[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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