REU Site: Differential Geometry, Mathematical Physics, Mathematical Finance, and Mathematics Education

University Of Connecticut, Storrs CT

Investigators

Abstract

This award provides funding for a three-year undergraduate research experience site at the University of Connecticut that supports nine students for ten weeks each summer. The project engages a diverse group of undergraduate students in research in several areas of mathematics and mathematics education. The main goal of this program is to contribute to the development of human resources in mathematical fields by engaging undergraduates, mostly from non-PhD-granting institutions, in research that yields publishable results, produces conference talks and posters, and inspires the students to pursue graduate studies and careers in mathematics, mathematics education, and other mathematically intensive disciplines. This site is supported by the Department of Defense in partnership with the National Science Foundation. Specific projects will vary from year to year. In pure and applied mathematics, typical projects will involve using computational tools or hands-on combinatorial arguments to investigate properties of basic examples that are expected to illuminate some larger part of the theory. Topics are expected to include problems from sub-Riemannian geometry, stochastic processes, analysis and mathematical physics on fractals and disordered media, and mathematical finance. Projects in mathematics education will vary depending on student interest, but the anticipated focus is on creating and refining curricular and pedagogical tools that support students in constructing, communicating, and critiquing mathematical arguments as a means of enhancing both conceptual understanding and practical quantitative reasoning. In addition to research experience, the program will give students practice in writing and presenting their work, teach them how to use software for mathematics (e.g. Mathematica and Matlab) and for writing mathematics (LATEX), and expose them to a broad range of mathematical topics through a weekly seminar series. Workshops on the graduate school applications process and ethical issues in scientific research will also be provided.