REU Site: UCSB Mathematics Summer Research Program for Undergraduates

University Of California-Santa Barbara, Santa Barbara CA

Investigators

Abstract

The UCSB Mathematics Summer Research Program for Undergraduates aims to provide a full research experience to undergraduate students in mathematics from different backgrounds. Over the course of the eight-week program, the students will learn to investigate and solve open problems in diverse areas of mathematics, to work in a collaborative environment, to communicate their mathematical results through talks and written reports, and to publish their findings in appropriate journals with the goal of disseminating their research. The program will expose the participants to daily life in graduate school, through interactions with graduate students, graduate advisors, faculty and postdocs in the UCSB math department. In addition, through professional development workshops, the participants will learn about different areas in industry that demand professionals with good research skills. Historically, the UCSB REU has not focused on a specific area of mathematics. However, the program intends to be accessible to students with a variety of backgrounds in mathematics. Thus, the research projects are likely to be in linear algebra, matrix analysis, numerical linear algebra, combinatorics and graph theory; that is, in areas that do not require extensive mathematical background from students. Examples of topics that have been studied in this program before include 1) primitive circulant matrices; 2) matrix polynomials and linearizations; 3) matrix equations; 4) parking functions; 5) Alexander and Jones polynomials; 6) sequential dynamical systems. The topics will change every year depending on the active research areas of the mentors involved in the program. The final goal is to expose the students to the techniques and methods used to tackle problems in these areas, to publish papers in refereed professional journals, and to participate and give talks in conferences for undergraduates. The REU concludes with a poster conference in which undergraduates doing summer research in all the UCSB departments present their results and make it accessible to non-experts in the area. Previous projects and publications as well as more information about the program can be found on the website http://math.ucsb.edu/REU. This site is supported by the Department of Defense in partnership with the NSF REU program. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.