| It's just that it is very much a "mathematics for engineers" style course. I think very few of the subjects outlined there give you a flavor for what "real" mathematics is really all about at all (except for algebra, which you do mention). Apart from the applied stuff you mention, the real core of a mathematics education involves, I think, 4 main areas with significant overlap Group A:
number theory, graph theory, combinatorics which shares concepts with Group B:
Algebra, Topology, complex analysis, differential geometry, metric spaces...etc which shares concepts with Group C:
Functional analysis, measure theory which shares concepts with Group D:
probability and statistics. As for the applied math that you mention, you should really need to add vector calculus and I'd highly encourage anyone to take a course on fluid mechanics (from a mathematics department instead of an engineering department) to get a real feel for vector calculus in action. |
Real analysis, complex analysis, topology, and number theory are there (topology and number theory are both listed as electives since most math programs categorize them as such). Graph theory, functional analysis, differential geometry, probability, and statistics are almost always either electives or graduate courses.
It’s funny, because most of the things you mention as “real math” are things that many math undergraduates don’t learn (not until graduate school at least) but that physics students learn as undergraduates (differential geometry, measure theory, functional analysis, etc.).