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REU in Applied Mathematics


This page contains program details for 2010. Check back later this fall for 2011 project descriptions and program details.

On This Page

Join our program and work with faculty and grad students
on cutting-edge research problems in Applied Mathematics
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2010 Dates and Stipend

Start: June 7, 2010
End: July 31, 2010
Stipend: $4,000

Contact Info

Ms. Lori J. Mueller
Administrative Coordinator
402-472-4319
lmueller2@unl.edu
REU Website

Who Should Apply

Related majors and areas
  • Mathematics
Eligibility
Participation in the Nebraska Summer Research Program is limited to students who meet the following criteria:
  • U.S. Citizen or Permanent Resident
  • Current undergraduate with at least one semester of coursework remaining before obtaining a bachelor's degree
For more information, refer to the eligibility page.

In this program, each project has unique prerequisites. See the Research and Mentors section for more details.


How to Apply

To apply, follow these application steps.

Application Timeline

  • Tuesday, December 8, 2009 — Application opens
  • Monday, February 15, 2010 — Priority deadline
  • Monday, March 1, 2010 — Application deadline
  • Monday, March 29, 2010 — Admission decisions complete
See more timeline information.


Benefits

  • Competitive stipend
  • Double-occupancy room and meal plan
  • Travel expenses to and from Lincoln
  • Campus parking and/or bus pass
  • Full access to the Campus Recreation Center, University Health Center, and campus library system
  • Wireless internet access
Learn more about academic and financial benefits.

Program Events

  • Campus and department orientation
  • Department seminars and presentations
  • Professional development workshops (e.g., applying to graduate school, taking the GRE)
  • Welcome picnic
  • Omaha day trip to Henry Doorly Zoo
  • Canoe and camping trip
  • Research symposium

Research and Mentors

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The Nebraska REU in Applied Mathematics is administered by the University of Nebraska-Lincoln Department of Mathematics and 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.

In 2010 our projects will include Life History of Plants, mentored by Professor Glenn Ledder and Fractional Calculus on Time Scales, mentored by Professor Al Peterson. Each project will also have a graduate student mentor.

The summer program has been funded by the National Science Foundation, and the 2010 Site is contingent upon continued funding.

The University of Nebraska-Lincoln Department of Mathematics has a national repletion for excellence in education and mentorship. For instance, the department recently received the 2009 AMS Award for Exemplary Program or Achievement in a Mathematics Department, in part in recognition of their research mentoring for undergraduates.

2010 Mentors and Projects

Glenn Ledder, Ph.D.
Mathematics
Life History of Plants
Prerequisite: An introductory course in ODEs. Familiarity with a scientific programming language is also desirable. All relevant biology will be presented during the early weeks of the project.

Various mathematical models have been used to determine plant fitness in terms of life history parameters and schedules and to determine the optimal life history for different scenarios, but there is a lot of room for new work.
Read more about this project
Various life history strategies are observed among plants. While most plants can be classified as annual or perennial, there are variations on these themes. Annual plants differ in timing, with some sprouting in the spring and others in the fall. Those that sprout in the fall may set seeds in the fall or overwinter and set seeds the following spring. A small number of annual plants flower in both the fall and the spring. Some perennials reproduce every year, while others save resources for occasional reproduction binges.

The distribution of resources between roots and shoots can be adapted to the individual plant’s micro-environment. Leaves can be delicate or sturdy, long-lived or short-lived, defended against herbivory by toxic chemicals or not. In all cases, the principle of natural selection suggests that a plant's actual life history is approximately the optimal life history for its environment and ecological niche, subject to limitations in genetic variation.

The students who work on this project will learn some of the models and methods that have already been developed for this area. Then they will work to identify a new feature to include in a model or a new scenario to study, construct an appropriate mathematical model, and analyze the model to see what biological phenomena it predicts. Analytical work may include methods of control theory, optimization, and/or dynamic programming, with some scientific computation.
Allan Peterson, Ph.D.
Mathematics
Fractional Calculus on Time Scales
Prerequisite: An introductory course in ODEs.

The focus of the project will be on fractional derivatives and fractional differential equations, and their generalization to time scales.
Read more about this project
The concept of time scales unifies and extends discrete time and continuous time. In this project students will study calculus and dynamical systems on time scales, which is a natural extension of the more familiar calculus and differential equations in continuous time. Fractional differential equations have applications in numerous diverse fields, including electrical engineering, chemistry, mathematical biology, control theory, and the calculus of variations. For instance, the fractional calculus may provide more mathematically accurate epidemic models.

Students will first learn about fractional derivatives and fractional differential equations in continuous time. They will then learn about the fractional calculus on arbitrary time scales. This is a very new topic, and hence has many new research areas to explore.