I found your comments interesting, @ucbalumnus, so I did a check of a LAC’s math offerings. The one I checked has 25 courses on the 300 or 400 level. This seems like a lot to me, but I don’t know enough to say what this would mean in terms of your hypothetical “very advanced in math” student.
Your post seems like a quite appropriate prompt for the OP’s next stage. For the moment, though, I think the intent was to illicit a Rorschach type of quick response. Not a bad idea, since the kind of answers provided may not be available elsewhere.