You want to learn more about both pure and applied mathematics. Pure math is very proof heavy which is excellent for self learning because you never have to tak

You want to learn more about both pure and applied mathematics. Pure math is very proof heavy which is excellent for self learning because you never have to take anything on faith. Proofs are meant to be very clear explanations. One of the best resources for learning in this way is to find books that are structured to have you develop the theory via the problem sets. Of the top of my head, Tao's Analysis books and Atiyah & MacDonald's Commutative Algebra book are exemplars of this style. These books often show the basic definitions, some results, and then break up remaining results into step by step problems. Proofs will be the hardest part to wrap your head around. Once you understand proofs, can read them, the remaining is going to be a question of time. Think of it like programming: you can't learn by reading, lectures, etc. You need to learn by doing. In this case, the doing is doing proofs.