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An Intuitive Guide to Linear Algebra (2012)

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Re: An Intuitive Guide to Linear Algebra (2012)

#11

Post by swiley »

addicted wrote: post #5
sushisource wrote: post #3

I love explainers like this, but it frankly makes me a little angry that the vast majority of the math teachers I had in highschool and college taught in the awful way described in the setup to the piece. Why is that? Has anyone studied it, or is there even a solid anecdotal explanation? The best one I can imagine is many of these professors simply don't care much for teaching and are more focused on their research,…

How much of this explainer however seems better to us precisely because of the more comprehensive knowledge and understanding we already have? For example the author uses the word function liberally in the explanation. However, when studying functions in school in math it was super complicated for me. It was only after I started programming, learning the programming language meaning of function, and then when I was r…

As someone who learned to program before taking any interesting math I was always so confused by the amount of early math classes spent explaining function notation.

It wasn't until I tried teaching people that I realized how odd the notation can seem.

Re: An Intuitive Guide to Linear Algebra (2012)

#13

Post by mathnovice »

formalsystem wrote: post #2

Viewing Linear Algebra as the study of linear operators instead of matrices makes everything so much simpler. Of course AB != BA Composition makes sense Inverse makes sense This is the book that helped me get it http://linear.axler.net/

I'm reading Strang's linear algebra book and he teaches it in terms of combining columns and rows which I think is a lot clearer than explaining it in terms of linear equations.

Re: An Intuitive Guide to Linear Algebra (2012)

#14

Post by adamnemecek »

If this interests you, you should check out the bivector community https://bivector.net/.

Join the discord https://discord.gg/vGY6pPk.

Check out a demo https://observablehq.com/@enkimute/animated-orbits

Also at the end of February, there is geometric algebra event in Belgium. https://bivector.net/game2020.html All the big names in the field will be there.

Re: An Intuitive Guide to Linear Algebra (2012)

#15

Post by swiley »

formalsystem wrote: post #2

Viewing Linear Algebra as the study of linear operators instead of matrices makes everything so much simpler. Of course AB != BA Composition makes sense Inverse makes sense This is the book that helped me get it http://linear.axler.net/

I really like "matrices are the coordinate form of linear transforms." In the LA class I took the professor made a pretty big deal out of that, first by defining "lexicographic matrix basis" so he could write out matrices as vectors and then talking about mapping between the three different ideas.

There's still stuff he said that I'm unpacking today... that was a dense class.

Re: An Intuitive Guide to Linear Algebra (2012)

#17

Post by jimhefferon »

addicted wrote: post #5
sushisource wrote: post #3

I love explainers like this, but it frankly makes me a little angry that the vast majority of the math teachers I had in highschool and college taught in the awful way described in the setup to the piece. Why is that? Has anyone studied it, or is there even a solid anecdotal explanation? The best one I can imagine is many of these professors simply don't care much for teaching and are more focused on their research,…

How much of this explainer however seems better to us precisely because of the more comprehensive knowledge and understanding we already have? For example the author uses the word function liberally in the explanation. However, when studying functions in school in math it was super complicated for me. It was only after I started programming, learning the programming language meaning of function, and then when I was r…

For sure there is an effect on Reddit and other places where someone will post a question such as, "I'm having trouble with my Calc class, what is a good book?" and people seriously answer Calculus on Manifolds.

Now, CoM is a classic, a real great book, but it is useful only to people who have reached a certain level of mathematical maturity. That, presumably, is not the questioner.

A version of this is that I also see people who write, "I didn't understand this topic when I took the course but now years later, I see it is all actually very easy."

(I call this Second Book Syndrome because I don't know of a common name for it. I understand this to be what Zen people mean by the "Gateless Gate," that after struggling with something at great length a person can come to see that there is no real difficulty. But I've never heard anyone else apply that name to this phenomenon and I'm not Zen trained so I'm not sure that is right either.)

Re: An Intuitive Guide to Linear Algebra (2012)

#18

Post by cycomanic »

addicted wrote: post #5
sushisource wrote: post #3

I love explainers like this, but it frankly makes me a little angry that the vast majority of the math teachers I had in highschool and college taught in the awful way described in the setup to the piece. Why is that? Has anyone studied it, or is there even a solid anecdotal explanation? The best one I can imagine is many of these professors simply don't care much for teaching and are more focused on their research,…

How much of this explainer however seems better to us precisely because of the more comprehensive knowledge and understanding we already have? For example the author uses the word function liberally in the explanation. However, when studying functions in school in math it was super complicated for me. It was only after I started programming, learning the programming language meaning of function, and then when I was r…

Actually a rather famous example of your point are the Feynman lectures. They are often hailed as a great, "easy" and intuitive explanation of physics. However, supposedly at the time, the undergrad students Feyman was teaching did not think their were all the rage. It was actually the grad students who retook the material and really enjoyed them. To support your point I think sometimes it is really necessary to have been exposed to the material and been able to grasp some part of it, then you are open to these type of explanations which really lift you over the hurdle of the things that you didn't quite get before.

Re: An Intuitive Guide to Linear Algebra (2012)

#19

Post by foxx-boxx »

vecter wrote: post #12

This is ok but nothing is as intuitive as 3B1B's series on YouTube that has been posted hundreds of times on HN [0]. Linear algebra is really about linear transformations of vector spaces, which is not captured in this blog post. [0] https://www.youtube.com/watch?v=fNk_zzaMoSs

Often these articles are written by students who either failed their exam or scared to fail it. People who actually know the subject get paid either for lectures or for real work.

Re: An Intuitive Guide to Linear Algebra (2012)

#20

Post by sandov »

vecter wrote: post #12

This is ok but nothing is as intuitive as 3B1B's series on YouTube that has been posted hundreds of times on HN [0]. Linear algebra is really about linear transformations of vector spaces, which is not captured in this blog post. [0] https://www.youtube.com/watch?v=fNk_zzaMoSs

Playlist link: https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...
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