What math to take after Linear Algebra? In Linear Algebra class we're covering Vector Spaces and it's the most fascinating thing that I've ever seen in mathematics class. I'll be majoring in Actuarial Science and I was hoping to take something abstract, what could I take? I would like to understand how to write proofs, and above all, see something that isn't calculus. I'm not at the university yet and the highest math offered is the one I'm taking at the moment. I'll be transferring after the summer.
I was hoping to take two classes that don't have to directly contribute to my major. I would consider them as a fun classes that I would do serious work. 
 A: If you like vector spaces and such, you'll probably like abstract algebra more broadly. An undergraduate class will cover group theory and may go further than that depending on the curriculum. You'll also be exposed to proof writing in earnest. Maybe look into rings, fields, modules and algebras over fields on your own time.
Moving away from algebra, you might try a course in topology or geometry, though the latter would likely involve calculus. The former might be a refreshing departure from your prior math education and would also sharpen your proof writing. Intersecting the two fields, you might try to find an introductory course in Lie theory, the study of Lie groups and Lie algebras.
Speaking to Tony's answer, it might be that your institution lists real analysis as a prerequisite to topology, though I find that logic to be sort of backwards as the former is a special case of the latter.
A: Most maths programs would have you next take real analysis (called fundamentals of analysis 1 at my university). You will study proofs, and more abstract maths. I would also recommend number theory.
A: Take Dynamical System, you won't regret it! One of my favourite math classes in college.
