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An Intuitive Guide to Linear Algebra (2012)

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Re: An Intuitive Guide to Linear Algebra (2012)

#81

Post by alacombe »

JadeNB wrote: post #31
alacombe wrote: post #21

Speaking for Linear Algebra, I learnt more reading for a few hours the appendix of "The Design of Rijndael: AES - The Advanced Encryption Standard" than I did in 6 months of theoretical university teaching full of useless technical terms and solutions in search of problems...

> solutions in search of problems... This sounds like it was meant to be pejorative, but it's what (applied) linear algebra, and applied mathematics more generally, is . Anyone can learn about a certain mathematical topic upon realising it's the one relevant to the problem they're facing—and learn it way more quickly, due to motivation and focus, than they would in a general-purpose course on the topic; the art is in…

Of course it was meant to be pejorative and that pretty much summarize my experience through university. In this particular case, the teacher wasn't giving a rat arse about his class and was merely there for the safe job, pension, sprinkles by some "research".

Anyhow, I disagree with that top-down approach, which seems to be very... European. I much prefer to follow a more logical path where the problem preclude the introduction to the solution.

Re: An Intuitive Guide to Linear Algebra (2012)

#83

Post by richard78459 »

id_ris wrote: post #61

I recently finished going through MIT OCW's linear algebra class from Gilbert Strang. Without the struggle of doing the assignments, reading the text, and watching the lectures, I don't think I would have ever learned the content. While content like this and that from 3blue1brown are commendable and useful, it simply would not have lodged the ideas into my head. Now that the ideas of things like vector spaces, norms,…

3blue1brown himself has told in his videos that they are not substitute for books and working out the exercise and he recommends reading from books and his videos are for inspiration and as a supplement.

Re: An Intuitive Guide to Linear Algebra (2012)

#84

Post by sci_c0 »

dundercoder wrote: post #22

Does something like this exist for differential equations?

May be this can help you:

https://www.youtube.com/playlist?list=PLZHQObOWTQDNPOjrT6KVl...

This is 3Blue1Brown's video series on Differential Equations. Do support him on Patreon if this really helps you.

Re: An Intuitive Guide to Linear Algebra (2012)

#85

Post by qazpot »

id_ris wrote: post #61

I recently finished going through MIT OCW's linear algebra class from Gilbert Strang. Without the struggle of doing the assignments, reading the text, and watching the lectures, I don't think I would have ever learned the content. While content like this and that from 3blue1brown are commendable and useful, it simply would not have lodged the ideas into my head. Now that the ideas of things like vector spaces, norms,…

> I think the real benefit accrues to the author who had to work out how to teach these concepts to others.

In college I learned more math when I was trying to build software for teaching math compared to when I was trying to learn math.

Re: An Intuitive Guide to Linear Algebra (2012)

#86

Post by ukj »

The only way to test if you've 'understood' something is to apply it to real-world problems.

If it works - then you understood it. If it doesn't - then you didn't.

"Understanding" without way of external verification seems no different to dopamine-chasing.

Measuring on output and all that...

Re: An Intuitive Guide to Linear Algebra (2012)

#87

Post by matteuan »

ukj wrote: post #86

The only way to test if you've 'understood' something is to apply it to real-world problems. If it works - then you understood it. If it doesn't - then you didn't. "Understanding" without way of external verification seems no different to dopamine-chasing. Measuring on output and all that...

The only way to test is if you talk with an expert and he says you have understood. There are many things in linear algebra that you can use in practice even when you didn't really understand them. This is the reason why self-studying certain topics is very hard, you still need (good) teachers to give you constant feedback.

Re: An Intuitive Guide to Linear Algebra (2012)

#88

Post by ukj »

matteuan wrote: post #87
ukj wrote: post #86

The only way to test if you've 'understood' something is to apply it to real-world problems. If it works - then you understood it. If it doesn't - then you didn't. "Understanding" without way of external verification seems no different to dopamine-chasing. Measuring on output and all that...

The only way to test is if you talk with an expert and he says you have understood. There are many things in linear algebra that you can use in practice even when you didn't really understand them. This is the reason why self-studying certain topics is very hard, you still need (good) teachers to give you constant feedback.

That seems like a verbalistic notion of 'understanding'.

How do I falsify the expert's claims about my understanding?

Re: An Intuitive Guide to Linear Algebra (2012)

#89

Post by stoddler »

id_ris wrote: post #61

I recently finished going through MIT OCW's linear algebra class from Gilbert Strang. Without the struggle of doing the assignments, reading the text, and watching the lectures, I don't think I would have ever learned the content. While content like this and that from 3blue1brown are commendable and useful, it simply would not have lodged the ideas into my head. Now that the ideas of things like vector spaces, norms,…

You don't learn by putting information into your head, you learn by retrieving information from your head.

Re: An Intuitive Guide to Linear Algebra (2012)

#90

Post by jimhefferon »

Koshkin wrote: post #35
Swizec wrote: post #27

Earlier quoted context omitted.

Once you understand monads, you lose the ability to explain monads. Hence the number of monads tutorials grows at an exponential rate as every new understander tries to explain them and fails. it's a fun problem in teaching

> Once you understand... you lose the ability to explain Sorry, this does not make sense to me.

Here is a link that helps me think about it: https://www.alanwatts.org/3-3-10-gateless-gate/ (I teach Math and a common complaint, against all math teachers, is "They obviously know the material but they cannot teach it." When I first heard AW talk about this it was a relevation for me because it so closely linked with my experience. You say to people "A vector space is a place for linear combinations to happen" and they don't get it, of course they don't get it, I wouldn't have gotten it, but that's what a vector space is. So you have to do lots of examples, and work around the edges, and somehow sit with it for a while. Anyway, I find that for me this link conveys the point of that quote about monads.)
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