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almostsuremath.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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francisbach.com
[AI summary] This text discusses the scaling laws of optimization in machine learning, focusing on asymptotic expansions for both strongly convex and non-strongly convex cases. It covers the derivation of performance bounds using techniques like Laplace's method and the behavior of random minimizers. The text also explains the 'weird' behavior observed in certain plots, where non-strongly convex bounds become tight under specific conditions. The analysis connects theoretical results to practical considerations in optimization algorithms. |
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julianzheng.com
[AI summary] The content outlines a book categorization system focusing on computer science, mathematics, natural science, applied science, and social science, with subcategories for various disciplines and topics. |
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