[susanrigetti]

I suggest taking another look at the list and comparing it to the required courses of the undergraduate math majors at the top 20 universities in the USA.

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.).

[mrjangles]

I have never met a physics student that even knows what functional analysis even is, despite it being at the core of quantum mechanics. I can't even imagine why someone in a physics department would learn about measure theory. True that any student learning General Relativity will get an introduction to differential geometry.