In the Williams College SMALL REU program, for ten weeks each summer (nine in residence at Williams and one at home), 25 to 40 undergraduates work on research projects under the direction of a faculty member in mathematics or statistics. There are usually between 4 and 7 groups each summer of various sizes. The summer culminates with presentations (at Williams and often at conferences), and most groups write up their work for submission to a research journal. There are weekly talks by faculty and students, both in mathematics and in related fields. Students are part of a vibrant scientific community; over 100 students do original research in mathematics and the sciences at Williams each summer, and there are a variety of academic and social activities bringing all the summer students and faculty together. Now in its fourth decade, participants are connected with alumni of the program who are able to provide excellent perspective, advice, and mentorship.

The goal of this REU is to introduce undergraduates to the excitement and challenge of doing original research in mathematics. Topics will be drawn from a variety of fields. Possible areas include algebraic geometry, Bayesian statistics, combinatorics, commutative algebra, computational geometry, CR structures, discrete geometry, dynamics and ergodic theory, graph theory, hyperbolic manifolds, knot theory, mathematical biology, mathematical physics, measure theory, minimal surfaces, number theory, probability, random matrix theory, representation theory, Riemannian geometry, symmetry groups, and tropical geometry. In the process, students learn lots of background material. They typically work in groups, meeting with advisors as needed, and are encouraged to present as well as publish their work, all valuable skills for graduate school as well as non-academic pursuits. A variety of mathematical activities and topics provides a rich intellectual environment; students live together and are constantly discussing their work, and attend weekly talks by the faculty so they learn the basics of all the different areas being investigated that summer. Our nation needs a wider appreciation and understanding of mathematics, and cannot afford to leave anyone out. We have increased the numbers of students from traditionally under-represented groups participating in the program over the last five years, as well as from community college backgrounds, and we are continuing to look for new and better ways to encourage applications from women, minorities, first generation college students, and other underrepresented groups. Students, faculty and the broader mathematics community will benefit from the presentation and publication of original research. Students will develop a lifetime network of peers and mentors, and many of them will pursue graduate studies, partially because of their REU experience. Almost all students publish papers in research journals and many present their results at national and international research conferences.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Program Officer
Michelle Manes
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Williams College
United States
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