How to learn mathematics: the asterisk method

Post by eru » Tue, Oct 26, 2021, 2:55 AM UTC

mkl wrote: post #33

GuB-42 wrote: post #12

Earlier quoted context omitted.

It seems like proof-based maths and applied maths are different fields. The latter is more closely related to engineering. I am the kind of person who likes to solve more practical problems but it is more of a hindrance in advanced maths, where you manipulate concepts that are too abstract for practical use, like infinities.

As an applied mathematician, I disagree. Proofs are often useful in applied maths, and most applied maths is much more closely related to pure maths than to engineering. Infinities show up in practical applied maths, but there are more abstract things that don't (yet).

Post by eru » Tue, Oct 26, 2021, 7:34 AM UTC

spekcular wrote: post #44

garmaine wrote: post #36

Earlier quoted context omitted.

That's an explanation that only makes sense from the perspective of pure math. Many of us engineers are wholly incapable of caring about the resolution of theoretical problems. Learning how to take a real world problem and map it into the domain of theory is a special skill that is not required for pure math, because it has an intrinsically messy interface into the real world. I suspect that a pure mathematician woul…

I don't think mathematicians look scornfully upon people doing the mapping between applied and theoretical domains. On the contrary, I think there's a lot of respect (and perhaps some envy). It's an entirely different set of skills, and a lot of great math has been inspired by applications, which would never have been possible if pure mathematicians worked in isolation. (The respect/envy comes from the fact that most…

Post by k__ » Tue, Oct 26, 2021, 6:10 PM UTC

randomswede wrote: post #73

k__ wrote: post #52

I noticed a great overlap in learning math and programming. Programming was easier for me to learn and now helps me to understand math a bit better. Coding a real project is the equivalent to math's proofs, I think. The book "Badass - Making Users Awesome" says, learning something just requires two steps. Perceptual exposure (of hundreds of correct examples) and deliberate practice. I think, math falls short in the f…

But, then does programming. In C, there's at least three (arguably more) ways of doing a loop. You can use for (...) { ... }, you can use while (...) { ... }, and you can use do { .... } while ( ... ). Of course, which one you pick depends on context. But, then, which one of sqrt or "raised to 1/2" you choose also depends on what's more convenient at the time.

Post by pkaye » Wed, Oct 27, 2021, 7:05 AM UTC

noduerme wrote: post #41

olau wrote: post #11

Earlier quoted context omitted.

Intuitively, it does make sense. If you only ever encounter something once, it probably does not make sense to spend brain resources storing it.

I think I've reinvented trigonometry at least fifteen times in my life when I needed to animate something roughly circular, spherical or wave-like. I still have no freakin clue which thing is a sin, cos or tan. I failed precalc (and they still let me work on video games!) But I do remember that a hypotenuse is the square root of A^2 + B^2 and from that I can pretty much figure out the rest.