Interactive Linear Algebra (2019)

#1

Post by natemcintosh » Fri, Aug 13, 2021, 1:03 PM UTC

Interactive Linear Algebra (2019)
textbooks.math.gatech.edu

Re: Interactive Linear Algebra (2019)

#2

Post by TrackerFF » Fri, Aug 13, 2021, 1:56 PM UTC

I really wish we'd have these kind of tools when I took Linear Algebra (or many other math and engineering courses, for that mater).

When I took it, it was purely proofs up and down on the blackboard, zero visualizations.

Re: Interactive Linear Algebra (2019)

#3

Post by iainctduncan » Fri, Aug 13, 2021, 2:00 PM UTC

I am excited to try this, thanks for posting!

Re: Interactive Linear Algebra (2019)

#4

Post by nicomeemes » Fri, Aug 13, 2021, 2:01 PM UTC

This is one of my favorite resources for learning about Linear Algebra. Helped me immensely when I took it last spring.

Re: Interactive Linear Algebra (2019)

#5

Post by criddell » Fri, Aug 13, 2021, 2:05 PM UTC

It would be nice if the items in the left column on the index page [1] were links to the context location.

[1]: http://textbooks.math.gatech.edu/ila/index-1.html

Re: Interactive Linear Algebra (2019)

#6

Post by scythmic_waves » Fri, Aug 13, 2021, 2:07 PM UTC

I've only just skimmed through this. And it's a subject I already know so I can't tell if it's actually a good resource. However, my initial impression is that I love it.

I think that textbooks, math textbooks in particular, are an example where print publishing does a disservice. (I'm counting PDFs here too.) By having to lay everything out in print form, you have to clutter up your explanations with examples and footnotes that take up physical room. Here, the examples are toggle-able. If I _want_ to explore an example, I can. But I don't need to. This kind of thing is especially helpful when reviewing content for, say, a test rather than learning it for the first time.

Also finding things in textbooks is a real pain. It's difficult to index things in a helpful way, so you just have these counting schemes in LaTeX that increment for every definition, theorem, etc. I'd love to be able to tag things then search the tags.

And that says nothing for when you want to explain something that's difficult with static images. Being able to interact with animations by zooming, panning, pausing, slowing down, speeding up, etc. is a boon. (I don't think I actually saw an example of a non-static image here, but I think my point still stands.)

All in all, I'd love to see more interactive textbooks. We've got this really expressive kind of document via the web. I think we should be taking advantage of it more.

Re: Interactive Linear Algebra (2019)

#7

Post by JadeNB » Fri, Aug 13, 2021, 2:58 PM UTC

scythmic_waves wrote: post #6

I've only just skimmed through this. And it's a subject I already know so I can't tell if it's actually a good resource. However, my initial impression is that I love it. I think that textbooks, math textbooks in particular, are an example where print publishing does a disservice. (I'm counting PDFs here too.) By having to lay everything out in print form, you have to clutter up your explanations with examples and fo…

> I think that textbooks, math textbooks in particular, are an example where print publishing does a disservice. (I'm counting PDFs here too.) By having to lay everything out in print form, you have to clutter up your explanations with examples and footnotes that take up physical room. Here, the examples are toggle-able. If I _want_ to explore an example, I can. But I don't need to. This kind of thing is especially helpful when reviewing content for, say, a test rather than learning it for the first time.

This sounds so much like a meeting of Lamport's idea of how to structure a proof (https://lamport.azurewebsites.net/pubs/proof.pdf) and the Stacks project (https://stacks.math.columbia.edu).

Re: Interactive Linear Algebra (2019)

#8

Post by ChrisArchitect » Fri, Aug 13, 2021, 3:14 PM UTC

Previous discussion:

2 years ago https://news.ycombinator.com/item?id=21628449

Re: Interactive Linear Algebra (2019)

#9

Post by chobytes » Fri, Aug 13, 2021, 3:23 PM UTC

scythmic_waves wrote: post #6

I've only just skimmed through this. And it's a subject I already know so I can't tell if it's actually a good resource. However, my initial impression is that I love it. I think that textbooks, math textbooks in particular, are an example where print publishing does a disservice. (I'm counting PDFs here too.) By having to lay everything out in print form, you have to clutter up your explanations with examples and fo…

I think I prefer physical textbooks for many reasons I wont get in to... but I do really like the interactive and visualization elements computers offer.

I feel like teaching kids some amount of coding to be able to play with math could be very helpful.

Re: Interactive Linear Algebra (2019)

#10

Post by Jtsummers » Fri, Aug 13, 2021, 3:46 PM UTC

chobytes wrote: post #9

scythmic_waves wrote: post #6

I've only just skimmed through this. And it's a subject I already know so I can't tell if it's actually a good resource. However, my initial impression is that I love it. I think that textbooks, math textbooks in particular, are an example where print publishing does a disservice. (I'm counting PDFs here too.) By having to lay everything out in print form, you have to clutter up your explanations with examples and fo…

I think I prefer physical textbooks for many reasons I wont get in to... but I do really like the interactive and visualization elements computers offer. I feel like teaching kids some amount of coding to be able to play with math could be very helpful.

That's one of the intents behind Logo, see the book Mindstorms by Papert.

Programming wasn't an end unto itself, but a means of exploring complex topics. Notebook-style programming is a great modern iteration of this, especially with the ability to produce interesting and complex visualizations of the underlying data and structures.