Advice from Math Majors?

Advanced Calculus is a senior-level class at my university that is also heavily proofs-based, so taking it to avoid Abstract Algebra doesn’t make sense if your courses are structured similarly to the ones at my university. If there’s anything along the lines of Introduction to Mathematical Thinking and Discrete Structures, you might want to take that as an intro to proofs course.

Again, Numerical Analysis often has ODEs as a prerequisite, and even if it’s not a prerequisite, it’s useful. I wouldn’t recommend talking them simultaneously.

It seems like a jumble of unrelated math courses. What is your goal? If you’re planning to do financial math or other specific area after college, it’s one thing, if you’re trying to sample various areas of math, it’s another. If you’re not completely sure you want to pursue a career in math, branching out is better, maybe take another science course, or a foreign language.

Yea, to take advanced calculus you need to take at least real analysis first.

Often there is an Advanced Calculus class, which is only requires Calculus III. That was what I meant. If I knew the school and its classes, I could advise you on classes. As indicated, I would recommend less advanced, less theoretical,and more focused on classes relevant to financial math.

I would be careful with taking random upper division math classes, as some are theoretical or more advanced than they may appear.

I have a math degree from Johns Hopkins, so I am not some student or someone off the street.

From that Spaces class, this looks like University of Iowa. I looked at the courses, and I would recommend considering the Introduction to Discrete Math and Introduction to the Theory of Numbers, which are less advanced sort of theoretical classes. Even though you are interested in financial math, you could consider the engineering differential equations and vector calculus classes.

Numerical Analysis and Financial Math are good choices, but the courses I mentioned are less advanced and theoretical than Abstract Algebra, ODE, and the spaces course.