Ask HN: How to self-learn math?

I'd start with this video to get an overview of all the topics and areas that mathematics entails (some might be unknown to you) https://www.youtube.com/watch?v=OmJ-4B-mS-Y . Then you go ahead and research a bit what sounds interesting to you and then you might google that topic and add "foundations" to that google search. It's just that most school/university math is heavily focused on analysis and algebra but there is so much more!

Khan Academy is pretty good, though in my experience most of the videos focus on the way high-school courses are structured rather than teaching in a method that is the most intuitive (if you're planning to dedicate more time than an average high-school class timetable then it would make sense to learn in a more methodical way than the "scatter shot" that most high school curricula use).

Unfortunately a lot of the good "starting out" maths textbooks I know of are basically university level (though it should be noted that first-year of university mathematics is basically re-learning all of your previous mathematics knowledge but with new insights). While I wouldn't stop you from trying to read a university-level textbook, most of them are structured in a way that requires some familiarity with the topic before reading.

I have just the book for you: the essentials of high school math for adults: http://www.lulu.com/shop/ivan-savov/no-bullshit-guide-to-mat...

If you like this one, you can followup with the MATH&PHYS book which covers mechanics (PHYS101) and calculus. And if you like that one, you can follow up with the liner algebra book.

All along the way, I recommend you try solving exercises and problems using pen and paper. Ideally you can also create custom "test questions" for yourself using SymPy https://minireference.com/static/tutorials/sympy_tutorial.pd... 1. start with a simple math question or equation related to what you're studying right now, 2. solve it by hand, 3. compare your answer with the answer obtained by SymPy.

Good luck on your journey. Math is very deep so don't be in a rush. Enjoy the views along the way!

If you love math, read the books that interest you most, and read about math used within the context of your interests. You will get much more out of that than reading books that others told you about. And you will also stick to it and turn it into something you enjoy rather than feeling guilty for not reading enough about math in a context you cant strongly relate to or be attracted to. Take advantage of your interests.

Ok, I'll take a crack at this:

Up to high-school level:

1. Precalculus: Precalculus: A Prelude to Calculus - Axler

2. Calculus: The Calculus Tutoring Book - Ash.

College:

3. Preparation for Collegel-level maths:

3a. General prep for high level maths: How to Study as a Mathematics Major - Alcock

3b. Proof writing: How to Prove It - A Structured Approach - Velleman OR Book of Proof (2nd ed) - Hammack (it's free!)

4. Mathematical Analysis:

4a. Good prep for Analysis: How to Think About Analysis - Alcock

4b. Understanding Analysis (2nd ed) - Abbott OR Yet Another Introduction to Analysis - Bryant (has full solutions) OR The How and Why of One Variable Calculus - Sasane OR Mathematical Analysis - A Straightforward Approach (2nd ed) - Binmore (has full solutions)

5. Discrete Mathematics (a combination of set theory, combinatorics, a bit of discrete probability and graph theory): Discrete Mathematics - Chetwynd, Diggle

6. Linear Algebra: Linear Algebra - A Modern Introduction (4th ed) - Poole

7. Probability: Introduction to Probability - Blitzstein, Hwang + online course https://projects.iq.harvard.edu/stat110

8. Statistics: (for Bayesian) Statistical Rethinking - A Bayesian Course with Examples in R and Stan - McElreath + online course https://www.youtube.com/playlist?list=PLDcUM9US4XdM9_N6XUUFr...

Usually you'll be doing courses on #4, #5, and #6 simultaneously.