Ask HN: Is there a website specialized in mathematics courses?

Can you speak towards what you self-studied to get to an undergraduate understanding of mathematics and what resources, or books you used in the process? I’m also interested in the resources you used or recommend for learning category theory.

Motivation and direction are important when starting out. I decided pretty early on that I wanted to be an algebraist, but would have to build some mathematical maturity before I could get there, so I had a rather shallow goal in the beginning: to be able to solve the previous years' math GRE papers. Off the top of my head, these were some of the books that I worked through:

1. Spivak's Calculus.

2. Johnstone's Notes on Set Theory and Logic.

3. Gamelin's Complex Analysis.

4. Hoffman & Kunz' Linear Algebra.

5. Dummit & Foote's Abstract Algebra; just the group theory.

6. Munkres' Topology; just the general topology.

Once I was happy with my preparation, I strived for a deeper understanding of Group Theory. I bumbled through Herstein, but didn't understand it very well. Then, I stumbled upon Artin's book, and worked through it using the outline provided on the MIT OCW course page, and I could confidently solve most of the exercises.

For category theory, the top resources that I would recommend are:

1. Mileweski's Category Theory for Programmers, the video lecture series. As is always the case with video lectures, this one can help motivate a Haskell programmer uninitiated in category theory.

2. Goldblatt's Topoi. It's fairly dated, but teaches category theory well, via its application to topoi.

3. MacLane's CatWork. I'm not especially fond of this one, but it's necessary to work through it.

The most important thing to understand when learning category theory is that it cannot be learnt in a vacuum: the subject is entirely vacuous, and you need to use it in other mathematical disciplines to give it meaning.

Good luck.

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/

I always appreciate when someone leaves the well-defined path and does something different, such as you self-studying Math and getting enrolled in a Masters program.

I am just curious about your process of actually joining the masters program. They usually require 2-3 letters of recommendation etc. How did you handle such requirements?

> Second, classroom lectures mainly act as a structured table-of-contents for working through various textbooks.

On a side note, actually studying math as an undergrad, I can't stress enough how much I agree with this, especially in a remote setup.

I started in late 2016. Initially, it was just during the weekends. I was a regular at the local coffee shop near my place in Boston: I'd go in with my iPad and some sheets of paper, spend 4~5 hours studying, while constantly consuming coffee. Then, I found a friend who had done a Bachelors in math, and we'd visit the local community college 3~4 times a week, and discuss general math and GRE problems on the blackboard for a couple of hours after work: it was a lot of fun.

In mid-2017, I moved to California and spent ~2 hours a day studying by myself, while maintaining a day job writing Haskell and Coq. Then, in late-2019, I quit my job and moved to India to study mathematics full-time (read: 4~6 hours every single day). I started meeting a professor at the local university once a week to discuss my solutions to problems in Miles Reid. We worked through Reid together. I also audited a course in algebraic topology at the university, simultaneously.

In mid-2019, I moved to Paris to continue studying part-time (1~2 hours a day) while working on a Coq project. After some shuffles, I found a professor I really liked, and we started working together. He wrote me the primary recommendation for the Masters program.

I hope the elaboration was more useful than two numbers.