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An illustrated introduction to linear algebra

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Re: An illustrated introduction to linear algebra

#81

Post by potbelly83 »

hn_throw_bs wrote: post #31

I don’t like these examples because IRL nobody does things this way. Try actual problems that require you to use these tools and the inter-relationships between them, where it becomes blindingly obvious why they exist. Calculus is a prime example and it’s comical most students find Calculus hard because their LA is weak. But Calculus has extensive uses, just not for doing basic carb counting.

Honestly all these cute websites give people a false sense that they're actually learning something. The only way to learn this stuff is get one of the million good LA books out there and work through the problems. But that's hard, so people look for shortcuts.

Re: An illustrated introduction to linear algebra

#82

Post by [deleted] »

cykill wrote: post #72

I know this is going to be super controversial, but I genuinely find illustrations of mathematical concepts below a minimum threshold of complexity totally useless and frequently detrimental. Below a certain level of complexity the human brain is much faster and efficient operating on abstract symbols, like 'x' and 'y'. You can solve equations and figure things out in a fraction of the time it takes you to visualize…

[deleted]

Re: An illustrated introduction to linear algebra

#83

Post by hn_throw_bs »

potbelly83 wrote: post #81
hn_throw_bs wrote: post #31

I don’t like these examples because IRL nobody does things this way. Try actual problems that require you to use these tools and the inter-relationships between them, where it becomes blindingly obvious why they exist. Calculus is a prime example and it’s comical most students find Calculus hard because their LA is weak. But Calculus has extensive uses, just not for doing basic carb counting.

Honestly all these cute websites give people a false sense that they're actually learning something. The only way to learn this stuff is get one of the million good LA books out there and work through the problems. But that's hard, so people look for shortcuts.

Yeah I think when students actually hit Calculus-level related rates, a small dim light starts to glow. Obviously it only gets brighter the less you have to hold onto and the more you have to mathematically present something that you are trying to reason about that all the tools start to make sense, the relationships are asking you “is this true in my case or do I need to take a step back?” and so forth.

I don’t have an axe to grind against the site I think it’s fine, but if someone wants to learn LA, a college level course followed by an intense grind of word problems and having to work backwards and forwards and finding flaws in answers might be a better way to develop the noggin for it. Just my 2c.

Re: An illustrated introduction to linear algebra

#85

Post by barrenko »

egonschiele wrote: post #77
barrenko wrote: post #62

Earlier quoted context omitted.

Ok, boy, I'm also reviewing LinAlg textbooks as we speak. Coming in with a similar interest for ML / AI. I've done math on KA academy up to linear algebra, with other resources / textbooks / et al. depending on the topic. People will recommend 3B1B, Strang (MIT OCW Lin Alg lessons). For me the 3B1B is too "intuitionist" for a first serious pass, and Strang can be wonderful but then go off on a tangent during a lectur…

That's quite the list! How does this one compare? Anything you think is missing?

https://www.math.ucdavis.edu/~linear/ (authors David Cherney, Tom Denton, Rohit Thomas and Andrew Waldron) - reminds me of category theory articles, so good.

Re: An illustrated introduction to linear algebra

#86

Post by rramadass »

xwowsersx wrote: post #7

This is great. I really appreciate visual explanations and the way you build up the motivation. I'm using a few resources to learn linear algebra right now, including "The No Bullshit Guide to Linear Algebra", which has been pretty decent so far. Does anyone have other recommendations? I've found a lot of books to be too dense or academic for what I need. My goal is to develop a practical, working understanding I can…

Suggestions for books/articles from a couple of my previous comments;

https://news.ycombinator.com/item?id=45110857

https://news.ycombinator.com/item?id=45088830

The OP's article though simple, still does not really explain things intuitively. The key is to understand the concept of a Vector from multiple perspectives/coordinate systems and map the operations on vectors to movements/calculations in the coordinate space (i.e. 2D/3D/n-space). Only then will Vector Spaces/Matrices/etc. become intelligible and we can begin to look at Physical problems naturally in terms of vectors/vector calculus.

The following are helpful here;

1) About Vectors by Banesh Hoffmann.

2) A History of Vector Analysis: The Evolution of the Idea of a Vectorial System by Michael Crowe.

Re: An illustrated introduction to linear algebra

#87

Post by xwowsersx »

barrenko wrote: post #62
xwowsersx wrote: post #7

This is great. I really appreciate visual explanations and the way you build up the motivation. I'm using a few resources to learn linear algebra right now, including "The No Bullshit Guide to Linear Algebra", which has been pretty decent so far. Does anyone have other recommendations? I've found a lot of books to be too dense or academic for what I need. My goal is to develop a practical, working understanding I can…

Ok, boy, I'm also reviewing LinAlg textbooks as we speak. Coming in with a similar interest for ML / AI. I've done math on KA academy up to linear algebra, with other resources / textbooks / et al. depending on the topic. People will recommend 3B1B, Strang (MIT OCW Lin Alg lessons). For me the 3B1B is too "intuitionist" for a first serious pass, and Strang can be wonderful but then go off on a tangent during a lectur…

Thank you very much I'll check out these resources. ROB101 looks really great.

I love the 3B1B videos, but I've noticed my attention tends to drift when watching videos. I've learned that I absorb information best through text. For me, videos work well as a supplement, but not as the main way to learn.

Thanks again.

Re: An illustrated introduction to linear algebra

#90

Post by xwowsersx »

i_don_t_know wrote: post #60
xwowsersx wrote: post #7

This is great. I really appreciate visual explanations and the way you build up the motivation. I'm using a few resources to learn linear algebra right now, including "The No Bullshit Guide to Linear Algebra", which has been pretty decent so far. Does anyone have other recommendations? I've found a lot of books to be too dense or academic for what I need. My goal is to develop a practical, working understanding I can…

I’ve really enjoyed this book: Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares https://web.stanford.edu/~boyd/vmls/

Thanks for the suggestion.
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