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.
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 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 naturally learn lots of background and are encouraged to present as well as publish their work, all invaluable for graduate school. The variety of mathematical activities provides a rich intellectual environment. 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, 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.