Research Experiences for Undergraduates
June 14 - August 6, 2010
The Department of Mathematics announces Summer 2010 Research Experiences for Undergraduates (REUs). Funding for these REUs comes from the National Science Foundation (NSF) Workforce in the Mathematical Sciences Program.
Participating students will receive a stipend, although the exact amount has not been determined at this time because our NSF funding is still pending. Descriptions of the programs and application guidelines are below.
REU on Geometric Visualization in Virtual Environments
Program Director: George K. Francis
E-mail: gfrancis@illinois.edu
Website: www.math.illinois.edu/~gfrancis
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 http://new.math.uiuc.edu for the role of mathematics in this enterprise.
Students in this program, http://new.math.uiuc.edu/im2008, 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 gfrancis@illinois.edu will be answered promptly.
REU on Evolutionary Games and Social Networks
Program Director: Robert G. Muncaster
E-mail: muncast@illinois.edu
Website: www.math.illinois.edu/~muncast
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 their friends while avoiding others. And good interactions can reinforce a frienship while bad ones can make a relationship worse. The study of interagent relationships falls within the discipline of sociology called 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 up to four background areas important to the understanding of evolutionary theory: conventional game theory (especially non-cooperative discrete games), Markov chains, graph theory, and dynamical systems 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.
Selected students will also explore some examples of simulation software packages that attempt to capture game playing behavior between actors, with and without relationship structures. One of these, AgentSim, will be a principal tool in allowing students to use computer simulations to discover new evolutionary results which might be establish rigorously.
As a Research Experience, each student will be exposed to the full breadth of issues connected with research in mathematics:
- working knowledge of TEX
- selecting a research question
- collaborative research discussions and exposure to an overall research environment
- writing up your research (abstracts, first drafts, final papers)
- meeting deadlines associated with research efforts
- presenting your research findings at a professional meeting (for undergraduates!)
By the end of the program, each student will understand the highs (and lows) that research in mathematics entails, and will have made many valuable personal and professional connections along the way.
How to Apply
Eligible applicants must be U.S. citizens or permanent residents. Pending full funding by the NSF we hope to fund 6 students in each program. For full consideration, application materials should be received by March 15, 2010.
To apply to the program, please send:
- A completed application form (you may print out the application form in pdf format or complete the online form.
- Statement of interest (1-2 typed pages).
- A list of math courses completed or currently being taken, with grades for those completed.
- Two letters of recommendation from professors who will comment on your mathematical potential, motivation and work habits.
- Send all application materials electronically to reu@math.uiuc.edu or by U.S. mail to:
Joseph Miles
Director of Undergraduate Studies
Department of Mathematics
University of Illinois at Urbana-Champaign
313 Altgeld Hall
1409 W. Green Street
Urbana, IL 61801
Questions
See the REU Frequently Asked Questions page. If you have further questions, contact Professor Joseph Miles at reu@math.uiuc.edu.