Bard College's REU will introduce students from a wide variety of backgrounds to mathematics research at a highly selective liberal arts college where mathematical and scientific research by undergraduates and faculty members is burgeoning. The problems given to students will be part of active and current research areas in pure and applied mathematics, mathematical physics, and mathematical computation. Throughout the summer, students will be exposed to theoretical constructs, computational techniques and real world applications, and will develop background and skills that will help to prepare them for further study or employment in a mathematics-related career.
As a way to broaden access to, and the impact of, mathematics in the larger community, Bard will offer some REU slots to talented sophomores who are just beginning to consider careers in mathematics, as well as to students who have decided to major in mathematics as late as their junior year. We are determined to make this experience a tipping point for students who are mathematically talented but undecided about whether to pursue a career in mathematics. Moreover, with its attention to students who arrive early or late to mathematics in their college careers, Bard's REU will help to retain mathematical talent that might otherwise disappear when individuals with unorthodox academic preparation fail to fit into more traditional math and science programs. Thus, Bard's REU will increase the base of U.S. citizens who are highly trained in mathematics. Moreover, Bard's REU will contribute to broadening this mathematically qualified base by prioritizing gender parity in the students selected, as well as diversity in race, ethnicity, and mathematical background.
The Bard Math REU is an eight week long summer immersion in mathematical research for undergraduates, which ran the summers of 2010, 2011, and 2012. Although we originally requested funding for 24 students (8 each summer for 3 summers), we were actually able to stretch our NSF funding to support 29 students. In addition, the NSF-funded students were part of a larger community of summer research students including students funded by their home institutions, as well as Bard students supported by the Bard Summer Research Institute. REU participants worked individually or in teams on cutting edge research projects, advised by Bard College faculty from the Mathematics and Computer Science programs. As part of its Science Initiative, Bard College has been increasing its science faculty, and it recently opened the Reem-Kayden Center for Science and Computing. All Bard College seniors pursue a year long senior project, which in the sciences must consist of original research. The REU takes this experience advising year-long undergraduate research projects and puts it to use advising intensive summer research projects. The REU provided our undergraduate participants with a serious introduction to mathematical research, exposing them to a rigorous research environment. It helped them develop the tools and skills necessary for mathematical research, as well as oral and written presentation skills. Each student made substantial contributions to their research projects, writing up their results in a robust final report, and giving well prepared presentations in two informal progress reports and a final talk in the last week of the program. In addition, we require and provided funding for our REU participants to present their research at conferences, including the annual Joint Mathematics Meetings and various undergraduate mathematics research conferences. It is our goal that our REU participants will go on to successful careers in mathematics and related fields, and that the skills they developed in the REU will prepare them for graduate school and beyond. The research projects funded by this grant included conventional mathematics topics of algebra, geometry, and combinatorics, including a topic applying fractal geometry to number theory. One applied topic studied the mathematics of supersymmetry, a physical theory on the cusp of being realized at the Large Hadron Collider at CERN, and REU participants advanced a supersymmetry research program proposed by S. James Gates, Jr., a member of PCAST (the President's Council of Advisors on Science and Technology). Other REU participants studied ecological stability analysis, with one project on solar greenhouse design and another modeling crop collapse using techniques from applied mathematics to compare using land for a single crop vs. using it for multiple crops. Computer Science topics included both theoretical computer science and applied topics in computational neuroscience, studying how birds learn their songs, and how to simplify language via computer. This research has resulted in one paper to be published in the International Journal of Number Theory, as well as more joint papers with REU participants in progress. In addition, REU faculty have given multiple talks at conferences about their work with REU students. But most importantly, the 29 students have given a total of 41 conference presentations on their REU research, including 15 talks and 26 poster presentations. Most of our REU students are now in graduate school, with some already having Masters Degrees and moving on to their Ph.D.s, while our younger students are planning to apply to graduate school. We also have one alumnus now working at Google. The Broader Impacts of this project were primarily to help develop the US workforce in mathematics and related fields. Our participants included not only the usual juniors one finds in REU programs, but also students earlier in their academic careers, with 2 first year students and 10 second year students, in the hope that early exposure to mathematical research will inspire and prepare these students to advance their mathematical studies. We also attempted to achieve gender parity, and of our 29 students total, we had 12 women and 17 men. In addition to their research work, we also had our REU students participate in the Bard Math Circle outreach program, where they played mathematical games and built geometric models with elementary school students at local libraries. We hope that this will interest our REU participants in and provide a model for further such outreach.
