REU Site: Nebraska REU in Applied Math

University Of Nebraska-Lincoln, Lincoln NE

Investigators

Abstract

This grant funds the Nebraska REU in Applied Mathematics, held at the University of Nebraska in Lincoln, Nebraska, and run by the Department of Mathematics. The PIs will offer projects during the summers of 2013, 2014 and 2015, and each project will last for eight weeks. Most of the projects are interdisciplinary as well as applied, and many incorporate computer exploration in order to gain insight into mathematical problems. There is an emphasis on mathematical biology, and the site will offer projects in herbivore-plant interactions, population movement along a river, and dynamics in recurrent neural networks. There will also be projects in differential equations, including discrete fractional calculus on time scales, nonlocal models for elasticity and diffusion, and finite element schemes for wave equations. REU students work in two teams of five undergraduates each, along with one or two faculty mentors and one graduate student mentor. Each group works together on one or more problems with a common theme. The main goal is to give the students a complete research experience, with attention given to defining good problems, solving problems and (in some projects) giving rigorous proofs, writing mathematics, and presenting work with a talk and a poster. This is achieved by using a structure carefully designed to make use of the strengths of talented undergraduates while compensating for their relative inexperience and limited background. The students meet with their mentors almost every weekday, and spend significant additional time with their graduate student mentors. Over the course of the eight weeks, the projects will gradually transition from a focus on preparation to an exclusive focus on research to a focus on preparing results for dissemination. Research, educational, and social activities will combine to cultivate an environment that emphasizes interaction and collaboration. The students document their work as a written report in professional mathematics style as results are produced. In the final week of the Site, the project teams devote the bulk of their energy to preparation of results for dissemination, which includes a group talk presented to the larger University of Nebraska-Lincoln mathematics community and a poster intended for presentation at the Joint Mathematics Meetings the following January. REU projects result in one or more conference presentations, and many also produce papers published in undergraduate or professional journals.