Ask HN: If you were to relearn math today, how would you approach it?

No matter your math background, how would you approach learning math again? Are there things you wish you had done sooner? What aspects of your personal math journey were impactful enough that you would definitely include in your relearning roadmap? I would like to hear everyone's thoughts and opinions.

I have a Statistics Master background but forgot most of the stuffs. Here is my plan:

I'd first have an objective in mind -- why do I need to relearn Math? For me it's because I want to study General Relativity in a rigorous way, so that needs some Math.

Then I'd break down the Math needed. I want to be safe so I'd include more Math than many people suggested online. Basically General Relativity can be approached by either tensor or differential geometry, so I'll take both. Now I check the prerequisites of them until I reach the root, probably Calculus and Linear Algebra.

Once I identify all courses I need to take, I'd go to MIT or other open course and download all assignments and final exams and go for them.

Of course in my case I need to take Physics classes interwoven, but your case may differ. I'd skip any material that is not required but also add some historical background.

In retrospect, much of my struggle with later math can be traced back to the tedium of trigonometry. I've struggled with memorization for as long as I can recall. The emphasis on memorizing the trig identities and relationships between the functions is at odds with that. It affects other subjects as well, so I know it's not just math. Obviously trig is a fundamental subset of math. In any case, had trig been taught alongside or in close relationship with the aspects of math where it's used, as a set of tools to solve problems – when and where to use it – not only would I have found it far more interesting, it would have clicked better.

Dimensional analysis is the term you're looking for.

Trig was actually one of the courses that helped me a lot in my later math degree, because I only had to memorize a few key facts and identities, and the rest were variations derivable from the key information. A lot of my earlier math courses "clicked" when I realized this. When I studied further areas of math I found that it was often the case that there was a large set of information to learn, but most of it could be derived from a small-ish core. If I studied and understood the core, and memorize the commonly used parts of the rest (couldn't help but memorize because it was common, didn't need special study effort) that most classes were straightforward.

But,

> In any case, had trig been taught alongside or in close relationship with the aspects of math where it's used

I took it concurrent with a physics course and we did apply trig quite a bit so my practice with it was more than just whatever was needed for the trig class itself.