New Math

Airika Yee, C’20, was starting her senior year as a mathematical economics major when she got an email about the Directed Reading Program (DRP), a nationwide initiative that pairs math graduate and undergraduate students for a semester of independent research, culminating in a final presentation.

“I really wanted to take a course in topology, but it never fit my schedule,” Yee says. “I saw the DRP as a chance to learn about an area of mathematics I’d never explored. I’ve had great experiences with grad students as TAs, so I knew I would to learn a lot.”

Mona Merling, Assistant Professor of Mathematics, knows how powerful the DRP can be for grad and undergrad students alike. She was a graduate student mentor in University of Chicago’s DRP and saw an opportunity to create a chapter at Penn in fall 2019. With support from the department and Dennis DeTurck, Robert A. Fox Leadership Professor and undergraduate chair of mathematics, as well as funding from the National Science Foundation, the program took off.   She’s now the faculty advisor. But the real work, she says, is done by the mentors and graduate student organizers Thomas Brazelton and George Wang.

When you’re teaching a class, neither you nor the student has much freedom in choosing what you study. The DRP is a valuable experience because we get the freedom to explore and dive into a student’s interests and challenges.

Brazelton and Wang recruit participants and match undergraduates to grad students who could help them learn more about the areas of math they want to pursue. From there, the mentor/mentee pairs create reading lists and schedule regular meetings to discuss texts and work on problems.

Reflecting on the graduate student interest, Brazelton says, “When you’re teaching a class, neither you nor the student has much freedom in choosing what you study. The DRP is a valuable experience because we get the freedom to explore and dive into a student’s interests and challenges.” 

Yee and Abby Timmel, C’20, a physics major and DRP mentee, agree about the benefits of working one-on-one.

“In math courses, you’re not able to go at your own pace and it’s frustrating, no matter if it’s too fast or too slow,” says Timmel, who was mentored by Brazelton. “Working with a mentor, there is always time to ask questions and make sure you really understand.”

Yee, who was mentored by graduate student Artur Saturnino for two semesters, comments on the program’s flexibility and openness. She says, “Artur and I could think about things in a conceptual way and not focus on finding the ‘right’ answer. That’s really different from other math courses I’ve taken.”

Any Path to Math

The DRP is for students interested in math, no matter their academic journeys or ultimate goals. Undergrad applicants have included students majoring in math, physics, computer science, and philosophy. The mentors are no exception.

“I had a weird path into math,” says Wang. “As an undergrad, I jumped around to a lot of majors and it wasn’t until very late that I really got a sense of what math was like and that I could enjoy it and imagine it as a career. I wish that resources like the DRP were available to me, and I want to help make sure that others have them.”

Timmel, for example, became interested in the program because she wanted to learn about areas of math that are relevant to physics. 

“My DRP project showed me a general perspective on math that could be helpful for me going forward in physics,” she says. “I studied category theory, which is very abstract. Instead of looking at distinct mathematical objects and what separates them, you look at the bigger picture. That type of outlook is useful, and I’ve heard that category theory can be applied to physics, but I haven’t gotten there yet.” 

Timmel plans to go to graduate school for physics, where she hopes to continue to study math and explore how it and physics complement one another.

Merling adds that women are better represented in DRP applicants than in math courses in general.

“We didn’t design the program that way,” she says, “but it’s a consequence of offering one-on-one instruction that is different from a traditional classroom. One-on-one mentoring can work against the stigmas surrounding underrepresented groups in math”

Just as Wang views the DRP as a resource for undergraduate students, Merling says it can also be valuable for graduate students as they progress in their careers. “I can feel the impact of the experience of mentoring undergraduates in the DRP on my growth as a mentor and advisor,” she explains. “I cherished the experience of learning along with my DRP students and watching them grow. It was a very formative experience.”

Going Remote

When classes went online as a result of the COVID-19 pandemic, so did the DRP.

“We kept up our reading and meeting schedule, but our online meetings were different because it had to be mostly verbal communication,” Timmel says.

Yee and her mentor found a creative solution, putting up white boards in their homes so they could talk through problems via video chat.

“Last semester, our presentations were in person, but this time we did it on a Zoom call,” says Yee. “I think they went really smoothly, and I was happy that we were all able to present what we learned.” 

Brazelton agrees, saying, “Despite the challenge, this cohort of students exceeded our expectations and delivered clear, engaging talks.”

“It was great to see a variety of captivating topics being covered from both applied math and pure math. Even with the disruptions in the semester, it was clear that the students had really mastered their topics,” Merling adds.

As they look to the future, the mentees and mentors agree: any curious undergraduates and graduate students should look into the DRP.

Merling explains, “For graduate students, the DRP mentoring experience teaches you a completely different skill set than classroom teaching: to learn to give the student the spotlight and listen to them, to let them take charge and have the freedom to go in the direction they are most drawn to, and let them be the expert in what they are learning about. You learn to provide just enough guidance to let them develop their academic independence.”

Yee valued both the challenge and the independence in her senior year.

“It would have been easy to wash up and not do anything,” she laughs. “But I’m really happy. It ended my Penn career in a positive way.”