Method of characteristics for first- and second-order partial differential equations, conservation laws and shocks, classification of second-order systems and applications.

Data science methods and their mathematical foundations: linear regression, classification, and clustering, kernel methods, regression trees and ensemble methods, dimension reduction.

Core topics in differential, including: Lie groups, curvature, and relations with topology.

This course will cover important topics in linear algebra not usually discussed in a first-semester course, featuring a mixture of theory and applications.