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Robotics 101 at UMich: Applied numerical linear algebra as intro linear algebra

robotics.umich.edu

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Re: Robotics 101 at UMich: Applied numerical linear algebra as intro linear algebra

#61

Post by mp05 »

lupire wrote: post #21
mp05 wrote: post #16

Earlier quoted context omitted.

Yes back in 2005 when I first went to undergrad as a mech engineering major, linear algebra was not a requirement. Our mechanics professors were highly irritated by this. 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…

Why can't professors set LA as a prereq for their courses? Or use it in their courses and earn students that they need to learn it so succeed?

It's up to department heads and dean and they're pressured by ABET and companies that write them checks.

Education is secondary; this is job training! We need to crank out people ready to drop into Boeing's way of doing things!

Re: Robotics 101 at UMich: Applied numerical linear algebra as intro linear algebra

#63

Post by sn9 »

caspper69 wrote: post #19
BeetleB wrote: post #14

Earlier quoted context omitted.

> For some reason linear algebra still isn't part of standard Mechanical Engineering course load (Calc 1, 2, 3, DiffEq) Wow. In my undergrad all engineering majors had to take linear algebra (calc 3 was optional for computer engineering).

This would have helped me get an actual CS degree 25 years ago instead of CS-lite (networking & server admin). 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…

You should check out Math Academy.

It schedules everything for you including the review so you just have to keep showing up to do the work.

Even as little as 30 minutes per day done consistently for months will have you make tremendous progress.

And once you master multivariable calculus, fields like probability and machine learning will be unlocked for you.

Re: Robotics 101 at UMich: Applied numerical linear algebra as intro linear algebra

#64

Post by sn9 »

mettamage wrote: post #52
redmerchant2 wrote: post #41

Earlier quoted context omitted.

Probably trying to transition from a SWE role to a ML one

I'd like to keep that option open yea, not sure if I want to. I just want to learn it, but I also want to prove to people that I can do it. This is one of the things I'm playing with. Not why I'm going to study it though, but yea, I might want to switch.

If it's ML you want, you should check out Math Academy.

They have courses on linear algebra and mathematics for machine learning.

No certificates, but you can always demonstrate your mastery in interviews.

You can always build a project as well.

Re: Robotics 101 at UMich: Applied numerical linear algebra as intro linear algebra

#65

Post by caspper69 »

caspper69 wrote: post #54
casey2 wrote: post #47

Earlier quoted context omitted.

A few hours per week simply isn't enough, the best success I've had studying was 6 hours a day, resting for 3 (leisure activity), "working" for 3 (class, commute, chores, related reading) and sleeping 12 hours. In books like Stewart, staring at a theorem until you can write it's proof should trivialize most problems in the book. If a method for solving a particular problem is too difficult for you maybe consider rese…

Thank you. I appreciate the feedback and the pointers.

I honestly don't think the problem is the textbook.

I have Stewart (both the standard version and Early Transcendentals), and I also have a book from 1967 by Tom Apostol (the 2 volume set that covers single & multivariable calculus, linear algebra, a subtle introduction to differential equations and some probability as well).

My gut feeling is that I just don't know the correct way to study math in general. I have no problem doing the work. But it feels more like mechanical or algorithmic solving than it does like true understanding. There is a difference. I can't deconstruct a problem and think in the abstract to come up with a different method to solve it.

And there always seem to be some fundamental truth that I'm always missing. A part of a proof here or an axiom there that seems obvious to other people who study these subjects that I just don't "see".

It's incredibly frustrating, because deep down I know I have the aptitude for this stuff. I guess that most subjects have always been easy for me. I could ace exams without cracking the book (or just skimming).

Math is not like that. You need to read. And then re-read. And then do. And then do some more. And then go back and re-read again to see what you missed. And there's a lot of things that are between the lines, and if you're not following it, those things fall by the wayside.

I just need to learn how to learn math. I need to learn how to deconstruct notation and proofs to truly understand them. And there's no shortcut. It's grind and grind until it all becomes clear. That sort of thing is just difficult for me.

Re: Robotics 101 at UMich: Applied numerical linear algebra as intro linear algebra

#66

Post by monadINtop »

caspper69 wrote: post #19
BeetleB wrote: post #14

Earlier quoted context omitted.

> For some reason linear algebra still isn't part of standard Mechanical Engineering course load (Calc 1, 2, 3, DiffEq) Wow. In my undergrad all engineering majors had to take linear algebra (calc 3 was optional for computer engineering).

This would have helped me get an actual CS degree 25 years ago instead of CS-lite (networking & server admin). 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…

If by 3d-calc you mean vector calculus then yeah I never actually understood any of it, I just moved on to differential forms and the tensor calculus and Riemannian geometry and then wondered why anyone bothered with 3d-calculus in the first place.

Most of the time I've found that the deeper I plunge into abstraction in math I get rewarded with an extremely elegant formalism. Its like upgrading your weapon in dark souls, the early game enemies get one-shotted when you go back.

Re: Robotics 101 at UMich: Applied numerical linear algebra as intro linear algebra

#67

Post by gessha »

kosmet wrote: post #35
krosaen wrote: post #24

Earlier quoted context omitted.

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…

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.

Re: Robotics 101 at UMich: Applied numerical linear algebra as intro linear algebra

#68

Post by krosaen »

a-dub wrote: post #50
krosaen wrote: post #24

Earlier quoted context omitted.

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…

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 e…

> 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.

Re: Robotics 101 at UMich: Applied numerical linear algebra as intro linear algebra

#69

Post by almostgotcaught »

frognumber wrote: post #33
RobbieGM wrote: post #7

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…

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 yea…

> 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?

Re: Robotics 101 at UMich: Applied numerical linear algebra as intro linear algebra

#70

Post by eigenman »

I taught numerical linear algebra in grad school and was really frustrated that even the applied math department took so long to build up to solving linear systems and eigen-decompsotions. The ordering of the material in the textbook is great, focusing on algorithms and decompositions.
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