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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

#71

Post by BeetleB »

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…

> It's that I hate calculus. Not the subject itself, just the grinding away at problem sets.

Most math majors I knew hated the standard calculus courses, for precisely this reason. It's taught this way because they're targeting engineers and some hard sciences (physics).

The reason is that for many of those majors (EE, physics), you will take courses where doing calculus is your daily bread and butter. You need to be as adept at it as algebra. Over 50% of HW problems in those courses will involve calculus. They really don't want students who understand circuits but can't do anything useful because they stumble on calculus.

They are the largest "customers" of the math department, so the department caters to them.

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

#72

Post by defrost »

BeetleB wrote: post #71
caspper69 wrote: post #19

Earlier quoted context omitted.

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…

> It's that I hate calculus. Not the subject itself, just the grinding away at problem sets. Most math majors I knew hated the standard calculus courses, for precisely this reason. It's taught this way because they're targeting engineers and some hard sciences (physics). The reason is that for many of those majors (EE, physics), you will take courses where doing calculus is your daily bread and butter. You need to be…

I swapped out from being an Engineering major (consistently in the top 5 scoring Engineering students out of a first year intake of 300) to being a math major for similar reasons - Engineering has a lot of rote learning grind exams, not so much exploration of deep fundementals.

The Math dept has numerours courses loosely covering similar material, Math 100 - first year math for math nerds, Math 110 - first math for engineering students, Math 120 - math for business majors, etc.

Math for math majors ( the 100 stream ) had 20 students in all (IIRC) most of whom now hold academic positions, Math 110 had the 300 engineering students, other streams had cross over students from business, medicine, law, et al.

Future mathematicians (and theoritical physicists, etc) are indeed the smallest group the Math Dept. catered for.

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

#73

Post by banku_brougham »

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…

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

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

#74

Post by tonyarkles »

BeetleB wrote: post #14
angry_moose wrote: post #4

Man this would have been nice when I was in school. 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…

> 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).

I did an EE/CS dual degree and there was a really interesting difference between the linear algebra courses offered in both departments.

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.

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

#75

Post by jamesliudotcc »

caspper69 wrote: post #65
caspper69 wrote: post #54

Earlier quoted context omitted.

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…

I feel what you're describing very viscerally. I have tried so many times as an adult to finally get linear algebra. Worked my way through Strang to eigenvalues and eigenvectors repeatedly. Still feel like I am failing to see something.

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I hear Apostol is hard. Like Spivak-level hard.

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