MathJax Quick Reference

Overview

MathJax makes it incredibly easy to typeset mathematics on a web page: Simply include the following script tags on your page and then enter Tex language markup between either the $ ... $ delimiters for inline, or the $$ ... $$ delimiters for block display.

Note: When using Markdown, you must escape the backslashes — \$ ... \$

CDN Includes Version 3

<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>

CDN Includes Version 4

<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@4/tex-mml-chtml.js"></script>

Below are several examples that demonstrate how to markup the most common types of mathematical expressions.

The most common symbols are defined in the sidebar and there are links to more info in the sidebar as well.

Also note that anyplace where MathJax is used on a web page, you can right click on the expression to pull up the context menu shown to the right. This is particularly handy for seeing how a particular expression is formed.

Expressions

Expression	Inline: $...$	Block: $$...$$
~ tilde	adds whitespace
\\\\ 2 backslashes	new line
x_2 subscript	$x_2$	$$x_2$$
x^2 superscript	$x^2$	$$x^2$$
{(x_{i+1}+1)}^{2\omega} {} grouping	${(x_{i+1}+1)}^{2\omega}$	$${(x_{i+1}+1)}^{2\omega}$$
\{x\in s\mid x\text{ is extra large}\} set definition	$\{x\in s\mid x\text{ is extra large}\}$	$$\{x\in s\mid x\text{ is extra large}\}$$
\bigcup union	$\bigcup$	$$\bigcup$$
\bigcap intersection	$\bigcap$	$$\bigcap$$
\Biggl\{ big left bracket	$\Biggl\{$	$$\Biggl\{$$
\Biggl(\biggl(\bigl( x \bigr) big left & right	$\Biggl(\biggl(\bigl( x \bigr)$	$$\Biggl(\biggl(\bigl( x \bigr)$$
\Biggl\{\biggl(\bigl[ x \bigr] big left & right	$\Biggl\{\biggl(\bigl[ (x) \bigr]$	$$\Biggl\{\biggl(\bigl[ (x) \bigr]$$
\Biggl\|( x - 1 )^3 \Biggr\|^2	$\Biggl\|( x - 1 )^3 \Biggr\|^2$	$$\Biggl\|( x - 1 )^3 \Biggr\|^2$$
\alpha~\beta greeks	$\alpha~\beta$	$$\alpha~\beta$$
\gamma~\Gamma greek cases	$\gamma~\Gamma$	$$\gamma~\Gamma$$
\omega~\Omega greek cases	$\omega~\Omega$	$$\omega~\Omega$$
\pi r^2	$\pi r^2$	$$\pi r^2$$
\frac{numerator}{denominator} fraction	$\frac{numerator}{denominator}$	$$\frac{numerator}{denominator}$$
\frac{(n++1)n}{2}	$\frac{(n++1)n}{2}$	$$\frac{(n++1)n}{2}$$
\int integral	$\int$	$$\int$$
\int_0^\infty integral	$\int_0^\infty$	$$\int_0^\infty$$
\sum summation	$\sum$	$$\sum$$
\sum_i^n	$\sum_i^n$	$$\sum_i^n$$
\sum_{i=0}^{n^3}	$\sum_{i=0}^{n^3}$	$$\sum_{i=0}^{n^3}$$
\prod_{i=0}^{n^3} product	$\prod_{i=0}^{n^3}$	$$\prod_{i=0}^{n^3}$$
\sqrt {25} = 5 square root	$\sqrt {25} = 5$	$$\sqrt {25} = 5$$
\left (\frac{\sqrt x}{y} \right)	$\left (\frac{\sqrt x}{y} \right)$	$$\left (\frac{\sqrt x}{y} \right)$$
\sqrt[3]{\frac xy} cube root of fraction	$\sqrt[3]{\frac xy}$	$$\sqrt[3]{\frac xy}$$
\\begin{bmatrix}a\\b\end{bmatrix} matrix	$\begin{bmatrix}a\\b\end{bmatrix}$	$$\begin{bmatrix}a\\b\end{bmatrix}$$
\lVert v \rVert_2^2 Normed vector space	$\lVert v \rVert_2^2$	$$\lVert v \rVert_2^2$$

Common Symbols

$\mathbb{R}$ → \mathbb{R}
$\neq$ → \neq
$\leqslant$ → \leqslant
$\geqslant$ → \geqslant
$\approx$ → \approx
$\equiv$ → \equiv
$\cong$ → \cong
$\sim$ → \sim
$\simeq$ → \simeq
$\partial$ → \partial
$\infty$ → \infty
$\nabla$ → \nabla
$\aleph$ → \aleph
$\ell$ → \ell
$\vee$ → \vee
$\wedge$ → \wedge
$\forall$ → \forall
$\exists$ → \exists
$\Longrightarrow$ → \Longrightarrow
$\cdots$ → \cdots
$\vdots$ → \vdots
$\therefore$ → \therefore

$\mathbb{N}$ → \mathbb{N}
$\pm$ → \pm
$\varnothing$ → \varnothing
$\angle$ → \angle
$\measuredangle$ → \measuredangle
$\sphericalangle$ → \sphericalangle
$\bigodot$ → \bigodot
$\triangle$ → \triangle
$\bigtriangleup$ → \bigtriangleup
$\square$ → \square
$\subset$ → \subset
$\supset$ → \supset
$\in$ → \in
$\emptyset$ → \emptyset
$\cup$ → \cup
$\cap$ → \cap
$\times$ → \times
$\div$ → \div
$\perp$ → \perp
$\parallel$ → \parallel
$\vec{a}$ → \vec{a}
$\bar{a}$ → \bar{a}
$\hat{a}$ → \hat{a}

Quadratic Equation

When $a \ne 0$, there are two solutions to $ax^2 + bx + c = 0$ and they are

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

Logarithms

$$\log_a N = x \iff N = a^x$$ $$\log N = x \iff N = 10^x$$ $$\ln N = x \iff N = e^x$$

Euler's Identity

$$e^{i\pi}+1=0$$

Fundamental Theorem of Calculus

$$\frac{df}{dt} = \lim_{h \to 0} \frac{f(t+h) - f(t)}{h}$$

The normal distribution

$$\Phi(x) = {\frac{1}{2\pi\sigma}e}^{\frac{(x-\mu)^2}{2\sigma^2}}$$

Shannon's Information Theory

$$H = -\sum p(x)\log p((x)$$

Shane Bow

Technology Consultant

I enjoy making things that serve the greater good — Software (and gadgets) that promote social values, improved quality of life, and learning.

I especially thrive on building strong close knit teams of developers based on superior leadership skills and wide ranging technical know-how and experience.

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