Hey Imartel -- I've been in a similar situation. I think my first starting point was "Mathematics and the Imagination" or "Gödel's Proof." Mathematics and the I

Hey Imartel -- I've been in a similar situation. I think my first starting point was "Mathematics and the Imagination" or "Gödel's Proof." Mathematics and the Imagination is a good high level overview, and would provide some foundational notions that'll reappear repeatedly -- but, it won't given you any practice in mathematical methods. For that I would recommend "What is Mathematics?" by Courant and Robbins. Can be pretty challenging, but you'll actually get somewhere if you put effort into it. If you haven't had much experience with proofs, it's worth focusing briefly on the process of proving explicitly as a preliminary. That's actually a good thing to do with another person or in a class -- can be pretty difficult to get some of the subtleties involved, and to know when you've done things correctly or not. I mention "Gödel's Proof" because it's the first thing I came across that informed me I am in fact interested in mathematical systems. I'm more interested in architectures than problem solving though. If you suspect that might be the case for yourself, might check it out -- it's about 100 pages.