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How to learn mathematics: the asterisk method

geometry.org

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Re: How to learn mathematics: the asterisk method

#31

Post by bjarneh »

pash wrote: post #26
bjarneh wrote: post #9

> If you read something which is difficult to understand, stop and think about it until you understand it clearly. Ahh, ok.

This is the essence of the method described in the link, and the ability to pull it off is called "mathematical maturity". How one acquires mathematical maturity is the matter of some debate.

> How one acquires mathematical maturity is the matter of some debate.

The asterisk method just reminded me about this (how to draw an owl):

https://www.reddit.com/r/funny/comments/eccj2/how_to_draw_an...

Re: How to learn mathematics: the asterisk method

#33

Post by mkl »

GuB-42 wrote: post #12
spekcular wrote: post #3

This is not bad advice, especially for people new to proof-based mathematics. (I've noticed more mathematically experienced people do something like the linked method intuitively, without writing things down.) But, it's only half the story. After you learn the definitions and theorems, you have to learn how to apply them to do computations and solve problems. This means working at least a few "easy" problems to learn…

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).

Re: How to learn mathematics: the asterisk method

#34

Post by sureglymop »

This is great advice and it is definitely how i learn best too.

But what do I do if i don't have the time necessary to do this always?

At my university i have 4 graded assignments i have to hand in every week and they always consume a lot of time. Between working on those there is barely any time to even study, except on the weekend, which by this method might be enough to study two subjects max. I feel like this works but not for the pace of a college degree.

Re: How to learn mathematics: the asterisk method

#35

Post by garmaine »

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?

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.

Re: How to learn mathematics: the asterisk method

#36

Post by garmaine »

spekcular wrote: post #29
eru wrote: post #22

Earlier quoted context omitted.

I agree with you, but I think you might misunderstand what GuB-42 means by 'practical'? Computing some homotopy groups of spheres is a good simple exercise for the right kind of abstract math. But probably not 'practical' by GuB-42's standards?

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 would look scornfully at that as a waste of time, as the whole point is the math doesn't depend on the particular instance. An applied mathematician / engineer on the other hand sees no point in the mathematics unless it is manifested in the form of physical problems.

Re: How to learn mathematics: the asterisk method

#37

Post by vymague »

spekcular wrote: post #3

This is not bad advice, especially for people new to proof-based mathematics. (I've noticed more mathematically experienced people do something like the linked method intuitively, without writing things down.) But, it's only half the story. After you learn the definitions and theorems, you have to learn how to apply them to do computations and solve problems. This means working at least a few "easy" problems to learn…

> 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.

Re: How to learn mathematics: the asterisk method

#38

Post by Cthulhu_ »

Learning to learn is such an important skill that a lot of people just miss. Speaking for myself and I think my brother who was unfortunately labeled 'gifted' at some point, learning came automatically - I just absorbed information - until it didn't. During primary and secondary school, I never had to 'knuckle down' and actually study.

Re: How to learn mathematics: the asterisk method

#39

Post by normac2 »

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

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

Re: How to learn mathematics: the asterisk method

#40

Post by verytrivial »

vymague wrote: post #37
spekcular wrote: post #3

This is not bad advice, especially for people new to proof-based mathematics. (I've noticed more mathematically experienced people do something like the linked method intuitively, without writing things down.) But, it's only half the story. After you learn the definitions and theorems, you have to learn how to apply them to do computations and solve problems. This means working at least a few "easy" problems to learn…

> 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.
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