https://www.youtube.com/playlist?list=PLdPQZLMHRjDK8ZbLIcq1Q...
Materials on Github:
See:
Bruner / Spiral Curriculum.
Ebbinghaus / Spacing effect
Hattie / Deep-surface-transfer learning
Chunking ("How People Learn" has a good copy on this)
Etc.
The way you do this is you take a course, and then you take more courses. After a few years, it all connects and makes sense. The first course, I find, is often best short, simplified, and applied. Once you get through that, you can go deeper.
Different angles are nice too. For linear algebra:
- Quantum computing
- Statistics and probability
- Machine learning
- Control theory
- Image processing
- Abstract algebra / groups / etc.
- Computer graphics
All come to mind.
On a mile-high level, this course seems ideal for a first pass. On a detailed level, I'm confused by some licensing issues.
At least that was my experience when I taught it. See https://bentilly.blogspot.com/2009/09/teaching-linear-algebr... for more detail on my experience.
I don't understand the point of this comment. On the one hand you're trying to encourage people by saying "don't feel bad you didn't get it the first time" but then you throw a mountain more work/terms/books at them? You think it's encouraging to a student to hear that if they didn't succeed in this robotics class because the LA coverage wasn't great ...... they should go take quantum computing, control theory, abstract algebra classes?
One of the umich grad school prereqs for economics was linear algebra, and it was literally just that - pure math.
Would highly recommend https://mathacademy.com/courses/linear-algebra or https://mathacademy.com/courses/mathematics-for-machine-lear...
I originally spent time working through practice problems from one of Strang's books, now really appreciate how systematic math academy is in assessing, building a custom curriculum, then doing spaced repetition.
For some reason linear algebra still isn't part of standard Mechanical Engineering course load (Calc 1, 2, 3, DiffEq) which made life extremely difficult in some of the later classes. I remember spending weeks brute forcing a lot of things that would have been trivial with a little bit of matrix math.
I took a superficially similar class as a 400 level elective but it assumed everyone already knew linear algebra going in, and it was a disaster.
Wow. In my undergrad all engineering majors had to take linear algebra (calc 3 was optional for computer engineering).
It's not that I can't do calculus, I took it in high school, and then again in my first go-round in CS. It's that I hate calculus. Not the subject itself, just the grinding away at problem sets.
I did a refresher in pre-calc, calc I, calc II & discrete mathematics during COVID at the local community college (was planning to finish the few credits I need for an actual CS BS) & I started calc III twice (but dropped both times). I even got a 4.0 on my first calc III exam (and this was an in-person class, so no online shenanigans).
I just have some kind of weird aversion to 3 dimensional calculus. I have convinced myself that I'm simply not smart enough to actually do the work. I understand it, I just get clammy with it.
Truth be told, maths are my kryptonite. Despite working with numbers all day every day for 30+ years, and writing a lot of software over the years (and not just CRUD, but games of all things), I am absolutely ashamed that I just can't seem to grok math with any rigor.
I have all the Stewart textbooks on my shelf, many textbooks from libgen (ones I've seen recommended on HN from people who went to much better universities than I attended), and I even work through problems a few hours per week. I just can't seem to make that leap from a guy who's "good with numbers" (from a layperson's perspective) to a guy who's good at math.
Maybe I need to break open one of my physics textbooks and actually use the calculus in an applied context and that will break whatever mental barrier I have (I've even watched all of the 3 blue 1 brown videos, countless youtube lectures, etc).
Michigan doesn't seem to require it as the College of Engineering core classes or as part of the BSME (checked because they're who this course is through):
https://me.engin.umich.edu/academics/undergrad/handbook/bach...
And my alma mater has a very similar progression.
For the EEs we were given a crash course in GE120, which all engineering students had to take. It covered how to use determinants, Gaussian elimination and matrix inversion, and those kinds of “basic” LA tools, plus some simple numerical methods stuff like Newton’s Method. In second year we had a short lab course that focused on how to use Matlab, and a circuits analysis course that pretty much forced us to learn how to represent large sets of equations in matrix form and invert them to solve all of the variables at once. Very very practical.
And then in third year I had to take a 200-level linear algebra course from the Math department to satisfy the requirements for the CS degree. I chose the honours version of it and… holy moly. I thought it was going to be a gimme class but it turned out to be very theory-heavy, of which I had learned almost none in engineering. The first month kicked my ass pretty hard. Once we got out of the low-level theory (which was truly amazing to take in) and into the more advanced things that I’d been using for 2 years but didn’t know “why”, everything changed. Many of my peers were struggling to understand why you’d want to do some of this stuff and I was just super excited to finally understand why the “just turn the crank” math I’d been doing actually worked.
I don't think this has changed much (but absolutely should). I've watched in real time as Micron representatives reject mechanical engineers and prefer résumés from industrial engineers for design roles due to their superior grasp on linear algebra and statistics. I'm paraphrasing but "it's easier to teach an IE how to do FEA than it is to teach a mechanical engineer DOE and Weibull analysis".
Or use it in their courses and earn students that they need to learn it so succeed?
Thankfully the companies I've worked for have done a really good job with advanced stats training.
https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-...
and that assumption seems to be there as well, so very glad of the posting of the Youtube links elsethread.
Graduate school definitely made up for lost time... LA was very front and center in the applied math courses.
After trying a couple of courses and books, I liked it the most because it gives a pretty deep overview of the concepts, alongside the numpy and matlab code, which I found refreshing.
It's has good amount of proofs and has sections designed to build your intuition, which I really appreciated.
Couldn’t agree more, Jack! Great times during 482… tranquil compared to the 470 slog that started immediately after every night :)
It is self-paced, so may not be what you're looking for, and it is expensive ($1250 if you have a BS already), but I seriously considered going this route before deciding to save big $$ and attend the local community college (which was actually a decent decision).
Program link: https://netmath.illinois.edu/
They offer 2 linear algebra courses, Math 257, which is Linear Algebra with Computer Applications (likely the "easy" applied version) and Math 416, Abstract Linear Algebra. Some of these Netmath courses do not have online lectures, but the Abstract LA course has video lectures from 2016.
From their site: "Math 416 is a rigorous, abstract treatment of linear algebra. Topics to be covered include vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalizability, and inner product spaces. The course concludes with a brief introduction to the theory of canonical forms for matrices and linear transformations."
When I was investigating what to do in order to solidify my math credentials (still a work in progress), I knew UofI was a good school, and figured credit in one of their courses (online or not) would not be a terrible investment. At a bare minimum it wouldn't be belittled or untrusted like other online certificates might.
Plus the credit should transfer anywhere, if that's important.
Just be warned that this is literally the graduate level linear algebra course taken by mathematics majors. If you are looking for applications, this might not be it. On the other hand, if you are looking for a deep understanding of the fundamentals - I would say you found it.
