Ask HN: Best resources to gain math intuition? • Hacker News Board

Re: Ask HN: Best resources to gain math intuition?

#81

Post by hyperpallium » Tue, Aug 27, 2019, 1:32 PM UTC

  You don't understand mathematics,
  you just get used to it - jvn

I used to want to understand math (intuition); now I think of it as learning a language: lots of vocab and rules with some pattern. You need to become fluent - practiced, like a cellist or cricketer.

It's also a language when someone is teaching it.

Prior knowledge is assumed; so it's difficult to detect that it is a gap that's making it difficult. When I finally realized my hard-won breakthroughs were about prior material, I dropped back to do that prior level... again and again.

This thorough approach is far too time-consuming for your needs. I really hope you find a quicker way - and please tell me!

Re: Ask HN: Best resources to gain math intuition?

#82

Post by vectorEQ » Tue, Aug 27, 2019, 1:39 PM UTC

i'm bad at math, lets say that first.

but for basic things, funny enough i feel like some of these math games / apps and math puzzle apps help me recognise patterns in numbers etc. better.

that being said, i hardly use maths ,certainly not advanced maths. but i do feel things like that are somewhat fun way to keep your senses a bit sharper.

in the end, practice makes perfect, but doing maths straight up is boring as hell to me, so i try my hand at little puzzle and maths games / apps to combat the boringness.

Re: Ask HN: Best resources to gain math intuition?

#83

Post by eric-brechemier » Tue, Aug 27, 2019, 1:48 PM UTC

I would recommend brilliant.org. From first-hand experience, this might be exactly what you are looking for: start from the basics and grow into complex matters, by solving one short problem at a time.

I think this is relevant with regards to your perceived lack of intuition: they have a way of making you discover the solution to complex problems by introducing complexity through a succession of simple problems, in a very piecemeal manner.

Re: Ask HN: Best resources to gain math intuition?

#84

Post by agumonkey » Tue, Aug 27, 2019, 2:25 PM UTC

croo wrote: post #78

agumonkey wrote: post #74

Earlier quoted context omitted.

There's a loophole. You read about people like Gauss who had insights long before they became math students. There's something to dig there.

Gauss definetly used a cheat code. Calculating before starting to talk, fixing errors in payrolls at age of 3... numbers came more naturally to that guy than talking. If something is to dig here is that the earlier you start the better you will be.

Aight he might have been wired differently, but there might be a thing or two to ask about their mindset when thinking.

Re: Ask HN: Best resources to gain math intuition?

#85

Post by locoman88 » Tue, Aug 27, 2019, 2:33 PM UTC

vectorEQ wrote: post #82

i'm bad at math, lets say that first. but for basic things, funny enough i feel like some of these math games / apps and math puzzle apps help me recognise patterns in numbers etc. better. that being said, i hardly use maths ,certainly not advanced maths. but i do feel things like that are somewhat fun way to keep your senses a bit sharper. in the end, practice makes perfect, but doing maths straight up is boring as…

Hope you don't call yourself engineer then

Re: Ask HN: Best resources to gain math intuition?

#86

Post by rainhacker » Tue, Aug 27, 2019, 3:39 PM UTC

I like 'Better Explained'[1]. It specifically focuses on intuitive understanding of mathematics.

A post I like is on adding numbers 1 to 100 [2]. The staple formula is n(n+1)/2, sum of arithmetic progression. How can we intuitively arrive that this formula?

> Technique 1: Pair Numbers Pairing numbers is a common approach to this problem. Instead of writing all the numbers in a single column, let’s wrap the numbers around, like this:

1 2 3 4 5

10 9 8 7 6

An interesting pattern emerges: the sum of each column is 11. As the top row increases, the bottom row decreases, so the sum stays the same.

Because 1 is paired with 10 (our n), we can say that each column has (n+1). And how many pairs do we have? Well, we have 2 equal rows, we must have n/2 pairs.

Number of Paris x Sum of Each Pair = (n/2) (n + 1) = n(n+1) / 2

[1] https://betterexplained.com/

[2] https://betterexplained.com/articles/techniques-for-adding-t...

Re: Ask HN: Best resources to gain math intuition?

#87

Post by enriquto » Tue, Aug 27, 2019, 3:45 PM UTC

rainhacker wrote: post #86

I like 'Better Explained'[1]. It specifically focuses on intuitive understanding of mathematics. A post I like is on adding numbers 1 to 100 [2]. The staple formula is n(n+1)/2, sum of arithmetic progression. How can we intuitively arrive that this formula? > Technique 1: Pair Numbers Pairing numbers is a common approach to this problem. Instead of writing all the numbers in a single column, let’s wrap the numbers ar…

This reasoning for adding consecutive numbers is ok, but for some people the geometric reasoning (that you are adding half of a full square plus the diagonal) will be much clearer and intuitive. It also allows a visual generalization to higher dimensions, where the formula is not so evident.

Re: Ask HN: Best resources to gain math intuition?

#88

Post by SkyMarshal » Tue, Aug 27, 2019, 4:48 PM UTC

james_s_tayler wrote: post #65

SkyMarshal wrote: post #25

Related question, anyone know any good resources for learning and developing intuition in Abstract Algebra? Especially ones that explain it well, like Calculus Made Easy did for Calculus. AA is a prereq for cryptography, category theory and and other areas of interest for CompSci. I asked this a few weeks ago but at an off peak time and not many folks saw the question. But I know HN probably has good recommendations…

The YouTube playlist on AA I linked has some extremely clear explanations. Depending on your level of familiarity already ymmv. I certainly got quite a lot out of it.

Thanks!

Re: Ask HN: Best resources to gain math intuition?

#89

Post by kalid » Tue, Aug 27, 2019, 6:50 PM UTC

kobiguru wrote: post #63

kalid wrote: post #4

Plug, but I have a blog for exactly this. As an EE/physics student you may appreciate this one on Euler's Formula: https://betterexplained.com/articles/intuitive-understanding...

Hey Kalid, I didn't know you roamed here. I love your site. I have recommended it to everyone who asked me for math resources. I really like your site. Thank you for building an amazing resource.

That's awesome to hear, thanks for helping share it :).

Re: Ask HN: Best resources to gain math intuition?

#90

Post by impendia » Tue, Aug 27, 2019, 7:13 PM UTC

The other answers have suggested a lot of particular references, many of which are excellent.

I'd add, speaking as a math professor: don't worry too much about holes and lack of intuition. The more you learn, the bigger you will feel like your holes are!

Whatever you choose, in my opinion it should involve solving lots of problems. Subject to that, I'd recommend simply that you dive in to any math subject that attracts your attention.