application of this type of research is in cryptography, a discipline that uses sophisticated patterns to encode information used by the government, financial institutions, the military, and other organizations who encrypt sensitive data.”

Lola is committed to her polynomial research, and is also passionate about teaching. Dartmouth’s Math Department does an excellent job training its PhD candidates to teach. After the masters degree in mathematics is conferred by the school, the department’s doctoral students are qualified to work as course instructors. However, before they’re allowed to teach undergraduates, these graduate students undergo an intensive teacher-training course. In this training course, graduate students learn the nuts and bolts of teaching: to successfully complete the program, the graduate students are required to design two weeklong courses for high school students on topics from the undergraduate math curriculum. Then, before they’re allowed to work as course instructors, these graduate students teach the two courses they designed over the summer.

“Though I enjoyed the training process, it was a little embarrassing,” explains Lola. “The department videotapes each of the summer courses that you teach, and the videotapes are then reviewed in a workshop. It’s worth it though—after you have your masters degree and have completed the training, you’re as qualified to teach as many adjunct professors, and can teach courses at Dartmouth.”

During her five years at Dartmouth, Lola has taught three different courses: two sections of calculus (Math 8 and Math 1) and one section of discrete probability (Math 20). While Lola was the chief instructor for each of these courses, a “teaching mentor” sat in on three of her classes each term to offer feedback on her teaching progress. In addition, she met with a “course chair,” whose role was to ensure that her choice of textbook, syllabus, and exam questions were consistent with the curriculum set by the department.

“While I enjoyed a large amount of freedom in the classroom, both my teaching mentor and course chair were there to guide me,” says Lola. “They checked in to make sure I was teaching effectively, and covering all of the required material.”

During her graduate career, Lola held three positions on Dartmouth’s Graduate Student Council (GSC): she first acted as the departmental representative for the Math department, was then elected Social Chair, and finally served as the Vice President of the GSC. Currently, Lola runs Dartmouth’s Graduate Vegetarians and Vegans club, is a Graduate Student Leader, and takes Persian and belly dancing classes.

Recently, Lola accepted a one-year postdoctoral position at the University of Georgia—her adviser is a Dartmouth Arts and Sciences Graduate Programs alumnus– and she’s also accepted a tenure track position at Oberlin College starting in the 2013-14 academic year.

by Wesley Whitaker