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algorithmsoup.wordpress.com | ||
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mikespivey.wordpress.com
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| | | | | Equations of the form $latex x^3 = y^2 + k$ are called Mordell equations. In this post we're going to prove that the equation $latex x^3 = y^2 -7$ has no integer solutions, using (with one exception) nothing more complicated than congruences. Theorem: There are no integer solutions to the equation $latex x^3 = y^2... | |
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dominiczypen.wordpress.com
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| | | | | For $latex A, B \subseteq \omega$ we write $latex A \subseteq^* B$ if $latex A\setminus B$ is finite, and we write $latex A\simeq^* B$ if $latex A\subseteq^* B$ and $latex B\subseteq^* A$. A tower is a collection $latex {\cal T}$ of co-infinite subsets of $latex \omega$ such that for all $latex A\neq B\in {\cal T}$... | |
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mathematicaloddsandends.wordpress.com
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| | | | | The function $latex f(x) = x \log x$ occurs in various places across math/statistics/machine learning (e.g. in the definition of entropy), and I thought I'd put a list of properties of the function here that I've found useful. Here is a plot of the function: $latex f$ is defined on $latex (0, \infty)$. The only... | |
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tom-e-white.com
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| | | I've always thought that Hadoop is a great fit for analyzing log files (I even wrote an article about it). The big win is that you can write ad hoc MapReduce queries against huge datasets and get results in minutes or hours. So I was interested to read Stu Hood's recent post about using Hadoop to analyze email log data: Here at Mailtrust, Rackspace's mail division, we are taking advantage of Hadoop to help us wrangle several hundred gigabytes of email log data that our mail servers generate each day. We'... | ||
