Ask HN: How to self-learn math?

https://github.com/desicochrane/data-science-masters

It's still evolving especially towards the latter parts - but the earlier math progression is pretty solid.

> If some 2-minute video gives you something actionable to do rather than going through a 2-hour chapter in textbook there is no point of going through 2-hour chapter. Knowledge is all about applying not learning the facts and saying it around to your friends I know it feels good but nothing comes out of it in real life.

There are optimal and suboptimal ways to learn things, sure. But some things legitimately cannot be reduced from a complicated textbook chapter to a straightforward YouTube video. You can improve exposition, but that comes with its own time efficiency trade-offs, and you won't meaningfully simplify the material without compromising significantly in depth of coverage. In particular, even extremely good video series like 3Blue1Brown's Linear Algebra have neither the breadth nor the depth to replace the material in any given chapter of e.g. Axler's Linear Algebra Done Right. The exposition is certainly clear, and you can get a nice overview, but you're actually not learning enough to apply the mathematics if you watch a video on it. Ironically, such a video is much more likely to leave someone able to talk about the subject but woefully incapable of actually doing it. The videos that can be used for learning are mostly lectures.

More importantly I think your conception of working through a chapter is incorrect. If you're spending a significant amount of time working through a textbook chapter, you're either 1) actively learning the material and doing the mathematics, not just passively reading it, or 2) you're not prepared for the material, and you're not learning efficiently. Finding a video to simplify the material doesn't resolve #2, it just disguises it. When you learn mathematics from a textbook, you should be applying the material by working through the exercises. You can't immediately jump into e.g. data analysis after learning linear algebra, and you certainly can't do so by watching a video on the subject.

I'm fully with you that replying to these questions with textbook recommendations is unhelpful, but not because they're textbooks. Textbooks are great! The hard reality is that you can't simplify most mathematics into an easily, quickly digested format, especially if you want to apply it. There are simply too many prerequisites for most material and too many unknown unknowns that can leave glaring blind spots. "There is no royal road to geometry" is a saying for precisely this reason.

They are very clear and straight to the point. She currently has courses on Fundamentals of Math, Algebra (I and II on the same course), Calculus (I, II, III, in separate courses) and Geometry and Trigonometry. She is also preparing some Probability & Statistics course and later a Linear Algebra one.

That is the only way I could self-learn Math without quitting after more than 12 years without doing math at all in real life. I was originally a Lawyer so I didn't care much for Math in school and didn't have anything relate to Math for all those years until now.

I tried a bunch of other paths, like challenges, For Dummies books, more advanced University open courses... Nothing stuck until her courses.

They are not free, but you can find basically permanent Udemy coupons to buy each course for USD 10.

Here is her profile: https://www.udemy.com/user/kristaking/

I'd strongly disagree with this. To the mathematically literate, concepts like "imaginary numbers", "prime numbers" and "logarithms" are just simply understood things which are familiar and have always been a part of your lexicon. These are actually wildly complex, abstract ideas which take years to fully grasp as an adult being first exposed to the material. Developing a mathematical intuition to the level of an advanced high schooler is no small feat for an adult with zero mathematical training. I'd strongly suggest anyone actually starting from zero mathematical knowledge to go back and spend time doing basic remedial math courses from the point of simple algebra and arithmetic with a good teacher to truly understand numbers first.