2013-08-12 13:21:38 +00:00
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<!doctype html>
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<html lang="en">
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<head>
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<meta charset="utf-8">
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2013-08-20 13:10:26 +00:00
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<title>reveal.js - Math Plugin</title>
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2013-08-12 13:21:38 +00:00
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<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">
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2014-04-06 08:09:25 +00:00
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<link rel="stylesheet" href="../../css/reveal.css">
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2013-08-23 18:57:11 +00:00
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<link rel="stylesheet" href="../../css/theme/night.css" id="theme">
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2013-08-12 13:21:38 +00:00
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</head>
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<body>
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<div class="reveal">
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<div class="slides">
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<section>
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2013-08-13 02:42:14 +00:00
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<h2>reveal.js Math Plugin</h2>
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<p>A thin wrapper for MathJax</p>
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2013-08-12 13:21:38 +00:00
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</section>
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<section>
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2013-08-13 02:42:14 +00:00
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<h3>The Lorenz Equations</h3>
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2013-08-13 03:01:35 +00:00
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2013-08-12 13:21:38 +00:00
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\[\begin{aligned}
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\dot{x} & = \sigma(y-x) \\
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\dot{y} & = \rho x - y - xz \\
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\dot{z} & = -\beta z + xy
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\end{aligned} \]
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</section>
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2013-08-12 13:24:29 +00:00
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<section>
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2013-08-13 02:42:14 +00:00
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<h3>The Cauchy-Schwarz Inequality</h3>
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2013-08-12 13:24:29 +00:00
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2013-08-13 04:10:14 +00:00
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<script type="math/tex; mode=display">
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\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
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</script>
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2013-08-12 13:24:29 +00:00
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</section>
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<section>
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2013-08-13 02:42:14 +00:00
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<h3>A Cross Product Formula</h3>
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2013-08-12 13:24:29 +00:00
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\[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
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\mathbf{i} & \mathbf{j} & \mathbf{k} \\
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\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
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\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0
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\end{vmatrix} \]
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</section>
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<section>
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2013-08-13 02:42:14 +00:00
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<h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>
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\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
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</section>
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<section>
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<h3>An Identity of Ramanujan</h3>
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2013-08-12 13:24:29 +00:00
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\[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
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1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
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{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
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</section>
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2013-08-13 02:42:14 +00:00
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<section>
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<h3>A Rogers-Ramanujan Identity</h3>
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\[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
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\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
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</section>
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<section>
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<h3>Maxwell’s Equations</h3>
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\[ \begin{aligned}
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\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
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\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
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\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}
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\]
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</section>
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2018-02-08 12:54:21 +00:00
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<section>
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<h3>TeX Macros</h3>
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Here is a common vector space:
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\[L^2(\R) = \set{u : \R \to \R}{\int_\R |u|^2 < +\infty}\]
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used in functional analysis.
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</section>
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2013-08-13 03:15:19 +00:00
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<section>
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<section>
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<h3>The Lorenz Equations</h3>
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<div class="fragment">
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\[\begin{aligned}
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\dot{x} & = \sigma(y-x) \\
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|
|
|
\dot{y} & = \rho x - y - xz \\
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|
|
|
|
\dot{z} & = -\beta z + xy
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\end{aligned} \]
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</div>
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</section>
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<section>
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<h3>The Cauchy-Schwarz Inequality</h3>
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<div class="fragment">
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\[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
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</div>
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</section>
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<section>
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<h3>A Cross Product Formula</h3>
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<div class="fragment">
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\[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
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|
|
|
|
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
|
|
|
|
|
\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
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|
|
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\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0
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\end{vmatrix} \]
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</div>
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</section>
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<section>
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|
|
|
|
<h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>
|
|
|
|
|
|
|
|
|
|
<div class="fragment">
|
|
|
|
|
\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
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|
|
|
|
</div>
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|
|
|
|
</section>
|
|
|
|
|
|
|
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<section>
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|
|
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<h3>An Identity of Ramanujan</h3>
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|
|
|
|
|
|
|
|
|
<div class="fragment">
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|
|
|
\[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
|
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|
|
|
1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
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|
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{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
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</div>
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</section>
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<section>
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<h3>A Rogers-Ramanujan Identity</h3>
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<div class="fragment">
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\[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
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\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
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</div>
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</section>
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<section>
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<h3>Maxwell’s Equations</h3>
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|
|
|
|
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|
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<div class="fragment">
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|
|
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\[ \begin{aligned}
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|
|
|
\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
|
|
|
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|
\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
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\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}
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\]
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</div>
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</section>
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2018-02-08 12:54:21 +00:00
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<section>
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|
|
|
|
<h3>TeX Macros</h3>
|
|
|
|
|
|
|
|
|
|
Here is a common vector space:
|
|
|
|
|
\[L^2(\R) = \set{u : \R \to \R}{\int_\R |u|^2 < +\infty}\]
|
|
|
|
|
used in functional analysis.
|
|
|
|
|
</section>
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2013-08-13 03:15:19 +00:00
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</section>
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2013-08-12 13:21:38 +00:00
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</div>
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</div>
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2014-04-06 08:09:25 +00:00
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<script src="../../js/reveal.js"></script>
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2013-08-12 13:21:38 +00:00
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<script>
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Reveal.initialize({
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2013-08-13 03:15:19 +00:00
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history: true,
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2013-08-13 02:42:14 +00:00
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transition: 'linear',
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2013-08-13 03:01:35 +00:00
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math: {
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2017-04-05 11:44:41 +00:00
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// mathjax: 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js',
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2018-02-08 12:54:21 +00:00
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config: 'TeX-AMS_HTML-full',
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TeX: {
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Macros: {
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R: '\\mathbb{R}',
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set: [ '\\left\\{#1 \\; ; \\; #2\\right\\}', 2 ]
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}
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}
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2013-08-13 03:01:35 +00:00
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},
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2013-08-12 13:21:38 +00:00
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dependencies: [
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2013-08-23 18:57:11 +00:00
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{ src: '../../plugin/math/math.js', async: true }
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2013-08-12 13:21:38 +00:00
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]
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});
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</script>
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</body>
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</html>
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