
Ask HN: Where can I do a self-study math degree online? - piqalq
My background is in CS and I’m currently working as an ML engineer, but I’m very eager to go back for a PhD soon.<p>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.<p>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.<p>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.
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ziddoap
This channel[1] (by the sounds of it) isn't exactly what your looking for, but
I feel like it's appropriate for the topic and might act as a supplement to
whatever course(s) you end up taking, depending on where you are having
difficulties.

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!

[1][https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw](https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw)

~~~
kyllo
Grant Sanderson has made a lot of great contributions to Khan Academy as well,
particularly in the Linear Algebra and Multivariable Calculus sections.

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dhkxh
> I’ve found that even trying to really study through books things like number
> theory, proofs, and integration takes huuuuge time investments.

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.

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throwawaymath
The University of Illinois at Urbana-Champaign offers a wide variety of
mathematics courses online for self-paced study[1]. The courses range from 100
- 400 level. 100 - 300 level courses confer undergraduate course credit at
UIUC, whereas 400 level courses are eligible for graduate credit. (Note that
you are not enrolled as a degree-seeking student in a mathematics program,
you're simply taking courses online).

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.

_____________________________

1\. [https://netmath.illinois.edu](https://netmath.illinois.edu)

2\. [https://netmath.illinois.edu/academics/certificate-
program](https://netmath.illinois.edu/academics/certificate-program)

3\. [https://cvn.columbia.edu/program/columbia-university-
applied...](https://cvn.columbia.edu/program/columbia-university-applied-
mathematics-certification-certificate)

------
gtani
Look at UIUC and Open University, MIT's OCW, community/junior colleges can
give you a big boost, there's probably a lot of other advice at /r/math,
/r/LearnMath and math.stackexchange.

Some older threads:

[https://news.ycombinator.com/item?id=19811715](https://news.ycombinator.com/item?id=19811715)

[https://news.ycombinator.com/item?id=18939913](https://news.ycombinator.com/item?id=18939913)

[https://news.ycombinator.com/item?id=19071050](https://news.ycombinator.com/item?id=19071050)

------
newen
I assume you're looking to do an ML PhD, so you probably don't need to learn
up on number theory. Mathematics is a huge topic, so you need to condense what
you're going to study down to a couple of courses. Also, ML doesn't use that
much actual maths, so you don't need to know proofs, real analysis, algebra,
differential equations, etc. Though doing a a decent proofs course is always
helpful everywhere.

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](https://news.ycombinator.com/item?id=19812266)
[2]
[https://www.youtube.com/playlist?list=PLA89DCFA6ADACE599](https://www.youtube.com/playlist?list=PLA89DCFA6ADACE599)

------
usgroup
University of London does post grad maths diplomas . They are solid and
somewhat structured for self study. They are also cheap .

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.

------
hackermailman
You should probably look up the undergrad math courses of the grad school you
want to go to, they will have lectures notes and textbook/chapter reading
recommendations so structured and you aren't going through enormous reference
books. Search the textbook name on youtube, often there will be some lectures
for it sometimes even by the author.

There's an ML math prep book [https://mml-book.com/](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](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](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.

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vymague
> I feel like this will be less so with a structured course and teacher.

There is no royal road to geometry. Try this:
[https://aimath.org/textbooks/approved-
textbooks/](https://aimath.org/textbooks/approved-textbooks/)

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arshadtskur
Not sure what you mean by online. Do you mean distance courses?

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).

~~~
bencollier49
I think your quote of 40% isn't right. From elsewhere on the net:

"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.

~~~
arshadtskur
In my experience Level 1 and 2 courses are not a match for normal Undergrad
courses, but certainly the Level 3 courses are.

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.

------
chrisseaton
> I’ve found that even trying to really study through books things like number
> theory, proofs, and integration takes huuuuge time investments

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.

------
bencollier49
The Open University in the UK is still a fairly solid bet, despite not quite
being what it used to be.

~~~
chrisseaton
What’s changed?

~~~
bencollier49
The range of choice in modules was radically cut and the cost of courses was
increased considerably.

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.

~~~
EliRivers
I did that; finished around 2015, I think. The fees went up while I was there,
but I have a half-memory that it went up in steps, or maybe if you were
already on it the hike wasn't so extreme.

In retrospect, paying somewhere around 3500 GBP for a masters (even if it was
basically "here's the textbook, see you in nine months for the exam!") that I
could do in my evenings and weekends was a bargain. I should have done more of
them.

------
gsruff
There are quite a few posts about this on HN, including this one 11 days ago.
[https://news.ycombinator.com/item?id=19811715](https://news.ycombinator.com/item?id=19811715)

------
la_fayette
[https://pimbook.org/](https://pimbook.org/)

~~~
faitswulff
The reviews on Amazon were not particularly kind - regardless, good reading if
you're interested in purchasing this book:
[https://www.amazon.com/gp/product/1727125452/ref=as_li_qf_as...](https://www.amazon.com/gp/product/1727125452/ref=as_li_qf_asin_il_tl?ie=UTF8&tag=mathinterpr00-20&creative=9325&linkCode=as2&creativeASIN=1727125452&linkId=ba980a3cac32bd38deeb15441b2f1151)

