American Institute Of Mathematics

Research by Undergraduates

Summer, 2005

The purpose of this program is to form a research team of undergraduates and mathematicians to investigate interesting unsolved problems in number theory and analysis.

The theme for this year is "Polynomials: random and not so random." We will investigate random polynomials, random matrices, and L-functions (which are part of number theory). While some projects will look at connections between these objects, others will focus specifically on L-functions or on polynomials. The explorations will take place both theoretically (pen and paper) and experimentally (on the computer).

The majority of the projects have an analytic flavor and will appeal to someone who enjoyed calculus, real analysis, or complex analysis. Taking courses in those subjects is helpful but not required. What is essential is an interest in mathematics and a willingness to work! Our experience has been that the ability to immerse yourself in the subject is more important than arriving with a lot of prior knowledge.

In addition to the significant scientific progress which will be accomplished by these teams, the participants will benefit by the opportunity to work closely with research mathematicians and with each other. This will expose the participants to the culture of research mathematics and will also provide an opportunity to learn interesting mathematics and computational techniques which are not normally encountered in the classroom.

Program philosophy

1. The AIM REU is run by active research mathematicians who select projects that are an integral part of their own research program.
2. Participants begin doing interesting work on their project on the first day. Nobody is ever told "You have to do a couple of weeks of background reading before you can begin your project."
3. Participants are exposed to the entire process of research, from exploration and conjecture, to proof and refinement, through writeup and presentation.
4. Each participant has their own project under the direction of a research mathematician. Students do not directly work together on projects.

Program details

Participants receive a stipend ($2500< stipend ≤ $3000) and a travel and housing allowance. Accommodations will be in a residential neighborhood a short walk from AIM. We expect to support 3 or 4 students.

This program is supported by a Focused Research Groups grant (FRG) from the National Science Foundation.

The application deadline for the 2005 REU has closed.

For more information email reu@aimath.org



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