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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
.
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 |
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
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} |
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 |
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} |
The \bm
command requires the bm
package.
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)
Each letter in the argument of the array represents a column.
l
: left aligned textc
: centered textr
: 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}
Matrices
Use one of the following environments.
matrix
: No delimiterpmatrix
: $($ delimiterbmatrix
: $[$ delimiterBmatrix
: $\{$ delimitervmatrix
: $\lvert$ delimiterVmatrix
: $\lVert$ delimiter
Use \\
to separate different rows, and &
to separate elements of each row.
\begin{bmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
\end{bmatrix}
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.