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 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.
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.
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 it assumed everyone already knew linear algebra going in, and it was a disaster.
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 and statistics. I'm paraphrasing but "it's easier to teach an IE how to do FEA than it is to teach a mechanical engineer DOE and Weibull analysis".
Same... I didn't have to take Linear Algebra in ChemE undergrad. DiffEq had a little bit of LA... and ChemE had few classes where bits of pieces of LA where introduced and applied.
Graduate school definitely made up for lost time... LA was very front and center in the applied math courses.
Chapter 13 of the textbook was added in January 2022. It covers separating hyperplanes, signed distance to a hyperplane, Max-margin Classifiers, a remark on Soft Margin Classifiers, and the Orthogonal Projection Operator. The additional material was added to support EECS 445, Machine Learning at Michigan.
For folks interested in 101 on linear algebra - I highly recommend book "Linear Algebra: Theory, Intuition, Code" by Mike X Cohen.
After trying a couple of courses and books, I liked it the most because it gives a pretty deep overview of the concepts, alongside the numpy and matlab code, which I found refreshing.
It's has good amount of proofs and has sections designed to build your intuition, which I really appreciated.
Chapter 13 of the textbook was added in January 2022. It covers separating hyperplanes, signed distance to a hyperplane, Max-margin Classifiers, a remark on Soft Margin Classifiers, and the Orthogonal Projection Operator. The material was added to support EECS 445, Machine Learning at Michigan.
For engineering we had to pick either multivariate calculus or linear algebra for more upper level math courses. I picked multivariate, and I'll say it was also my least enjoyable there. I look back wondering what would have gone different if I picked linear algebra instead, but who knows, maybe I'd have just as blech of an experience with that. Lot of great classes in the EECS department though.
MATH 217 was one of my favorites! Ive heard that the math department can be a little unenthusiastic about the non-major courses, but overall it’s a really welcoming place in my experience.
I love Linear Algebra. I took it in college almost 20 years ago and I still use it everyday. The higher level maths almost broke me academically. And it was a course in LA that really kept my head in the game. Even now, when I'm talking to students I try and encourage them to take the class if it's available.
For me LA was spread across several courses (I was at Michigan in engineering too), and I never got enough internalization of when it was useful from these, sadly. It definitely seemed more useful that a lot of the higher level maths, like you imply.
What's the best online credential for doing linear algebra? I like to do some self-studying but also, I'd like some form of "evidence" that I actually know my stuff and don't have t constantly explain that I do
I can't personally vouch for the program as I have not attended, but the University of Illinois offers quite a few mathematics courses online geared toward high school students, distance learners, and those preparing for grad school.
It is self-paced, so may not be what you're looking for, and it is expensive ($1250 if you have a BS already), but I seriously considered going this route before deciding to save big $$ and attend the local community college (which was actually a decent decision).
They offer 2 linear algebra courses, Math 257, which is Linear Algebra with Computer Applications (likely the "easy" applied version) and Math 416, Abstract Linear Algebra. Some of these Netmath courses do not have online lectures, but the Abstract LA course has video lectures from 2016.
From their site: "Math 416 is a rigorous, abstract treatment of linear algebra. Topics to be covered include vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalizability, and inner product spaces. The course concludes with a brief introduction to the theory of canonical forms for matrices and linear transformations."
When I was investigating what to do in order to solidify my math credentials (still a work in progress), I knew UofI was a good school, and figured credit in one of their courses (online or not) would not be a terrible investment. At a bare minimum it wouldn't be belittled or untrusted like other online certificates might.
Plus the credit should transfer anywhere, if that's important.
I like Lay, it's one of the few math books anyone can read cover to cover, prove every statement and solving every problem, with no experience. It's like the Thomas' calculus equivalent linear algebra. If you do the work you'll get an easy A and will have built a great foundation for further engineering or theoretical study.
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.
dotancohen|1 year ago
https://www.youtube.com/playlist?list=PLdPQZLMHRjDK8ZbLIcq1Q...
Materials on Github:
https://github.com/michiganrobotics/rob101
RobbieGM|1 year ago
frognumber|1 year ago
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.
pxmpxm|1 year ago
One of the umich grad school prereqs for economics was linear algebra, and it was literally just that - pure math.
tptacek|1 year ago
byefruit|1 year ago
angry_moose|1 year ago
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 it assumed everyone already knew linear algebra going in, and it was a disaster.
BeetleB|1 year ago
Wow. In my undergrad all engineering majors had to take linear algebra (calc 3 was optional for computer engineering).
mp05|1 year ago
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 and statistics. I'm paraphrasing but "it's easier to teach an IE how to do FEA than it is to teach a mechanical engineer DOE and Weibull analysis".
WillAdams|1 year ago
https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-...
and that assumption seems to be there as well, so very glad of the posting of the Youtube links elsethread.
cashsterling|1 year ago
Graduate school definitely made up for lost time... LA was very front and center in the applied math courses.
profgrizzle|1 year ago
tptacek|1 year ago
alexk|1 year ago
After trying a couple of courses and books, I liked it the most because it gives a pretty deep overview of the concepts, alongside the numpy and matlab code, which I found refreshing.
It's has good amount of proofs and has sections designed to build your intuition, which I really appreciated.
profgrizzle|1 year ago
trillic|1 year ago
jackschultz|1 year ago
semperdark|1 year ago
yardie|1 year ago
gertlex|1 year ago
mettamage|1 year ago
caspper69|1 year ago
It is self-paced, so may not be what you're looking for, and it is expensive ($1250 if you have a BS already), but I seriously considered going this route before deciding to save big $$ and attend the local community college (which was actually a decent decision).
Program link: https://netmath.illinois.edu/
They offer 2 linear algebra courses, Math 257, which is Linear Algebra with Computer Applications (likely the "easy" applied version) and Math 416, Abstract Linear Algebra. Some of these Netmath courses do not have online lectures, but the Abstract LA course has video lectures from 2016.
From their site: "Math 416 is a rigorous, abstract treatment of linear algebra. Topics to be covered include vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalizability, and inner product spaces. The course concludes with a brief introduction to the theory of canonical forms for matrices and linear transformations."
When I was investigating what to do in order to solidify my math credentials (still a work in progress), I knew UofI was a good school, and figured credit in one of their courses (online or not) would not be a terrible investment. At a bare minimum it wouldn't be belittled or untrusted like other online certificates might.
Plus the credit should transfer anywhere, if that's important.
sn9|1 year ago
casey2|1 year ago
eigenman|1 year ago