REU Site: Mathematical Modeling at UCLA

University Of California-Los Angeles, Los Angeles CA

Investigators

Abstract

This award provides funding for a three-year REU site to support twelve undergraduate students for eight summer weeks each year to perform frontier level research. Student participants will learn to build mathematical models for problems from across the sciences. Research projects will focus on three areas: (1) Biology: how fungal spores cooperate to create networks; (2) Social sciences: mathematical patterns underlying urban crime; and (3) Physics: predicting the catastrophes that occur when industrial or geophysical slurries start to flow. Students will be recruited from outside the spheres normally reached by mathematics REU activities, including community college students and mathematics education students, and an existing university framework will be utilized to attract under-represented groups. Research activities are carefully designed to ensure that students with widely differing levels of experience are empowered to contribute vitally to each project. Additional outreach efforts will be made to enrich teaching of mathematical modeling in high school and middle school classrooms across California. Mathematics education students recruited to the REU site will create new lesson plans and teaching materials based on their research experiences and test them in real classrooms. These lesson plans will then be shared with teachers for wider use. The modeling topics involve different application areas, including newly emerging interfaces between mathematics and fungal biology and between mathematics and criminology. Specific projects will include: (1) Analyzing spore cooperation and competition within microfluidic chambers, and modeling these interactions using evolutionary game theory; (2) Looking for scaling laws in the spatial and temporal patterns of gang violence in East Los Angeles; (3) Analyzing the flow of particle-laden fluid under gravity using the theory of shocks. REU participants will study a broad spectrum of modeling methods including differential equations, stochastic and agent based models, and scaling theory. All projects require that modeling be fused with real data, which in two of the projects will be collected by students themselves through experiments. Participants will receive training in model fitting, image analysis, scaling, data analysis, and error estimation. The program is designed to create immersive research experiences for students ranging from students early in their college careers to advanced undergraduates contemplating graduate school, as well as future expert teachers. A final goal of the program is the creation of field-tested learning materials based on the REU projects that will be taught to hundreds of middle school and high school teachers annually.