The Nebraska REU in Applied Mathematics is administered by the University of Nebraska-Lincoln Department of Mathematics and is funded by the National Science Foundation. The REU site was established in 2002.
Our program strives to give students as full of a research experience as possible, including background reading and exercises in their subject; the skills needed on how to define a good problem, how to solve the problem and (in many projects) give rigorous proofs; and the tools for writing mathematics and giving a talk or presenting a poster. We also offer research, educational, and social activities that cultivate an environment which emphasizes interaction and collaboration.
Summer scholars meet with their mentors almost every weekday. At the conclusion of the 8-week program, students present their research. Often the summer projects result in presentations at a national conferences and research publications. We believe that the participants leave the Nebraska REU Site with an appreciation for the methods of mathematical discovery and have a meaningful and rigorous educational experience.
The University of Nebraska-Lincoln Department of Mathematics has a national reputation for excellence in education and mentorship. In recognition of their research mentoring for undergraduates, the department received the 2009 AMS Award for Exemplary Program or Achievement in a Mathematics Department.
Where Can You Find the Population in a River?
Prerequisites: A course in ordinary differential equations and an interest in population dynamics and ecology. For best results, we will look for team members who bring specific additional skills to the group, such as experience in ecology, mathematical modeling, partial differential equations, and numerical analysis.
Riverine ecosystems are heterogeneous, as flow velocity and nutrient levels vary considerably with depth and nearness to the river bank. These environmental differences lead to gradients in the population sizes of species in the river, particularly those that do not have significant capability of moving against the current. In this project, we focus on the variations in flow velocity and nutrient levels at different water depths, with the aim of studying the influence of the variations on steady state population distributions. Models will consist of coupled systems of ordinary differential equations in different zones and/or partial differential equations that treat depth as a continuous variable. The models will be scaled and studied with a combination of analytical, asymptotic, and numerical methods. The first week of the project will consist of a tutorial on basic mathematical modeling in population dynamics and stability analysis of differential equation systems.
Prerequisites: A calculus sequence and a one-semester course in Differential Equations.
Gottfried Leibniz and Guilliaume L'Hopital are believed to have first sparked curiosity into the idea of fractional calculus during a 1695 overseas correspondence on the possible meaning for a one-half derivative. By the late 19th century, combined efforts by several mathematicians — most notably Liouville, Grunwald, Letnikov and Riemann — led to a fairly solid understanding of fractional calculus in the continuous setting. Since then, the number of known applications for fractional calculus has grown greatly. There are applications of fractional derivatives in the fields of viscoelasticity, capacitor theory, electrical circuits, electroanalytical chemistry, neurology, diffusion, control theory and statistics.