In high school I was a good maths student and took AP Calculus BC my freshman year and got a 5 and then took Multivariable Calculus, Linear Algebra, Differential Equations, Introduction to Mathematical Proof, Real Analysis, Complex Analysis, and Abstract Algebra through a dual enrollment program at the University of Maryland-College Park and at a local community college and received mostly A's and B's but I struggled quite a bit with a lot of the proofs and problem sets in the more difficult courses. Next year, I will start college I will probably take courses such as abstract algebra and topology my first year and by second year start graduate level math coursework but I am extremely worried that I am ill-prepared for the level of abstraction in these courses and that my college GPA will get destroyed immediately. My questions are:
What is the recommended number of math courses per semester at that level?
How do I make sure I do not overwhelm myself and burnout?
What courses are good preparation for graduate school in maths and how should I pace myself? Should I try to specialize in a specific field of math this early?
What is a good academic pathway for someone like me?
If my school offers a combined BS-MA degree for math and I could complete it in 4 years, is it worth it? And is it riskier to graduate early from college (in 2-3 years) and then apply directly to a doctorate program? If so, what are the risks?
Finally, how do I learn whether or not I will do well in research and whether getting a doctorate degree is a right decision for me? How do people usually find out? What process should I go through before applying?
Any advice/encouragement/experiences would be very much appreciated. Thank you. Is there anyone who has been through a similar situation?