[ams, math, latex, tex, cheatsheet]


Overview

This is a quick overview of the main \(\LaTeX\) commands to render mathematical expressions.

We also provide a compiled PDF version of this cheatsheet.


Commands

Packages

The main package to load is amsmath. More symbols are included in amssymb.

Tip

You can load packages in the preamble: \usepackage{amsmath}

Typeset

  • For text style (inline) math, use: $...$. This is inline: $E=mc^2$
  • For display style math, which breaks the paragraph: \begin{equation} ... \end{equation} (numbered equation) or \[ ... \] (non-numbered). This is a display equation: $$E=mc^2$$

Greek letters

Lowercase

$\alpha$ \alpha $\beta$ \beta $\gamma$ \gamma
$\delta$ \delta $\epsilon$ \epsilon $\varepsilon$ \varepsilon
$\zeta$ \zeta $\eta$ \eta $\theta$ \theta
$\vartheta$ \vartheta $\iota$ \iota $\kappa$ \kappa
$\lambda$ \lambda $\mu$ \mu $\nu$ \nu
$\xi$ \xi $\pi$ \pi $\varpi$ \varpi
$\rho$ \rho $\varrho$ \varrho $\sigma$ \sigma
$\tau$ \tau $\upsilon$ \upsilon $\phi$ \phi
$\varphi$ \varphi $\chi$ \chi $\psi$ \psi
$\omega$ \omega

Uppercase

$\Gamma$ \Gamma $\Delta$ \Delta $\Theta$ \Theta
$\Lambda$ \Lambda $\Xi$ \Xi $\Pi$ \Pi
$\Sigma$ \Sigma $\Upsilon$ \Upsilon $\Phi$ \Phi
$\Psi$ \Psi $\Omega$ \Omega
Tip

To ensure a consistent style throughout the document, use:

\renewcommand{\epsilon}{\varepsilon}  
\renewcommand{\theta}{\vartheta}  
\renewcommand{\rho}{\varrho}  
\renewcommand{\phi}{\varphi}

Mathematical font

$$\mathcal{A} \, \mathcal{B} \, \mathcal{C} \, \mathcal{D} \, \mathcal{E} \, \mathcal{F} \, \mathcal{G} \, \mathcal{H} \, \mathcal{I} \, \mathcal{J} \, \mathcal{K} \, \mathcal{L} \, \mathcal{M} \, \mathcal{N} \, \mathcal{O} \, \mathcal{P} \, \mathcal{Q} \, \mathcal{R} \, \mathcal{S} \, \mathcal{T} \, \mathcal{U} \, \mathcal{V} \, \mathcal{W} \, \mathcal{X} \, \mathcal{Y} \, \mathcal{Z}$$

Use \mathcal{\text{letter}}.

Superscript and subscript

$\LaTeX$ Code $\LaTeX$ Code
$x^y$ x^y $x^{a+b}$ x^{a+b}
$x_y$ x_y $x_{a+b}$ x_{a+b}

Root

Type $\LaTeX$ Code
Square root $\sqrt{x}$ \sqrt{x}
N-th root $\sqrt[N]{x}$ \sqrt[N]{x}

Dots

Type $\LaTeX$ Code
Multiplication dot $\cdot$ \cdot
Three centered dots $\cdots$ \cdots
Three baseline dots $\ldots$ \ldots
Three diagonal dots $\ddots$ \ddots
Three vertical dots $\vdots$ \vdots

Spaces

Type Code
Negative space \!
Thinnest space \,
Thin space \:
Medium space \;
1em space \quad
2em space \qquad

Braces

$\LaTeX$ Code
$\overbrace{ … }^{ \text{text over brace} }$ \overbrace{ ... }^{ \text{text over brace} }
$\underbrace{ … }_{ \text{text under brace} }$ \underbrace{ ... }_{ \text{text under brace} }

Accents

$\LaTeX$ Code $\LaTeX$ Code $\LaTeX$ Code
$\hat{a}$ \hat{a} $\bar{a}$ \bar{a} $\mathring{a}$ \mathring{a}
$\check{a}$ \check{a} $\dot{a}$ \dot{a} $\vec{a}$ \vec{a}
$\tilde{a}$ \tilde{a} $\ddot{a}$ \ddot{a} $\widehat{AAA}$ \widehat{AAA}

Operators

\sin \cos \arcsin \arccos \sinh
\cosh \tan \arctan \log \ln
\max \min \sup \inf \tanh
\cot \sec \csc \det

Tip

To define a custom operator: \DeclareMathOperator{\argmax}{argmax}.

Modulo

$\LaTeX$ Code
$a \bmod b$ a \bmod b
$a \equiv b \pmod{m}$ a \equiv b \pmod{m}

Fractions

\frac{ ... }{ ... }

For instance, 3/4 can be displayed as $\frac{3}{4}$.

Symbol stacking

$\LaTeX$ Code
$\overset{ A }{ B }$ \overset{ ... }{ ... }
$\underset{ A }{ B }$ \underset{ ... }{ ... }

First argument is the main symbol, second argument is the symbol to put over or under the main symbol.

Big operators

$\LaTeX$ Code $\LaTeX$ Code
$\displaystyle \int_{a}^{b}$ \int_{a}^{b} $\displaystyle \sum_{k=0}^{n}$ \sum_{k=0}^{n}
$\displaystyle \prod_{k=0}^{n}$ \prod_{k=0}^{n} $\displaystyle \lim_{x \to 0}$ \lim_{x \to 0}
Tip

For multiple integrals, use: $\iint$ \iint $\,\, \iiint$ \iiint etc.

For a closed path integral, use: $\oint$ \oint

Delimiter size

Change the delimiter size by adding one of these modifiers immediately before the delimiter itself: \big \Big \bigg \Bigg.

Let $\LaTeX$ determine the correct size using \left and \right immediately before the opening and closing delimiters, respectively.

Absolute value and norm

$\LaTeX$ Code
$\lvert x \rvert$ \lvert x \rvert
$\lVert x \rVert$ \lVert x \rVert

The same can be achieved by defining:

\usepackage{mathtools}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}

Use starred variants \abs* and \norm* to produce the correct delimiter height for any kind of equation.

Arrows

$\LaTeX$ Code $\LaTeX$ Code $\LaTeX$ Code
$\uparrow$ \uparrow $\downarrow$ \downarrow $\updownarrow$ \updownarrow
$\Uparrow$ \Uparrow $\Downarrow$ \Downarrow $\Updownarrow$ \Updownarrow
$\leftarrow$ \leftarrow or \gets $\rightarrow$ \rightarrow or \to $\leftrightarrow$ \leftrightarrow
$\Leftarrow$ \Leftarrow $\Rightarrow$ \Rightarrow $\Leftrightarrow$ \Leftrightarrow
$\mapsto$ \mapsto $\longleftarrow$ \longleftarrow $\longrightarrow$ \longrightarrow
$\longleftrightarrow$ \longleftrightarrow $\Longleftarrow$ \Longleftarrow $\Longrightarrow$ \Longrightarrow
$\Longleftrightarrow$ \Longleftrightarrow $\longmapsto$ \longmapsto

Binary relations

$\LaTeX$ Code $\LaTeX$ Code $\LaTeX$ Code
$\ne$ \ne $\le$ \le $\ge$ \ge
$\equiv$ \equiv $\ll$ \ll $\gg$ \gg
$\doteq$ \doteq $\sim$ \sim $\simeq$ \simeq
$\subset$ \subset $\supset$ \supset $\approx$ \approx
$\subseteq$ \subseteq $\supseteq$ \supseteq $\cong$ \cong
$\in$ \in $\ni$ \ni $\propto$ \propto
$\mid$ \mid $\parallel$ \parallel $\perp$ \perp
Tip

It’s possible to negate these symbols by prefixing them with \not (for example: $\not\equiv$ with \not\equiv).

Binary operators

$\LaTeX$ Code $\LaTeX$ Code $\LaTeX$ Code
$\pm$ \pm $\mp$ \mp $\cdot$ \cdot
$\div$ \div $\times$ \times $\setminus$ \setminus
$\star$ \star $\cup$ \cup $\cap$ \cap
$\ast$ \ast $\circ$ \circ $\bullet$ \bullet
$\oplus$ \oplus $\ominus$ \ominus $\odot$ \odot
$\oslash$ \oslash $\otimes$ \otimes $\smallsetminus$ \smallsetminus

Logic symbols

$\LaTeX$ Code $\LaTeX$ Code $\LaTeX$ Code
$\lor$ \lor $\land$ \land $\neg$ \neg
$\exists$ \exists $\nexists$ \nexists $\forall$ \forall
$\implies$ \implies $\iff$ \iff $\models$ \models

Other symbols

Symbol $\LaTeX$ Code
Infinity $\infty$ \infty
Partial derivative $\partial$ \partial
Empty set $\emptyset$ \emptyset
Nabla $\nabla$ \nabla
Angle brackets $\langle x \rangle$ \langle x \rangle

Multi line equation

Use the multline environment.

\begin{multline}
    ...
\end{multline}

To align equations, use the align environment. Specify the alignment position with & and separate equations with \\.

\begin{align}
    ... &= ...\\
    ... &= ...
\end{align}

Vectors

$\LaTeX$ Code
$\vec{x}$ \vec{x}
$\bm{x}$ \bm{x}
Warning

The \bm command requires the bm package.

Tip

Best practice to easily switch between types:

\usepackage{bm}
\renewcommand{\vec}{\bm}

Arrays

Use the array environment. Use \\ to separate rows, and & to separate elements of each row. To produce large delimiters around the array, use \left and \right followed by the desired delimiter.

\[\left( \begin{array}{lcr} a & b & c \\ d & e & f \\ g & h & i \end{array} \right)\]
\left(
\begin{array}{lcr}
      a & b & c \\
      d & e & f \\
      g & h & i
\end{array}
\right)

Each letter in the argument of the array represents a column.

  • l: left aligned text
  • c: centered text
  • r: right aligned text

Cases

Use the cases environment. Use \\ to separate different cases, and & for correct alignment.

\[\begin{cases} x & \text{if } x > 0 \\ 0 & \text{if } x \le 0 \end{cases}\]
\begin{cases}
  x & \text{if } x > 0 \\
  0 & \text{if } x \le 0
\end{cases}

Matrices

Use one of the following environments.

  • matrix: No delimiter
  • pmatrix: $($ delimiter
  • bmatrix: $[$ delimiter
  • Bmatrix: $\{$ delimiter
  • vmatrix: $\lvert$ delimiter
  • Vmatrix: $\lVert$ delimiter

Use \\ to separate different rows, and & to separate elements of each row.

\[\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ \end{bmatrix}\]
\begin{bmatrix}
      1 & 2 & 3 \\
      4 & 5 & 6 \\
\end{bmatrix}
Tip

To produce a small matrix, useful for inline math, use the smallmatrix environment: $\left[\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}\right]$.

\left[\begin{smallmatrix}
a & b \\\\ c & d
\end{smallmatrix}\right]

Blackboard bold

$\mathbb{A}$ \mathbb{A} … $\mathbb{R}$ \mathbb{R}

Include the package bbm for these symbols. All letters are supported.


Contributed by Manuele Macchia