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

247 points by vinchuco 10y ago

tgb 10y ago
I like these! Work related to number 9 came up just three days ago: https://news.ycombinator.com/item?id=14114876 https://news.ycombinator.com/item?id=14114876
cyber_dude 10y ago
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=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x... [2] https://github.com/3b1b/manim https://github.com/3b1b/manim
- BucketSort 10y ago
  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 https://www.youtube.com/watch?v=mvmuCPvRoWQ&t=385s
- jaddood 10y ago
  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.
aardvark291 10y ago
If you want a printed version: https://www.amazon.com/Thirty-three-Miniatures-Mathematical-Algorithmic-Applications/dp/0821849778/ https://www.amazon.com/Thirty-three-Miniatures-Mathematical-...
leni536 10y ago
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.
- stabbles 10y ago
  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_operators https://en.wikipedia.org/wiki/Spectral_theory_of_compact_ope...
fithisux 10y ago
If you enjoy this, Matousek and Vondrak have a better one. http://webbuild.knu.ac.kr/~trj/Combin/matousek-vondrak-prob-ln.pdf http://webbuild.knu.ac.kr/~trj/Combin/matousek-vondrak-prob-...
- gmiller123456 10y ago
  >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.
mrcactu5 10y ago
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 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 https://arxiv.org/abs/1009.6077 ( Discrete Complex Analysis and Probability )
morenoh149 10y ago
Which of these miniatures is most relevant to CS or real-world software problems?

247 points by vinchuco 10y ago

tgb 10y ago

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

cyber_dude 10y ago

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=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x... [2] https://github.com/3b1b/manim https://github.com/3b1b/manim

BucketSort 10y ago
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 https://www.youtube.com/watch?v=mvmuCPvRoWQ&t=385s
jaddood 10y ago
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.

aardvark291 10y ago

If you want a printed version: https://www.amazon.com/Thirty-three-Miniatures-Mathematical-Algorithmic-Applications/dp/0821849778/ https://www.amazon.com/Thirty-three-Miniatures-Mathematical-...

leni536 10y ago

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.

stabbles 10y ago
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_operators https://en.wikipedia.org/wiki/Spectral_theory_of_compact_ope...

fithisux 10y ago

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

gmiller123456 10y ago
>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.

mrcactu5 10y ago

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

morenoh149 10y ago

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