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Comment by RobbieGM | Hacker News Reader

I took this course 3 years ago. I found it fast-moving, and it focused a lot more on applications than fundamentals, which meant it was more wide than it was deep. This didn't turn out so well when I decided to study ML later and needed stronger linear algebra fundamentals, but it was a fun course. There were a couple interesting course projects, one of which was using linear algebra to balance a (simulated) 2D robot.

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No one, and let me repeat that, no one "gets" linear algebra, differential equations, or frequency domain on the first pass. It takes years to absorb and multiple passes.

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.

Not with the way it is taught. But if the course structure is changed slightly to have reinforcement of early concepts woven through the course, people learn much better.

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.

> No one, and let me repeat that, no one "gets" linear algebra, differential equations, or frequency domain on the first pass. It takes years to absorb and multiple passes...

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?

Really for my linear algebra courses in pure math i was comfortable--but some applications courses would help me understand the usefulness.

Tangent, but how does that course make anything "more equitable" as per the video?

One of the umich grad school prereqs for economics was linear algebra, and it was literally just that - pure math.

Where do you feel the gaps were for what you needed for ML? Downthread, Jesse Grizzle notes they've added some stuff in 2023 (it's on Github I think?) to support an ML class.

What would you recommend for building a strong linear algebra foundation?

UMich has a couple other linear algebra courses that might be better for that: MATH 214, MATH 217 are the numbers if I remember correctly. 217 is known for having a high workload and greater rigor, but some say it's worth it even for non-Math majors.

In terms of books, I would say Linear Algebra Done Right. The book requires some background to understand efficient. But, once you have some background, it is very good for having a systematic and rigorous understanding of Linear Algebra theory

LADR is the SICP of linear algebra.

If you can handle it, fabulous. If not, you're really in deep doo-doo. There did not seem to be a half-way to me. Astounding exercises, and also some are astoundingly hard.

Anything by Gilbert Strang

https://youtube.com/playlist?list=PLE7DDD91010BC51F8

Also a big fan of Strang. "Linear algebra and its applications" has problem sets with solutions for odd number questions.

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.

I took 18.085 (applied linear algebra) as a grad student at MIT. The best taught math course I've ever taken. Strang is a fantastic teacher.

After working with math academy, any form of video learning seems so inefficient. I think people lose a lot of time watching these videos thinking that they are learning without applying anything by themselves.

It’s $50/month online course. As effective as it can be, I can’t justify this expense for myself, as much as I’m fascinated by math.

i don't really care how many people i respect liked it, i have to be honest, i hated strang's "linear algebra and its applications."

there's a strang text on computational science that was much more my speed (less of the baby talk and repetitive manual arithmetic exercises) and i think that some of the revisions that came later (+ "learning with data") were better.

i did not find doing endless exercises of gaussian elimination or qr factorization by hand on small matrices to be all that enlightening.

this michigan course looks awesome!

> less of the ... repetitive manual arithmetic exercises

I think this post (from a math academy employee) has a good argument for why these sorts of exercises are important. It's about basic arithmetic, but I think it applies to tedious things like performing gaussian elimination on small matrices as well.

https://www.justinmath.com/if-you-want-to-learn-algebra-you-...

I like to come at it from both angles - higher level with useful applications, and then lower level "I could maybe implement this if I had to" exercises. The latter are tedious, and hard to motivate effort for without the former. Ultimately, as the post argues, I agree that if you don't understand the lower level (tedious) operations, you will only get so far in your ability to apply LA.

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