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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.

The kind of math taught in this this class generally covers the same topics as Calculus I-III, Linear Algebra, and Analysis. But it starts completely from the beginning, from first principles. So you have to start with number theory, set theory, and other fundamentals and build up to things like derivatives, the fundamental theorem of calculus, the various theorems of linear algebra, etc, proving everything with complete rigor. You really get super solid understanding of all the intricate, abstract details that are glossed over in math classes designed for science and engineering majors.

And like I said, for most people, even most people in highly qunatiative fields, that kind of stuff is useless. It's only useful for people who want to spend their lives proving thoerems.