Overview

$\LaTeX$, a powerful typesetting system, is widely used for creating professional documents with complex formatting, especially in academic domains. It empowers you to convey complex mathematical ideas with precision.

This cheat sheet serves as your guide to mastering the main $\LaTeX$ commands that allow you to render mathematical expressions in your documents.

We also provide a compiled PDF version of this cheat sheet. Print it out or save it on your computer ensuring that you have easy access whenever you require it!

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

{{% wide-table %}} | | | | | | |
|-------------|-------------|------------|------------|---------------|---------------| | $\alpha$ | \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 | {{% /wide-table %}}

Uppercase

{{% wide-table %}} | | | | | | | |-------------|-------------|------------|------------|---------------|---------------| | $\Gamma$ | \Gamma | $\Delta$ | \Delta | $\Theta$ | \Theta | | $\Lambda$ | \Lambda | $\Xi$ | \Xi | $\Pi$ | \Pi | | $\Sigma$ | \Sigma | $\Upsilon$ | \Upsilon | $\Phi$ | \Phi | | $\Psi$ | \Psi | $\Omega$ | \Omega | {{% /wide-table %}}

Tip

To ensure a consistent style throughout the document, use: latex \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

{{% wide-table %}} | $\LaTeX$ | Code | $\LaTeX$ | Code | |---------|-------|-----------|-------------| | $x^y$ | x^y | $x^{a+b}$ | x^{a+b} | | $x_y$ | x_y | $x_{a+b}$ | x_{a+b} | {{% /wide-table %}}

Root

{{% wide-table %}} | Type | $\LaTeX$ | Code | |-------------|-----------------|---------------| | Square root | $\sqrt{x}$ | \sqrt{x} | | N-th root | $\sqrt[N]{x}$ | \sqrt[N]{x} | {{% /wide-table %}}

Dots

{{% wide-table %}} | 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 | {{% /wide-table %}}

Spaces

{{% wide-table %}} | Type | Code | |----------------|----------| | Negative space | \! | | Thinnest space | \, | | Thin space | \: | | Medium space | \; | | 1em space | \quad | | 2em space | \qquad | {{% /wide-table %}}

Braces

{{% wide-table %}} | $\LaTeX$ | Code | |----------------|----------| | $\overbrace{ ... }^{ \text{text over brace} }$ | \overbrace{ ... }^{ \text{text over brace} } | | $\underbrace{ ... }_{ \text{text under brace} }$ | \underbrace{ ... }_{ \text{text under brace} } | {{% /wide-table %}}

Accents

{{% wide-table %}} | $\LaTeX$ | 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} | {{% /wide-table %}}

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

{{% wide-table %}} | $\LaTeX$ | Code | |-----------------------|-----------------------| | $a \bmod b$ | a \bmod b | | $a \equiv b \pmod{m}$ | a \equiv b \pmod{m} | {{% /wide-table %}}

Fractions

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

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

Symbol stacking

{{% wide-table %}} | $\LaTeX$ | Code | |-----------------------|-----------------------| | $\overset{ A }{ B }$ | \overset{ ... }{ ... } | | $\underset{ A }{ B }$ | \underset{ ... }{ ... } | {{% /wide-table %}}

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

Big operators

{{% wide-table %}} | $\LaTeX$ | 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} | {{% /wide-table %}}

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

{{% wide-table %}} | $\LaTeX$ | Code | |-------------------|-------------------| | $\lvert x \rvert$ | \lvert x \rvert | | $\lVert x \rVert$ | \lVert x \rVert | {{% /wide-table %}}

The same can be achieved by defining:

latex
\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

{{% wide-table %}} | $\LaTeX$ | 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 | {{% /wide-table %}}

Binary relations

{{% wide-table %}} | $\LaTeX$ | 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 | {{% /wide-table %}}

Tip

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

Binary operators

{{% wide-table %}} | $\LaTeX$ | 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 | {{% /wide-table %}}

Logic symbols

{{% wide-table %}} | $\LaTeX$ | Code | $\LaTeX$ | Code | $\LaTeX$ | Code | |-------------|-------------|-------------|-------------|-----------|-----------| | $\lor$ | \lor | $\land$ | \land | $\neg$ | \neg | | $\exists$ | \exists | $\nexists$ | \nexists | $\forall$ | \forall | | $\implies$ | \implies | $\iff$ | \iff | $\models$ | \models | {{% /wide-table %}}

Other symbols

{{% wide-table %}} | 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 | {{% /wide-table %}}

Multi line equation

Use the multline environment.

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

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

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

Vectors

{{% wide-table %}} | $\LaTeX$ | Code | |----------|------| | $\vec{x}$ | \vec{x} | | $\bm{x}$ | \bm{x} | {{% /wide-table %}}

Warning

The \bm command requires the bm package.

Tip

Best practice to easily switch between types: latex \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) $

latex
\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} $

latex
\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} $

latex
\begin{bmatrix}
      1 & 2 & 3 \\
      4 & 5 & 6 \\
\end{bmatrix}

Tip

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

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