I find that the best way I learn is by writing or typing because I actively engage with the math at hand. Consequently, I would describe my notes as broadly falling into one of two categories: Either fleshed out or condensed proofs from texts, class, or monographs. That being said, I acknowledge the absurdity of this old habit.
Occasionally, I strive for speed rather than conciseness and lucidity. During such occasions, experience has shown that I may give long, over-wrought proofs for statements which have a much shorter proof. If you believe that you have found a proof for which this is the case, or simply have a slicker proof, feel free to email me! Finally, some stylistic remarks: I abuse the ease of creating table of contents, so I break up my notes into smaller files.
At some point (?) I'll get around to uploading and organizing everything. You may deduce my plan from the skeleton I have left.
|Analysis (Broadly)||The Stone-Weierstrass Theorem, Filter Bases and Tychonoff's Theorem, Construction of Measures and Regularity of Measures, Measurable Functions and Integration, Product Measures, Fubini's Theorem and More Integration, Modes of Convergence, Elements of Functional Analysis|
|Algebra||Elements of Group Theory, p-Sylow Theorems, On Solvable and Simple Groups, On Abelian Groups, On Semidirect Products, (the following is incomplete and in a somewhat rough state) Semisimplicity and Representation Theory||Point-Set Topology|