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The Essence of Linear Algebra [video]

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Re: The Essence of Linear Algebra [video]

#31

Post by 75dvtwin »

allengeorge wrote: post #25

I have to echo what the posters above have already said: I learned linear algebra way back in the day, and it's only now, watching the videos, that I suddenly _got_ matrix multiplication etc. I'm not joking when I say I almost cried with joy. These videos are incredible, and I'm so sad I didn't see them earlier in my life.

Same here, felt like 'crying with joy'. I have been struggling to really understand and internalize eigen vectors for years now (even I used them for some of my lab work). With this visualization, I felt like it had opened another, previously closed, door for me. I would like to donate to this author (and octave's author, on a separate note).

Re: The Essence of Linear Algebra [video]

#32

Post by mathgenius »

I'm just starting to realize that there are whole other levels of depth of understanding underneath this geometric intuition. So if you manage to grasp what is in these videos, don't stop! It keeps getting deeper and more mysterious, [1][2].

[1] https://en.wikipedia.org/wiki/Rank%E2%80%93nullity_theorem#R...

[2] http://math.ucr.edu/home/baez/week233.html

Re: The Essence of Linear Algebra [video]

#35

Post by espeed »

Other good STEM video channels/series:

Dave Ackley's series "Hyperspace Academy", "Robust First Computing", and "Artificial Life" are well animated: https://www.youtube.com/user/DaveAckley/

Vsause's video on "The Banach–Tarski Paradox": https://www.youtube.com/watch?v=s86-Z-CbaHA (mindblown)

XylyXylyX channel's series on "What is a Tensor?" and "What is a Manifold?": https://www.youtube.com/user/XylyXylyX/playlists

Socratica's series on "Abstract Algebra": https://www.youtube.com/playlist?list=PLi01XoE8jYoi3SgnnGorR...

Mathologer's channel on all-things math: https://www.youtube.com/channel/UC1_uAIS3r8Vu6JjXWvastJg

Ben Garside's series "Vector Spaces": https://www.youtube.com/channel/UCu5cg_Jd9XSJL_CHUskgkGw/pla...

PatrickJMT's channel on calculus, game theory...(too many to list): https://www.youtube.com/user/patrickJMT/playlists

Numenta's (http://numenta.com) series "HTM School" on the Hierarchical temporal memory (https://en.wikipedia.org/wiki/Hierarchical_temporal_memory) model for ANNs: https://www.youtube.com/playlist?list=PL3yXMgtrZmDqhsFQzwUC9...

Dan Shiffman's series "The Nature of Code: Simulating Natural Systems with Processing": https://www.youtube.com/user/shiffman/playlists?shelf_id=6&s...

Re: The Essence of Linear Algebra [video]

#37

Post by mindcrime »

malikNF wrote: post #3

Wow thanks for posting this link. I was wondering does anyone know more channels (or any other resource) just like this one, for Statistics and Calculus?

One of the best channels that I've found for Calculus is:

https://www.youtube.com/channel/UCoHhuummRZaIVX7bD4t2czg

He also has a Statistics series, as well as some pre-calculus / basic algebra stuff.

Re: The Essence of Linear Algebra [video]

#38

Post by CamperBob2 »

DanAndersen wrote: post #23

These videos are a treasure and I watch every new video that 3Blue1Brown puts out. They saved me last year when I had a graduate-level numerical linear algebra class and was struggling to grok the true meaning of all this linear algebra stuff (an embarrassing situation for a computer-graphics guy to be in!). Things that had always been "insert formula X to get result Y" started making a lot more sense. The videos als…

What is it about the state of math education that this kind of explanation is not there in every class?

Computational skill is used as a proxy for understanding because educators, just like the rest of us, are lazy-ass human beings. The authors of standardized tests don't care if you know what an eigenvalue is, only that you can calculate one.

Or, put more charitably: teaching math is hard as hell.

Like so many other aspects of our lives, modern math education in the US grew out of a knee-jerk response to a perceived crisis -- the launch of Sputnik, in this case -- that wasn't very well thought out. Schools were required to measure kids' progress in math and science quantitatively, precisely, and repeatably. And just as in other fields, once a measurement becomes a target, it ceases to be a good measurement.

Re: The Essence of Linear Algebra [video]

#39

Post by espeed »

elviking wrote: post #34

I went to a top school in the US and I got a major in CS without ever taking linear algebra, which in hindsight seems completely crazy. Every major in science or eng. should have this as part of the mandatory curriculum.

Hmm...it's been core curriculum in my school's CS department since I was there (almost 20 years ago) -- this is the first time I've seen visualizations like this though.

The next evolution will be to make these type of video lectures/visualizations interactive by implementing the math animation engine in JavaScript/ClojureScript and syncing it with the audio.

Re: The Essence of Linear Algebra [video]

#40

Post by espeed »

afarrell wrote: post #9

These explainations are fantastic! Does anyone know of a literature class that examines different technical explainations and analyses why they are successful and where they fail?

Bret Victor's essays, demos, and talks focus on this topic:

http://worrydream.com/

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