Following the feedback on my earlier post about self‑studying pure math, I wanted to share a concrete example of lecture notes built around the principle “try to solve everything yourself first”.
This is an advanced linear algebra course aimed at readers who have already seen a standard linear algebra course and want to go deeper. It covers topics such as dual spaces, tensor products, complexification, Jordan normal form over the reals, and spectral theorems for normal operators. The emphasis is on conceptual understanding rather than the computational skills that are usually trained in a matrix‑algebra course. The first three lectures are intended to build the necessary prerequisites.
This style of learning has been actively developed in recent years. If this particular course feels too fast‑paced, you might consider starting with a more traditional text, or with an inquiry‑based introduction to proofs or linear algebra, and then returning to this material. If there is interest, I can also share the problem sets that typically accompany this course in a small‑group setting.
I would be very interested in your comments, critique, and suggestions, both on the course itself and on which approach to learning linear algebra left you with the best memories.