Good evening guys, I now announce that I am entering the second *hard* half of mathematics, in college! Courses I have finished: Calculus I Calculus II Calculus III Differential Equations Linear Algebra Foundations of Mathematics Operations Research I am registered for two math courses next semester: Complex Analysis Theory of Numbers Now, as you can see, the courses I am registered for are certainly different than the courses I have been in (or are they?) and I am honestly quite worried about what the semester will hold. I haven't really been involved in any proof-heavy mathematics course instead of the introduction to proofs ones. What should I expect, and how can I best prepare myself to do well? I hope to one day get a PhD in mathematics. Note: I have a sciency background, especially in biology, chemistry, and physics.