Topics in Theoretical Computer Science: An Algorithmist's Toolkit
MIT's graduate course, taught by Jonathan Kelner, surveys geometric techniques that recur across modern algorithm design rather than sticking to one problem domain. Lectures move through linear and semidefinite programming, spectral graph theory, metric embeddings, and convex geometry, showing how each tool cuts through problems in optimization, approximation algorithms, and combinatorics. The course materials on MIT OpenCourseWare include full lecture notes for each session and problem sets that ask students to apply the techniques to concrete algorithmic questions rather than just follow proofs. There is no video lecture series, so the notes carry the course, but they are detailed enough to substitute for one, building from basic linear algebra and probability up to research-level constructions like Cheeger's inequality and low-distortion embeddings. It suits students who already have a solid grounding in algorithms and want to see the mathematical machinery behind the techniques they have been using as black boxes. Free to audit, as with all MIT OpenCourseWare content.