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The Art of Linear Algebra [pdf]

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Re: The Art of Linear Algebra [pdf]

#21

Post by SamBam »

ChicagoBoy11 wrote: post #16

I never understood why we don't do more of this stuff in school, and how calculus instead became the defacto advanced math curriculum in most high-schools. Students grow up working on their basic algebraic operations, solving equations, etc. Liner Algebra introduces them to the universe that lies just beyond those techniques, has very readily applicable uses, lends itself excellently to simulation/connections to comp…

I would say that calculus is more relevant to the sciences, is it not?

Possibly not Calculus 2, but at least getting an intuitive understanding of rates of change, second derivatives, and area under a curve seems pretty critical for all the sciences.

Re: The Art of Linear Algebra [pdf]

#23

Post by ivansavz »

ChicagoBoy11 wrote: post #16

I never understood why we don't do more of this stuff in school, and how calculus instead became the defacto advanced math curriculum in most high-schools. Students grow up working on their basic algebraic operations, solving equations, etc. Liner Algebra introduces them to the universe that lies just beyond those techniques, has very readily applicable uses, lends itself excellently to simulation/connections to comp…

There is a nice "opinion piece" by Strang that echoes what you're saying here: Too Much Calculus (and not enough LA) https://siags.siam.org/siagla/articles/Strang2001.pdf

Re: The Art of Linear Algebra [pdf]

#24

Post by dls2016 »

Grustaf wrote: post #18
ChicagoBoy11 wrote: post #16

I never understood why we don't do more of this stuff in school, and how calculus instead became the defacto advanced math curriculum in most high-schools. Students grow up working on their basic algebraic operations, solving equations, etc. Liner Algebra introduces them to the universe that lies just beyond those techniques, has very readily applicable uses, lends itself excellently to simulation/connections to comp…

Both calculus and linear algebra are fundamental for further studies, but I'm not sure linear algebra is more approachable? I personally find geometry and algebra more interesting, but it seems to me that derivatives are more fundamental than matrices. But maybe that's just my bias from being educated like that.

What if I told you the derivative is a linear operator? (matrix meme style)

Re: The Art of Linear Algebra [pdf]

#26

Post by wbsss4412 »

Grustaf wrote: post #18
ChicagoBoy11 wrote: post #16

I never understood why we don't do more of this stuff in school, and how calculus instead became the defacto advanced math curriculum in most high-schools. Students grow up working on their basic algebraic operations, solving equations, etc. Liner Algebra introduces them to the universe that lies just beyond those techniques, has very readily applicable uses, lends itself excellently to simulation/connections to comp…

Both calculus and linear algebra are fundamental for further studies, but I'm not sure linear algebra is more approachable? I personally find geometry and algebra more interesting, but it seems to me that derivatives are more fundamental than matrices. But maybe that's just my bias from being educated like that.

This begs the question: more fundamental to what?

At a high school level, you have students who are either engaged and will likely learn both subjects eventually, or students who aren’t as engaged and are just looking to take their “last math class”. In my opinion, it makes more sense to offer a choice or at least focus on the curriculum that keeps students are that age to most engaged.

As someone who has studied both subjects, I’d go with linear algebra 9 times out of 10, the exception being if someone wanted to also study physics.

Re: The Art of Linear Algebra [pdf]

#27

Post by SavantIdiot »

ChicagoBoy11 wrote: post #16

I never understood why we don't do more of this stuff in school, and how calculus instead became the defacto advanced math curriculum in most high-schools. Students grow up working on their basic algebraic operations, solving equations, etc. Liner Algebra introduces them to the universe that lies just beyond those techniques, has very readily applicable uses, lends itself excellently to simulation/connections to comp…

I think highschool tries to expose you to as much as possible. I did get a tiny bit of linear algebra at the end of my senior year in calc, but back then PCs pretty much didn't exist. I think today LA is more applicable to programming than integrals, series & expansions, continuity, etc... so maybe times have changed.

Re: The Art of Linear Algebra [pdf]

#28

Post by SavantIdiot »

wbsss4412 wrote: post #26
Grustaf wrote: post #18

Earlier quoted context omitted.

Both calculus and linear algebra are fundamental for further studies, but I'm not sure linear algebra is more approachable? I personally find geometry and algebra more interesting, but it seems to me that derivatives are more fundamental than matrices. But maybe that's just my bias from being educated like that.

This begs the question: more fundamental to what? At a high school level, you have students who are either engaged and will likely learn both subjects eventually, or students who aren’t as engaged and are just looking to take their “last math class”. In my opinion, it makes more sense to offer a choice or at least focus on the curriculum that keeps students are that age to most engaged. As someone who has studied bot…

The question seems to be: should integration and differentiation be taught before matrix operations, or after?

IMHO, since linear algebra is largely a tool for solving differential equations, I think calculus should be taught first, as the fundamental knowledge.

Re: The Art of Linear Algebra [pdf]

#29

Post by [deleted] »

dls2016 wrote: post #24
Grustaf wrote: post #18

Earlier quoted context omitted.

Both calculus and linear algebra are fundamental for further studies, but I'm not sure linear algebra is more approachable? I personally find geometry and algebra more interesting, but it seems to me that derivatives are more fundamental than matrices. But maybe that's just my bias from being educated like that.

What if I told you the derivative is a linear operator? (matrix meme style)

[deleted]

Re: The Art of Linear Algebra [pdf]

#30

Post by wbsss4412 »

SavantIdiot wrote: post #28
wbsss4412 wrote: post #26

Earlier quoted context omitted.

This begs the question: more fundamental to what? At a high school level, you have students who are either engaged and will likely learn both subjects eventually, or students who aren’t as engaged and are just looking to take their “last math class”. In my opinion, it makes more sense to offer a choice or at least focus on the curriculum that keeps students are that age to most engaged. As someone who has studied bot…

The question seems to be: should integration and differentiation be taught before matrix operations, or after? IMHO, since linear algebra is largely a tool for solving differential equations, I think calculus should be taught first, as the fundamental knowledge.

I’m not really sure where you got the idea that it’s largely a tool for solving differential equations. Certainly that is an application, but that isn’t the only use case.
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