Department of Mathematics University of Illinois Department of Mathematics
Academic Programs People Research Areas Publications Courses Seminars and Conferences Positions Search

Research Experiences for Undergraduates

June 12 - August 5, 2006

The Department of Mathematics announces Summer 2006 Research Experiences for Undergraduates (REUs). Funding for these REUs comes from a National Science Foundation (NSF) Workforce in the Mathematical Sciences Program.

Participating students will receive a stipend of $3,200. Participants will be responsible for the cost of travel, food and housing (dormitory housing with full board is available at a cost of about $1,700 for the eight-week program). Descriptions of the programs and application guidelines are below. There are funds for travel to conferences where participants present papers. There are also some funds for books and supplies.

Housing Information
Frequently Asked Questions about REUs

REU on Geometric Visualization in Virtual Environments

Program Director: George K. Francis

Visualization of mathematical phenomena and their transmutations is a maturing field of geometical computer graphics. Though opportunities to learn and practice this discipline are now plentiful, few universities have as long a tradition and as broad a base of application as Illinois. See for the role of mathematics in this enterprise.

Students in this program,, work with current researchers in diverse areas of mathematics, science and technology, who use a common programming platform, Syzygy. This distributed graphics system powers cluster based virtual environments such as the CAVE, CUBE and CANVAS at UIUC, the DiVE at Duke, and the PORTAL at the Technical University of Berlin.

Students in all majors and at all levels of expertise are encouraged to apply. All will learn to express themselves effectively in TeX and presentation graphics. There will be opportunities to publish or present papers at conferences. Specific questions addressed to will be answered promptly.

REU on Evolutionary Games and Social Networks

Program Director: Robert G. Muncaster

Have you ever wondered why we drive on the right-hand side of the road? Or why our political system is essentially two-party? Or even why men once opened doors for women as a matter of etiquette? These are examples of institutional structures or norms of behavior that have evolved into their current forms through a process of adaptive decision making. EVOLUTIONARY GAME THEORY, the mathematical discipline that studies such problems, has seen a great deal of activity in recent years.

When individuals interact with others in an evolutionary setting, relationships between the game players can have a significant impact on what happens. Individuals tend to choose to interact with friends while avoiding others. And good interactions can reinforce a frienships while bad ones can make relationships worse. The study of interagent relationships falls within the sociology discipline of SOCIAL NETWORKS.

This summer research experience will provide a select group of undergraduates the opportunity to explore evolutionary game theory, social network theory and their interconnections and make their own contributions to the subject. Working as a group, the students selected will explore three background areas important to the understanding of evolutionary theory conventional game theory (especially non-cooperative discrete games), Markov chains, and graph theory. With an exposure to these topics in place, we will move into the theory of evolutionary games and social networks and study some of the main results that have been found concerning how actors adapt to the playing of a game and how institutions or norms arise.

The students will also explore some examples of simulation software that attempt to capture game playing behavior between actors that exhibit relationship structures. One of these, AgentSim, will be a principal tool in allowing students to use computer simulation to discover new evolutionary results which might be establish rigorously.

How to Apply

Eligible applicants must be U.S. citizens or permanent residents. We expect to fund 6 students in each program. We will begin reading applications and making appointments on March 10, 2006. But we will continue to accept applications, space permitting, until the end of March.

To apply to the program, please send:

Questions about this application should be directed to Randy McCarthy,

Department of Mathematics

Last modified April 25, 2006