Strong duality for linear programs

In this post, we prove the strong duality theorem for linear programs, which says that if either the primal or dual is feasible, then their optimal values are equal.

Interior point method

In this post, we begin describing a basic interior point method to solve a linear program. We follow material from these notes by Professor Michel Goemans (relevant lectures are 6,7 and 8), filling in the details.

Basic properties of the Laplacian

In this post, we lay out the basics of spectral graph theory - the study of graph structure through the lens of linear algebra. Some of this material is based on a lecture for 6.854 given by Professor Aleksander Madry, and these notes by Professor Dan Spielman.