HACKER Q&A
📣 dalleh

Is there a website specialized in mathematics courses?


I have a BSc in computer engineering and part of the major was just a couple of calculus and discrete math courses. I want to expand my knowledge in mathematics through online courses. Is there a specialized website that offers courses in various mathematics fields?


  👤 impendia Accepted Answer ✓
I am a math professor. In my observation, there is a huge amount of material available on the web, but it isn't very centralized -- especially at the upper levels.

My advice would be to get a book on any topic which interests you, read through it, and do a significant number of the exercises. You might try Epp's Discrete Mathematics, Hefferon's Linear Algebra, Colley's Vector Calculus, Dudley's Elementary Number Theory, Spivak or Apostol's Calculus (these go far beyond ordinary freshman calculus), Pinter's A Book of Abstract Algebra, among many others. Some of these books are expensive to buy new, but just buy older editions.

Resources like Khan Academy and 3blue1brown are also fantastic, and I have shared some of these with my students. I'd recommend using these as a supplement; if you rely on them solely then you'll develop vague intuition but not much else.

Also, with the pandemic, there are a huge number of traditional university courses that have moved online, and you could probably enroll in one for not too much money. Check the RateMyProfessor reviews -- you want a mix of positive reviews claiming the prof inspired them, and negative reviews complaining that work was expected. I have a RateMyProfessor review which complains bitterly that "homework is graded for accuracy and not completion". :)


👤 artagnon
I've self-taught myself undergraduate-level Mathematics, and am currently enrolled in an advanced Masters program specialized in higher category theory at Université de Paris. Here are some thoughts:

First, the amount I learnt on a day-to-day basis from self-studying in my free time pales in comparison to the amount I learnt from a structured course ending with an exam, in which you have to commit to studying 2~4 hours of math every single day.

Second, classroom lectures mainly act as a structured table-of-contents for working through various textbooks. The problem sheets they distribute in the tutorials are very helpful, as is the discussion of problems that some students might have got stuck in.

Graduate-level math textbooks are fantastic, and the authors have poured 10+ years of their lives writing them. No online course with cute interactive video can substitute them. Having said that, there are some video lectures that can act as good motivation for studying a subject. For instance, Wildberger's lectures on algebraic topology (find them on YouTube) are a great starting point for the subject.

You first have to decide on what you want to learn, by looking through various fields, and narrow your scope. Mathematics is a huge discipline, and you have to decide what you like, and work through the prerequisites in a disciplined manner.

I cannot emphasize the importance of working through exercises enough. All mathematics textbooks have exercises at the end of each section, a subset of which you must work through.

Having said all this, you might find the following site interesting: it contains a lot of unpolished notes from studying various math textbooks, but it requires a lot more work to be useful to a larger audience. Look through it, and pick something you like. On request, I might find the time to add some material.

https://artagnon.com


👤 sabas123
I would advice against resources like KA and 3B1brown.

I'm a firm believer that you don't truly understand material unless you also understand a proof for it. Ane while those resources are AMAZING for simple intuition building, they aren't sufficient.

Go pick up a book about proofs to develop mathematical maturity and then delve into some undergrad books for analysis (Abbott) or linear algera (Axler)


👤 laichzeit0
I'd like more math professors to make recordings of their courses. E.g. here is a pure gem [1]. This is a recording of a real analysis course from Rudin's principles of mathematical analysis (aka Baby Rudin aka the architect of many beginning mathematics students' misery). Anyone that's worked through this book knows the world of pain you're about to enter. I'd love if there was a similar recording for say, Charles Pugh's real mathematical analysis. I mean he's still alive, dunno if he still lectures from his book, but why not record one of those? It would be game changing for those who self-study.

Here's another request: Terrence Tao does a recording of a measure theory course.

Personally I find the Khan Academy, 3B1brown stuff to be a waste of time. It's too elementary and cutesy. That is not anything like what I've experienced real mathematics to be like. It is a continuous painful struggle.

[1] https://www.youtube.com/watch?v=ab41LEw9oiI&list=PLun8-Z_lTk...


👤 qz2
MIT OCW: https://ocw.mit.edu/courses/mathematics/

I mostly fudge together what I need from that and Khan Academy when I’ve forgotten something fundamental.


👤 iflp
It's probably way easier to decide on a subject you want to learn more about, and find the most approachable textbook / lecture notes on e.g. StackExchange. It doesn't make sense to choose courses (or even subjects to learn) based on whether video lectures are available.

I don't maintain a collection of these, but I can probably recommend

* Stephen Abbott, Understanding Analysis, for mathematical analysis and a little bit of real analysis

* David Williams, Probability with Martingales, for advanced probability

* Dym and McKean, Fourier Series and Integrals

Alternatively if you have a more cursory interest, you can probably check out Metacademy [1] which provides roadmaps to learning a variety of math (and ML) concepts.

[1]: https://metacademy.org/browse


👤 strangattractor
You may try https://mitpress.mit.edu/books/street-fighting-mathematics. It is free.

If you like learning math by programming https://greenteapress.com/wp/think-complexity-2e/ also free.


👤 smukherjee19
I heard this from a senior colleague of mine that he's been working through the book "How to prove it: A Structured Approach"[1] that show how to prove things in mathematics, and has quite good exercises.

Perhaps a hands-on approach such as solving the exercises while working through this book will prove beneficial and is complimentary to watching, say, KA or 3B1B.

[1]: https://www.amazon.com/How-Prove-Structured-Daniel-Velleman/...


👤 Alexss
https://realnotcomplex.com/ has a wide range of free textbooks and video courses collected

👤 auroranil
https://tutorial.math.lamar.edu/ is a good place to review continuous maths.

👤 isaacaderogba
As an alternative to getting a textbook, I would strongly recommend Krista King's maths courses. They're available through Udemy or her personal website [1][2].

Each section has a 1) written explanation, 2) video explanation with an exercise walkthrough and a 3) set of exercises. Each exercise also has a well-written walkthrough in case you can't solve them.

I've been working through them part-time for 4 months now, and it's honestly the first time that maths has clicked for me (I've found that most books tend to skip concepts which leave me lost).

[1] https://www.udemy.com/user/kristaking/ [2] https://www.kristakingmath.com/


👤 rramadass
I suggest spending less time with online lectures/videos etc. and more time with actual Books. The online stuff should be an adjunct to your study of books. Also it is best if you look at books dealing with a survey of all the relevant topics required for Science/Engineering before delving into specialized ones. To that end, i can recommend the following;

Mathematical Techniques: An Introduction for the Engineering, Physical, and Mathematical Sciences by Jordan and Smith - This book is really accessible.

Mathematical Methods for Physics and Engineering: A Comprehensive Guide by Riley, Hobson, Bence - A more advanced coverage of topics than the one above.

Mathematics for Physicists: Introductory Concepts and Methods by Altland and Delft - The coverage is excellent but somewhat challenging to read.


👤 app4soft
> part of the major was just a couple of calculus and discrete math courses

On Coursera[0] there are a lot of courses on math[1], including on discrete math[2].

[0] https://en.wikipedia.org/wiki/Coursera

[1] https://www.coursera.org/courses?query=mathematics

[2] https://www.coursera.org/courses?query=discrete%20mathematic...


👤 joeblau
This is one I’ve heard a lot on the Data Skeptic podcast. Great for math and science.

https://brilliant.org/


👤 chrisweekly
Slight tangent given it's not all about "courses" per se, but my all-time favorite math-related website -- https://betterexplained.com -- is remarkably good at aiding in the development of intuition and deep understanding. Enjoy!

👤 errantspark
Khan Academy is great for this.

👤 posed
Personal opinion: Mathematics should be learned with a piece of paper, a pencil and a sheet full of problems.

👤 henearkr
My own way to expand my knowledge was by going through textbooks and with a heavy support of Math StackExchange.

Maths is a very written-oriented domain, but still if you are more a video-oriented learner you can probably find a lot on Youtube, and a lot of great researchers have videos there.


👤 klunger
I am not sure what your "discrete math courses" were and if you have already taken these but, the Linear Algebra and Differential Equations courses on Kahn Academy are solid intros to the basics of those subjects.

👤 BatteryMountain
Doing Khan Academy then 3Blue1Brown got me through many mental blocks when it came to math stuff. I used KA during university and it really helped me, but wish 3BlueBrown existed back then as it has even better visualizations - this was key for me to make math interesting and to see why certain levers exist in math and what happens when you pull them (how changing formula variable values changes outputs).

https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw


👤 Arun2009
If you are in India, NPTEL courses are a possibility, but I've heard that it can be a hit or a miss depending on the lecturer. You get to write regular assignments, and a proctored exam for a certificate.

👤 ben_w
I’m working through the entirety of brilliant.org right now; some of its courses are specifically maths, and the skill level goes from introductory courses all the way up to maths-degree level topics.

👤 swiley
As much as I really hate to say it, youtube seems to have the best collection of recorded math lectures I can find anywhere. OCW has quite a few but only the ones from MIT. One of my professors only uploaded to youtube (and I think he was doing this without the administration knowing, they were generally hostile to recorded lectures and the official policy was that recordings of lectures should never be shared to non students for some reason.)

Besides that good math books are usually very cheap. I would highly recommend those over a website.


👤 saivan
I'm making youtube videos

https://www.youtube.com/channel/UCafIamqsRUHoRT4496jgvMQ

And I'm also working on a website that has a fair bit of the foundations:

https://treena.org/

Admittedly, we don't have a huge amount of the higher stuff yet. But we are making our way through steadily :) Hopefully it's of some help to you


👤 stakkur
I highly recommend http://schoolyourself.org/ over just about anything else (Khan Academy, etc.) It's free, and has a great interactive user experience. Algebra through Calculus.

👤 rbtprograms
I'm in the same boat as you and I just started taking classes at my local community college/university. Options are affordable and lots of online offerings.

👤 redwoolf
What sort of mathematics ought one to study if interested in designing programming languages?

👤 21eleven
Is there something like leetcode.com but for math?

👤 rorykoehler
I had the best results from mit ocw https://ocw.mit.edu/index.htm

👤 moonbug
books are still a thing.