Speaker
Description
This talk will discuss the integration of undergraduate research and project-based learning in both abstract and computational linear algebra. Specifically, it will highlight a research training course focused on the mathematical foundations of machine learning and the analysis of human brain connectivity.
Throughout a summer research program and a Python-based numerical linear algebra course, students are trained to apply computational linear algebra, matrices, and graph theory concepts to real-world datasets. The central project involves investigating structural brain networks derived from $90\times 90$ connectivity matrices obtained from MRI data. Furthermore, students analyze the spectra of adjacency matrices and use computational linear algebra tools to identify structural patterns and hubs within human brain networks.
We will discuss that by engaging students in data-driven projects, students develop proficiency in numerical methods in linear algebra while learning the concept of eigenvalues, eigenvectors, and graph representations. Also, this presentation will reflect on student learning outcomes and the pedagogical benefits of using data to fill the gap between classroom theory and interdisciplinary research.