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mkatkov.wordpress.com | ||
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thehighergeometer.wordpress.com
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| | | | | Here's a fun thing: if you want to generate a random finite $latex T_0$ space, instead select a random subset from $latex \mathbb{S}^n$, the $latex n$-fold power of the Sierpinski space $latex \mathbb{S}$, since every $latex T_0$ space embeds into some (arbitrary) product of copies of the Sierpinski space. (Recall that $latex \mathbb{S}$ has underlying... | |
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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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mathematicaloddsandends.wordpress.com
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| | | | | I recently learned of Craig's formula for the Gaussian Q-function from this blog post from John Cook. Here is the formula: Proposition (Craig's formula). Let $latex Z$ be a standard normal random variable. Then for any $latex z \geq 0$, defining $latex \begin{aligned} \mathbb{P}\{ Z \geq z\} = Q(z) = \dfrac{1}{\sqrt{2\pi}} \int_z^\infty \exp \left( -... | |
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rapuran.wordpress.com
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