Immersive Linear Algebra (2015)

http://immersivemath.com/ila/index.html

by oumua_don17 • 2 years ago

876 71 2 years ago

immersivemath.com

whereismyacc3• 2 years ago

ah sick people from my uni

it's pretty messy tbh but it's a good idea

greymalik• 2 years ago

What’s messy about it?

bbor4• 2 years ago

It’s possible I’m alone in this, but the textbook / vaguely “academic” style of site always comes across as messy to me. That said, I think we’re spoiled by vaporware that invests huge money into style and flashy visuals — as anyone who’s been in school during the Blackboard/Piazza era knows, education software does not have to be pretty to be popular.

whereismyacc3• 2 years ago

maybe the layout just messed up on the resolution I looked at it with, there were boxes all over the place, the spinny thing on the main page scaled out of its bounding box. also I think it would be helpful to have some consistent design cues for which elements are interactive or what you can do with them.

if nothing else I feel each interactive canvas should have some kind of description of what you can do with it so you don't have to trial & error

dahart2• 2 years ago

I tried look at this page on an iPhone, and the figures kept resizing and the page was reflowing whenever I tried interacting with the diagrams, sometimes looking messy. That makes me thing it’s possible the parent was at an odd resolution that does look bad.

akam4n4n• 2 years ago

looks like the future of education. especially with VR

lambdaba• 2 years ago

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

bbor4• 2 years ago

Looks incredible! All this needs is a little bit of conversational AI magic in the background to filter and modulate the content according to plain-English student questions and its go time.

Note that this was finished in 2019, so now would be the perfect time for someone to polish this up and expand it to the rest of math! Assuming this is threeJS, you could get an open-source file format going for simulations, and even host crowdsourced applications of it to existing popular math textbooks by Figure/page #. I mean, linear algebra is cool, but the market for good free geometry education is limitless

Does anyone know if the big names in math education offer simulations yet, or is it all animations/images/videos still?

EDIT: definitely ThreeJS — love the vector chapter. What this needs is true spatial computing support - not pages with nested simulations, but site-wide (SPA-wide) simulated objects. What if every student in geometry class could have their own simulation on their Chromebook as they read/follow along? I can’t wait.

fallingsquirrel2• 2 years ago

It really pains me to see someone suggesting adding AI to a book like this. Current AIs are infamously bad at math. The last thing we need is ChatGPT misplacing a minus sign and confusing readers or setting back their understanding by weeks.

dhosek2• 2 years ago

I remember a friend reviewing some math before starting grad school was stymied by a typo in her textbook for an inordinate amount of time. It’s really vital that instructional materials avoid errors as much as humanly possible. AI right now ain’t it.

lupire3• 2 years ago

Please read the comment carefully before parroting a canned retort. It doesn't say what you think it says.

CamperBob22• 2 years ago

You clearly have no idea how effective an interactive conversation with a text can be. An AI doesn't have to be "good at math" to be useful. People (and programs) who are "good at math" are a dime a dozen. To be useful to a student, a language model just has to be good at answering questions about math.

That part works, right now. Try it. Go to ChatGPT4 and pretend you're a student who is having trouble grasping, say, what a determinant is. See how the conversation unfolds, then come back and tell us all how "infamously bad" the experience was. Better still, ask it about something you've had trouble understanding yourself.

bbor4• 2 years ago

The AI isn't doing math, the AI is curating the textbook material. In the same way that you have a host of different faculties that enable you to excel in all that you excel at, there is more to math (and math pedagogy) than arithmetical consistency

boomskats• 2 years ago

Just taking something like the threejs GLTFExporter and combining it with modelviewer.dev on the fly could enable a 'view in AR' button compatible with both SceneViewer and Quick Look (i.e. most mobile devices available today).

jimmySixDOF• 2 years ago

+1 for Spatial Computing here -- I see immersive here and just think 2D animations of 3D concepts, good start though it may be, is leaving possibilities on the table. 3D consumed inside a fully 6DOF 3D animated space is a better environment to transfer meaning. These collections of links could be piped into WebXR with just a little tweaking and really be immersive.

ubj• 2 years ago

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• 2 years ago

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

smburdick• 2 years ago

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!

WillAdams• 2 years ago

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... )

vitalnodo2• 2 years ago

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

vitalnodo2• 2 years ago

https://explorabl.es/

https://github.com/blob42/awesome-explorables

akdas• 2 years ago

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/

jovial_cavalier• 2 years ago

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

nutanc3• 2 years ago

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

doubloon• 2 years ago

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

__rito__• 2 years ago

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/)

ibobev• 2 years ago

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.

stared2• 2 years ago

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/).

Abishek_Muthian• 2 years ago

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

teleforce• 2 years ago

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• 2 years ago

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)

tunnuz• 2 years ago

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.

jgalt212• 2 years ago

Love the bootstrap 3. Clean, it works, and embraces the principle of least surprise.

brnaftr361• 2 years ago

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!

stared2• 2 years ago

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).

javajosh• 2 years ago

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

fuzztester2• 2 years ago

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

Maybe a CSS issue ...

fuzztester2• 2 years ago

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

gerdesj• 2 years ago

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?

doctorhandshake• 2 years ago

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.

ethanholt1• 2 years ago

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.

flandish• 2 years ago

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

lupire3• 2 years ago

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.

citizen_friend3• 2 years ago

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?

nutanc3• 2 years ago

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/

huygens63632• 2 years ago

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?

citizen_friend3• 2 years ago

Yes. And the latest iteration of JavaScript/canvas has had longevity, but it doesn’t have the robustness of a JPEG. What you describe would be interesting.

nutanc3• 2 years ago

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.

hannofcart• 2 years ago

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/

wdh5052• 2 years ago

One critique that glares in my face is "you changed the textbooks via hackers and now my children's development is your fault". These accusations fly when money (e.g. big textbook starts a media campaign) is on the line. As such, these interactive apps need to be able to handle that level of criticism if in a public school (before college).

These applications probably need to be client side only enabled and a hash that agrees to the hash of the "approved curriculum" for most parents to think that this might be okay, or a read-only USB rental from the school library that gets verified when it is checked back in.

I will not let the government install unknown tech on my computer, but I am willing to download a read only file. I do not want to have my children learning "new math" and be able to point at the technology as the problem "because hackers" or some other BS that has sounds true but has a high amount of effort to disprove coming while chatting with parents at a bus stop or PTA meeting.

https://en.wikipedia.org/wiki/Brandolini%27s_law

oivey• 2 years ago

It’s a web page.

dahart2• 2 years ago

I’ve never seen this particular accusation anywhere, do you have examples? You’re worried that someone will hack a math textbook to teach incorrect math that’s not obviously wrong or obviously hacked, but misleading and damaging to math education somehow? Or what kind of threat exactly are you imagining? Who’s got a secret plan to corrupt math education, and how does that work when math involves exercises and proofs? Brandolini’s Law certainly finds application in politics, but it’s news to me if anyone has ever taken the time to intentionally develop fake but believable academic curricula. Why would someone go to that level of effort, what would be the political agenda, and what makes you think it would get very far without getting caught and taken down?

wdh5052• 2 years ago

I don't necessarily think that math is where this critique is the strongest. As you say, this happens most in political arguments, and this critique is strongest when talking about history books. I listened to a rant about this once and I think it is adjacent enough to be relevant as a critique here:

While I attended a church in a different state, the Sunday school teacher decided to get on a talking point aka rant about how history books are going to be changed via an opaque technology process to save kids backs from heavy textbooks and this was the BIG BAD. The entire topic kinda blindsided me at the time as I was leaning toward khan academy and other progressive teaching techniques at the time. (Still do, but i have had a number of bad experiences with subscription models for knowledge that is a prerequisite for certain jobs).

I bet that math textbooks are the more exact science, so it will probably pass over well, but some people (conservatives who don't trust change) will probably mount resistance if not addressed.

I just wanted to say that there are two sides (monetary incentives) to the question "should we adopt", and it directly shapes the narrative (and may cause a narrative to change into a political one).

Regarding "never heard of deliberately fake curriculum", i agree that i havent seen a deliberately fake math curriculum, but i have seen a number of "montressouri schools" that have no credentials and have not updated based on science for years. Most "charter schools" have a similar standard.

Omnipresent• 2 years ago

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

nextworddev• 2 years ago

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

the-mitr• 2 years ago

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?

Immersive Linear Algebra (2015)

Related Stories