The Summer Undergraduate Research Experience in Pure and Applied Mathematics (SUREPAM) at the University of Wisconsin-Eau Claire is an eight week program designed for ten undergraduate students. The students will become part of a thriving multidisciplinary summer research community. The participants will work in two-person teams. Each team will prepare presentations which will expose all participants to a variety of projects, both pure and applied. Our research topics will include: Banach spaces, combinatorics, fluid dynamics and elasticity, Lie groups, deformation algebras, non-standard analysis, and wavelets and signal processing. The program offers strong prospects for the students to obtain meaningful results in mathematics. The research mentors have solid records of successful research collaboration with undergraduate students and have developed research programs accessible to undergraduates. External faculty mentors and other visitors will broaden the perspective of both the students and mentors. Students will write a scientific research paper, and present their research at an on-campus Workshop to be held during the eighth week of the program. Some of the research problems have industrial applications and this will increase awareness of possible career options. Each student receives a stipend, housing, and funds for travel from and to his or her home institution. Preference will be given to students who are engaged with faculty from their home institutions in a study or a research project related to their anticipated project prior to their arrival at SUREPAM. This possibility of involving faculty from the students' home institutions will serve as a catalyst for expanding mathematics research opportunities for more undergraduates and will build ties between students and faculty from different universities. Eau Claire is located 90 miles east of the Minneapolis / St Paul metropolitan area. The students will have the opportunity to visit some of the many famous attractions of the region, including the Minnesota Science Museum and the Mall of America.

Project Report

at the University of Wisconsin-Eau Claire was funded by an NSF-REU Site grant with additional support from the University. The program ran over four summers, received over 300 applications from across the United States, and the provided 47 undergraduate mathematics students with faculty mentored research projects drawn from a wide variety of topics, including: Cohomology and Deformation Theory, Mathematical Biology, Modeling of Fluid Flow, Wavelets, Noise Removal, Mathematical Analysis of Music, Invariant Theory, Numerical Solutions of Physical Problems, Time Scale Calculus, Functional Analysis, Non-Archimedean Analysis, Algebraic Combinatorics and Dynamical Systems. Research mentors included UW-Eau Claire faculty as well as several faculty from other universities with a strong record of mentoring undergraduates. As soon as students were accepted into the program they were sent background materials so that they arrived well prepared. They presented their partial results at weekly seminars, wrote up their results in the form of a journal article and presented their results at the annual Summer Mathematics Workshop, which included guest presenters and evaluators, as well as presentations by students from other REU programs. Faculty at the students’ home institutions often helped them prepare before the summer and assisted with their research after they returned. As of this writing, SUREPAM students have coauthored 9 articles accepted for publication in peer-reviewed research journals and another 5 have been submitted and are under review. In addition, the students have made numerous presentations and posters at regional and national professional meetings. At least 23 students have gone on to graduate programs in the mathematical sciences (many are still undergraduates) and a number have earned prestigious awards and scholarships. Some of the research results from the SUREPAM program have direct applications, for example, models of blood flow in an artery, fluid flow across a membrane, or signal denoising. Typically, applications from "pure" research" are not realized for many years; for example, many algorithms that make internet security possible rely on mathematics discovered 200 years ago. However, the main goal of the SUREPAM program is to transform students from the mode of "do the homework-the answer is in the back of the book" into the mode of "research mathematics–the answer is not known, in fact the questions may not be known." We are confident that we have achieved this goal.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Noel Brady
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University of Wisconsin-Eau Claire
Eau Claire
United States
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