Mathematic in LaTeX

How To Write Mathematical Equations, Expressions, and Symbols with LaTeX: A cheatsheet.

1 What is LaTeX?

LaTeX is a programming language that can be used for writing and typesetting documents. It is especially useful to write mathematical notation such as equations and formulae.

2 How to use LaTeX to write mathematical notation

There are three ways to enter “math mode” and present a mathematical expression in LaTeX:

1. inline (in the middle of a text line)
2. as an equation, on a separate dedicated line
3. as a full-sized inline expression (displaystyle)

2.1 inline

Inline expressions occur in the middle of a sentence. To produce an inline expression, place the math expression between dollar signs ($ ). For example, typing $E=mc^2$ yields $E=mc^2$ .

2.2 equation

Equations are mathematical expressions that are given their own line and are centered on the page. These are usually used for important equations that deserve to be showcased on their own line or for large equations that cannot fit inline. To produce an inline expression, place the mathematical expression between the symbols \[ and \] . Typing \[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\] yields$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$  (1)

2.3 displaystyle

To get full-sized inline mathematical expressions use \displaystyle . Typing I want this $\displaystyle \sum_{n=1}^{\infty} \frac{1}{n}$, not this $\sum_{n=1}^{\infty} \frac{1}{n}$. yields: I want this $\displaystyle \sum_{n=1}^{\infty}\frac{1}{n}$ , not this $\sum_{n=1}^{\infty}\frac{1}{n}.$

3 Symbols (in math mode)

3.1 The basics

As discussed above math mode in LaTeX happens inside the dollar signs ($...$ ), inside the square brackets \[...\] and inside equation and displaystyle environments. Here’s a cheatsheet showing what is possible in a math environment:

description	command	output
addition	+	$+$
subtraction	-	$-$
plus or minus	\pm	$\pm$
multiplication (times)	\times	$\times$
multiplication (dot)	\cdot	$\cdot$
division symbol	\div	$\div$
division (slash)	/	$/$
simple text	\text{text}	$\text{text}$
infinity	\infty	$\infty$
dots	1,2,3,\ldots	$1,2,3,\ldots$
dots	1+2+3+\cdots	$1+2+3+\cdots$
fraction	\frac{a}{b}	$\frac{a}{b}$
square root	\sqrt{x}	$\sqrt{x}$
$n$ th root	\sqrt[n]{x}	$\sqrt[n]{x}$
exponentiation	a^b	$a^{b}$
subscript	a_b	$a_{b}$
absolute value	|x|	$|x|$
natural log	\ln(x)	$\ln(x)$
logarithms	\log_{a}b	$\log_{a}b$
exponential function	e^x=\exp(x)	$e^{x}=\exp(x)$
deg	\deg(f)	$\deg(f)$
degree	\degree	$\degree$
arcmin	^\prime	$^\prime$
arcsec	^{\prime\prime}	$^{\prime\prime}$
circle plus	\oplus	$\oplus$
circle times	\otimes	$\otimes$
equal	=	$=$
not equal	\ne	$\ne$
less than	<	$<$
less than or equal to	\le	$\le$
greater than or equal to	\ge	$\ge$
approximately equal to	\approx	$\approx$

3.2 Functions

description	command	output
maps to	\to	$\to$
composition	\circ	$\circ$

3.3 Greek and Hebrew letters

command	output	command	output
\alpha	$\alpha$	\tau	$\tau$
\beta	$\beta$	\theta	$\theta$
\chi	$\chi$	\upsilon	$\upsilon$
\delta	$\delta$	\xi	$\xi$
\epsilon	$\epsilon$	\zeta	$\zeta$
\varepsilon	$\varepsilon$	\Delta	$\Delta$
\eta	$\eta$	\Gamma	$\Gamma$
\gamma	$\gamma$	\Lambda	$\Lambda$
\iota	$\iota$	\Omega	$\Omega$
\kappa	$\kappa$	\Phi	$\Phi$
\lambda	$\lambda$	\Pi	$\Pi$
\mu	$\mu$	\Psi	$\Psi$
\nu	$\nu$	\Sigma	$\Sigma$
\omega	$\omega$	\Theta	$\Theta$
\phi	$\phi$	\Upsilon	$\Upsilon$
\varphi	$\varphi$	\Xi	$\Xi$
\pi	$\pi$	\aleph	$\aleph$
\psi	$\psi$	\beth	$\beth$
\rho	$\rho$	\daleth	$\daleth$
\sigma	$\sigma$	\gimel	$\gimel$

3.4 Vectors

description	command	output
vector	\vec{v}	$\vec{v}$
vector	\mathbf{v}	$\mathbf{v}$
norm	||\vec{v}||	$||\vec{v}||$

3.5 Set theory

description	command	output
set brackets	\{1,2,3\}	$\{1,2,3\}$
element of	\in	$\in$
subset of	\subset	$\subset$
subset of	\subseteq	$\subseteq$
contains	\supset	$\supset$
contains	\supseteq	$\supseteq$
union	\cup	$\cup$
intersection	\cap	$\cap$
big union	\bigcup_{n=1}^{10}A_n	$\displaystyle \bigcup_{n=1}^{10}A_{n}$
big intersection	\bigcap_{n=1}^{10}A_n	$\displaystyle \bigcap_{n=1}^{10}A_{n}$
empty set	\emptyset	$\emptyset$
power set	\mathcal{P}	$\mathcal{P}$
minimum	\min	$\min$
maximum	\max	$\max$
supremum	\sup	$\sup$
infimum	\inf	$\inf$
limit superior	\limsup	$\limsup$
limit inferior	\liminf	$\liminf$
closure	\overline{A}	$\overline{A}$

3.6 Logic

description	command	output
not	\sim	$\sim$
and	\land	$\land$
or	\lor	$\lor$
if...then	\to	$\to$
if and only if	\leftrightarrow	$\leftrightarrow$
logical equivalence	\equiv	$\equiv$
therefore	\therefore	$\therefore$
there exists	\exists	$\exists$
for all	\forall	$\forall$
implies	\Rightarrow	$\Rightarrow$
equivalent	\Leftrightarrow	$\Leftrightarrow$

3.7 Calculus

description	command	output
derivative	\frac{df}{dx}	$\displaystyle \frac{df}{dx}$
derivative	\f'	$f'$
partial derivative	\frac{\partial f} {\partial x}	$\displaystyle \frac{\partial f}{\partial x}$
limits	\lim_{x\to \infty}	$\displaystyle \lim_{x\to \infty}$
summation	\sum_{n=1}^{\infty}a_n	$\displaystyle \sum_{n=1}^{\infty}a_n$
product	\prod_{n=1}^{\infty}a_n	$\displaystyle \prod_{n=1}^{\infty}a_n$
integral	\int	$\displaystyle\int$
double integral	\iint	$\displaystyle\iint$
triple integral	\iiint	$\displaystyle\iiint$

3.8 Number theory

description	command	output
divides	|	$|$
does not divide	\not |	$\not |$
greatest common divisor	\gcd	$\gcd$
ceiling	\lceil x \rceil	$\lceil x\rceil$
floor	\lfloor x \rfloor	$\lfloor x \rfloor$

3.9 Geometry and trigonometry

description	command	output
angle	\angle ABC	$\angle ABC$
degree	90^{\circ}	$90^{\circ}$
triangle	\triangle ABC	$\triangle ABC$
segment	\overline{AB}	$\overline{AB}$
sine	\sin	$\sin$
cosine	\cos	$\cos$
tangent	\tan	$\tan$
cotangent	\cot	$\cot$
secant	\sec	$\sec$
cosecant	\csc	$\csc$
inverse sine	\arcsin	$\arcsin$
inverse cosine	\arccos	$\arccos$
inverse tangent	\arctan	$\arctan$

4 Symbols (in text mode)

The followign symbols do not have to be surrounded by dollar signs.

description	command	output
dollar sign	\$	$
percent	\%	%
ampersand	\&	&
pound	\#	#
backslash	\textbackslash	\
left quote marks	``	“ right quote marks & '' & ”
single left quote	`	‘ single right quote & ' & ’
hyphen	X-ray	X-ray
en-dash	pp. 5--15	pp. 5–15
em-dash	Yes---or no?	Yes—or no?

5 Writing LaTeX notation in Authorea

Authorea supports LaTeX writing, but you don’t have to know LaTeX to use Authorea! In order to insert LaTeX in an Authorea document:

1. Create a new document
2. Click on the Insert button in the toolbar and then select LaTeX from the dropdown.

Here are some tips for writing LaTeX in Authorea:

1. Click anywhere outside of the LaTeX block to render it.
2. Hover on Preview to see a Preview of the rendered content.
3. Do not paste an entire LaTeX article! Instead import documents from your homepage.
4. Only type LaTeX content in a LaTeX block, i.e. everything you would write after \begin{document} .
5. Do not type preamble (e.g. documentclass), frontmatter, macros or figures.
6. To add macros (newcommands) and packages, click Settings $\rightarrow$  Edit Macros
7. Use the Insert Figure button to insert images (and data).
8. Use math mode for equations, e.g. $\mathcal L_{EM}=-\frac14F^{\mu\nu}F_{\mu\nu}$ .
9. Try the citation tool (click cite) to find and add citations, or use \cite{} .
10. To insert more LaTeX blocks click Insert $\rightarrow$  LaTeX.
11. You can use sectioning commands like \section{},\subsection{},\subsubsection{} to add headings.1

6 Further reading

Interested in finding out more about LaTeX? Check out these examples of how LaTeX can be used to write mathematical equations, and follow these instructions to create powerful documents in LaTeX on Authorea, beyond mathematics.