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matheuscmss.wordpress.com | ||
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mattbaker.blog
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| | | | | In my last blog post, I discussed a simple proof of the fact that pi is irrational. That pi is in fact transcendental was first proved in 1882 by Ferdinand von Lindemann, who showed that if $latex \alpha$ is a nonzero complex number and $latex e^\alpha$ is algebraic, then $latex \alpha$ must be transcendental. Since... | |
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qchu.wordpress.com
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| | | | | (Part I of this post ishere) Let $latex p(n)$ denote the partition function, which describes the number of ways to write $latex n$ as a sum of positive integers, ignoring order. In 1918 Hardy and Ramanujan proved that $latex p(n)$ is given asymptotically by $latex \displaystyle p(n) \approx \frac{1}{4n \sqrt{3}} \exp \left( \pi \sqrt{ \frac{2n}{3}... | |
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mycqstate.wordpress.com
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| | | | | [7/9/17 Update: Following a suggestion by Oded Regev I upgraded Section 1 from "probabilistic functions" to "matrix-valued functions". This hopefully makes it a more useful, and interesting, mid-point between the classical analysis of BLR and the non-abelian extension discussed afterwards. I also fixed a bunch of typos -- I apologize for the many remaining ones.... | |
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tcsmath.github.io
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| | | Using the mirror descent framework for MTS | ||
