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

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.

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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.

Doing unit conversions where the units are treated as a kind of that can be multiplied and cancelled was a game changer for me. When it was first taught to me, I thought it was pointless.

Looking back, it should have been taught closer to 1st grade, not 7th.

Dimensional analysis is the term you're looking for.

I learnt Math by being forced to, in the same way as CS. If I had to learn today or teach it I would start by motivating the subject.

Speak about how linear algebra is cool and the basis of ML algorithms. If I were to teach algorithms, I wouldn't start by theory I would start with a problem that would take minutes to compute an answer.

I was taught CS in an abysmal way. I was taught system deisgn by drawing retarded diagrams of entities and how long they leave instead of taking an example of some social network with millions of users and having a real world discussion of it before moving to theory. I think professors suck and are doing it just to teach the class and don't care about it.

Number theory - motivate the example with RSA. Linear algebra - motivate the teaching of the class with ML and autodiff. Functional programming - this was the worst. I had this class at 18, no one sat down to explain to me why it was just one class after the other of boring theory.

Having a purpose in mind - what are you learning the “math” for?

For me, I want to dive into matrices, vector operations for game engine programming

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.

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.

> 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,

Yes! Trig is key for later math, and that's why I place learning it better as central to my retrospective. I struggle so much with memorization, though, that I was having to derive from first principles all the time.

The question and this comment[1] help me narrow down my real question which is

I want to learn enough mathematics that will help me to understand and learn about ML/AI and newer research and furthermore quantum computing.

Is that even possible? If so which topics I can target first? That will help me refactor and rebuild my foundational mathematical knowledge

1. https://news.ycombinator.com/item?id=42933232

Doing Math Academy right now and I'd say it's working well. https://www.mathacademy.com/ I just started with Math Foundations 1 and relearning from the beginning :)

I kept at mathacademy for about 6-8 months and completed Foundations 1, which was mostly a review of things I'd forgotten. Once I got to Foundations 2 and started regularly failing quizzes, I had to let it go. In my opinion, the pedagogy of "learn this one method to deal with this one problem type, we'll teach you why it works later" is great for young learners and their sponge-like memory, but I'm well into middle age and my memory is shot. I failed quizzes because I forgot the rote method for the solutions, even though I mechanically understood the method and had completed several problems just like it. Taking copious notes might have helped, but there are only so many hours in the day and flipping through notes during timed quizzes is tough. Not saying don't try it, definitely do (especially if your memory's still sharp), but if you start failing, don't be too hard on yourself.

Khan Academy. Assuming "math" here is the sort used by programmers, engineers, and most scientists.

If you're talking "math" as used by mathematicians and some physicists (Proofs, disciplines that end in "theory") etc... no idea!

Set theory, mathematical logic and proof makes sense to learn early on. Maybe even after strong command of arithmetic. These things are very portable to thinking generally. They'll change the way you see in a way you can't unlearn.

More about logarithms. I would like to know and understand formal proofs and logic. I should have practiced much more.

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