Mathematics typesetting is done using MathJax. The feature is off by default for performance reason. You must enable MathJax by inserting the line

math: true

in the front matter of your Markdown file.

Inline maths

Inline some mathematics by single dollar signs $. This inlining $y = f(x)$ would render as $y = f(x)$.

Donec et odio pellentesque $y = mx + b$ diam volutpat commodo sed egestas. Eget dolor morbi non arcu risus quis varius quam. Lorem donec massa sapien faucibus et molestie ac feugiat. Aliquam purus sit amet luctus venenatis lectus. In ante metus dictum at $\sqrt{3x-1}+(1+x)^2$ tempor commodo ullamcorper a. Purus in $t^3 + pt + q = 0$ massa tempor nec feugiat. Nam libero justo $\cos(3\theta) = \frac{3q}{2p} \sqrt{\frac{-3}{p}}$ laoreet sit amet cursus. Nunc pulvinar sapien et ligula ullamcorper malesuada proin.

Block maths

Use double dollar signs to typeset a block of mathematics. This code

$$
x
=
\frac{
  -b \pm \sqrt{b^2 - 4ac}
}{
  2a
}
$$

would render as:

\[x = \frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a }\]

The Cauchy-Schwarz inequality:

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

Equation numbering

Consider the integral:

\[\begin{equation} \label{eqn_integral} \int_{-\infty}^{\infty} \exp(x^2) \; dx = \sqrt{\pi}. \end{equation}\]

The integral (\ref{eqn_integral}) has a closed form solution, i.e. $\sqrt{\pi}$.

Standard normal distribution:

\[\frac{1}{\sqrt{2\pi}} \int_{-\infty}^{\infty} \exp(-x^2/2) \; dx = 1.\]

A matrix:

\[\begin{equation} \label{eqn_matrix_2x2} O = \begin{bmatrix} \cos\phi & \sin\phi \\ -\sin\phi & \cos\phi \end{bmatrix}. \end{equation}\]

The matrix (\ref{eqn_matrix_2x2}) is $2 \times 2$. The general $m \times n$ matrix is:

\[A_{mn} = \begin{pmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{pmatrix}.\]