
Ask HN: What are the good online maths university programs - tjomk
About 10 years ago I graduated with master&#x27;s in CS but haven&#x27;t been using maths a lot, and want to catch up on that. I do not need a university diploma, but I was still thinking about enrolling because of the structured program. Are there any online alternatives to that, free or not, that I could do during the quarantine?
======
vmilner
In "Learn X the hard way" style, I'm planning to refresh my maths degree
fundamentals by working through some of the Cambridge Tripos material at
[https://www.maths.cam.ac.uk/undergrad/studentreps/tripos-
spe...](https://www.maths.cam.ac.uk/undergrad/studentreps/tripos-specific-
resources)

(particularly the Dexter Chua notes). This may be too hard without tutor
support, but I figure I can always find easier material if it gets too tough.

------
xupybd
I'm not sure what you want to learn but I found MIT to be very helpful when
doing my engineering degree. I find the lectures in my own university hard to
follow and wanted to look for more resources. I found that MIT had amazing
lecturers that took difficult topics and explained them simply.
[https://ocw.mit.edu/courses/find-by-
topic/#cat=mathematics](https://ocw.mit.edu/courses/find-by-
topic/#cat=mathematics)

------
rollinDyno
When you say catch up on do you mean you want to review what you’ve already
learned or you actually want to catch up with the literature in what used to
be your field?

If the former, I don’t see why you would go through a structured programme
again, you already know what the knowledge tree looks like and you can google
for the best textbooks or youtube videos for each topic or course.

~~~
tjomk
Bad wording, sorry. I meant to refresh the knowledge I already have and learn
the new things, ie go deeper into the maths topics.

What I studied during my cs course was just the basics: linear algebra,
mathematical analysis, probability theory, and physics. All beginner levels.

I do need to refresh my knowledge from 10 years ago in order to move forward.
I was thinking about taking the time off from work and spending a year in a
library reading books and learning more. The problem is that I don't really
know which direction to take, what are the good books for that. And this is
something I hoped a university program would solve.

~~~
rmrfstar
It is impossible to usefully answer the question without having an objective
in mind.

If you want to become a research mathematician through self-study, then
working through the qualifying exam syllabus for an established math program
could be helpful [1].

If you want practical skills in the fields you have listed, then a great way
to get them is to work through Gilbert Strang's OCW linear algebra course and
Feynman's lectures on physics. That means doing the problem sets, _all_ of
them. The former will give you linear algebra, the latter will give you
_useful_ analysis/probability/physics. If you diligently solve the P-sets, you
will probably be in better shape than 99% of people leaving university with a
BS/MS in math/stats/physics.

It is very easy to go down a rabbit hole that is not useful to a practitioner.
This is particularly true in analysis and probability theory. Almost no one
but a research mathematician needs to know about Lebesgue measures or Radon-
Nikodym derivatives or whatever.

[1] [https://www.math.harvard.edu/graduate/study-the-
qualifying-e...](https://www.math.harvard.edu/graduate/study-the-qualifying-
exam/the-qualifying-exam-syllabus/)

~~~
tjomk
This is exactly what I was looking for (and why I was asking for a university
course) - hints what to study, which books and lectures to use.

I'm not looking for a research career in maths but rather to refresh my
existing knowledge and deepen it even further.

Thanks a lot for the suggestions.

------
downshun
Khan academy

