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Relearning math as an adult

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Re: Relearning math as an adult

#11

Post by SuperNinKenDo »

Well, it's essentially an ad/shout-out for the mate's product, but if the value is there, the value is there. I can't afford the subscription price and don't care much for subscriptions these days anyway, but I'd love to found my own education company in the future, so wishing nothing but the best, and happy to see someone hopefully being able to make some money in the spacez even when free alternatives like Khan Academy are already established.

Edit: The original post has no value in explaining how the author is learning maths other than to say that they're using the Math Academy platform, and taking notes. Useless to anybody not interested in a $49/month subscription to a semi-open beta. I would almost characterise the title of the post as a bait and switch after further consideration.

Re: Relearning math as an adult

#12

Post by redcobra762 »

hintymad wrote: post #10

It looks how do do proofs is at university level in the US. I wonder why other countries start to teach kids how to do proofs from grade 7. They start with rigorous proofs in Euclidean geometry, the move to solid geometry, then to proofs in elementary functions, sets, number theories, and etc, then to polynomials and simple discrete maths and analytic geometry. By the time a kid graduates high school. using things li…

We did proofs in 7th grade as part of geometry, in a semi-rural United States middle school.

Re: Relearning math as an adult

#13

Post by tnecniv »

trws wrote: post #7
boxfire wrote: post #3

I may be biased as I am a trained Mathematician, but I always feel when someone says "Math is Hard", that is because they had bad teachers. Math is easy if you build up from fundamentals, not like physics education where you say "but lets delete everything before because it had an oversimplifying assumption", rather if you build your knowledge entirely sequentially from things you know or assume, you build up a toolb…

I probably had crummy teachers in some places, but my experience was that math up through linear algebra made sense and wasn’t all that bad, but that calculus was a huge bag of “if it looks kinda like this try this thing, and if the result looks kinda right it probably worked, if not try this other thing” such that I could never form a framework for it in my head. Also didn’t help when teachers in some things would s…

In hindsight, that’s because high school calculus doesn’t teach you how things work and just teaches you a bag of tricks so you can grind through problems. There’s a certain number of tricks you should know, I.e., you should be able to take some simple integrals and derivatives, but for higher math, you run into complicated things where the tricks don’t work or don’t exist. Some of the tricks are actually really useful, but you have to fully internalize where they come from, e.g., integration by parts just comes from rearranging the chain rule, and, if you know that, you can apply it to more exotic derivatives.

I did well in HS calculus but struggled in college math because the bag of tricks approach doesn’t work there. It took a lot of effort for me to undo the bad habits I learned from K-12 math and learn the good stuff, but it paid off.

Also, it’s well known that eventually professional mathematicians hate certain kinds of math. There’s the classic divide between analysists (those that do calculus-type stuff) and algebrists (those that do things like group theory, and linear algebra goes here). You don’t have to like it all, and something you don’t appreciate the first time you see it, you may enjoy later

Re: Relearning math as an adult

#14

Post by hintymad »

redcobra762 wrote: post #12
hintymad wrote: post #10

It looks how do do proofs is at university level in the US. I wonder why other countries start to teach kids how to do proofs from grade 7. They start with rigorous proofs in Euclidean geometry, the move to solid geometry, then to proofs in elementary functions, sets, number theories, and etc, then to polynomials and simple discrete maths and analytic geometry. By the time a kid graduates high school. using things li…

We did proofs in 7th grade as part of geometry, in a semi-rural United States middle school.

Good to know. I guess education in the US has local standards? I have this impression of the US not teaching proof because in a number of introductory math classes in my college, the profs dedicated chapters to teach basics of induction, how to write proofs, and etc.

Re: Relearning math as an adult

#15

Post by fiforpg »

> but I needed a good reason that would justify the time investment

It should be understood though that there are cases when math(-like) language is abused, leading to overcomplication and obscurantism [1]. In mathematics, there is always the temptation of formalizing for formalization's sake. Indeed, 99% of pure math is non-constructive ("there exists a group such that", "the algorithm converges in O(N) steps"), as opposed to the practical CS and applied math ("here are the runtimes on real world data") which are likely the primary concerns of the HN crowd.

None of this can diminish the sheer impractical appeal of pure math and pure CS, not unlike that of poetry, but I would rather not oversell either of the two.

[1] A good illustration is a rant by Cosma Shalizi at http://bactra.org/notebooks/nn-attention-and-transformers.ht..., recently posted on HN.

Re: Relearning math as an adult

#16

Post by Jtsummers »

hintymad wrote: post #14
redcobra762 wrote: post #12

Earlier quoted context omitted.

We did proofs in 7th grade as part of geometry, in a semi-rural United States middle school.

Good to know. I guess education in the US has local standards? I have this impression of the US not teaching proof because in a number of introductory math classes in my college, the profs dedicated chapters to teach basics of induction, how to write proofs, and etc.

Every state sets its own curriculum, with varying degrees of freedom for the districts and schools within the states. The federal level has standards, which students are generally tested against in various standardized tests, that are tied to federal funding.

Multiple curricula can satisfy the same standards, at least on paper if not in practice. So states are, more or less, free to teach things how they want. However, they're also strongly driven by the textbook industry, which turns on the two biggest textbook purchasers: Texas and California. So a lot of the textbooks (and associated curriculum material) available for purchase in the rest of the states are driven by whatever those two states are pushing.

Re: Relearning math as an adult

#17

Post by hnbad »

6d6b73 wrote: post #5

$49/student/month? That's excessive.

It's not cheap. Given that it sounds like this is something you want to deliberately spend time on rather than just an app to use when you're bored it might be worth it but probably not so much if you can't use the knowledge professionally somehow.

Re: Relearning math as an adult

#18

Post by AlchemistCamp »

6d6b73 wrote: post #5

$49/student/month? That's excessive.

Compared to what? They have a track-record of students not even old enough to be in high school yet passing AP Calculus BC exams.

Here in Taiwan, where I live, it's not that uncommon for people to pay 5x that price per month on supplementary math courses for their kids.

https://twitter.com/_MathAcademy_/status/1708542077695574292

Re: Relearning math as an adult

#19

Post by redcobra762 »

hintymad wrote: post #14
redcobra762 wrote: post #12

Earlier quoted context omitted.

We did proofs in 7th grade as part of geometry, in a semi-rural United States middle school.

Good to know. I guess education in the US has local standards? I have this impression of the US not teaching proof because in a number of introductory math classes in my college, the profs dedicated chapters to teach basics of induction, how to write proofs, and etc.

I would have still appreciated that refresher in a college class on content I learned 7-8 years prior.

Re: Relearning math as an adult

#20

Post by AlchemistCamp »

dcw303 wrote: post #8

I've been doing similar for about a year. My target is to learn the math needed to make 3d games, so basically algebra, geometry, calculus and linear algebra. I started with brilliant.org, and while I liked the level of polish in the interactive lessons, I found the lesson structure to be out of sequence, often referring to things that haven't been covered yet. They didn't seem to have put as much thought into pedago…

I totally agree with you on the value in using Chat GTP when stuck.

What's the scope of The Art of Problem Solving? How far does the series go?

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