These videos are posted any time linear algebra is mentioned. I find it almost comical at this point. What good is this intuition? I struggle to understand the value that these videos bring, but I'm not saying there is no value. I'm just lost, and kind of jealous because I need a deep understanding of linear algebra for work.
Those are good videos, and I also endorse them. However, you will not truly know what is going on until you solve some real problems with them.
One interesting option that computer programmers have to understand linear algebra that most people do not is that you could go do some stuff with computer graphics. Grab three.js, and then once you've followed some tutorial somewhere to get a triangle on the screen, start doing things, but do them manually, including implementing matrix multiplication yourself. Modern graphics has moved so far up the stack nowadays that you probably shouldn't say that you "know 3D graphics" after that exercise, because you'll know 3D graphics circa 1995. But you will have a much better intuition for linear algebra, and those videos will either make sense, or be trivially obvious to you.
(One of the reasons why the linear algebra videos can be so helpful is that it has historically been very easy to take an entire class on the topic and just grind numbers, without ever getting to that level of intuition. Differential equations, if you took physics that did not use them, can have a very similar problem, where you just grind through problems for a semester with no motivation.)
It's not just linear algebra, 3blue1brown also has an entire series on undergraduate calculus, and series on Statistics, Linear Algebra II and Group Theory are in the works. Plus a large number of excellent videos on miscellaneous math topics.
I think I understand what you're saying -- one needs more than just cool videos and cool intuition. You need to do exercises. This is a point made multiple times in those very videos.
But, the intuition provided in those videos is absolutely excellent. As an example, look at the explanation of change-of-basis in the linear algebra I series.
Ah, the videos come with pointers to exercises? I'm quite excited about https://www.edukera.com/ and possibilities for interactive learning through automated theorem proving. Thanks!
Actually, there are not many pointers to exercises. I believe they may be planning to add some written materials, so maybe in the future, but not currently.
The videos suggest pausing and trying to figure the next bit out yourself and a couple of the videos do end with a suggestion to prove something yourself.
For me personally, understanding why it is done on a deeper level than is commonly taught helps me consolidate the concept more comprehensively and permanently.
I think what stands out about those videos is that people who have no prior higher math education still get a shadow of intuition of what's actually going on, and people who already 'grokked' the concepts still got an alternative, simpler view on those concepts, resulting in at least a view 'a-ha!' moments for almost everyone.
Grant (the 3Blue1Brown guy) has an uncanny ability to explain difficult concepts and the fundamental intuition behind them. In many of his videos, he explains topics from the perspective of a person inventing that topic (such as in his first Calculus video [1]). I can't recommend his videos enough.
It works for a lot of people, I'm just looking for something else, exercise-based computer-checked proofs to teach mathematics, something like that. Want it bad.
