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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.
ellisv 2y ago
Anything by Gilbert Strang https://youtube.com/playlist?list=PLE7DDD91010BC51F8 https://youtube.com/playlist?list=PLE7DDD91010BC51F8
krosaen 2y ago
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 https://mathacademy.com/courses/linear-algebra or https://mathacademy.com/courses/mathematics-for-machine-learning 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.
- a-dub 2y ago
  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 2y ago
    > 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-need-to-have-automaticity-on-basic-arithmetic/ 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.
- javiramos 2y ago
  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 2y ago
  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 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.

ellisv 2y ago

Anything by Gilbert Strang https://youtube.com/playlist?list=PLE7DDD91010BC51F8 https://youtube.com/playlist?list=PLE7DDD91010BC51F8

krosaen 2y ago

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 https://mathacademy.com/courses/linear-algebra or https://mathacademy.com/courses/mathematics-for-machine-learning 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.

a-dub 2y ago
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 2y ago
  > 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-need-to-have-automaticity-on-basic-arithmetic/ 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.
javiramos 2y ago
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 2y ago
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 2y ago