Immersive Linear Algebra (2015)

[WillAdams]

Very cool!

Does anyone have a list of other similar texts?

There's:

- Geometry: Joyce's Java version of Euclid's _Elements_: https://mathcs.clarku.edu/~djoyce/java/elements/elements.htm...

- Physics: https://www.motionmountain.net/

- Chemistry: The Elements by Theodore Gray https://apps.apple.com/us/app/the-elements-by-theodore-gray/...

A nifty thing my kids enjoyed was the website version of the book, _Bembo's Zoo_ (which sadly is no longer on-line: https://soundeffects.fandom.com/wiki/Bembo%27s_Zoo_(Websites... )

[vitalnodo]

https://schoolyourself.org/ with different ideas about

https://www.youtube.com/watch?v=4cQIbZa7P80 Computer-Assisted Instruction

http://dmentrard.free.fr/GEOGEBRA/Maths/export4.25/golf.html some people manage to create some applets in geogebra

https://xenaproject.wordpress.com/2022/07/29/teaching-formal... a way to teach theorem proving

maybe I'll remember something else and add it here

[nutanc]

This was the core premise on which Innings2 books was made. In this day and age textbooks can be made interactive. So, the CBSE math syllabus (main syllabus in India) was made interactive for 6th to 10 grades.

https://books.innings2.com/demo

[__rito__]

You might like these-

- Matrix Arcade (https://yizhe-ang.github.io/matrix-explorable//)

- Computational Discovery on Jupyter (https://computational-discovery-on-jupyter.github.io/Computa...)

- Nature Inspired Programming Recipes (https://github.com/clever-algorithms/CleverAlgorithms)

- A Little Calculus (https://papl.cs.brown.edu/2018/func-as-data.html#%28part._.A...)

- The Matrix in Computer Science (https://cs.brown.edu/courses/cs053/current/lectures.htm)

- Discrete Mathematics and Functional Programming (https://cs.wheaton.edu/~tvandrun/dmfp/)

- A Programmer's Introduction to Mathematics (https://pimbook.org/)

- Complexity Explorer (https://www.complexityexplorer.org/)

- Learn Physics with Functional Programming (https://nostarch.com/learn-physics-functional-programming)

- Seeing Theory (https://seeing-theory.brown.edu/)

- Coding The Matrix (https://codingthematrix.com/)

[stared]

I created a list of Interactive Machine Learning, Deep Learning, and Statistics websites (https://p.migdal.pl/interactive-machine-learning-list/), which includes Immersive Linear Algebra, among other things.

For a broader range of subjects, there is a list of Explorables (https://explorabl.es/).

[akdas]

I started on two resources on different topics. One day, I want you invest a good amount of time into building them out.

https://cstheory.avikdas.com/

https://nesdev.avikdas.com/

[doubloon]

its not animated but its really nicely illustrated in html friendly layout

https://www.c82.net/euclid/book1/

and this is animated, and interactive, for polyhedra

https://polyhedra.tessera.li/dodecahedron/operations

[ibobev]

I created a list of links to various freely available online learning resources about computer programming, math, and science:

https://github.com/bobeff/programming-math-science

Most of them are collected from HN posts.

[jovial_cavalier]

One on complex analysis - https://complex-analysis.com/

[Abishek_Muthian]

Here's a modern version for Euclid's Elements- https://www.c82.net/euclid/

[brnaftr361]

Thank God people are moving towards this modality. I have a fervent hatred for textbooks and publishers. The former are antiquated, static, badly formatted, and often ride with distracting garbage in the margin, or worse inline. It makes actually reading them far more difficult than needs be, with unremarkable asides that may span pages and that are easy to get pulled into. While I understand that they have a purpose, they aren't for everyone so having a platform with the dynamism of a webpage is something that I hope will inevitably lend itself to future development along this course. Not to mention being able to have interactive questions that give quick feedback rather than requiring turning through pages to find out if you're on the right track... And this interactive stuff is just an excellent means to drive meaning from terse and difficult to explain systems.

Cheers to the folks that put this together, a thousand thanks for the travails you've been through to blaze these trails!

[stared]

See Seskir et al., "Quantum games and interactive tools for quantum technologies outreach and education", Optical Engineering 61(8), 081809(2022), https://doi.org/10.1117/1.OE.61.8.081809 (open access, but if you prefer ArXiv, https://arxiv.org/abs/2202.07756).

While it is focused on quantum mechanics & quantum computing, sections 3.2 Science-based Games, and 3.3 Explorable Explanations, discuss this medium (full disclaimer - I am one of the lead authors).

[smburdick]

My undergrad math professor created one of the first fully online linear algebra texts: http://linear.ups.edu/html/fcla.html It's integrated with Sage, a Python library for studying (among other things) number theory. Another prof at the same university also wrote his own linear book, using a lot more illustrations, but as a traditional textbook.

I see this book as a solid evolution in both directions. Nicely done!

[citizen_friend]

My gut reaction to this sort of thing is that textbooks work great and have a timeless quality. But with a little more thought, they certainly aren't optimal. Being able to see a video, hear a sound, or play with a figure can be powerful learning. I think my hesitation comes from the fact that this stuff just doesn't seem to have longevity (think educational java applets) and tends to be proprietary (shitty Pearson learning hw). How can we get newer media as robust as text and pngs?

[nutanc]

It does not have to do with the book or any other medium. It comes from the learner. You are right about the problems mentioned.

1. Stuff does not have longevity. This is because most of the new tools are outside curriculum. This does not encourage students to learn something extra.

2. Proprietary. Books providing add ons have a different goal. They want to sell their books. So the addons or just that. Add ons. They are not complete.

These were some of the thoughts which encouraged us to build [1]. Keep it curriculum focused so kids don't learn anything extra. No books to sell :)

[1] https://books.innings2.com/

[huygens6363]

If only there was some kind of magic device that has basic input facilities coupled with some kind of simple graphics output.

I jest, but I think a very basic computational platform - think 6502-style - with simple graphics could be standardized upon and anointed as universal educational computation base.

If you don’t touch the instruction set this can go a long way. The outputs of course need to be universal, but we have some experience with outputting stuff on machines. I think we are able to come to some sort of useable situation.

Think PDF or whatever with built-in NES emulator.

Is that what you have in mind?

[hannofcart]

It's not really a textbook but at this stage, 3Blue1Brown courses almost needs an obligatory mention for how fantastic they are.

https://www.3blue1brown.com/

[teleforce]

Previous posts on HN:

1) 2015 (78 comments):

https://news.ycombinator.com/item?id=10183725

2) 2019 (140 comments):

https://news.ycombinator.com/item?id=19264048

[dang]

Thanks! Macroexpanded:

Immersive Linear Algebra - https://news.ycombinator.com/item?id=26294588 - Feb 2021 (3 comments)

Immersive Linear Algebra (2016) - https://news.ycombinator.com/item?id=19264048 - Feb 2019 (140 comments)

Immersive Linear Algebra – textbook with fully interactive figures (2015) - https://news.ycombinator.com/item?id=13904881 - March 2017 (74 comments)

Immersive Linear Algebra – A free interactive online book - https://news.ycombinator.com/item?id=10183725 - Sept 2015 (78 comments)

[ethanholt1]

I hope that this sets a standard for future textbooks/publications. I haven’t been able to grasp several concepts in math unless I was able to properly visualize it, which most modern textbooks do with a terribly compressed and unsaturated JPG.

[ubj]

This looks like a fantastic resource. After a quick scan, I couldn't find any information on how this book was programmed / created. Does anyone know if a particular framework was used, or if this was all coded by hand?

[ayhanfuat]

Looks like the authors rolled out their own https://immersivemath.com/ila/javascript/samillustration3d.j...

[tunnuz]

I studied physics-based rendering from a book by one of the two authors (T. A-M), and it was written excellently. I'll have a look at this for sure, as I need a refresher every now and again.

[the-mitr]

A naive question: I see that they are using mathjax for the displaying mathematics content. But what are they using to create the interactive diagrams?

[akam4n4n]

looks like the future of education. especially with VR

[lambdaba]

I remember Jaron Lanier describing this vision of learning through VR, where a student in class would "become the triangle" in learning trig, etc.

[nextworddev]

Feel like a treatment of SVD is a must for an entry level Linear Algebra course

[fuzztester]

The navigation links at the bottom of the home page are too small on my phone.

Maybe a CSS issue ...

[javajosh]

Would love to see this done with geometric algebra AKA Clifford algebra.

[fuzztester]

The web site says math, but it seems to be only about linear algebra.

[gerdesj]

Which "subject" would you normally ascribe linear algebra to?

It looks like this is a first module within the Immersive math system. No doubt there will be more.

Why not look at what is presented rather than what is not?

[Omnipresent]

Are there such immersive math courses geared more towards middle / high schoolers?

[nutanc]

Cool to see stuff like this which makes math fun for everyone. I love stuff like this because it brings together two things I love, math and programming.

I mean textbooks are cool. But with the tools available to us we should be able to make almost any textbook interactive. It will need effort, pedagogy, programming skills and design. But it's certainly worth it.

Making an effort with this. Started with 6th to 10th grade math. Let's see how this goes.

[doctorhandshake]

Hell yeah. Linear algebra was a hole in my math education and has turned out to be far more relevant to my work than the calculus I spent so much time on. I’ve been teaching myself piecemeal on an as-needed basis but this looks like a great opportunity to finally get a cohesive overview.

[flandish]

I like this. I feel like I’m too old, at 45, to relearn and this may help!

[lupire]

The biggest barrier to learning is having a real motivating need to learn the thing. Young people aren't as dissolutioned about the uselessness of what they are learning relative to all the demands of adult life.

I've learned amazing things when I had a real reason pop pup, after a decade of idly wanting to learn it.