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An introduction to functional analysis for science and engineering

arxiv.org

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Re: An introduction to functional analysis for science and engineering

#11

Post by [deleted] »

throwaway81523 wrote: post #8
oakinnagbe wrote: post #6

Genuine question: does the writing tool matter at all here if the exposition is clear and mathematically correct? I’ve seen great notes written in Word, LaTeX, and even slides—quality seems independent of format.

I would say it's not statistically independent. See https://scottaaronson.blog/?p=304 item #1. So we get to add another exception, which is fine.

[deleted]

Re: An introduction to functional analysis for science and engineering

#12

Post by anioko1 »

throwaway81523 wrote: post #8
oakinnagbe wrote: post #6

Genuine question: does the writing tool matter at all here if the exposition is clear and mathematically correct? I’ve seen great notes written in Word, LaTeX, and even slides—quality seems independent of format.

I would say it's not statistically independent. See https://scottaaronson.blog/?p=304 item #1. So we get to add another exception, which is fine.

Interesting!

Re: An introduction to functional analysis for science and engineering

#13

Post by dieselgate »

From my undergrad engineering math I understand some context here but am getting confused after a decade of programming. Words like "compact" and "closure" [0] probably do not translate directly to the mathematics space from software development - but don't really expect them to...

Thanks for the post it's a good kick in the rear to explore conceptually what eigenvalues/vectors are again!

[0]: from looking up "compact operator" https://en.wikipedia.org/wiki/Compact_operator

Re: An introduction to functional analysis for science and engineering

#14

Post by mswphd »

oakinnagbe wrote: post #6

Genuine question: does the writing tool matter at all here if the exposition is clear and mathematically correct? I’ve seen great notes written in Word, LaTeX, and even slides—quality seems independent of format.

both no in principle, and when you're used to reading LaTeX, word is ugly. It's a milder form of how if these notes were handwritten it wouldn't matter, but it would also be less appealing than them being typeset well.

Re: An introduction to functional analysis for science and engineering

#18

Post by wolfi1 »

iamcreasy wrote: post #17

Does anyone know any applied functional analysis book? I have strong linear algebra foundation, but no real analysis.

if you take the spectral theorem, for example, there is a direct connection between linear algebra and functional analysis, basically it's linear algebra in infinite dimensions

Re: An introduction to functional analysis for science and engineering

#19

Post by srean »

iamcreasy wrote: post #17

Does anyone know any applied functional analysis book? I have strong linear algebra foundation, but no real analysis.

I love this one

https://ia801706.us.archive.org/7/items/in.ernet.dli.2015.14...

Luenberger, Optimization By Vector Space Methods.

Although it is about a specific application, optimization, it is a good book to get a sense of infinite dimensional vector spaces. I would also recommend Halmos. His book surreptitiously introduces you to that subset of linear algebraic notions that survive inti infinite dimensional spaces.

Re: An introduction to functional analysis for science and engineering

#20

Post by oakinnagbe »

throwaway81523 wrote: post #8
oakinnagbe wrote: post #6

Genuine question: does the writing tool matter at all here if the exposition is clear and mathematically correct? I’ve seen great notes written in Word, LaTeX, and even slides—quality seems independent of format.

I would say it's not statistically independent. See https://scottaaronson.blog/?p=304 item #1. So we get to add another exception, which is fine.

That feels more like a selection effect than a property of the writing tool itself.
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