In Gems of Linear Algebra (Winter 2027), 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 
Knowledge of linear algebra at the level of the first quarter of the Fundamentals of Higher Mathematics sequence is required for this class.
In winter 2027, this class will meet for ten consecutive weeks. Everyone will attend lectures online on Mondays from 6:30–8:30 PM Pacific time, from January 4th through March 8th. Online students will attend problem sessions on Tuesdays from 5:30–7:30 PM Pacific time, from January 5th through March 9th. In-person students will attend problem sessions on Wednesdays from 6:30–8:30 PM Pacific time, from January 6th through March 10th.
Applications for the winter 2027 class are due November 22nd, 2026. After that, we will continue to accept applications on a rolling basis while spots remain. Click here to apply!
