Highly abstract math is not for everyone, both in terms of ability to grasp it, as well the need to know it.
The vast majority of people in quantitative disciplines do not need the stuff. Engineers don't need it. Even most physicists don't need it; only the really abstract theory guys need it. Some abstract economic and financial theorists might find it useful, but most don't.
This is a course that you only really need to pass if you want to be a mathematician who spends his life proving theorems. If you're an undergraduate, it's a very good idea to figure out whether this sort of thing is for you or not very early in your college career. Most who attempt it find it's not for them, and so they drop. That's how it should by.
My undergraduate institution also had a class like this, and I dropped by the middle of the first semester. If I stuck it out, I probably could have gotten a B-, but after talking with my advisors, I realized that the class wasn't necessary unless I wanted to be a mathematician, something I definitely did not want to be. I went and took the standard advanced calculus sequence that science and engineering majors take, and that proved to be an excellent move. It in no way hindered my ability to go get into a top Ph.D. program in Finance.
I took Calculus I, Calculus II, Linear Algebra and Matrices, Sequences and Series, Calculus of Several Variables, Probability and Statistics, the course with first order and second order equations, etc. that I can’t remember the name of, and Advanced Calculus For Engineers. Actually I dropped Sequences and Series and audited the rest after everyone in the class failed the midterm because the lectures were completely different from what he really wanted us to know. He erased what he wrote before you could even write it down. I did well on the redo midterm, but decided drop it anyway. I did write a program years later that generated Bessel Functions with Series, but even those kinds of advanced functions aren’t usually necessary with home computers and numerical integration. I wish I’d taken them all at the smaller less competitive college I started out in. I would have felt much more confident. Every once in awhile some guy would start talking about Hilbert Spaces to try to impress everybody, but my conclusion was that that kind of math wasn’t that practical. I think that was taught in an advanced upper level class though, not an advanced Freshman class.
Differential Equations. That’s the name of the course I couldn’t think of. Also the lowest grade I ever got in a math class, a B!