How come nobody ever told me Linear Algebra was the best? I

>>8823339
For the same reason nobody gets excited over algebra or Calc 1. Take linear 2 and see if you're still excited by it

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I never focused on linear algebra because there are already millions of experts in that area. If you like to use linear algebra to describe Nature, then you should do that. Its formalism truncates from the parameter space the ability to define irrational topology. How would you write a pi by Phi matrix?

>>8823339
Both "calc 3" (by this I assume you mean multivariate / vector calc) and diffEQ make very heavy use of linalg techniques. They "feel completely arbitrary" to you because you learned them while not having a foundation in linalg.

For better or for worse, at this point, this is by design.

Back in the 60's and 70's at least, linalg was actually a prerequisite to those courses. You enrolled in undergrad and took calc 1 -> calc 2 -> linalg , in that order, before you could take anything else.

Nowadays, math is taught in "passes" over the same topic, with the "curtain" pulled back a little further on each iteration. First you learned geometry, then you learned trigonometry, then you learned calc2, then you learned basic complex analysis, etc. each time realizing that the "facts" you were taught 2-3 years ago can be derived from the facts you're learning today.

>>8823345
>he didn't get excited over algebra and calc when he was a kid

>>8823370
>each time realizing that the "facts" you were taught 2-3 years ago can be derived from the facts you're learning today.

I'm fucking triggered. I've never been properly taught about conic sections, save for parabolas, and I was lucky enough to have an optics prof that actually made a section of the course dedicated to basic complex analysis. It has yet to even be mentioned in a math course.

>>8823339
How do I get into Linear? I'm near the end of a Computational Linear Algebra class and I don't get it at all. I feel like I'm just running arbitrary algorithms on arrays, with no rhyme or reason. Whenever I read the theory, it just seems like a load of words I can't conceptualize or visualize.

Is there a good lecture series that really makes sense of it? A textbook? Short tutorials or explainers?

>>8823370

holy shit

>>8823424

This series gives a pretty good overview of the basic concepts:

https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

>>8823509
I love you

>>8823370
Why though, fucking why though?

I'm nearing the end of an intro analysis course and we just jumped right into solving IVPs with Euler's/Runge-Kutta methods despite the fact that differential eqs was not a pre-req to this class. Maybe it's just my uni's math department but I feel like the curriculum is all over the place.

>>8823509
I'm so happy he's doing the same thing for calculus. Only content creator that motivates me to donate

>>8823370
linear algebra is a very beautiful glimpse of how math works: it gives structure to things you study. it turns out vector spaces are such simple structures that they can be described completely and you get tons of nice results without much effort.

mathematics is about giving order to things and understanding them. it's a shame you've been misled into thinking math is the dry plug and chug you do in calculus and other "math" for engineers.

I hope you give math a chance because it sounds like you really might like it. Hoffman & Kunze is a great book for linear algebra you can grab. If you want to see what's actually up with calculus, you can also start learning Real Analysis (another entry level math class) from Tao's Analysis I.

>>8823424
H&K

>>8824274
>Tao's Analysis
For what purpose? Everything there is left as an exercise, so if you don't already know it you won't learn shit

>>8824289
what are you talking about? he forces you to fill in details into his proofs so you have to read carefully. maybe you're not reading carefully? maybe you're used to skimming quickly and fooling yourself into thinking you're learning?

Tao is very light and friendly, the exercises that you're mentioning, sewn into the text, are routine manipulations that mimic others that he already did before. if you don't get it, backtrack and read again. the idea is that reading a textbook is not a passive experience, it should be active and you should be trying to prove results before the proof is shown to you.

>>8824311
How can you mimic his proofs if almost all of them are "See exercise this and this"?

>>8823509
Is there anything else like this? He doesn't cover all the topics of my Linear course.

>>8825208
Khan academy is always good for more practical examples and computational stuff. What isn't present here that is present in your linear course?

>>8823339
get a book like for your next course
this is the single most applicable course for a math major

https://www.amazon.com/Fundamentals-Matrix-Computations-David-Watkins/dp/0470528338/