Alright I'll give you a basic overview of what I've taken really quick: Calc I-Diff Eqs (Boyce and DiPrima, nothing special for my Calc courses) Linear Algebra (Strang) and a course in Abstract Algebra (Dummit and Gallian) Discrete (Rosen) and an elementary Stats class Since my school is not especially strong on math, but has two or three strong professors, my adviser is having me take up to three directed studies next semester before I transfer out. My goal is to double major in Physics/Math somewhere. Here are some topics/subjects I want to cover: PDE Analysis (Real and Complex) Point Set Topology Differential Geometry Lie Groups/Lie Algebra Clifford Algebra Division Algebras! and probably some other topics I can't come up with off the top of my head. Now, I've been told that some of the topics are probably waaaaaaaaay above my head, but I mentioned them to give you an idea of my direction. Like, I believe he said I had a long way to go before I can get to Clifford Algebra, but Lie Algebra he thinks I can get through after Analysis and maybe some more Abstract Algebra. He told me that it would be very difficult (at a small school) to find a differential geometer...so that's something I'm probably going to have to put off and so forth. The professors who I can work with are specialized as follows: the first did a lot of research into harmonic analysis, but feels he would be willing to teach me Point Set Topology along with someone else doing Analysis, he taught me Linear Algebra and is my adviser. The second is a surprisingly well published mathematician who did his PhD under Rudin and will teach anything Analysis related, maybe Lie Algebra with the recommendation of my adviser. The third just got his PhD from a relatively small school, but he does a lot of interesting work in Combinatorics and Abstract Algebra (he's teaching my Abstract course now). Does anyone have any recommendations on what I should ask to study? I'm asking to do a Real Analysis direct study (so I can cover material at a different depth than the course offered) and Abstract Algebra directed study (maybe in Groups?), but the option of doing Topology is really appealing as well. If anyone comes up with something of a reasonable level they think I should consider, let me know. I'm looking at mostly "advanced undergraduate" and early graduate material. Thanks in advanced for your help! I'm really hoping I can make things work out and have an awesome set of courses next semester.