[HN Gopher] Robotics 101 at UMich: Applied numerical linear alge...
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       Robotics 101 at UMich: Applied numerical linear algebra as intro
       linear algebra
        
       Author : jamesliudotcc
       Score  : 164 points
       Date   : 2025-01-08 13:11 UTC (9 hours ago)
        
 (HTM) web link (robotics.umich.edu)
 (TXT) w3m dump (robotics.umich.edu)
        
       | dotancohen wrote:
       | Youtube playlist for the course:
       | 
       | https://www.youtube.com/playlist?list=PLdPQZLMHRjDK8ZbLIcq1Q...
       | 
       | Materials on Github:
       | 
       | https://github.com/michiganrobotics/rob101
        
       | trillic wrote:
       | MATH 214 (intro to Linear) was the least enjoyable class during
       | my undergraduate at Umich. This seems like a better intro.
        
         | jackschultz wrote:
         | 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 wrote:
           | > 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 wrote:
             | 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 wrote:
         | 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 wrote:
       | 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.
        
         | WillAdams wrote:
         | Currently watching:
         | 
         | 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 wrote:
         | > 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).
        
           | angry_moose wrote:
           | Maybe some schools do but it's baffling to me its not a
           | universal requirement. It'd be dramatically more useful than
           | Calc3 for most engineers.
           | 
           | Michigan doesn't seem to require it as the College of
           | Engineering core classes or as part of the BSME (checked
           | because they're who this course is through):
           | 
           | https://me.engin.umich.edu/academics/undergrad/handbook/bach.
           | ..
           | 
           | And my alma mater has a very similar progression.
        
             | lupire wrote:
             | The Robotics concentration requires Linear (Matrix)
             | Algebra.
             | 
             | And some upper level courses have a prerequisite.
             | 
             | But indeed it does seem a avoidable for many MechE majors.
             | 
             | Funny thread about UM engineering students avoiding taking
             | UM math classes. https://www.reddit.com/r/uofm/comments/15w
             | 18gv/reminder_you_...
        
             | Sanzig wrote:
             | First year linear algebra is a requirement in Canada for
             | national accreditation of any engineering program.
        
           | caspper69 wrote:
           | 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 (was
           | planning to finish the few credits I need for an actual CS
           | BS) & I started calc III twice (but dropped both times). I
           | even got a 4.0 on my first calc III exam (and this was an in-
           | person class, so no online shenanigans).
           | 
           | I just have some kind of weird aversion to 3 dimensional
           | calculus. I have convinced myself that I'm simply not smart
           | enough to actually do the work. I _understand_ it, I just get
           | clammy with it.
           | 
           | Truth be told, maths are my kryptonite. Despite working with
           | numbers all day every day for 30+ years, and writing a lot of
           | software over the years (and not just CRUD, but games of all
           | things), I am absolutely ashamed that I just can't seem to
           | grok math with any rigor.
           | 
           | I have all the Stewart textbooks on my shelf, many textbooks
           | from libgen (ones I've seen recommended on HN from people who
           | went to much better universities than I attended), and I even
           | work through problems a few hours per week. I just can't seem
           | to make that leap from a guy who's "good with numbers" (from
           | a layperson's perspective) to a guy who's good at math.
           | 
           | Maybe I need to break open one of my physics textbooks and
           | actually use the calculus in an applied context and that will
           | break whatever mental barrier I have (I've even watched all
           | of the 3 blue 1 brown videos, countless youtube lectures,
           | etc).
        
           | antman wrote:
           | We had the basic Linear Algebra in high school
        
         | mp05 wrote:
         | 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 resumes 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".
        
           | angry_moose wrote:
           | Yeah, stats is the other major deficiency in the course load.
           | I think one course is required but its basically high school
           | level "check out these normal distributions, 68-95-99.7,
           | here's a Z-score, see you later".
           | 
           | Thankfully the companies I've worked for have done a really
           | good job with advanced stats training.
        
           | lupire wrote:
           | 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?
        
         | cashsterling wrote:
         | 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.
        
       | yardie wrote:
       | 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 wrote:
         | 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 wrote:
       | 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.
        
         | byefruit wrote:
         | What would you recommend for building a strong linear algebra
         | foundation?
        
           | RobbieGM wrote:
           | 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 wrote:
           | 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
        
           | ellisv wrote:
           | Anything by Gilbert Strang
           | 
           | https://youtube.com/playlist?list=PLE7DDD91010BC51F8
        
           | krosaen wrote:
           | 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 a custom
           | curriculum, then doing spaced repetition.
        
             | javiramos wrote:
             | I took 18.085 (applied linear algebra) as a grad student at
             | MIT. The best taught math course I've ever taken. Strang is
             | a fantastic teacher.
        
             | kosmet wrote:
             | 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.
        
         | tptacek wrote:
         | 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.
        
         | frognumber wrote:
         | 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.
        
           | btilly wrote:
           | 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.
        
       | profgrizzle wrote:
       | 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 wrote:
       | 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 wrote:
         | This is (one of?) the authors of the course, for what it's
         | worth. Welcome to HN! Pelt him with questions, everybody. :)
        
       | alexk wrote:
       | 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 wrote:
       | 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 wrote:
         | Who are you trying to prove this to?
        
         | caspper69 wrote:
         | 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/
         | 
         | 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.
        
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