typing mathematical symbols into emacs using the TeX input method

You can type mathematical symbols into emacs using the TeX input method.
 C-\ TeX <enter> \ohm \therefore \pi 
C-\ will toggle the input method on and off. Note the \ indicator in the bottom left of the status bar.

$$\LaTeX$$ Equations in WordPress using MathJax

I came accross this great tool for displaying mathematical equations the other day. MathJax not only supports $$\LaTeX$$ syntax but also renders the equations as pure text, so no unsightly images and they scale beautifully. You can also right click on the equation and see it’s $$\LaTeX$$ code.

The code for MathJax is open source, but if you don’t want to go to the bother of installing it yourself, you can use it on their CDN.

There are a couple of plugins to enable MathJax in WordPress. I’m using the Simple MathJax plugin. I’ve not tried the others.

To use MathJax simply mark up your equation with $…$. If you want to have an equation inline, use $$…$$. You can also inline equations in the post title.

Here are a few examples taken from the MathJax site:

The Lorenz Equations

\begin{aligned}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x – y – xz \\
\dot{z} & = -\beta z + xy
\end{aligned}

The Cauchy-Schwarz Inequality

$\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$

A Cross Product Formula

$\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix}$

The probability of getting $$k$$ heads when flipping $$n$$ coins is

$P(E) = {n \choose k} p^k (1-p)^{ n-k}$

An Identity of Ramanujan

$\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } }$

A Rogers-Ramanujan Identity

$1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for |q|<1}.$

Maxwell’s Equations

\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}