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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
Who are you trying to prove this to?
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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.
First year linear algebra is a requirement in Canada for national accreditation of any engineering program.
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What would you recommend for building a strong linear algebra foundation?
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
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.
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 $$…
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.
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> 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).
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…
Do all the homework problems check the answer in the back of the book. You’ll make it.
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> 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).
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…
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.
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…
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…
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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…
What do these acronyms mean?—IE, FEA, DOE?
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.
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What would you recommend for building a strong linear algebra foundation?
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…
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!