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A comment on Robotics 101 at UMich: Applied numerical linear algebra as intro linear algebra. Parent comment

Re:Robotics 101 at UMich: Applied numerical linear algebra a... by frognumber on Wednesday January 08, 2025 @02:21PM (#42637509)
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.

[ Parent | on HN ]
Re:Robotics 101 at UMich: Applied numerical linear algebra a... by btilly on Wednesday January 08, 2025 @03:38PM (#42638203)
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.

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Re:Robotics 101 at UMich: Applied numerical linear algebra a... by almostgotcaught on Thursday January 09, 2025 @01:46PM (#42648632)
> 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?

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Re:Robotics 101 at UMich: Applied numerical linear algebra a... by banku_brougham on Thursday January 09, 2025 @06:38PM (#42650990)
Really for my linear algebra courses in pure math i was comfortable--but some applications courses would help me understand the usefulness.
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