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Relearning math as an adult

gmays.com

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Re: Relearning math as an adult

#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 toolbag that applies literally everywhere.

So math isnt hard. Learning random bits of math out of context is hard. Climb the ladder once, you have it for life.

Hopefully for this person that sticks.

Re: Relearning math as an adult

#4
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…

This assumes that climbing the ladder comes easy. To me at least, it doesn't. It requires tedious labor, and lots of repetition for every single step. That's the main difference I keep noticing between me and people who say they like math or find it easy. They just look at each step of the ladder once, and immediately "get" it, sometimes even skipping steps. In contrast, I need to repeatedly step up and down the ladder multiple times, until I can take the next step.

Re: Relearning math as an adult

#6
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…

> Math is easy if you build up from fundamentals

To a certain point, I guess. Most people hit a wall of abstraction at some point, either because the abstraction is too hard or because the abstraction stops being relevant so the person loses drive to learn. For me, the wall is model theory and the second course of abstract algebra. They are both too hard and too abstract for me to push through.

Re: Relearning math as an adult

#7
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 say “oh this is much easier and more straightforward with calculus”, even without a prerequisite for it, and proceed to only explain concepts with calculus half or more of the class had never learned. One of these days I need to find a way to get it the right way.

Re: Relearning math as an adult

#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 pedagogy as Math Academy as described in TFA.

So I gave up on that and instead have been shipping several kilograms of dead tree across the pacific in the form of The Art Of Problem Solving series of textbooks. They are great, the lesson structure and building up of complex ideas from first principles is outstanding. They will humble you though, as the exercises are tough. They're also quite expensive but IMHO worth it.

Math Academy does look interesting, If I was not halfway through my series I would probably take a look. But I do enjoy having reference books on hand. Many times I've jumped back to brush up on a topic that has slipped from memory.

I solve my exercises with the most low tech solution possible, but I like the freedom it gives me to try new approaches, and nothing beats the latency between idea to ink on paper.

edit: also wanted to add that I've enrolled Chat GPT4 as my tutor. Contrary to many other's experiences that I've read, I find it to generally be very good at reasoning in this level of mathematics. It's helped me many times when I've gotten stuck. And on the occasions where it bullshitted its way to an incorrect answer, I always challenge it if I don't understand, and we ultimately find out if it hallucinated something (rare, can usually be fixed by restating the problem), or I gave it the wrong input to start with (unfortunately more common than I'd like)

Re: Relearning math as an adult

#9
Can anyone help me with some questions about this program? (I assume the founders will see this thread once they notice the HN hug of death)

1. How exactly is AI being used here? Is there an AI chat-bot that I can ask for help? Do you generate problem-sets with AI? Check answers with AI? Is it GPT-4?

2. Do you utilize Spaced-Repetition in any way? Have you found that to be useful?

Thank you

Re: Relearning math as an adult

#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 like proof by induction or by contradiction is like a second nature. And no, I'm not talking about elite kids, but curriculum requirements for all the STEM students.
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