things i really want to learn

I have started my PhD and I’ve realized I want to learn a bunch of important things. Not all of them are directly relevant to my PhD topic.

In order of importance:

1. Real Analysis I (80% done) - I still need to learn about pointwise convergence, uniform convergence and more importantly metric spaces (and a bit of topology). Liebl. I also want to do 3 chapters in Liebl volume II. Problem is I’m struggling to find time.
2. Intro to manifolds by Loring Tu. Idk how many chapters to do.
3. SAGT - spectral graph theory - first 4 chapters and then the heat kernel chapter.I want to understand the connection between the heat kernel and the Laplacian on graphs.
4. Measure theory. Maybe not super relevant by maybe first 4 chapters of Folland. I also want to understand the connection between measure theory and probability theory.
5. Basic SDE theory
6. Information theory.
7. Functional analysis (MIT has an OCW course)
8. Dynamical systems by Srogatz. Kind of low priority.