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How to learn mathematics: the asterisk method

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Re: How to learn mathematics: the asterisk method

#11
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.

Re: How to learn mathematics: the asterisk method

#12

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.

Re: How to learn mathematics: the asterisk method

#13
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.

Re: How to learn mathematics: the asterisk method

#15
post #11
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.

First covid vaccine dose provokes a short-term response; second dose provokes a long-term immunity response.

Parallel adaptation of probability estimation?

Re: How to learn mathematics: the asterisk method

#17
>> 3. Start copying the relevant part of the book or the lecture notes to a (paper) note-pad by hand.

When I started learning to code. I remember people would buy the famous books and do an intellectual dive into them.

As for me I bought 'SAM's Learn C in 21 Days.' Then for the next one month like a dumb bot I would just read the code and type it out on my desktop. Religiously. Like wake up everyday spend significant part of the day just to read and write code into the editor and run it. Most of the time I had a hazy understand of what I was doing.

But surprisingly this approach worked better than the intellectual fantasising exercise(Most of my friends quit after a while). I've used this technique of using dumbest possible method to study anything useful in everything I've touched since. Including workout and fitness.

Over the years I've also wondered why it works. One reason is when you just wake up everyday and do this ritual, you are basically spending time with the subject. Add a month or two to this journey it's now a habit. Even though your understanding is relatively poor, you haven't quit at a point most people quit. You are comfortable doing work in the subject and therefore you are already scoring wins everyday. This not only builds confidence, it will eventually take you to higher levels.

Turns out the hardest part of learning and doing anything is sticking with a subject for long. Once you have practice the hard parts become easy.

Re: How to learn mathematics: the asterisk method

#18
> Connections can only be made between ideas when they are in the mind to be connected.

This is probably true. I always used to try to understand to avoid the bother of rote learning... but the truth is, I probably examined it so intensively while trying to understand, that I rote learned without realizing it.

Re: How to learn mathematics: the asterisk method

#20
post #12

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.

Especially in abstract mathematics, you must practice computations with basic examples (e.g. computing some homotopy groups of spheres). If you cannot do this, you haven't actually grasped the mathematical content of the reading. The abstractions exist precisely because they are concise, powerful ways to deal with various examples.
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