REU Site: Mathematics Research Experience for Undergraduates

Suny College At Potsdam, Potsdam NY

Investigators

Abstract

This project is the continuation of a successful eight-week Summer Research Experience for Undergraduates (REU) in mathematics at SUNY Potsdam, with the cooperation of Clarkson University, in Potsdam, NY. Students will work daily in groups of 3 or 4 with an advisor on an original research problem in mathematics, specifically in the areas of algebraic graph theory, topological graph theory, analysis and algebra. More specifically, in the first year of the program, we propose that one group will study the impact of additive and multiplicative noise on the stability of systems of differential equations with an emphasis on systems that arise from biological applications. Another group will examine graphs that have a flat spatial embedding (an embedding for which every cycle bounds a disk that intersects the graph only along its boundary). Another group will study dynamic equations on time scales (a time scale is a nonempty, closed subset of the real numbers). In particular, students will calculate Taylor monomials when the time scale is the Cantor set. Finally, another group will examine quantum walks on graphs, which has implications for quantum computations and algorithms. We will nationally recruit math majors who have completed 2 or preferably 3 years of undergraduate course-work. Women, minorities, students with disabilities, and students from schools with limited research opportunities will be especially encouraged to apply. We have ambitious goals for our students. We would like to help them build their confidence in their ability to do research independently, and to help them build their appreciation and understanding of the vast field of mathematics. We also want to help them to improve their oral and written communication skills. Each group will present their results to the other students, at least twice during the eight weeks. Students will be encouraged to present their results at a national meeting. Each group will also use LaTex to prepare a paper on their work. We will further introduce our students to the mathematics profession through hosting a weekly guest speaker, and by presenting a panel on graduate school. Most math majors are not exposed to the process of mathematical research as undergraduates. We believe that our program provides a valuable added dimension to any serious math major's education. We believe they will go back to their home institutions with a much broader understanding of the process of mathematical discovery and dissemination. We will also mentor our students as they go through revising their work, and presenting at conferences. We believe that many of our students will want to go on to further study of mathematics in graduate school as a result of participating in our program. A few will choose not to, but they will enter society with a greater understanding and appreciation of mathematics.