REU Site: California State University, Fresno Research Experiences in Mathematics

California State University-Fresno Foundation, Fresno CA

Investigators

Abstract

The California State University, Fresno summer REU will serve 24 students during the summers of 2016-2018. The objectives of the program are: (1) to involve and engage undergraduate students in research in mathematics; (2) to increase the involvement of underrepresented and minority students in such research and to encourage them to consider attending graduate school; and (3) to afford students from institutions with limited research opportunities the chance to experience mathematics research. Students will work in pairs on research problems of current interest, often building on work completed by past participants of the program. Each year, a senior faculty mentor will pair up with a junior mentor in supervising student research, so as to broaden the impact of mentoring and collaboration. The program will continue to provide its participants with a supportive and welcoming environment, in which students are challenged to grow academically as well as professionally. To this end the program will provide workshops on improving writing and speaking skills, research methods, and general attributes of academia. The research areas for this cycle will be knot theory, complex analysis, analytic number theory, statistics, finite geometry and combinatorics, and applied mathematics. More explicitly, participants will study knot and link invariants, the distribution of zeros of entire functions, exact zero loci of polynomial families whose generating function is rational, volatility modeling, minimal dominating sets and blocking sets in finite geometries, and numerical implementations of computing algorithms. Students will give weekly presentations, and will complete three final products: a polished 20 minute talk, a professional poster, and an article quality research report. Guest speakers will give lectures on topics intended to broaden students' mathematical horizons, and will engage program participants in scientific discourse, both encouraging students to delve deeper into their research topic, and validating their efforts to date. The Fresno State REU will continue to participate in the NSF REU program-wide effort to involve underrepresented minority students in research and to inform all students about career opportunities available to them both in academia and otherwise. Students will leave the program having studied a small area of mathematics deeply, having improved their oral and written skills, having made new friends and connections, and ready to be further challenged as an undergraduate student, graduate student, or industry professional.