# School of Science Outreach

### Shaping the Future of Mathematics

**For High School Students: RSI**

On an early August morning last summer, high school student Patricia Li presented her project, “On the Number of Permutations with a Given Number of Cycles and Left-to-Right Maxima,” to an audience of peers, MIT graduate students, and professors. Like the other high school mathematics students in the audience, Patricia had spent six weeks of her summer at the 25th Annual Research Science Institute (RSI), devoting many hours and much patience to solving a specially assigned research problem. Both her project and her presentation went quite well, but first Patricia had a lot to learn about academic research and writing. Patricia has been part of advanced mathematics programs before. In fact, she was a member of the first U.S. team to go to the China Girls Mathematical Olympiad in 2007. But, she says, in other math programs, “you know problems can be solved in a short amount of time—but not here.” As for writing papers, she says “they only care whether the answer is right and is basically understandable.” At RSI, Patricia not only learned to work her way through longer, more complex problems, but also to meet the more rigorous standards of academic writing, where the key is striking the difficult balance between concision and rigor.

MIT has hosted the intensive six-week summer program since 1996, attracting around 75 of the most talented high school students in mathematics, science, and engineering. In addition to attending university-level courses, each RSI participant is assigned a graduate student mentor who designs a research problem tailored to the student’s own talents and interests. The mentors meet with their students daily, guiding them through their project and helping them prepare the presentations of research that conclude the program. RSI students frequently submit their projects to the nation’s most prestigious competitions in math, science, and technology. This year, RSI participant Eric K. Larson won second place in the Siemens-Westinghouse Competition, with two more students, Noah Arbesfeld and Maxim Rabinovich, named as semi-finalists. Sana Raoof, whose research provided new insight into how mathematical knot theory could help resolve classic biochemical problems, was selected as a winner of the Intel International Science Fair. One of the top three winners from about 1,550 young scientists from 51 countries, regions, and territories, she took home a $50,000 prize.

**For MIT Students: SPUR **

The Mathematics Department also runs the Summer Program in Undergraduate Research (SPUR), which is similar to the RSI program. Founded by Professor Hartley Rogers in 1996, the program gives ten MIT undergraduates, mostly math majors, the chance to experience graduate-level work. Like RSI, SPUR runs for six weeks, offering each student advanced seminars and a graduate student mentor. SPUR participants also meet weekly with program director and professor David Jerison. Many students publish papers based on the projects they complete at SPUR, and often go on to graduate school. Last year, Galyna Dobrovolska, a co-recipient of the Alice T. Schafer Prize for Excellence in Mathematics by an Undergraduate Woman awarded by the Association for Women in Mathematics, was able to co-publish her work in algebraic combinatronics. Her paper, “Solving the Support Containment Conjecture,” resolves a significant open problem, and has been noted by other researchers in the field. Galyna appreciated her research with Professor Pavel Etingoff, the support she received from Professor Victor Guillemin, and her classroom experiences with Professor Michael Artin, whom she says “teaches algebra so inspirationally.” Galyna is now a graduate student in the Mathematics Department at MIT.

Both RSI and SPUR perform the important work of encouraging talented students to choose and stay in the field of mathematics—the supportive and stimulating environment often convinces them to study math at MIT. Not only do the students benefit from training in advanced theory and research, but MIT also draws higher-quality students, and the graduate mentors who teach them gain valuable teaching experience and new insight into their own research. Adam Sealfon, an RSI student working on an aspect of algorithms that may have important applications for computational graph theory, was impressed by his experience at MIT and said he planned to apply. He believes that “the really amazing thing about RSI is the community at every level, from students to counselors to tutors to administrators. Everyone’s really approachable and really nice—and really smart … . I’ve learned a lot about what it means to research and to collaborate with other researchers.”