In the mean time, I’ve noticed my maths isn’t as strong as I’d like it to be. That aside, I’ve also taken a big interest into calculus.
Are there any online courses (free or non-free) that would allow me to learn mathematics either through self study, or as a MOOC? I’ll gladly take undegrad level courses. I just want something structured.
I’ve found that even trying to really study through books things like number theory, proofs, and integration takes huuuuge time investments. I feel like this will be less so with a structured course and teacher.
You have 16 weeks from the date of registration to complete each course. The courses themselves have weekly homework, two midterms and a final. You must find an eligible proctor to complete the midterms and final in person, but otherwise you need not go anywhere. Each course costs about $1500 - 2000. The lectures for each unit are video recordings of lectures in the corresponding course onsite at UIUC. There is also a certificate you can earn, but it's primarily focused on completion of lower-level courses.[2] Your homeworks are graded (with feedback) by a lecturer or math TA at the university. There are also remote office hours available.
UIUC is probably the highest caliber mathematics program which offers something like this. It's generally difficult to find a top ~20 math university willing to support online, self-paced study for credit. The ones which do offer such a system are usually very expensive[3] or predominantly focus on lower-level courses like a simple calculus sequence.
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1. https://netmath.illinois.edu
2. https://netmath.illinois.edu/academics/certificate-program
3. https://cvn.columbia.edu/program/columbia-university-applied...
He has an amazing ability to break math down into intuitive visuals which highlight the underlying nature of math, rather than being hyper focussed on a specific problem. For myself, the videos have allowed me to pick up other/adjacent math concepts significantly easier because I've developed a signficantly better understanding of what's happening "under the hood", so to speak.
Might be worth a quick look at least!
Yep, that's how to do it if you want to do it well. Practice. There's a reason why these degrees take so long. I would advise against just about any online course where you only watch videos and get the feeling that you've learned something while in reality you retain close to nothing.
Some older threads:
https://news.ycombinator.com/item?id=19811715
I would start with linear algebra. This post [1] links to a great course. Then you might want to do a course on multivariate calculus and a course on optimization but it's not really required. Second, I would do this [2] course on machine learning.
After these two courses, which would probably take you 3 to 4 months if you have a job, then you'll have a better idea of what math courses to take.
Final note, when I say do a course, I mean watch a lecture, take notes like you would do in a real class, go to the course website, go through the lecture notes, do the homework set associated with the lecture, and then go to the next lecture. Just watching the lecture, especially for a math lecture, especially of you're not familiar with the subject, is not as helpful.
[1] https://news.ycombinator.com/item?id=19812266 [2] https://www.youtube.com/playlist?list=PLA89DCFA6ADACE599
There's an ML math prep book https://mml-book.com/ which is basically a crash course, and a series of lectures here for a background in math for an intro machine learning course at CMU https://www.youtube.com/user/professorgeoff though note they aren't as long as they seem, as these were live lectures so they start late, have breaks between exercises, etc. If you've read the Elements of Statistical Learning 2e you likely know much of this already.
Personally my recommendation is go through a Wilberger course, this set of undergrad lectures is for the Stillwell book 'Mathematics and it's History' https://www.youtube.com/playlist?list=PL55C7C83781CF4316 it will intuitively cover differential geometry, topology, group theory, polynomials etc, to the depth of Stillwell's book and if you see something that interests you or that you forgot, then you can pursue it taking formal courses. I'd recommend his Linear Algebra course too on the same youtube channel he uses clear definitions for everything so when you get to abstract 3D vector spaces it makes sense.
Anybody with a complete shit background in math like I used to have try the Wildberger foundations playlists on the same channel watching how he writes proofs, then pick up some large book written by Knuth and start attempting the exercises as a weekly hobby, which will now be possible to do. This is also how you retain these skills by using them on a regular basis, at least for me anyway.
There is no royal road to geometry. Try this: https://aimath.org/textbooks/approved-textbooks/
Aside from that find yourself a tutor over Skype and crack on.
Just be sure you know what you’re getting yourself into. Unless you are one of the tiny number of people that have a genuine interest in maths, be prepared to slog through things you find senseless or boring in order to get to the prize. Further, and I think this is very true: there are no shortcuts. If you can implement something like mastery learning you will be all the better for it and if you don’t you may just regret it.
Finally, think really carefully about how you’re going to retain the maths you learn because if you don’t you can be sure that a month after your exam you won’t remember a scooby.
I am based in the UK, and we have the Open University. I am currently taking a Mathematics and Physics degree with them.
The content is not directly equivalent to an undergraduate degree (probably around 40% of a normal undergraduate here in the UK). But they have lectures, assignments and examinations and you get a proper degree certificate at the end.
I have friend who is Spanish and he has been taking a distance Mathematics course with a Spanish University. That again seemed to be an excellent course (he is heavily into Category Theory).
"Former students of the OU appying for a Masters at Cambridge have a 23% chance of getting of an offer. That's a bit below average but shows it is more than possible."
The level 1 courses are less complex than first-year regular uni because they'll take anyone and they have to get them up to par. But it quickly scales up.
At level 2 maths I covered all the core subjects (i.e. differential equations, multi-variable calculus, fourier analysis, etc.) But each of these was just a chapter in the course (approx. 2 weeks of study). Whereas in normal undergrad they would be perhaps 8-10 weeks worth of lectures each.
But level 3 were certainly really great. The Quantum Mechanics covered everything up to perturbation theory, and the Cosmology module was very comprehensive and the Pure Maths courses covered Group Theory up to Sylow Theorems and Metric Spaces.
So, certainly if someone is considering a Maths course I would recommend the OU. But the cost is way too high for what you get.
Well yeah, it's like three years of full-time study to get to an undergraduate level. Doing that part time is going to take you a decade or so. You need to put the time in. I'm not sure there's a shortcut.
There's no 'Royal road', as they say.
You used to be able to get a very interesting degree in maths with chosen specialisms in various pure and applied areas for about £3600. Might have been a bit more for people from outside the UK, but not massively.
There's little choice of courses now.
