The Nebraska REU in Applied Mathematics will offer summer research projects for undergraduates in 2010, 2011 and 2012. We will host ten undergraduates for eight weeks starting in early June. Each project is supervised by a faculty mentor or pair of mentors, and each project will have a graduate student assistant. The faculty serving as mentors have extensive experience mentoring undergraduate research. We intent to give the students as full a research experience as possible, including how to define a good problem, how to solve the problem and (in most projects) give rigorous proofs, how to write mathematics, and how to give a talk and present a poster. All of the projects are in Applied Mathematics, and more than half of the projects have an interdisciplinary component. Many emphasize the role of computer exploration in gaining insight into mathematical problems. The students will meet with their faculty and graduate student mentors almost every weekday. We have planned research, educational and social activities which will cultivate an environment which emphasizes interaction and collaboration. Our goal is to make sure that the students leave the Nebraska REU Site with an appreciation for the methods of mathematical discovery, have a meaningful, enjoyable and rigorous educational experience, and increase the likelihood that the students will continue with their mathematical and scientific studies.
Detailed project descriptions, including prerequisites, are posted on the web by the preceding November. The students choose those projects they wish to apply for, and order them according to preference. The application deadline is March 1. We intend to continue to have an approximately even gender balance among the students, and to target students from non-Ph.D. granting institutions. The University of Nebraska Office of Graduate Studies will assist us with recruiting, since they have extensive experience and infrastructure for recruitment of students from underrepresented groups.
The University of Nebraska ran the Nebraska REU in Applied Mathematics in the summers of 2010, 2011 and 2012. Each Site ran for eight weeks. During these summers seven faculty and seven graduate students mentored eight projects, involving 31 undergraduate participants. The program structure was designed to give students a research experience that follows a project through from conception to dissemination. Nebraska REU students learned how to define and solve problems, how to prove results, and how to present work to the mathematics community. Nebraska REU students worked in teams. Each team had three, four or five undergraduates, along with one or two faculty mentors and one graduate student mentor. Each project began with a concentrated tutorial on the mathematical and scientific context for the project and mathematical background that students might not have seen in their courses. Over the first two weeks, the focus gradually changed to research, with most groups working full time at research by the third week. The students documented their work in written reports in professional mathematics style as results were obtained. In the final week of each Site, the project teams devoted the bulk of their energy to preparation of results for dissemination, which includes a group talk presented to the larger UNL mathematics community and a poster presented at the Joint Mathematics Meetings the following January. The selection process for undergraduate participants focused on students from non-PhD granting institutions and first-generation college students; this ensured participation by students who will benefit most from the program, thereby helping to increase the number of talented undergraduates who choose careers in mathematics research and teaching. We promoted undergraduate research mentoring in the larger mathematics community by pairing graduate students with experienced faculty mentors. The projects offered were: 2010: Life History of Plants. This group worked on an optimization problem in plant life history theory. 2010-Calculus on Time Scales, 2011-Fractional Calculus, The students studied the discrete nabla fractional calculus. 2011: Metapopulation Modeling and Analysis. This group learned about modeling demographic stochasticity with Markov models. They also learned about density dependent deterministic models. 2011: Discrete Modeling of Biological Systems I. The students studied a continuous model for Th-cell differentiation based on a previously published discrete model. 2012: Discrete Modeling of Biological Systems II. The students studied how the design of experiments affects the network inference problem, which is to use the data of a dynamical system to infer the network. The goal was to determine how the generation of the initial data affects the inferred network. 2012: Quantum Calculus. The students extended many results known in the $q$-calculus (quantum calculus, which has very important applications in quantum theory). This includes a q-Laplace transform, which has several similar properties to the continuous Laplace transform. 2012: Peridynamics Models in Heat Conduction and Elasticity. The students worked in the area of peridynamics, a theory that has been successful in modeling phenomena in materials with discontinuities, or propagation of fractures. As of August 2013, the 2010, 2011 and 2012 Sites resulted in three published papers, one accepted paper, one submitted paper, and three papers in progress.
