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almostsuremath.com | ||
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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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terrytao.wordpress.com
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| | | | | In preparation for my upcoming course on random matrices, I am briefly reviewing some relevant foundational aspects of probability theory, as well as setting up basic probabilistic notation that we... | |
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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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margint.blog
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| | | Once upon a time, Paul Adams and I were standing next to our teams' desks, discussing something as we noticed a helicopter hovering over nearby buildings. Easily distracted as I am, we started to observe it and wondering where it was going. The chopper slowly drifted to the side and it seemed as if it... | ||
