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I was having a discussion with one of my old math professors from my community college (I'm in a four year university by the way) about my major in the STEM field. I asked her about how much math do computer scientists and physicists take compared to a mathematician. She told me that the only important math classes that those two majors need are differential equations and linear algebra, and discrete math for CS majors (which I understand). She tells me that all those math classes (Calculus, Diffy Q, Algebra) are all baby stuff and that real mathematicians take/use Analysis, Abstract Algebra, Topology, etc and you won't be seeing CS or physics majors using abstract algebra or any other high level math course (complex analysis may be of some importance to physics majors). Linear Algebra is probably closer to what pure mathematicians do since its not just about matrices and eigenvalues, but proving abstract theorems if they are true or exist, she told me and I have taken a linear algebra class before so I understand.

But i'd imagine that some CS and physics majors take more higher level math courses. I think some CS majors who take advanced math courses take more purer math courses as they deal with logic and some physics majors take more applied math courses like probability or partial diffy-q, is that right?

Also, how important would abstract algebra be to a CS major? I've always wondered if that would be more important than say discrete math, which most CS majors take, and discrete math is very logical and proof based, just like abstract algebra.