To be honest most of those are covered at a good-enough level in the sophomore and junior years of a math undergrad. You don't need measures, differential geometry, or even epsilon-delta analysis to do ML which pins the calculus requirements pretty much to whatever proper multivariable calc class one takes in their sophomore year
Edit: if my school wasn't so obsessed with teaching CS majors diffeq (probably just as a gpa filter...), they could already fit in the requisite math for a solid ML understanding
I would argue that you need measure and differential geometry to understand Support Vector Machine and the kernel trick properly.
I think my contention is less things like being formally introduced to ‘epsilon-delta analysis’ (not sure what that is) but more that people trying to cut corners by skipping a semester of differential calculus tend to also skip a big part of the explanation around how models really work. They tend to not grasp what is convergence, get very confused in higher dimensions, and assume ‘harmless’ short-hands like: ”you should aways normalise your data, in some cases, you need to, but why actually remember why, just do it”; “as long as it’s not overfitting, the model is fine” -- without really much recourse when things are not acting as expected.
You need differential calculus in R^n, but there's no need for the full force of differential geometry. Also, I don't think that measure gains much in terms of understanding, but it certainly is needed to do some proofs the proper way.
I agree that cutting corners is something I would be super skeptical of in this degree. It should really be an offshoot of a mathematics program, not a CS program with the bare minimal mathematics included. It's end goal is probably PR, money grab, and pumping out students that are really attractive for doing analytics grunt work.
Edit: if my school wasn't so obsessed with teaching CS majors diffeq (probably just as a gpa filter...), they could already fit in the requisite math for a solid ML understanding