4 ms·

Unless you mean some sort of differential topology, those are rigorously covered in and respectable math undergraduate.

by physguy1123 8y ago

bertil 8y ago
I believe that’s the point of contention: I’ve you’ve gone through those programs, you are a graduate.
- physguy1123 8y ago
  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
  - bertil 8y ago
    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.
    - physguy1123 8y ago
      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.

Unless you mean some sort of differential topology, those are rigorously covered in and respectable math undergraduate.

bertil 8y ago

I believe that’s the point of contention: I’ve you’ve gone through those programs, you are a graduate.

physguy1123 8y ago
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
- bertil 8y ago
  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.
  - physguy1123 8y ago
    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.