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2008 Summer REU Program

The University of Georgia announces an REU program which will run two summer student research groups of 7-9 students in each of the years 2008 and 2009. The program will admit students from across the country for a fast-paced and challenging research experience working closely with our mathematics faculty. Students will work closely with UGA faculty and graduate students on a problem of current interest in mathematics research. The REU program is linked to our well-regarded graduate program in mathematics, and students accepted into the REU program will be advised on their preparations for graduate study.

The two 2008 REU programs will run from May 19-July 11 and June 9-July 27 at the University of Georgia. Housing, meal plan, travel support and a stipend will be provided. Course credit is also available. "Following NSF rules, students must be U.S. citizens or permanent residents to receive REU stipends."

The topics for this year are:

Ecological Modelling -- May 19 - July 11, 2008

Group Leader: Caner Kazanci

Temperature, blood pressure and specific enzyme levels are typical health indicators for human beings. For a healthy person, the values of these indicators lie in specific intervals. Defining similar health indicators for ecological systems is a major question in ecosystems ecology. Over the years there have been many efforts in this direction, resulting in many formulas that claim to represent the health of an ecosystem. However most of these formulations are relative measures, and are not universal to all ecosystems. One such example is the cycling index: The higher the cycling in an ecosystem, the higher the utilization of mass and energy within the system before it is lost due to respiration and other factors. Therefore cycling index is believed to represent ecosystem health. However, there is no specific interval for cycling index that identifies a healthy ecosystem.

Our objective is to come up with a solid universal non-relative ecosystem health indicator, such as body temperature. We tackle this problem by combining mathematical, computational and statistical approaches. We developed an online software called EcoNet (http://eco.engr.uga.edu \url{}) for simulation and analysis of ecological models. EcoNet is capable of measuring most currently available ecosystem health indicators.

In this project, students will use real ecological field data (gathered from over 40 ecosystems) and EcoNet to compare current ecological health indicators, and investigate new mathematical
definitions of ecosystem health.

Background: Students should have a course in linear algebra and in differential equations. The project will involve substantial use of computers, and students should be interested in learning to program.

Numerical Analysis -- June 9 - July 27, 2008

Group Leader: Dr. Ming-Jun Lai

Multivariate splines are smooth functions composed of piecewise polynomials defined on triangulations. These functions in the univariate setting are a major tool for describing curves and tensor product surfaces on computer which have been used in many area of research and industrial applcations for curve and surface visualization and simulations.  As finite elements, these functions are a standard tool for the numerical solution of partial differential equations.

In this REU program, we will study the general theory of multivariate splines and use them for scattered data interpolation and fitting, surface design, and to solve PDE numerically. We first spend three weeks on the basic theory of multivariate splines using the monograph "Spline Functions on Triangulations" written by Dr. Lai and his coauthor Larry Schumaker. Then we will spend two weeks learning how to use multivariate splines for data fitting problems including programming in MATLAB. Finally we will spend another two weeks learning how to use multivariate splines for numerical solution of partial differetial equations. Some examples of MATLAB programs will be given as a starting point. Students will use them to develop and solve more sophisticated problems.

Background: Students should have multivariable calculus and one course in differential equations. Some experience with computer programming is preferable, but all students must be interested in and willing to learn MATLAB programming and numerical simulation.

 

Application materials will be due on February 29, 2008 including a transcript, a statement on why you are interested in each project, and two letters of recommendation from faculty. Recommendation letters may be e-mailed directly to Laura Ackerley, laura@math.uga.edu. Decisions will be announced before March 15, 2008. Please download the application form <here> and send application materials to

UGA REU Program
Attn: Laura Ackerley
UGA Math Department
Boyd GSRC
Athens, GA 30602

Further inquiries can be directed to Laura Ackerley or to the group leaders directly.

Past UGA REUs