Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

How to learn mathematics: the asterisk method

geometry.org

Post reply on HN
Print view View original

41–50 of 79 posts

Re: How to learn mathematics: the asterisk method

#41

Post by noduerme »

olau wrote: post #11
babuskov wrote: post #6

I did this during university, but made it much more efficient. I wrote a program that would work like this: - while reading, instead of copying, the software would ask me to enter "facts" in form of questions with the most important piece of knowledge being the answer. I would type the question and the answer into the software - much faster than writing anyway - after I have gone through all the material, I would sta…

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.

Re: How to learn mathematics: the asterisk method

#42

Post by Trex_Egg »

normac2 wrote: post #39
thevinter wrote: post #7

Earlier quoted context omitted.

You've implement some lite version of Spaced Repetition! There's a tool that does exactly that and it's called Anki

This. There's also Mnemosyne, SuperMemo, and others. More here: https://www.gwern.net/Spaced-repetition

This site has many useful methods and lists its technicality in details. Thanks.

Re: How to learn mathematics: the asterisk method

#43

Post by Trex_Egg »

verytrivial wrote: post #40
vymague wrote: post #37

Earlier quoted context omitted.

> This is not bad advice I was going to say this article was a bad advice. I second the solving problems approach. It's pretty mainstream opinion really, at least among math/phys students. You can try to follow the article and feel you "understand" the topic. And still unable to solve any of the homework problems, let alone exams.

Reading is necessary but insufficient, but you can at least make it efficient -- that's what the article is covering I think.

I second this

Re: How to learn mathematics: the asterisk method

#44

Post by spekcular »

garmaine wrote: post #36
spekcular wrote: post #29

Earlier quoted context omitted.

It is a little hard for me to interpret their comment. I took it as meaning that the learning strategies should differ for pure and applied mathematics, hence my response. Maybe another way to say this is: pure math is just a kind of applied math where the applications are resolving theoretical problems. Essentially all of the big mathematical programs/fields/whatever were created to solve or understand some Big Cent…

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 mathematicians don't have those skills but recognize their value.)

I'm thinking in particular of a lot of stuff in mathematical physics and PDEs.

Re: How to learn mathematics: the asterisk method

#45

Post by amadsen »

thevinter wrote: post #7
babuskov wrote: post #6

I did this during university, but made it much more efficient. I wrote a program that would work like this: - while reading, instead of copying, the software would ask me to enter "facts" in form of questions with the most important piece of knowledge being the answer. I would type the question and the answer into the software - much faster than writing anyway - after I have gone through all the material, I would sta…

You've implement some lite version of Spaced Repetition! There's a tool that does exactly that and it's called Anki

Yeah this is spaced repetition. In this case the purpose is to memorize facts. But the asterisk method asks if you understand a concept. The purpose of revisiting asterisks is not to aid memorization via spaced repetition but to check if the understanding has improved after reading additional chapters. This seems like an important distinction.

Re: How to learn mathematics: the asterisk method

#47

Post by eggy »

hyperpallium2 wrote: post #15
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.

First covid vaccine dose provokes a short-term response; second dose provokes a long-term immunity response. Parallel adaptation of probability estimation?

Not long enough to require a third or fourth booster per Israel and some other countries, so not a good analogy unless we're all bad COVID students.

Re: How to learn mathematics: the asterisk method

#48

Post by hyperpallium2 »

garmaine wrote: post #35
hyperpallium2 wrote: post #15

Earlier quoted context omitted.

First covid vaccine dose provokes a short-term response; second dose provokes a long-term immunity response. Parallel adaptation of probability estimation?

To the best of my knowledge the first COVID vaccine dose immune response is not short-term, except in the sense that it is weaker and therefore will fade below an effective level in a smaller amount of time. But it fades at the same rate as the second dose. The second dose just "raises" the response level higher than the first dose got it.

Couldn't find my original source, but here's another:

> The second shot has powerful beneficial effects that far exceed those of the first shot,” Pulendran said. “It stimulated [...], a terrific T-cell response that was absent after the first shot alone, and a strikingly enhanced innate immune response.

https://med.stanford.edu/news/all-news/2021/07/immune-system...

Re: How to learn mathematics: the asterisk method

#49

Post by iamacyborg »

shurane wrote: post #13
babuskov wrote: post #6

I did this during university, but made it much more efficient. I wrote a program that would work like this: - while reading, instead of copying, the software would ask me to enter "facts" in form of questions with the most important piece of knowledge being the answer. I would type the question and the answer into the software - much faster than writing anyway - after I have gone through all the material, I would sta…

Have you ever tried learning a spoken language by doing this? Like another commenter mentioned, it sounds a lot like Anki Spaced Repetition. It's very cool that you just rediscovered it, though.

Duolingo certainly takes this method to an extreme. I’m not sure about spoken but I’m much better now at reading Spanish than I was this time last year
Post reply on HN