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RobbieGM | 1 year ago

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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frognumber|1 year ago

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.

almostgotcaught|1 year ago

> 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?

banku_brougham|1 year ago

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

pxmpxm|1 year ago

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.

tptacek|1 year ago

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.

byefruit|1 year ago

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

krosaen|1 year ago

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.

RobbieGM|1 year ago

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.

gauge_field|1 year ago

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