9 ms·

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

296 points by jamesliudotcc 2y ago

casey2 2y ago
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.
eigenman 2y ago
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 2y ago
Youtube playlist for the course: https://www.youtube.com/playlist?list=PLdPQZLMHRjDK8ZbLIcq1Q2PQobIi68dpv https://www.youtube.com/playlist?list=PLdPQZLMHRjDK8ZbLIcq1Q... Materials on Github: https://github.com/michiganrobotics/rob101 https://github.com/michiganrobotics/rob101
trillic 2y ago
MATH 214 (intro to Linear) was the least enjoyable class during my undergraduate at Umich. This seems like a better intro.
- jackschultz 2y ago
  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.
  - jumploops 2y ago
    > Lot of great classes in the EECS department though. Couldn’t agree more, Jack! Great times during 482… tranquil compared to the 470 slog that started immediately after every night :)
    - jackschultz 2y ago
      I totally remember 482 (Operating Systems for those reading) being really interesting. Story I remember is one of the final projects and dealing with locks in C++ world where I'd get close to full solution, but some errors from the locks, then I'd make a change and suddenly those previous failing tests passed but new ones failed. I didn't realize that could happen. Great times. And I really liked how we did it all in C++ (other than computer vision 442 that was in matlab) rather than Python which some places do. Having that lower level understanding of languages in school makes understanding code so much easier, and something I didn't have to learn on my own.
- semperdark 2y ago
  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.
angry_moose 2y ago
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.
- cashsterling 2y ago
  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.
- WillAdams 2y ago
  Currently watching: https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-fall-2010/video_galleries/video-lectures 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.
- BeetleB 2y ago
  > 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).
  - deleted 2y ago
    [deleted]
  - tonyarkles 2y ago
    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.
yardie 2y ago
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.
- gertlex 2y ago
  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.
RobbieGM 2y 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.
- pxmpxm 2y 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.
- byefruit 2y ago
  What would you recommend for building a strong linear algebra foundation?
  - RobbieGM 2y 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 2y 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
    - fn-mote 2y ago
      LADR is the SICP of linear algebra. If you can handle it, fabulous. If not, you're really in deep doo-doo. There did not seem to be a half-way to me. Astounding exercises, and also some are astoundingly hard.
profgrizzle 2y ago
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.
profgrizzle 2y ago
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.
- tptacek 2y ago
  This is (one of?) the authors of the course, for what it's worth. Welcome to HN! Pelt him with questions, everybody. :)
alexk 2y ago
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.
mettamage 2y ago
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
- sn9 2y ago
  Who are you trying to prove this to?
  - redmerchant2 2y ago
    Probably trying to transition from a SWE role to a ML one
    - mettamage 2y ago
      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.
      - sn9 2y ago
        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.
    - mp05 2y ago
      The writing is certainly all over the wall, in bold red ink.
- caspper69 2y ago
  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). Program link: https://netmath.illinois.edu/ 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.

296 points by jamesliudotcc 2y ago

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.

eigenman 2y ago

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 2y ago

Youtube playlist for the course: https://www.youtube.com/playlist?list=PLdPQZLMHRjDK8ZbLIcq1Q2PQobIi68dpv https://www.youtube.com/playlist?list=PLdPQZLMHRjDK8ZbLIcq1Q... Materials on Github: https://github.com/michiganrobotics/rob101 https://github.com/michiganrobotics/rob101

trillic 2y ago

MATH 214 (intro to Linear) was the least enjoyable class during my undergraduate at Umich. This seems like a better intro.

jackschultz 2y ago
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.
- jumploops 2y ago
  > Lot of great classes in the EECS department though. Couldn’t agree more, Jack! Great times during 482… tranquil compared to the 470 slog that started immediately after every night :)
  - jackschultz 2y ago
    I totally remember 482 (Operating Systems for those reading) being really interesting. Story I remember is one of the final projects and dealing with locks in C++ world where I'd get close to full solution, but some errors from the locks, then I'd make a change and suddenly those previous failing tests passed but new ones failed. I didn't realize that could happen. Great times. And I really liked how we did it all in C++ (other than computer vision 442 that was in matlab) rather than Python which some places do. Having that lower level understanding of languages in school makes understanding code so much easier, and something I didn't have to learn on my own.
semperdark 2y ago
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.

angry_moose 2y ago

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.

cashsterling 2y ago
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.
WillAdams 2y ago
Currently watching: https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-fall-2010/video_galleries/video-lectures 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.
BeetleB 2y ago
> 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).
- deleted 2y ago
  [deleted]
- tonyarkles 2y ago
  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.

yardie 2y ago

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.

gertlex 2y ago
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.

RobbieGM 2y 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.

pxmpxm 2y 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.
byefruit 2y ago
What would you recommend for building a strong linear algebra foundation?
- RobbieGM 2y 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 2y 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
  - fn-mote 2y ago
    LADR is the SICP of linear algebra. If you can handle it, fabulous. If not, you're really in deep doo-doo. There did not seem to be a half-way to me. Astounding exercises, and also some are astoundingly hard.

profgrizzle 2y ago

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.

profgrizzle 2y ago

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.

tptacek 2y ago
This is (one of?) the authors of the course, for what it's worth. Welcome to HN! Pelt him with questions, everybody. :)

alexk 2y ago

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.

mettamage 2y ago

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

sn9 2y ago
Who are you trying to prove this to?
- redmerchant2 2y ago
  Probably trying to transition from a SWE role to a ML one
  - mettamage 2y ago
    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.
    - sn9 2y ago
      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.
  - mp05 2y ago
    The writing is certainly all over the wall, in bold red ink.
caspper69 2y ago
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). Program link: https://netmath.illinois.edu/ 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.