Gems of Linear Algebra

In Gems of Linear Algebra (Winter 2023), we will look at some especially interesting applications and theorems in linear algebra. For instance, you may know what determinants are, but do you know how determinants can be used to solve combinatorial problems? It turns out that many combinatorial problems have solutions that can be expressed very cleanly in terms of determinants.

Another common theme in this class is spectral graph theory. Given a graph, we can associate a certain matrix to it. The eigenvalues of this matrix can tell us many interesting things about the graph. A concrete problem we will solve is showing that the complete graph on 10 vertices is not the union of three disjoint Petersen graphs.

Then there’s the question of matrix multiplication. The standard method of multiplying two n\times n matrices takes around n^3 operations. But there are faster algorithms, and we’ll look at some of them.

Knowledge of linear algebra at the level of the first quarter of the Fundamentals of Higher Mathematics sequence is required for this class.

This class will meet January 9–March 15. Everyone will attend lectures online on Mondays from 6:30–8:30 PM Pacific time. Online students will attend problem sessions on Tuesdays from 5:00–7:00 PM Pacific time. In-person students will attend problem sessions on Wednesdays from 6:30–8:30 PM Pacific time.