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<section>
<h2>reveal.js Math Plugin</h2>
<p>Render math with KaTeX, MathJax 2 or MathJax 3</p>
</section>
<section>
<h3>The Lorenz Equations</h3>
\[\begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho
x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned} \]
</section>
<section>
<h3>The Cauchy-Schwarz Inequality</h3>
<script type="math/tex; mode=display">
\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)
</script>
</section>
<section>
<h3>A Cross Product Formula</h3>
\[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} &
\mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} &
\frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v}
& \frac{\partial Y}{\partial v} & 0 \end{vmatrix} \]
</section>
<section>
<h3>
The probability of getting \(k\) heads when flipping \(n\) coins is
</h3>
\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
</section>
<section>
<h3>An Identity of Ramanujan</h3>
\[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
</section>
<section>
<h3>A Rogers-Ramanujan Identity</h3>
\[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
</section>
<section>
<h3>Maxwell’s Equations</h3>
\[ \begin{aligned} \nabla \times \vec{\mathbf{B}} -\, \frac1c\,
\frac{\partial\vec{\mathbf{E}}}{\partial t} & =
\frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} &
= 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\,
\frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}}
\\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned} \]
</section>
<section>
<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>
<section>
<section>
<h3>The Lorenz Equations</h3>
<div class="fragment">
\[\begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & =
\rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned} \]
</div>
</section>
<section>
<h3>The Cauchy-Schwarz Inequality</h3>
<div class="fragment">
\[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n
a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
</div>
</section>
<section>
<h3>A Cross Product Formula</h3>
<div class="fragment">
\[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i}
& \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u}
& \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial
X}{\partial v} & \frac{\partial Y}{\partial v} & 0
\end{vmatrix} \]
</div>
</section>
<section>
<h3>
The probability of getting \(k\) heads when flipping \(n\) coins
is
</h3>
<div class="fragment">
\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
</div>
</section>
<section>
<h3>An Identity of Ramanujan</h3>
<div class="fragment">
\[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}}
= 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
</div>
</section>
<section>
<h3>A Rogers-Ramanujan Identity</h3>
<div class="fragment">
\[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
</div>
</section>
<section>
<h3>Maxwell’s Equations</h3>
<div class="fragment">
\[ \begin{aligned} \nabla \times \vec{\mathbf{B}} -\, \frac1c\,
\frac{\partial\vec{\mathbf{E}}}{\partial t} & =
\frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}}
& = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\,
\frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & =
\vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0
\end{aligned} \]
</div>
</section>
<section>
<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>
</section>
</div>
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R: "\\mathbb{R}",
set: ["\\left\\{#1 \\; ; \\; #2\\right\\}", 2],
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