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$\LaTeX{}$ Guide

Document classes

Packages

Title

Class	Effect
$\texttt{book}$	Default is two sided
$\texttt{report}$	No `\part` divisions
$\texttt{article}$	No `\part` or `\chapter` divisions
$\texttt{letter}$	Letter
$\texttt{slides}$	Large sans-serif font

Used at the very beginning of a document:
\documentclass{class}. Write \begin{document} to start contents and \end{document} to end the document.

Common documentclass options

Effect	Code
Font size	`10pt` / `11pt` / `12pt`
Paper size	`letterpaper` / `a4paper`
Use two columns	`twocolumn`
Set margins for two-sided	`twoside`
Landscape orientation Must use `dvips-t landscape`	`landscape`
Double-space lines	`draft`

Usage: \documentclass[opt,opt]{class}.

Packages

Effect	Package
Use 1 inch margins	`fullpage`
Set margins with `\marginsize{l}{r}{t}{b}`	`anysize`
Use $n$ columns with `\begin{multicols}{n}`	`multicol`
Use $\LaTeX{}$ symbol font	`latexsym`

Use before \begin{document}. Usage: \usepackage{package}.

If using MathJax for html write \require{package}.

Title

Effect	Package
Author of document	`\author{text}`
Title of document	`\title{text}`
Date	`\date{text}`

These commands go before \begin{document}. The declaration \maketitle goes at the top of the document.

Miscellaneous documents classes

Use \pagestyle{empty} for an empty header, footer and no page numbers.

Document Structure

Text environments

Lists

References

Floating bodies

\part{title}
\chapter{title}
\section{title}
\subsection{title}
\subsubsection{title}
\paragraph{title}
\subparagraph{title}

Section commands can be followed with an *, like \section*{title} , to suppress heading numbers. \setcounter{secnumdepth}{x} supresses heading numbers of depth $> x$ , where chapter has depth $0$ .

Text environments

Code	Description
`\begin{comment}`	Comment block (not printed)
`\begin{quote}`	Indented quotation block
`\begin{quotation}`	with indented paragraphs
`\begin{verse}`	Quotation block for verse

Lists

Code	Description
`\begin{enumerate}`	Numbered list
`\begin{itemize}`	Bulleted list
`\begin{description}`	Description list
`\itemtext`	Add an item
`\item[x]text`	Use $x$ instead of normal bullet or number Required for descriptions

Examples for enumerate versions

Code	Description
`\begin{enumerate}[a]`	$a,b,c, \ldots$
`\begin{enumerate}[(a)]`	$(a),(b),(c), \ldots$
`\begin{enumerate}[a)]`	$a),b),c), \ldots$
`\begin{enumerate}[a.]`	$a.,b.,c., \ldots$
`\begin{enumerate}[i]`	$i,ii,iii, \ldots$

References

Code	Description
`\label{marker}`	Set a marker for cross-reference, often of the form `\label{sec:item}`
`\ref{marker}`	Give section/body number of marker
`\pageref{marker}`	Give page number of marker
`\footnote{text}`	Print footnote at bottom of page

Floating bodies

Code	Description
`\begin{table}[place]`	Add numbered table
`\begin{figure}[place]`	Add numbered figure
`\begin{equation}[place]`	Add numbered equation
`\caption{text}`	Caption for the body

The place is a list valid placements for the body. t=top, h=here, b=bottom, p=separate page, !=place even if ugly. Captions and label markers should be within the environment.

Text properties

Font face

Font size

Verbatim text

Justification

Miscellaneous text properties

Text color

Hyperlinks

Font face

Code	Declaración	Effect
`\textrm{text}`	`{\rmtext}`	$\textrm{Serif family}$
`\textsf{text}`	`{\sftext}`	$\textsf{Sans serif family}$
`\texttt{text}`	`{\tttext}`	$\texttt{Typewriter family}$
`\textmd{text}`	`{\mdtext}`	$\textmd{Medium series}$
`\textbf{text}`	`{\bftext}`	$\textbf{Bold series}$
`\textup{text}`	`{\uptext}`	$\textup{Upright shape}$
`\textit{text}`	`{\ittext}`	$\textit{Italic shape}$
`\textsl{text}`	`{\sltext}`
`\textsc{text}`	`{\sctext}`
`\emph{text}`	`{\emtext}`
`\textnormal{text}`	`{\normalfonttext}`	$\textnormal{Document font}$
`\underline{text}`		$\underline{Underline}$

Size	Example
`\tiny`	${\tiny tiny}$
`\scriptsize`	${\scriptsize scriptsize}$
`\footnotesize`	${\footnotesize footnotesize}$
`\small`	${\small small}$
`\normalsize`	${\normalsize normalsize}$
`\large`	${\large large}$
`\Large`	${\Large Large}$
`\LARGE`	${\LARGE LARGE}$
`\huge`	${\huge huge}$
`\Huge`	${\Huge Huge}$

Verbatim text

Code	Description
`\begin{verbatim}`	Verbatim environment
`\begin{verbatim*}`	Spaces are shown as $\textvisiblespace$
`\verb!text!`	Text between the delimiting characters (in this case `!` is verbatim)

Justification

Environment	Declaración
`\begin{center}`	`\centering`
`\begin{flushleft}`	`\raggedright`
`\begin{flushright}`	`\raggedleft`

Miscellaneous text properties

\linespread{x} changes the line spacing by the multiplier $x$ .

Use \boxed{a} or \Aboxed{a} to enclose in a box any text or equation.

$a$

This does not work in Katex but you can use CSS instead:

.katex { border: 0.0625em solid currentcolor; padding: 0.5em; }

Text color

To use colors from xcolor package write \usepackage{xcolor}. To define new color names use \definecolor{new name}{RGB}{r,g,b}. Then \textcolor{blue}{a_{n}} renders as $\color{blue}{a_{n}}$ . If using Katex for html \color{blue}{a_{n}} renders as $\color{blue}{a_{n}}$ .

Accessing additional named colours

Additional named colours can be accessed via the following xcolor package options:

dvipsnames: loads 68 named colours (CMYK)
svgnames: loads 151 named colours (RGB)
x11names: loads 317 named colours (RGB)

As an example: \usepackage[dvipsnames]{xcolor}.

Hyperlinks

Import the package hyperref to hyperlink your references. Typically, it should be the last package imported to avoid problems. The link formatting can be done after the package declaration like the following example:

\hypersetup{
  colorlinks=true,
  linkcolor=blue,
  filecolor=magenta,
  urlcolor=cyan,
  pdftitle={Example},
  pdfpagemode=FullScreen,
}
\urlstyle{same}

Code	Description
`\hypersetup{ ... }`	Setting these options configures the behavior of links within the document. Each parameter should be separated by commas, following the syntax of parameter=value
`colorlinks=true`	The links will display a color, with red as the default
`linkcolor=blue`	Blue indicates internal links, which are generated by cross-referenced elements
`filecolor=magenta`	Links to local files will be shown in magenta colour
`urlcolor=cyan`	Links to web sites are set to cyan colour
`urlstyle{same}`	By default, links are printed in monospaced fonts. This command alters their appearance to match the rest of the text style
`\href{https://johzu.com}{Something Linky}`	This command accepts two parameters: the URL for the link (http://www.overleaf.com in this instance) and the text to be displayed as the clickable link (in this case, 'Something Linky')
`\url{https://johzu.com}`	This command displays the passed parameter URL as an active link, particularly helpful for document printing purposes
`\href{run:./file.txt}{File.txt}`	The \href{run:./file.txt}{File.txt} command outputs the text 'File.txt' as a clickable link that directs to a local file named 'file.txt' within the present working directory. Observe the 'run:' prefix preceding the file path.
`\hyperlink{thesentence}{any sentence}`	The function generates a clickable element with the text "any sentence," linking to the location identified by "thesentence."
`\hypertarget{thesentence}{this sentence}`	The command takes two parameters enclosed in braces. The initial parameter serves as a distinct identifier for this sentence, while the second parameter, "this sentence," will be printed in its usual format.

Text-mode symbols

Symbols

Accents

Dashes

Line and page breaks

Spaces

Miscellaneous text-mode symbols

Use \ as an escape character:

Symbol	Code
$\&$	`\&`
$\%$	`\%`
$\$$	`\$`
$\#$	`\#`
$\_$	`\_`
$\{ \}$	`\{ \}`

Symbols

Symbol	Code	Name
$\&$	`\&`	ampersand
$\checkmark$	`\checkmark`	check mark
$\^{}$	`\^{}`, `\textasciicircum{}`	circumflex
$\dag$	`\dag`	dagger obelisk obelus
$\$$	`\$`	dollar sign
$\ddag$	`\ddag`	double dagger diesis
$\ldots$	`\ldots`	ellipsis
$\#$	`\#`	number sign primorial
$\%$	`\%`	percent sign
$\P$	`\P`	pilcrow
$\pounds$	`\pounds`	pound sign
$\qedsymbol$, $\qedhere$, $ \qed $	`$\qedsymbol$, $\qedhere$, $\qed$`	quod erat demonstrandum
$\S$	`\S`	section sign
$\~{}$	`\~{}`, `\textasciitilde{}`	tilde
$\_$	`\_`	underscore
$\mid$	`\\|`, `\mid`, `\textpipe`, `\textbar`	vertical bar (pipe)
$\textvisiblespace$	`\textvisiblespace`	open box
$\clubsuit$	`\clubsuit`	clubs
$\diamondsuit$	`\diamondsuit`	diamonds
$\heartsuit$	`\heartsuit`	hearts
$\spadesuit$	`\spadesuit`	spades
$\flat$	`\flat`	flat
$\natural$	`\natural`	natural
$\sharp$	`\sharp`	sharp

Accents

Symbol	Code	Name
$\textnormal{\`o}$	`\‘o`	grave accent
$\textnormal{\'o}$	`\’o`	acute accent
$\textnormal{\^{o}}$	`\^{o}`	circumflex
$\textnormal{\~{o}}$	`\~{o}`	tilde
$\textnormal{\={o}}$	`\={o}`	macron
$\textnormal{\.{o}}$	`\.{o}`	overdot
$\textnormal{\"{o}}$	`\"{o}`	diaeresis umlaut
$\textnormal{\v{o}}$	`\v{o}`	caron há $\textsf{\v{c}}$ ek
$\textnormal{\H{o}}$	`\H{o}`	double acute accent hungarumlaut
$\textnormal{\c{c}}$ $\textnormal{\c{o}}$	`\c{c}` `\c{o}`	cedilla
$\textnormal{\d{o}}$	`\d{o}`	underdot
$\textnormal{\b{o}}$	`\b{o}`	bar under the letter
$\textnormal{\u{o}}$	`\u{o}`	breve
$\textnormal{\r{o}}$	`\r{o}`	overring
$\textnormal{\t{oo}}$	`\t{oo}`	tie tie bar top ligature
$\textnormal{\OE}$	`\OE`	uppercase ethel
$\textnormal{\oe}$	`\oe`	lowercase ethel
$\textnormal{\AE}$	`\AE`	uppercase ash
$\textnormal{\ae}$	`\ae`	lowercase ash
$\textnormal{\AA}$	`\AA`	uppercase a with overring
$\textnormal{\aa}$	`\aa`	lowercase a with overring
$\textnormal{\O}$	`\O`	uppercase o with slash
$\textnormal{\o}$	`\o`	lowercase o with slash
$\textnormal{\k}$	`\k`	ogonek
$\textnormal{\L}$	`\L`	uppercase l with bar
$\textnormal{\l}$	`\l`	lowercase l with bar
$\textnormal{\i}$	`\i`, `\imath`	dotless i (untittled)
$\textnormal{\j}$	`\j`, `\jmath`	dotless j (untittled)
$\textnormal{\ss}$	`\ss`	eszett
$\sout{a}$	`\sout{a}`	strikethrough

Dashes

Name	Source	Example	Usage
hyphen	-	X $\textnormal{-}$ ray	In words
en-dash	-	1 $\textnormal{-}$ 5	Between numbers
em-dash	—	Yes $\textnormal{—}$ or no?	Punctuation

Line and page breaks

Code	Description
`\\`	Begin new line without new paragraph
`\\*`	Prohibit pagebreak after linebreak
`\kill`	Don’t print current line
`\pagebreak`	Start new page
`\noindent`	Do not indent current line

Spaces

Code	Description
`\quad`	space equal to the current font size (= 18 mu)
`\,`	3/18 of \quad (= 3 mu)
`\:`	4/18 of \quad (= 4 mu)
`\;`	5/18 of \quad (= 5 mu)
`\!`	-3/18 of \quad (= -3 mu)
`"\ "`	equivalent of space in normal text
`\qquad`	twice of \quad (= 36 mu)

Miscellaneous text-mode symbols

Code	Description
`\today`	February 17, 2023
`\sim`	Prints $\sim$ instead of `\~{}`, which makes $\textnormal{\~{ }}$ .
`˜`	Space, disallow linebreak $\texttt{(W.J.\~{ }Clinton)}$ .
`\@.`	Indicate that the $\texttt{.}$ ends a sentence when following an uppercase letter.
`\hspace{l}`	Horizontal space of length $l$ (Ex: l = $\texttt{20pt}$ ).
`\vspace{l}`	Vertical space of length $l$ .
`\vspace{w}{h}`	Line of width $w$ and height $h$ .

Tabular environments

Tabbing environment

Tabular environment

Tabular column specification

Tabular elements

Tabbing environment

\= Set tab stop.
\> Go to tab stop.
Tab stops can be set on “invisible” lines with \kill at the end of the line. Normally \\ is used to separate lines.

Tabular environment

\begin{array}[pos]{cols}
\begin{tabular}[pos]{cols}
\begin{tabular*}{width}[pos]{cols}

Tabular column specification

Code	Description
`l`	left-justified column.
`c`	centered column.
`r`	right-justified column.
`p{width}`	paragraph column with text vertically aligned at the top
`m{width}`	paragraph column with text vertically aligned in the middle (requires array package)
`b{width}`	paragraph column with text vertically aligned at the bottom (requires array package)
`@{decl}`	Insert $decl$ instead of inter-column space.
`\|`	Inserts a vertical line between columns
`\|\|`	Inserts a double vertical line between columns

Tabular elements

\hline Horizontal line between rows.
\cline {x-y Horizontal line across columns $x$ through $y$ .
\multicolumn{n}{cols}{text} A cell that spans $n$ columns, with cols column specification.

Math mode

Mathematical font face

Sensible size examples

Letters

Other symbols

Arrows

Delimiters

Accents

Elementary math control sequences

Non-italic function names

Fills, leaders and ellipses

Useful environments

Inline math	Displayed math
`$...$`	`\[...\]`
$...$	`$$...$$`
	`\begin{equation}` `...` `\end{equation}`
	`\begin{equation}` `...` `\end{equation}`

Mathematical font face

Code	Package	Effect
`\mathrm{text}`		$\mathrm{Serif\ family}$
`\mathit{text}`		$\mathit{Italic\ shape}$
`\mathbf{text}`		$\mathbf{Boldface\ series}$
`\mathsf{text}`		$\mathsf{Sans\ serif\ family}$
`\mathtt{text}`		$\mathtt{Typewriter\ family}$
`\bm{text}`		$\bm{Mathematical\ boldface}$
`\boldmath{text}`	amssymb	$\bm{Mathematical\ boldface}$
`\mathnormal{text}`		$\mathnormal{Mathematical\ normal}$
`\mathcal{text}`		$\mathcal{Calligraphic}$
`\Bbb{TEXT}`	amsfonts/amssymb	$\Bbb{OPEN}$
`\mathbb{TEXT}`	amsfonts, amssymb	$\mathbb{OPEN}$
`\frak{text}`		$\frak{Fraktur}$
`\mathfrak{text}`	eufrak, amsfonts, amssymb	$\mathfrak{Fraktur}$
`\mathscr{text}`	mathrsfs	$\mathscr{RSFS\ FONT}$
`\mathds{text}`	dsfont

Sensible size examples

Inline	Displayed	Code	Name
$\frac{x}{y}$	$\frac{x}{y}$	`\frac{x}{y}`	fraction
$\int$	$\int$	`\int`	integral
$\iint$	$\iint$	`\iint`	surface integral
$\iiint$	$\iiint$	`\iiint`	volume integral
$\oint$	$\oint$	`\oint`	contour integral
$\oiint$	$\oiint$	`\oiint`	closed surface integral
$\prod_{k=1}^{n}$	$\prod_{k=1}^{n}$	`\prod_{k=1}^{n}`	product
$\sqrt[n]{x}$	$\sqrt[n]{x}$	`\sqrt[n]{x}`	radical symbol
$s_{x}$	$s_{x}$	`s_{x}`	subscript
$\sum_{k=1}^{n}$	$\sum_{k=1}^{n}$	`\sum_{k=1}^{n}`	summation
$s^{x}$	$s^{x}$	`s^{x}`	superscript

Letters

Greek alphabet

Name	Code	Uppercase	Variant	Lowercase	Variant
alpha	`\Alpha`, `\alpha`	$\Alpha$		$\alpha$
beta	`\Beta`, `\beta`	$\Beta$		$\beta$
gamma	`\Gamma`, `\varGamma`, `\gamma`	$\Gamma$	$\varGamma$	$\gamma$
delta	`\Delta`, `\varDelta`, `\delta`	$\Delta$	$\varDelta$	$\delta$
epsilon	`\Epsilon`, `\epsilon`, `\varepsilon`	$\Epsilon$		$\epsilon$	$\varepsilon$
zeta	`\Zeta`, `\zeta`	$\Zeta$		$\zeta$
eta	`\Eta`, `\eta`	$\Eta$		$\eta$
theta	`\Theta`, `\varTheta`, `\theta`, `\vartheta`	$\Theta$	$\varTheta$	$\theta$	$\vartheta$
iota	`\Iota`, `\iota`	$\Iota$		$\iota$
kappa	`\Kappa`, `\kappa`, `\varkappa`	$\Kappa$		$\kappa$	$\varkappa$
lambda	`\Lambda`, `\varLambda`, `\lambda`	$\Lambda$	$\varLambda$	$\lambda$
mu	`\Mu`, `\mu`	$\Mu$		$\mu$
nu	`\Nu`, `\nu`	$\Nu$		$\nu$
xi	`\Xi`, `\varXi`, `\xi`	$\Xi$	$\varXi$	$\xi$
omicron	`\Omicron`, `\omicron`	$\Omicron$		$\omicron$
pi	`\Pi`, `\pi`, `\varPi`, `\varpi`	$\Pi$	$\varPi$	$\pi$	$\varpi$
rho	`\Rho`, `\rho`, `\varrho`	$\Rho$		$\rho$	$\varrho$
sigma	`\Sigma`, `\varSigma`, `\sigma`, `\varsigma`	$\Sigma$	$\varSigma$	$\sigma$	$\varsigma$
tau	`\Tau`, `\tau`	$\Tau$		$\tau$
upsilon	`\Upsilon`, `\varUpsilon`, `\upsilon`	$\Upsilon$	$\varUpsilon$	$\upsilon$
phi	`\Phi`, `\varPhi`, `\phi`, `\varphi`	$\Phi$	$\varPhi$	$\phi$	$\varphi$
chi	`\Chi`, `\chi`	$\Chi$		$\chi$
psi	`\Psi`, `\varPsi`, `\psi`	$\Psi$	$\varPsi$	$\psi$
omega	`\Omega`, `\varOmega`, `\omega`	$\Omega$	$\varOmega$	$\omega$

Archaic Greek

Name	Code	Uppercase	Lowercase	Variant
digamma	`\digamma`		$\digamma$

Hebrew letters

Name	Code	Symbol
aleph	`\aleph`	$\aleph$
beth	`\beth`	$\beth$
gimel	`\gimel`	$\gimel$
daleth	`\daleth`	$\daleth$

Other letters

Symbol	Code	Name
$\backepsilon$	`\backepsilon`	backepsilon
$\Bbbk$	`\Bbbk`	blackboard-bold lowercase k
$\circledR$	`\circledR`	registered trademark symbol
$\circledS$	`\circledS`
$\copyright$	`\copyright`	copyright symbol/sign
$\ell$	`\ell`	cursive l
$\eth$	`\eth`	eth
$\Game$	`\Game`
$\hbar$	`\hbar`	h-bar reduced Plancks’s constant
$\hslash$	`\hslash`
$\Im$	`\Im`	imaginary part
$\imath$	`\imath`
$\delta$ , $d\hspace{-0.08em}\bar{}\hspace{0.1em}$	`\delta`, `d\hspace{-0.08em}\bar{}\hspace{0.1em}`	inexact diferential
$\infty$	`\infty`	infinity
$\jmath$	`\jmath`
$\mho$	`\mho`
$\nabla$	`\nabla`	nabla, del
$\partial$	`\partial`	partial derivative
$\Re$	`\Re`	real part
$\wp$	`\wp`	power set, Weierstrass elliptic functions

Degree $^{\circ}$ Ex: 22^{\circ}\mathrm{C}: $22^{\circ}\mathrm{C}$ .

Other symbols

Agrupations

Symbol	Code	Name
$\bigcap_{i=a}^{b}$	`\bigcap_{i=a}^{b}`	set intersection
$\bigcup_{i=a}^{b}$	`\bigcup_{i=a}^{b}`	set union
$\biguplus_{i=a}^{b}$	`\biguplus_{i=a}^{b}`	disjoint/discriminated union
$\bigwedge_{i=a}^{b}$	`\bigwedge_{i=a}^{b}`
$\bigvee_{i=a}^{b}$	`\bigvee_{i=a}^{b}`
$\bigsqcup_{i=a}^{b}$	`\bigsqcup_{i=a}^{b}`	disjoint/discriminated union
$\prod_{i=a}^{b}$	`\prod_{i=a}^{b}`	product
$\coprod_{i=a}^{b}$	`\coprod_{i=a}^{b}`	coproduct
$\sum_{i=a}^{b}$	`\sum_{i=a}^{b}`	summation
$\bigodot_{i=a}^{b}$	`\bigodot_{i=a}^{b}`	Hadamard product
$\bigoplus_{i=a}^{b}$	`\bigoplus_{i=a}^{b}`	direct sum
$\bigotimes_{i=a}^{b}$	`\bigotimes_{i=a}^{b}`	Kronecker product

Bars

Symbol	Code	Name	Symbol	Code
$\smallsetminus$	`\smallsetminus`	set diference
$\setminus$	`\setminus`	set diference	$/$	`/`
$\backslash$	`\backslash`		$\not$	`\not`
$\diagdown$	`\diagdown`		$\diagup$	`\diagup`

Symbol	Code	Name
$\mid$	`\mid`	divides
$\nmid$	`\nmid`	non-divisibility
$\vert$	`\vert`
$\Vert$	`\Vert`
$\lVert$	`\lVert`
$\rVert$	`\rVert`
$\parallel$	`\parallel`	is parallel with
$\nparallel$	`\nparallel`	is not parallel with
$\\|$	`\\\|`

Symbol	Code	Name
$\shortmid$	`\shortmid`
$\nshortmid$	`\nshortmid`
$\shortparallel$	`\shortparallel`
$\nshortparallel$	`\nshortparallel`

Operations

Symbol	Code	Name
$\surd$	`\surd`	root
$\dotplus$	`\dotplus`
$\pm$	`\pm`	plus-minus sign
$\mp$	`\mp`	minus-plus sign
$\prime$	`\prime`	prime symbol
$\backprime$	`\backprime`
$\ast$	`\ast`	asterisk, Khatri-Rao product
$\times$	`\times`	cross/vector product
$\ltimes$	`\ltimes`	semidirect product of normal factor to the left
$\rtimes$	`\rtimes`	semidirect product of normal factor to the right
$\leftthreetimes$	`\leftthreetimes`	semidirect product to the left
$\rightthreetimes$	`\rightthreetimes`	semidirect product to the right
$\star$	`\star`
$\bigstar$	`\bigstar`
$\circ$	`\circ`	circle, Hadamard product of matrices
$\sout{\circ}$	`\sout{\circ}`	plimsoll, thermodynamic quantity in the standard state
$\bullet$	`\bullet`
$\cdot$	`\cdot`	scalar/dot product
$\centerdot$	`\centerdot`
$\div$	`\div`	division
$\divideontimes$	`\divideontimes`
$\oplus$	`\oplus`	direct sum, exclusive disjunction, astronomical Earth, symbol
$\ominus$	`\ominus`	symmetric difference
$\circledast$	`\circledast`
$\circledcirc$	`\circledcirc`
$\odot$	`\odot`	Hadamard product of power series, astronomical Earth symbol, vector out of the page
$\otimes$	`\otimes`	Kronecker product, tensor product, dyadic product,vector into the page
$\circleddash$	`\circleddash`
$\oslash$	`\oslash`	Hadamard division
$\bigcirc$	`\bigcirc`
$\Box$	`\Box`
$\boxplus$	`\boxplus`
$\boxminus$	`\boxminus`
$\boxdot$	`\boxdot`
$\boxtimes$	`\boxtimes`
$\frown$	`\frown`	cap product
$\smile$	`\smile`	cup product
$\smallfrown$	`\smallfrown`	cap product
$\smallsmile$	`\smallsmile`	cup product
$\amalg$	`\amalg`	disjoint union
$\Join$	`\Join`
$\lhd$	`\lhd`
$\rhd$	`\rhd`
$\unlhd$	`\unlhd`
$\unrhd$	`\unrhd`
$\wr$	`\wr`	wreath product
$\intercal$	`\intercal`	Transposed matrix

Geometry

Symbol	Code	Name
$\vartriangleleft$	`\vartriangleleft`
$\blacktriangleleft$	`\blacktriangleleft`
$\vartriangleright$	`\vartriangleright`
$\blacktriangleright$	`\blacktriangleright`
$\vartriangle$	`\vartriangle`
$\blacktriangle$	`\blacktriangle`
$\triangledown$	`\triangledown`
$\blacktriangledown$	`\blacktriangledown`
$\square$	`\square`	it is necessary that, it is probable that, it is obligatory that, it is believed that, D’Alembert operator
$\blacksquare$	`\blacksquare`	end of proof
$\lozenge$	`\lozenge`	it is possible that, it is not necessary that, it is not probable that
$\blacklozenge$	`\blacklozenge`
$\triangle$	`\triangle`	triangle
$\bowtie$	`\bowtie`
$\bigtriangleup$	`\bigtriangleup`
$\bigtriangledown$	`\bigtriangledown`
$\Diamond$	`\Diamond`	it is possible that, it is not necessary that, it is not probable that
$\diamond$	`\diamond`
$\triangleleft$	`\triangleleft`
$\triangleright$	`\triangleright`
$\ntriangleleft$	`\ntriangleleft`
$\ntriangleright$	`\ntriangleright`
$\ntrianglelefteq$	`\ntrianglelefteq`
$\ntrianglerighteq$	`\ntrianglerighteq`
$\angle$	`\angle`	angle symbol
$\measuredangle$	`\measuredangle`
$\sphericalangle$	`\sphericalangle`
$\vdash$	`\vdash`	turnstile, proves
$\dashv$	`\dashv`
$\vDash$	`\vDash`	double turnstile, models
$\Vdash$	`\Vdash`
$\Vvdash$	`\Vvdash`
$\nvdash$	`\nvdash`	does not prove
$\nvDash$	`\nvDash`	not true
$\nVdash$	`\nVdash`
$\nVDash$	`\nVDash`
$\perp$	`\perp`	is perpendicular with
$\not\perp$	`\not\perp`	is not perpendicular with
$\parallel$	`\parallel`	is parallel with
$\nparallel$	`\nparallel`	is not parallel with
$\asymp$	`\asymp`	is asymptotic to
$\models$	`\models`	models

Logic

Symbol	Code	Name
$\exists$	`\exists`	existential quantification
$\exists!$	`\exists!`	uniqueness quantification
$\nexists$	`\nexists`	there is no
$\Finv$	`\Finv`
$\forall$	`\forall`	universal quantification
$\land$	`\land`	logical conjunction
$\wedge$	`\wedge`	logical conjunction
$\lor$	`\lor`	logical (inclusive) disjunction
$\vee$	`\vee`	logical (inclusive) disjunction
$\barwedge$	`\barwedge`	sheffer stroke, NOT AND, NAND
$\doublebarwedge$	`\doublebarwedge`	conjunction with double bar
$\veebar$	`\veebar`	logical (exclusive) disjunction
$\neg$ , $\lnot$	`\neg`, `\lnot`	negation
$\top$	`\top`	tautology
$\bot$	`\bot`	contradiction
$\because$	`\because`	because
$\therefore$	`\therefore`	therefore

Relations

Symbol	Code	Name
$=$	`=`	is equal to
$:=$	`:=`	defines to
$\triangleq$	`\triangleq`	defines to
$\overset{\mathrm{def}}{=}$	`\overset{\mathrm{def}}{=}`	defines to
$\overset{\frown}{=}$	`\overset{\frown}{=}`	corresponds to
$\bumpeq$	`\bumpeq`
$\Bumpeq$	`\Bumpeq`
$\eqcirc$	`\eqcirc`
$\dot=$	`\dot=`	approaches the limit
$\doteq$	`\doteq`	approaches the limit
$\circeq$	`\circeq`
$\cong$	`\cong`	is congruent to, is isomorphic to
$\doteqdot$	`\doteqdot`
$\risingdotseq$	`\risingdotseq`	approximately equal to or the image of
$\fallingdotseq$	`\fallingdotseq`	image of or approximately equal to
$\equiv$	`\equiv`	is equivalent to
$\neq$ , $\ne$	`\neq`, `\ne`	is not equal to

Proportion

Symbol	Code	Name
$\propto$	`\propto`	is proportional to
$\varpropto$	`\varpropto`	is proportional to

Similarity or approximation

Symbol	Code	Name
$\approx$	`\approx`	is approximately
$\thickapprox$	`\thickapprox`	is approximately
$\approxeq$	`\approxeq`
$\cong$	`\cong`	is congruent/isomorphic to
$\simeq$	`\simeq`	is similar or equal to, asymptotically equal to
$\eqsim$	`\eqsim`
$\sim$	`\sim`	is similar to
$\thicksim$	`\thicksim`	is similar to
$\backsim$	`\backsim`
$\backsimeq$	`\backsimeq`
$\nsim$	`\nsim`	is not similar to
$\ncong$	`\ncong`	is not congruent/isomorphic to

Comparison

Symbol	Code	Name
$\lessdot$	`\lessdot`
$\gtrdot$	`\gtrdot`
$<$	`<`	is less than
$>$	`>`	is greater than
$\leq$ , $\le$	`\leq`, `\le`	is less than or equal to
$\geq$ , $\ge$	`\geq`, `\ge`	is greater than or equal to
$\leqq$	`\leqq`
$\geqq$	`\geqq`
$\leqslant$	`\leqslant`	is less than or equal to
$\geqslant$	`\geqslant`	is greater than or equal to
$\eqslantless$	`\eqslantless`
$\eqslantgtr$	`\eqslantgtr`
$\lesssim$	`\lesssim`
$\gtrsim$	`\gtrsim`
$\lessapprox$	`\lessapprox`	less-than or approximate
$\gtrapprox$	`\gtrapprox`	greater-than or approximate
$\lessgtr$	`\lessgtr`
$\gtrless$	`\gtrless`
$\lesseqgtr$	`\lesseqgtr`
$\gtreqless$	`\gtreqless`
$\lesseqqgtr$	`\lesseqqgtr`
$\gtreqqless$	`\gtreqqless`
$\ll$	`\ll`	much less than
$\gg$	`\gg`	much greater than
$\lll$ , $\llless$	`\lll`, `\llless`
$\ggg$ , $\gggtr$	`\ggg`, `\gggtr`
$\nless$ , $\not<$	`\nless`, `\not<`	is not less than
$\ngtr$ , $\not>$	`\ngtr`, `\not>`	is not greater than
$\lnsim$	`\lnsim`
$\gnsim$	`\gnsim`
$\lnapprox$	`\lnapprox`
$\gnapprox$	`\gnapprox`
$\lneq$	`\lneq`
$\gneq$	`gneq`
$\lneqq$	`\lneqq`
$\gneqq$	`\gneqq`
$\lvertneqq$	`\lvertneqq`
$\gvertneqq$	`\gvertneqq`
$\nleq$	`\nleq`	is not less than or equal to
$\ngeq$	`\ngeq`	is not greater than or equal to
$\nleqq$	`\nleqq`
$\ngeqq$	`ngeqq`
$\nleqslant$	`\nleqslant`	is neither less than nor equal to
$\ngeqslant$	`\ngeqslant`	is neither greater than nor equal to

Order

Symbol	Code	Name
$\curlywedge$	`\curlywedge`
$\curlyvee$	`\curlyvee`
$\prec$	`\prec`	precedes
$\succ$	`\succ`	succeeds
$\preceq$	`\preceq`	precedes or equals
$\succeq$	`\succeq`	succeeds or equals
$\precsim$	`\precsim`
$\succsim$	`\succsim`
$\precapprox$	`\precapprox`
$\succapprox$	`\succapprox`
$\curlyeqprec$	`\curlyeqprec`
$\curlyeqsucc$	`\curlyeqsucc`
$\preccurlyeq$	`\preccurlyeq`
$\succcurlyeq$	`\succcurlyeq`
$\nprec$	`\nprec`	does not precede
$\nsucc$	`\nsucc`	does not succeed
$\npreceq$	`\npreceq`	neither precedes nor equals
$\nsucceq$	`\nsucceq`	neither succedes nor equals
$\precnsim$	`\precnsim`
$\succnsim$	`\succnsim`
$\precnapprox$	`\precnapprox`
$\succnapprox$	`\succnapprox`
$\precneqq$	`\precneqq`
$\succneqq$	`\succneqq`

Sets

Symbol	Code	Name
$\empty$	`\empty`	empty set
$\emptyset$	`\emptyset`	empty set
$\varnothing$	`\varnothing`	empty set
$\uplus$	`\uplus`	multiset addition disjoint union
$\cap$	`\cap`	set intersection
$\cup$	`\cup`	set union
$\in$	`\in`	is member of
$\ni$ , $\owns$	`\ni`, `\owns`	has member owns
$\notin$	`\notin`	is not member of
$\pitchfork$	`\pitchfork`	transversal intersection
$\subset$	`\subset`	is a proper subset of
$\supset$	`\supset`	is a proper superset of
$\subseteq$	`\subseteq`	is a subset of
$\supseteq$	`\supseteq`	is a superset of
$\subseteqq$	`\subseteqq`
$\supseteqq$	`\supseteqq`
$\not\subset$	`\not\subset`	is not a proper subset of
$\not\supset$	`\not\supset`	is not a proper superset of
$\nsubseteq$	`\nsubseteq`	is not a subset of
$\nsupseteq$	`\nsupseteq`	is not a superset of
$\nsubseteqq$	`\nsubseteqq`
$\nsupseteqq$	`\nsupseteqq`
$\subsetneq$	`\subsetneq`
$\supsetneq$	`\supsetneq`
$\varsubsetneq$	`\varsubsetneq`
$\varsupsetneq$	`\varsupsetneq`
$\subsetneqq$	`\subsetneqq`
$\supsetneqq$	`\supsetneqq`
$\varsubsetneqq$	`\varsubsetneqq`
$\varsupsetneqq$	`\varsupsetneqq`
$\sqcap$	`\sqcap`
$\sqcup$	`\sqcup`	disjoint/discriminated union
$\sqsubset$	`\sqsubset`
$\sqsupset$	`\sqsupset`
$\sqsubseteq$	`\sqsubseteq`
$\sqsupseteq$	`\sqsupseteq`
$\doublecap$ , $\Cap$	`\doublecap`, `\Cap`	double intersection
$\doublecup$ , $\Cup$	`\doublecup`, `\Cup`	double union
$\Subset$	`\Subset`
$\Supset$	`\Supset`
$\between$	`\between`
$\complement$	`\complement`	complement

Most relations can be negated by prefixing them with \not.

Symbol	Code	Name
$\not\equiv$	`\not\equiv`	is not equivalent
$\notin$	`\notin`	is not member of
$\ne$	`\ne`	is not equal

Arrows

Symbol	Code	Name
$\leftarrow$ , $\gets$	`\leftarrow`, `\gets`
$\longleftarrow$	`\longleftarrow`
$\rightarrow$ , $\to$	`\rightarrow`, `\to`	material implication, yield(s), produce(s), net forward reaction
$\longrightarrow$	`\longrightarrow`
$\nleftarrow$	`\nleftarrow`
$\nrightarrow$	`\nrightarrow`
$\uparrow$	`\uparrow`	substance in a gaseous state
$\downarrow$	`\downarrow`	substance in a solid state
$\leftrightarrow$	`\leftrightarrow`	material equivalence, resonance, mesomerism
$\longleftrightarrow$	`\longleftrightarrow`
$\updownarrow$	`\updownarrow`
$\nleftrightarrow$	`\nleftrightarrow`
$\leftleftarrows$	`\leftleftarrows`
$\rightrightarrows$	`\rightrightarrows`	uniform convergence
$\upuparrows$	`\upuparrows`
$\downdownarrows$	`\downdownarrows`
$\leftrightarrows$	`\leftrightarrows`
$\rightleftarrows$	`\rightleftarrows`	reaction in both directions
$\twoheadleftarrow$	`\twoheadleftarrow`
$\twoheadrightarrow$	`\twoheadrightarrow`
$\dashleftarrow$	`\dashleftarrow`
$\dashrightarrow$	`\dashrightarrow`
$\leftarrowtail$	`\leftarrowtail`
$\rightarrowtail$	`\rightarrowtail`
$\leftrightsquigarrow$	`\leftrightsquigarrow`
$\rightsquigarrow$ , $\leadsto$	`\rightsquigarrow` `\leadsto`
$\mapsto$	`\mapsto`	maplet
$\longmapsto$	`\longmapsto`	maplet
$\nearrow$	`\nearrow`
$\searrow$	`\searrow`
$\nwarrow$	`\nwarrow`
$\swarrow$	`\swarrow`
$\circlearrowleft$	`\circlearrowleft`
$\circlearrowright$	`\circlearrowright`
$\curvearrowleft$	`\curvearrowleft`
$\curvearrowright$	`\curvearrowright`
$\looparrowleft$	`\looparrowleft`
$\looparrowright$	`\looparrowright`
$\hookleftarrow$	`\hookleftarrow`
$\hookrightarrow$	`\hookrightarrow`
$\Lsh$	`\Lsh`
$\Rsh$	`\Rsh`
$\Leftarrow$	`\Leftarrow`
$\Longleftarrow$	`\Longleftarrow`
$\Rightarrow$	`\Rightarrow`	material implication
$\Longrightarrow$ $\implies$	`\Longrightarrow` `\implies`
$\Uparrow$	`\Uparrow`
$\Downarrow$	`\Downarrow`
$\Leftrightarrow$	`\Leftrightarrow`	material equivalence
$\Longleftrightarrow$	`\Longleftrightarrow`
$\nLeftarrow$	`\nLeftarrow`
$\nRightarrow$	`\nRightarrow`
$\Updownarrow$	`\Updownarrow`
$\nLeftrightarrow$	`\nLeftrightarrow`
$\Lleftarrow$	`\Lleftarrow`
$\Rrightarrow$	`\Rrightarrow`
$\leftharpoonup$	`\leftharpoonup`
$\leftharpoondown$	`\leftharpoondown`
$\rightharpoonup$	`\rightharpoonup`
$\rightharpoondown$	`\rightharpoondown`
$\upharpoonleft$	`\upharpoonleft`
$\upharpoonright$ , $\restriction$	`\upharpoonright` `\restriction`
$\downharpoonleft$	`\downharpoonleft`
$\downharpoonright$	`\downharpoonright`
$\leftrightharpoons$	`\leftrightharpoons`
$\rightleftharpoons$	`\rightleftharpoons`	equilibrium arrows, equilibrium
$\multimap$	`\multimap`

The \buildrel macro puts one symbol over another. The format is \buildrel⟨superscript⟩\over⟨relation⟩.

\buildrel\alpha\beta\over\longrightarrow $\buildrel\alpha\beta\over\longrightarrow$

f(x) \; {\buildrel\rm def\over=} \; x + 1
$f(x) \; {\buildrel\rm def\over=} \; x + 1$

Delimiters

Symbol	Code	Name
$\lbrack$ , $[$	`\lbrack`, `[`	left square bracket left bracket
$\rbrack$ , $]$	`\rbrack`, `]`	right square bracket right bracket
$\lbrace$ , $\{$	`\lbrace`, `\{`	left curly bracket left brace
$\rbrace$ , $\}$	`\rbrace`, `\}`	right curly bracket right brace
$\langle$	`\langle`	left angle bracket left chevron
$\rangle$	`\rangle`	right angle bracket right chevron
$\vert$ , $\$	`\vert`, `\\|`	boxed text
$\Vert$ , $\\|$	`\Vert`, `\\\|`
$\lceil$	`\lceil`	left ceiling
$\rceil$	`\rceil`	right ceiling
$\lfloor$	`\lfloor`	left floor
$\rfloor$	`\rfloor`	right floor
$\ulcorner$	`\ulcorner`	top left corner, Gödel number (left)
$\urcorner$	`\urcorner`	top right corner, Gödel number (right)
$\llcorner$	`\llcorner`	bottom left corner
$\lrcorner$	`\lrcorner`	bottom right corner
$[\![$	`[\![`	mathematical left white square bracket
$]\!]$	`]\!]`	mathematical right white square bracket
$(\!($	`(\!(`	left double parenthesis
$)\!)$	`)\!)`	right double parenthesis

Left and right delimiters will be enlarged if they are prefixed with \left or \right. Each \left must have a matching \right, one of which may be an empty delimiter \left. or \right.. For example \int_{a}^{b} x^{2} dx = \left. \frac{1}{3} x^{3} \right\vert_{a}^{b} = \left\lbrack \frac{1}{3}b^{3}\right\rbrack - \left\lbrack \frac{1}{3}a^{3}\right\rbrack produces:

$\int_{a}^{b} x^{2} dx = \left. \frac{1}{3} x^{3} \right\vert_{a}^{b} = \left\lbrack \frac{1}{3}b^{3}\right\rbrack - \left\lbrack \frac{1}{3}a^{3}\right\rbrack$

To specify a particular size, use the following:

\bigl(, \bigr), $\bigl( \bigr)$
\Bigl(, \Bigr), $\Bigl( \Bigr)$
\biggl(, \biggr), $\biggl( \biggr)$

You can also write \bigm for a large delimiter in the middle of a formula, or just \big for one that acts as an ordinary symbol. For example:

\biggl\lbrace\Bigl[\bigl( a\bigm\vert^{c}_{b} \bigr)\Bigr]\biggr\rbrace $\biggl\lbrace\Bigl[\bigl( a\bigm\vert^{c}_{b} \bigr)\Bigr]\biggr\rbrace$

Accents

Code	Symbol	Name
`\acute`	$\acute{a}$	acute
`\bar`	$\bar{a}$	bar
`\breve`	$\breve{a}$	breve
`\check`	$\check{a}$	check
`\dot`	$\dot{a}$	dot
`\ddot`	$\ddot{a}$	double dot
`\grave`	$\grave{a}$	grave
`\hat`	$\hat{a}$	hat, circumflex
`\mathring{x}`	$\mathring{x}$	ring
`\tilde`	$\tilde{a}$	tilde
`\vec`	$\vec{a}$	vector
`\overset{*}{X}`	$\overset{*}{X}$
`\underset{*}{X}`	$\underset{*}{X}$
`\sideset{}{'}\sum`	$\sum^{\prime}$
`\sideset{_1^2}{_3^4}\sum`	$_1^2\!\sum_3^4$
`\widehat`	$\widehat{abc}$	expanding hat
`\widetilde`	$\widetilde{abc}$	expanding tilde
`\overline{abc}`	$\overline{abc}$	overline
`\underline{abc}`	$\underline{abc}$	underline
`\overbrace{abc}`	$\overbrace{abc}$	overbrace
`\underbrace{abc}`	$\underbrace{abc}$	underbrace
`\overleftarrow{abc}`	$\overleftarrow{abc}$
`\overrightarrow{abc}`	$\overrightarrow{abc}$
`\overleftrightarrow{abc}`	$\overleftrightarrow{abc}$
`\underleftarrow{abc}`	$\underleftarrow{abc}$
`\underrightarrow{abc}`	$\underrightarrow{abc}$
`\underleftrightarrow{abc}`	$\underleftrightarrow{abc}$
`\xleftarrow[under]{over}`	$\xleftarrow[under]{over}$
`\xrightarrow[under]{over}`	$\xrightarrow[under]{over}$

The \skew⟨number⟩ command shifts accents for proper positioning,the larger the ⟨number⟩, the more right the shift. Compare

\hat{\hat{A}} gives $\hat{\hat{A}}$ , skew6\hat{\hat{A}} gives $\skew6\hat{\hat{A}}$.

Elementary Math Control Sequences

Example	Code	Name
$\overline{x + y}$	`\overline{x + y}`	overline a formula
$\underline{x + y}$	`\underline{x + y}`	underline a formula
$\sqrt{x + y}$	`\sqrt{x + y}`	square root
$\sqrt[n]{x + y}$	`\root [n]\of{x + y}`, `\sqrt[n]{x + y}`	higher degree roots
${n + 1\over 3}$	`{n + 1\over 3}`	fraction
${n + 1\atop 3}$	`{n + 1\atop 3}`	no line fraction
${n + 1\choose 3}$	`{n + 1\choose 3}`	binomial coefficient
${n + 1\brace 3}$	`{n + 1\brace 3}`	braced fraction
${n + 1\brack 3}$	`{n + 1\brack 3}`	bracketed fraction

The following code specify a style for typesetting formulas.
\displaystyle, \textstyle, \scriptstyle, \scriptscriptstyle

Non-Italic Function Names

Example	Code	Name
$\arccos$	`\arccos`	arccosine
$\arcsin$	`\arcsin`	arcsine
$\arctan$	`\arctan`	arctangent
$\arg$	`\arg`	argument of complex number
$\cos$	`\cos`	cosine
$\cosh$	`\cosh`	hyperbolic cosine
$\cot$	`\cot`	cotangent
$\coth$	`\coth`	hyperbolic cotangent
$\csc$	`\csc`	cosecant
$\deg$	`\deg`	degree
$\det$	`\det`	determinant
$\dim$	`\dim`	dimension
$\exp$	`\exp`	exponential function
$\gcd$	`\gcd`	greatest common divisor
$\hom$	`\hom`	hom-class
$\inf$	`\inf`	infimum of a set
$\ker$	`\ker`	kernel
$\lg$	`\lg`	common logarithm ( $\log_{10}$ , $\log_{2}$ )
$\lim$	`\lim`	limit (sequence, function)
$\varinjlim$	`\varinjlim`
$\varprojlim$	`\varprojlim`
$\varliminf$	`\varliminf`
$\varliminf$	`\varliminf`
$\varlimsup$	`\varlimsup`
$\liminf$	`\liminf`	limit inferior
$\limsup$	`\limsup`	limit superior
$\ln$	`\ln`	natural logarithm $\left(\log_{e}\right)$
$\log$	`\log`	logarithm $\left(\log_{10}\right)$ , $\left(\log_{e}\right)$
$\max$	`\max`	maximum of a set
$\min$	`\min`	minimum of a set
$\Pr$	`\Pr`	projection (linear algebra)
$\sec$	`\sec`	secant
$\operatorname{sgn}$	`\operatorname{sgn}`	sign/signum function
$\sin$	`\sin`	sine
$\sinh$	`\sinh`	hyperbolic sine
$\sup$	`\sup`	supremum of a set
$\tan$	`\tan`	tangent
$\tanh$	`\tanh`	hyperbolic tangent
$\operatorname{zzz}_{0}^{1}$	`\operatorname{zzz}\_{0}^{1}`	generic operator

mod with parentheses a \pmod{m}: $a \pmod{m}$

mod without parentheses a \bmod m: $a \bmod m$

The following examples use \mathop to create function names.

Example	Code	Plain $\TeX{}$ Definition
`\def\lim{\mathop{\rm lim}}`	`\lim_{x\to2}`	$\lim_{x\to2}$
`\def\log{\mathop{\rm log}\nolimits}`	`\log_2`	$\log_{2}$

Fills, Leaders and Ellipses

Text or Math mode: \dots $\dots$

Math mode:

Example	Code
$\centerdot$	`\centerdot`
$\dotsb$	`\dotsb`
$\dotsc$	`\dotsc`
$\dotsi$	`\dotsi`
$\dotsm$	`\dotsm`
$\dotso$	`\dotso`
$\ldots$	`\ldots`
$\cdots$	`\cdots`
$\vdots$	`\vdots`
$\ddots$	`\ddots`

The following fill space with the indicated item.
\hrulefill, \rightarrowfill, \leftarrowfill, \dotfill

The general format for constructing leaders is:
\leaders⟨boxorrule⟩\hskip⟨glue⟩ repeat box or rule.
\leaders⟨boxorrule⟩\hfill fill space with box or rule.

Useful environments

Name	Code	Example
cases	`f(n) = \begin{cases}` `n/2 & n \text{ is even} \\` `3n + 1 & n \text{ is odd}` `\end{cases}`	$f(n) = \begin{cases} n/2 & n \text{ is even} \\ 3n+1 & n \text{ is odd} \end{cases}$
split	`\begin{equation}` `\begin{split}` `e^{x} & = \sum^{\infty}_{n = 0}\frac{x^{n}}{n!} \\` `&= 1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + ...` `\end{split}` `\end{equation}`	$\begin{equation}\begin{split} e^{x} & = \sum^{\infty}_{n = 0} \frac{x^{n}}{n!} \\ &= 1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + ... \end{split}\end{equation}$
gather	`\begin{gather}` `a_1=b_1+c_1\\` `a_2=b_2+c_2-d_2+e_2` `\end{gather}`	$\begin{gather} a_1=b_1+c_1\\ a_2=b_2+c_2-d_2+e_2 \end{gather}$
align	`\begin{align}` `a_1& =b_1+c_1\\` `a_2& =b_2+c_2-d_2+e_2` `\end{align}`	$\begin{align} a_1& =b_1+c_1\\ a_2& =b_2+c_2-d_2+e_2 \end{align}$
matrix (parentheses)	`\begin{pmatrix}` `a_{1} & a_{2} \\` `a_{3} & a_{4}` `\end{pmatrix}`	$\begin{pmatrix} a_{1} & a_{2} \\ a_{3} & a_{4} \end{pmatrix}$
matrix (brackets)	`\begin{bmatrix}` `a_{1} & a_{2} \\` `a_{3} & a_{4}` `\end{bmatrix}`	$\begin{bmatrix} a_{1} & a_{2} \\ a_{3} & a_{4} \end{bmatrix}$
matrix (vertical line)	`\begin{vmatrix}` `a_{1} & a_{2} \\` `a_{3} & a_{4}` `\end{vmatrix}`	$\begin{vmatrix} a_{1} & a_{2} \\ a_{3} & a_{4} \end{vmatrix}$

Arrays can be used to create matrices, columns with several equations or calculate the least common multiple.

\left( \begin{array}{rrr|r} -1 & 2 & 3 & 3 \\ 4 & -5 & 6 & 2 \\ 7 & 8 & -9 & 1 \end{array} \right)

$\left( \begin{array}{rrr|r} -1 & 2 & 3 & 3 \\ 4 & -5 & 6 & 2 \\ 7 & 8 & -9 & 1 \end{array} \right)$

\left( \begin{array}{rclc} -1 & 2 & 3 & 3 \\ 4 & -5 & 6 & 2 \\ 7 & 8 & -9 & 1 \end{array} \right)

$\left( \begin{array}{rclc} -1 & 2 & 3 & 3 \\ 4 & -5 & 6 & 2 \\ 7 & 8 & -9 & 1 \end{array} \right)$

\left\lbrace \begin{array}{rr} -x+2y-3z & = 3 \\ 4x+5y+6z & = 2 \\ 7x+8y+9z & = 1 \end{array} \right.

$\left\lbrace \begin{array}{rr} -x+2y-3z & = 3 \\ 4x+5y+6z & = 2 \\ 7x+8y+9z & = 1 \end{array} \right.$

\begin{array}{rllr} 5x &=& 10 & 8y &=& 24 \\ x &=& 2 & y &=& 3 \end{array}

$\begin{array}{rllr} 5x &=& 10 & 8y &=& 24 \\ x &=& 2 & y &=& 3\end{array}$

\begin{array}{r|lr|l} 56 & 2 & 104 & 2 \\ 28 & 2 & 52 & 2 \\ 14 & 2 & 26 & 2 \\ 7 & 7 & 13 & 13 \\ 1 & & 1 \end{array}

$\begin{array}{r|lr|l} 56 & 2 & 104 & 2 \\ 28 & 2 & 52 & 2 \\ 14 & 2 & 26 & 2 \\ 7 & 7 & 13 & 13 \\ 1 & & 1 \end{array}$

\begin{array}{|r|r|} \hline 1 & 2 \\ \hline 3 & 4 \\ \hline \end{array}

$\begin{array}{|r|r|} \hline 1 & 2 \\ \hline 3 & 4 \\ \hline \end{array}$

Bibliography and citations

Citation types

BibTex entry types

Bibtex fields

Common BibTeX style files

BibTex example

When using $\mathrm{B\scriptstyle IB}\TeX{}$ , you need to run $\LaTeX{}$ , $\mathrm{B\scriptstyle IB}\TeX{}$ , and $\LaTeX{}$ twice more to resolve dependencies.

Citation Types

Entry	Description
`\cite{key}`	Full author list and year. (Watson and Crick 1953)
`\citeA{key}`	Full author list. (Watson and Crick)
`\citeN{key}`	Full author list and year. Watson and Crick (1953)
`\shortcite{key}`	Abbreviated author list and year.
`\shortciteA{key}`	Abbreviated author list.
`\shortciteN{key}`	Abbreviated author list and year.
`\citeyear{key}`	Cite year only. (1953)

All the above have an $\texttt{NP}$ variant without parentheses; Example: \citeNP.

Bibtex entry types

Entry	Description
`@article`	Journal or magazine article
`@book`	Book with publisher
`@booklet`	Book without publisher
`@conference`	Article in conference proceedings
`@inbook`	A part of a book and/or range of pages
`@incollection`	A part of book with its own title
`@manual`	Technical documentation
`@mastersthesis`	Master’s thesis
`@misc`	If nothing else fits
`@phdthesis`	PhD. thesis
`@proceedings`	Proceedings of a conference
`@techreport`	Tech report, usually numbered in series
`@unpublished`	Unpublished

Bibtex fields

Entry	Description
`address`	Address of publisher, not necessary for major publishers
`author`	Names of authors
`booktitle`	Title of book when part of it is cited
`chapter`	Chapter or section number
`edition`	Edition of a book
`editor`	Names of editors
`institution`	Sponsoring institution of tech report
`journal`	Journal name
`key`	Used for cross reference when no author
`month`	Month published. Use 3-letter abbreviation
`note`	Any additional information
`number`	Number of journal or magazine
`organization`	Organization that sponsors a conference
`pages`	Page range (2,6,9-12)
`publisher`	Publisher’s name
`school`	Name of school (for thesis)
`series`	Name of series of books
`title`	Title of work
`type`	Type of tech report, example: "Research Note"
`volume`	Volume of a journal or book
`year`	Year of publication

Not all fields need to be filled.

Common BibTeX style files

Entry	Description
`abbrv`	Standard
`alpha`	Standard
`plain`	Standard
`abstract`	$\texttt{alpha}$ with abstract
`apa`	APA
`unsrt`	Unsorted

The $\LaTeX{}$ document should have the following two lines just before \end{document}, where $\texttt{bibfile.bib}$ is the name of the $\mathrm{B\scriptstyle IB}\TeX{}$ file.

\bibliographystyle{plain}
\bibliography{bibfile}

BibTeX example

The $\mathrm{B\scriptstyle IB}\TeX{}$ database goes in a file called $\texttt{file.bib}$ , which is processed with $\texttt{bibtex file}$ .

@String{N = {Nature}}
@Article{WC:1953,
  author = {James Watson and Francis Crick},
  title = {A structure for Deoxyribose Nucleic Acid},
  journal = N,
  volume = {171},
  pages = {737},
  year = 1953
}

Inline math	Displayed math
`\(...\)`	`\[...\]`
$...$	`$$...$$`
	`\begin{equation}` `...` `\end{equation}`
	`\begin{equation}` `...` `\end{equation}`

Sections

Contents

LaTeX \LaTeX{} LATE​X Guide

Document classes

Common documentclass options

Packages

Title

Miscellaneous documents classes

Document Structure

Text environments

Lists

Examples for enumerate versions

References

Floating bodies

Text properties

Font face

Font size

Verbatim text

Justification

Miscellaneous text properties

Text color

Accessing additional named colours

Hyperlinks

Text-mode symbols

Symbols

Accents

Dashes

Line and page breaks

Spaces

Miscellaneous text-mode symbols

Tabular environments

Tabbing environment

Tabular environment

Tabular column specification

Tabular elements

Math mode

Mathematical font face

Sensible size examples

Letters

Greek alphabet

Archaic Greek

Hebrew letters

Other letters

Other symbols

Agrupations

Bars

Operations

Geometry

Logic

Relations

Proportion

Similarity or approximation

Comparison

Order

Sets

Arrows

Delimiters

Accents

Elementary Math Control Sequences

Non-Italic Function Names

Fills, Leaders and Ellipses

Useful environments

Bibliography and citations

Citation Types

Bibtex entry types

Bibtex fields

Common BibTeX style files

BibTeX example

$\LaTeX{}$ Guide