[HN Gopher] Robotics 101 at UMich: Applied numerical linear alge...
___________________________________________________________________
Robotics 101 at UMich: Applied numerical linear algebra as intro
linear algebra
Author : jamesliudotcc
Score : 280 points
Date : 2025-01-08 13:11 UTC (1 days 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.
| bigger_cheese wrote:
| Linear Algebra was a first year subject for me as well. I
| studied Engineering in Australia.
| 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).
| downrightmike wrote:
| Maybe stop torturing yourself for a bit. Sounds miserable.
| caspper69 wrote:
| Such is life. We all have regrets, and being sloppy and
| indifferent with math in my youth is a big one for me. If
| I had done it then, I wouldn't have to try so hard now.
| liontwist wrote:
| There are deep concepts behind multi variable cal. But if
| you just want to pass the course, memorizing problem shapes
| through practice will get you through calc 3.
|
| Do all the homework problems check the answer in the back
| of the book. You'll make it.
| caspper69 wrote:
| One day, God willing, lol.
| casey2 wrote:
| A few hours per week simply isn't enough, the best success
| I've had studying was 6 hours a day, resting for 3 (leisure
| activity), "working" for 3 (class, commute, chores, related
| reading) and sleeping 12 hours.
|
| In books like Stewart, staring at a theorem until you can
| write it's proof should trivialize most problems in the
| book.
|
| If a method for solving a particular problem is too
| difficult for you maybe consider researching and/or
| inventing some new method to solve these problem. People
| created these methods in the first place because earlier
| methods were too tricky
|
| Or just focus on work that doesn't require hundreds of
| hours to gain proficiency. As long as you have time every
| day to stop, think, and come up with an idea that solves a
| problem you won't become intellectually unfit.
| caspper69 wrote:
| Thank you. I appreciate the feedback and the pointers.
| caspper69 wrote:
| 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 problem doing the
| work. But it feels more like mechanical or algorithmic
| solving than it does like true understanding. There is a
| difference. I can't deconstruct a problem and think in
| the abstract to come up with a different method to solve
| it.
|
| And there always seem to be some fundamental truth that
| I'm always missing. A part of a proof here or an axiom
| there that seems obvious to other people who study these
| subjects that I just don't "see".
|
| It's incredibly frustrating, because deep down I know I
| have the aptitude for this stuff. I guess that most
| subjects have always been easy for me. I could ace exams
| without cracking the book (or just skimming).
|
| Math is not like that. You need to read. And then re-
| read. And then do. And then do some more. And then go
| back and re-read again to see what you missed. And
| there's a lot of things that are between the lines, and
| if you're not following it, those things fall by the
| wayside.
|
| I just need to learn how to learn math. I need to learn
| how to deconstruct notation and proofs to truly
| understand them. And there's no shortcut. It's grind and
| grind until it all becomes clear. That sort of thing is
| just difficult for me.
| jamesliudotcc wrote:
| Maybe your problem is Stewart? I used that textbook and
| was successful, but it's not for everyone. For example,
| beginning calculus with limits is another bit of
| misguided conventional wisdom. I still don't get limits,
| really. Serge Lang's calculus book takes the approach to
| just roll with an intuitive notion of limits, saving
| rigor for analysis. Which seems better.
|
| Gilbert Strang has a textbook, also more intuitive and
| applied. Free PDF provided by MIT. Sylvanus Thompson's
| book is recommended here, again, intuitive, applied.
|
| Other comments here, 3 hours isn't enough, use Math
| Academy, nobody gets it on the first approach, all seem
| relevant. One of the textbooks recommended here says in
| the preface that it's for a second course in Linear
| Algebra. Analysis is just calculus the second (or third)
| go round, and it's said to be the hardest class in a math
| major.
|
| I am in your boat, but about linear algebra instead of
| calculus. This is what I try to get myself over the hump.
| sn9 wrote:
| You should check out Math Academy.
|
| It schedules everything for you including the review so you
| just have to keep showing up to do the work.
|
| Even as little as 30 minutes per day done consistently for
| months will have you make tremendous progress.
|
| And once you master multivariable calculus, fields like
| probability and machine learning will be unlocked for you.
| monadINtop wrote:
| If by 3d-calc you mean vector calculus then yeah I never
| actually understood any of it, I just moved on to
| differential forms and the tensor calculus and Riemannian
| geometry and then wondered why anyone bothered with
| 3d-calculus in the first place.
|
| Most of the time I've found that the deeper I plunge into
| abstraction in math I get rewarded with an extremely
| elegant formalism. Its like upgrading your weapon in dark
| souls, the early game enemies get one-shotted when you go
| back.
| BeetleB wrote:
| > 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.
| 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?
| mp05 wrote:
| It's up to department heads and dean and they're pressured
| by ABET and companies that write them checks.
|
| Education is secondary; this is job training! We need to
| crank out people ready to drop into Boeing's way of doing
| things!
| gnubison wrote:
| What do these acronyms mean?--IE, FEA, DOE?
| angry_moose wrote:
| IE == Industrial Engineering: broad, but generally
| "Engineering of Systems" instead of a physical product.
| Laying out factories, setting up supply chains, etc. It's
| morphed a little bit from the original field so the name
| isn't super accurate.
|
| FEA == Finite Element Analysis: advanced method of
| predicting the strength of a product via numerical
| simulation.
|
| DOE == Design of Experiments: evaluation of how the outputs
| of a system change as you vary the inputs. At a high level,
| you build model of the system, then vary all the inputs
| through their entire range and to build a response surface
| of the output.
| mp05 wrote:
| > It's morphed a little bit from the original field so
| the name isn't super accurate.
|
| I'm currently doing a masters in IMSE--Industrial and
| Management Systems Engineering--and yeah it's changed
| since the 70s or whenever it had its real heyday (they
| come in waves).
|
| The updated curriculum for undergrad is essentially the
| same as a mechanical engineering for the first two years,
| but as they wander off into advanced mechanics and
| fluids, IMSE students are doing time studies, factory
| design (FLOW!), and lots of stats and algorithms.
|
| I've actually had the pleasure of getting to gripe to our
| school's Industrial Advisory Board which seems mostly
| full of Boeing people. They want to know if the
| curriculum serves the students well and I preach to them
| that, actually, if you spend 6 or 9 extra credits on
| proper software engineering that you've created a
| monster... but they don't listen. Some even get kind of
| offended because they think that a career in project
| management is a fine way to go about life (why go to
| engineering school?)
|
| Sorry programming blows your mind? Perhaps that's why we
| need to teach it? I've done a lot of ERP integrations in
| my career and I'm not sure who they think is most
| qualified to do those sorts of things.
| 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
| fn-mote wrote:
| 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.
| 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.
| gessha wrote:
| It's $50/month online course. As effective as it can be,
| I can't justify this expense for myself, as much as I'm
| fascinated by math.
| a-dub wrote:
| i don't really care how many people i respect liked it, i
| have to be honest, i hated strang's "linear algebra and its
| applications."
|
| there's a strang text on computational science that was
| much more my speed (less of the baby talk and repetitive
| manual arithmetic exercises) and i think that some of the
| revisions that came later (+ "learning with data") were
| better.
|
| i did not find doing endless exercises of gaussian
| elimination or qr factorization by hand on small matrices
| to be all that enlightening.
|
| this michigan course looks awesome!
| krosaen wrote:
| > less of the ... repetitive manual arithmetic exercises
|
| I think this post (from a math academy employee) has a
| good argument for why these sorts of exercises are
| important. It's about basic arithmetic, but I think it
| applies to tedious things like performing gaussian
| elimination on small matrices as well.
|
| https://www.justinmath.com/if-you-want-to-learn-algebra-
| you-...
|
| I like to come at it from both angles - higher level with
| useful applications, and then lower level "I could maybe
| implement this if I had to" exercises. The latter are
| tedious, and hard to motivate effort for without the
| former. Ultimately, as the post argues, I agree that if
| you don't understand the lower level (tedious)
| operations, you will only get so far in your ability to
| apply LA.
| 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.
| almostgotcaught 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...
|
| I don't understand the point of this comment. On the one hand
| you're trying to encourage people by saying "don't feel bad
| you didn't get it the first time" but then you throw a
| mountain more work/terms/books at them? You think it's
| encouraging to a student to hear that if they didn't succeed
| in this robotics class because the LA coverage wasn't great
| ...... they should go take quantum computing, control theory,
| abstract algebra classes?
| pxmpxm wrote:
| 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.
| 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?
| redmerchant2 wrote:
| Probably trying to transition from a SWE role to a ML one
| mettamage wrote:
| 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 wrote:
| 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 wrote:
| The writing is certainly all over the wall, in bold red
| ink.
| 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.
| fn-mote wrote:
| > 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
|
| Just be warned that this is literally the graduate level
| linear algebra course taken by mathematics majors. If you are
| looking for applications, this might not be it. On the other
| hand, if you are looking for a deep understanding of the
| fundamentals - I would say you found it.
| caspper69 wrote:
| Thank you for posting that info. I'd hate for the guy to
| want the applied computer-centric linear algebra only to
| find himself neck deep in a super rigorous course that
| might go deeper that he intended! Oof.
|
| I should have posted the Math 257 description too. It also
| has lectures online as well as a synchronous Zoom
| component:
|
| Introductory course incorporating linear algebra concepts
| with computational tools, with real world applications to
| science, engineering and data science. Topics include
| linear equations, matrix operations, vector spaces, linear
| transformations, eigenvalues, eigenvectors, inner products
| and norms, orthogonality, linear regression, equilibrium,
| linear dynamical systems and the singular value
| decomposition.
| mettamage wrote:
| I'm from Europe, I suspect the credentials would still stand.
| casey2 wrote:
| 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 wrote:
| 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.
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