Miniatures: Mathematical and Algorithmic Applications of Linear Algebra [pdf]

Posted by vinchuco on Monday April 17, 2017 @01:04AM
from the kam.mff.cuni.cz dept.

http://kam.mff.cuni.cz/~matousek/stml-53-matousek-1.pdf

( 11 comments | 247 points | on HN )

Re:Miniatures: Mathematical and Algorithmic Applications of ... by cyber_dude on Monday April 17, 2017 @10:45PM (#14136119)

Essence of linear algebra [1] , in 3blue1brown youtube channel totally changed my perspective on Linear Algebra. One of the best channels in YouTube I have seen so far. He makes his videos using the animation engine [2] he built himself.

[1] https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...

[2] https://github.com/3b1b/manim

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Re:Miniatures: Mathematical and Algorithmic Applications of ... by BucketSort on Monday April 17, 2017 @11:00PM (#14136168)

That whole channel is amazing! I can start just listing all the videos by virtue of picking out awesome ones, but check out the one he did on Euler's formula[1]. Blew my mind.

[1]https://www.youtube.com/watch?v=mvmuCPvRoWQ&t=385s

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Re:Miniatures: Mathematical and Algorithmic Applications of ... by jaddood on Tuesday April 18, 2017 @02:21AM (#14136877)

I didn't know pretty much anything about linear algebra, but by watching the series, I felt deep enlightenment. Also, the videos they have done about topology really made me believe everything is, in essence, geometry.

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Re:Miniatures: Mathematical and Algorithmic Applications of ... by tgb on Monday April 17, 2017 @09:00PM (#14135745)

I like these! Work related to number 9 came up just three days ago: https://news.ycombinator.com/item?id=14114876

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Re:Miniatures: Mathematical and Algorithmic Applications of ... by fithisux on Tuesday April 18, 2017 @08:50AM (#14138371)

If you enjoy this, Matousek and Vondrak have a better one. http://webbuild.knu.ac.kr/~trj/Combin/matousek-vondrak-prob-...

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Re:Miniatures: Mathematical and Algorithmic Applications of ... by gmiller123456 on Tuesday April 18, 2017 @01:54PM (#14141143)

>If you enjoy this, Matousek and Vondrak have a better one.

Curious as to why you would say that. Having a cursory look at both, they don't appear to be even close to discussing the same things. The link you provided is much more theoretical, and about probability.

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Re:Miniatures: Mathematical and Algorithmic Applications of ... by aardvark291 on Tuesday April 18, 2017 @12:38AM (#14136526)

If you want a printed version: https://www.amazon.com/Thirty-three-Miniatures-Mathematical-...

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Re:Miniatures: Mathematical and Algorithmic Applications of ... by mrcactu5 on Tuesday April 18, 2017 @09:54AM (#14138798)

example 12, "Tiling a Rectangle by Squares" is rather unique; it was discussed in Stanislav Smirnov's Fields medal lecture in 2010

https://en.wikipedia.org/wiki/Squaring_the_square

In his lecture he puts the square tilings in a rather serious context (the theory of electrical networks)

https://arxiv.org/abs/1009.6077 ( Discrete Complex Analysis and Probability )

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Re:Miniatures: Mathematical and Algorithmic Applications of ... by leni536 on Tuesday April 18, 2017 @03:57AM (#14137132)

I think the most amazing thing is that Linear Algebra works the same for any fields, not just R and C. Applying it to finite fields is a great trick.

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Re:Miniatures: Mathematical and Algorithmic Applications of ... by stabbles on Tuesday April 18, 2017 @05:06AM (#14137351)

And some of the familiar linear algebra theorems extend to infinite dimensional spaces. For instance spectral theory of compact operators [1]

[1] https://en.wikipedia.org/wiki/Spectral_theory_of_compact_ope...

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Re:Miniatures: Mathematical and Algorithmic Applications of ... by morenoh149 on Tuesday April 18, 2017 @10:34AM (#14139109)

Which of these miniatures is most relevant to CS or real-world software problems?

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