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Founded in 2021, the program pairs undergraduates with graduate and postdoc mentors to study advanced concepts in math in a supportive and collaborative environment.
When doctoral student Richard Haburcak, Guarini '20, '23, reached out to Jenny Song '23 about hosting an information session for his newly created Directed Reading Program, the math major and president of the Dartmouth chapter of the Association of Women in Mathematics was intrigued.
Founded in 2021, the Directed Reading Program enables undergraduates to explore advanced math concepts of their choosing, guided by a graduate or postdoc mentor. The program culminates with a final presentation on the topic to peers, graduate students, postdocs, professors, friends, and family.
Song was drawn to the idea of getting to explore a complex subject in a supportive and collaborative setting. "I wanted to see more advanced math without signing up for a graduate-level course, since the thought of that was scary to me," Song says.
Not only did Song host the info session—she also ended up participating in the program herself.
"The DRP strives to increase diversity in mathematics and foster a supportive environment for students to explore mathematics," says Haburcak, who created the program with input and support from his math department peers, particularly from the program's faculty advisor, Asher Auel.
"We want to give students the chance to see math the way that mathematicians see math, to see the human side of math, and to be able to learn about topics that you usually don't have the chance to study until much later," Haburcak says.
Inclusive From the Start
Any interested undergraduate student can apply to the DRP—they don't even need to be a math major—and the application process is minimal by design.
"We want the program to be as inclusive as possible, so we don't ask for recommendation letters or nominations; student interest is the only requirement," Haburcak says. (Some projects on more advanced topics do have prerequisites, so that students and mentors can hit the ground running.)
Students can review the project offerings on the DRP website and choose the one that most interests them, or they can propose their own topic to study. Participants spend about four hours each week reading and doing math problems on their chosen topic, meeting about once a week with their mentors to discuss their reading and exercises. The cost of books is covered by the program.
Haburcak said he's never had any problem attracting mentors to the program..
"All I have to do is tell people that the program is running, and mentors will submit tons of interesting ideas for projects," Haburcak says. "I am consistently blown away by the enthusiasm of both the mentors and undergraduate students."
"As soon as I heard about the Directed Reading Program, I wanted to get involved," says Juanita Duque Rosero, Guarini '21, '23, a doctoral student in mathematics with a focus on computational number theory and arithmetic geometry, and who served as Song's mentor.
Not only was Duque Rosero excited by the prospect of exploring advanced math with motivated undergraduates, but she also felt a strong connection to the program's mission of fostering diversity in the field.
"As a woman in mathematics, I know firsthand the challenges that women in mathematics can face," she says. "The DRP was a great opportunity to not only share my passion for the subject but also to support a fellow woman pursuing math."
It was Duque Rosero who first suggested to Haburcak to connect with the Dartmouth chapter of the Association of Women in Mathematics.
Alex Wilson, Guarini '20, '23, who focuses on algebraic combinatorics, became a mentor after learning about it in a unique way: He was Haburcak's roommate.
"Richard was developing the idea for the DRP while we were working from home during the first summer of the pandemic, and as one of his roommates I was there as a sounding board from the beginning," says Wilson, who recalls the formative effect of studying math beyond the lecture hall.
"When I was an undergraduate, I found exposure to mathematics outside of the classroom—such as through attending seminars or reading courses, akin to what we do in the DRP—helpful in my deciding to pursue the math I study today."
Projects and Presentations
Topics explored in the DRP have ranged from machine learning and game theory to elliptic curves and bioeconomics. The 23 projects available for the upcoming spring term examine subjects such as quantum information theory, p-adic numbers, polynomials, and matrix groups.
When mentors and undergraduates meet each week, they typically discuss their impressions of the week's reading; engage in exercises pulled from the reading; and ask questions about the material. "Maybe the book presented a theorem that it's always possible to arrange a deck of cards so that it has certain properties, and so we attempt to make such an arrangement," Wilson says.
"My main goal for the program was that students felt capable and developed a
positive attitude towards advanced mathematics," says Duque Rosero, who served as a mentor twice. "I focused on creating a supportive and encouraging environment for my students."
This was particularly helpful for Song, who says she was initially nervous to present her work at the end of the term but found the environment and reception warm. "Everyone was so supportive, and no one was there to ask me difficult questions that I wouldn't have been able to answer," she says.
Indeed, Haburcak describes these presentations as "a celebration of what the students have learned during the term" and great opportunities for even seasoned math experts to learn something new. "They're like mini classes where I can get a great introduction to a math topic that I have no background in," he says.
Not surprisingly, mentors cite the presentations as their proudest moments working with students.
"It's really wonderful to see them take some ownership of the material and decide what they want to share with the rest of the community," Wilson says.
"Much like a poem or work of art, every time you re-read a subject you notice different pieces," Wilson says. "That's especially true when you are working with someone who is seeing and reacting to the material for the first time and asking questions you might not have expected or making connections with their own experiences."
"It was inspiring to see how my students took the material that we covered over the term and made it their own," agrees Duque Rosero, adding that she was "blown away by the quality of the presentations. The students put a tremendous amount of effort into their work, and it showed. Witnessing their progress and enthusiasm was a source of great joy and fulfillment."