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matheuscmss.wordpress.com | ||
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qchu.wordpress.com
(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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mattbaker.blog
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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terrytao.wordpress.com
Many modern mathematical proofs are a combination of conceptual arguments and technical calculations. There is something of a tradeoff between the two: one can add more conceptual arguments to try ... |
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jaketae.github.io
So far on this blog, we have looked the mathematics behind distributions, most notably binomial, Poisson, and Gamma, with a little bit of exponential. These distributions are interesting in and of themselves, but their true beauty shines through when we analyze them under the light of Bayesian inference. In today's post, we first develop an intuition for conditional probabilities to derive Bayes' theorem. From there, we motivate the method of Bayesian inference as a means of understanding probability. |
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