I recently taught a linear algebra class. Before I taught it, Momchil Konstantinov recommended I check out the Youtube channel 3Blue1Brown (produced by Grant Sanderson), which apparently had some nice videos about linear algebra. I was too busy preparing to teach. Once marking the exam was over, I thought I would relax by taking his advice and seeing someone else's take on linear algebra.
My mind was blown.
If you haven't already seen these videos, you should watch them (whether you're a nonmathematician or a tenured professor or anyone in between). The aim of the videos is to attempt to convey some of the intuition behind linear algebra (vectors, matrices, determinants, eigenvectors etc) using stunning visuals and extremely well-thought out narrative.
Leaving aside the visuals for a moment, the narrative is perfect:
- It bothers to point out many of the small nuances which most mathematicians leave out in their explanations and which (having now taught linear algebra) I know my students didn't get first time round.
- It selects a well-motivated path through the material, showing the
viewer where the idea for a matrix comes from. Happily, I can say
that my lectures followed a broadly similar course, but I can say
without a doubt that Grant Sanderson did it better (for example,
focusing on better examples first). I think his presentation is
pretty much optimal.
However, the visuals are what really set this apart from other online maths videos.
The visuals are mathematical animations produced in Python, and my immediate thought was: that's what linear algebra looks like in my head, that's what's going on in my head when I try to explain to people about linear algebra. The trouble is, I struggle to get these moving 2- or 3-d pictures out of my head and into the heads of students. I try to draw things, and I move my arms around, but I've never seen anything that conveys the ideas as well as these animations.
My next thought was: it must have taken hours to produce these, there's no way I'd have time to do that for each lecture. Indeed, on reading more about Grant Sanderson (the person behind 3blue1brown), I discovered that this whole project started as a showcase for his Python graphics library, so the point was to develop amazing graphics for use in educational videos. You can imagine my joy to find that his Python library manim is available (open source) from his GitHub page.
I already downloaded it and will be playing with it in the coming months. There are various things I really want to use it to demonstrate (mutation of polygons and some of the stuff about Lagrangian torus fibrations I've been lecturing about in the last year).
Next time I teach linear algebra, 3Blue1Brown will be there alongside Halmos's "Finite-dimensional vector spaces" as recommended viewing.