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

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What is LaTeX?

LaTeX is a programming language that can be used for writing documents. It is especially useful to write mathematical notations: equations, formulae, etc. LaTeX makes special symbols and equations look good! Note: you don’t have to learn LaTeX to use Authorea. You can write mathematics in Authorea using a visual equation editor. If you’re interested in using LaTeX, keep reading.

Writing mathematical notation in LaTeX

Authorea supports LaTeX, a powerful typesetting program that renders beautiful mathematics. In order to insert a LaTeX block in your document, select Insert from the editor toolbar, and select LaTeX. More instructions here. There are three ways to present a mathematical expression— inline (in the middle of a text line), as an equation, on a separate dedicated line, and as a full-sized inline expression (displaystyle).

Inline mathematical expressions

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 \(E=mc^2\).

Equations

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 \[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

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 \(\sum_{n=1}^{\infty}\frac{1}{n}.\)

Symbols (in math mode)

The basics

Math mode in LaTeX happens inside the dollar signs ($...$ ), inside the square brackets \[...\] and inside equation and displaystyle environments.

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 \(\approx\)

Functions

description command output
maps to \to \(\to\)
composition \circ \(\circ\)

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