Mathematical Expressions

Introduction

LaTeX's mathematical typesetting capabilities make it a compelling choice for writing technical documents. This article introduces the most basic commands to start writing mathematics with LaTeX.

For example, writing basic equations with LaTeX is simple:

home/new.tex
\documentclass{article}
\begin{document}

The well known Pythagorean theorem \(x^2 + y^2 = z^2\) was 
proved to be invalid for other exponents. 
Meaning the next equation has no integer solutions:

\[ x^n + y^n = z^n \]

\end{document}

As you can see, the way equations are displayed depends on the delimiters, in this case \[...\] and $...$.

Mathematical Modes

LaTeX allows two writing modes for mathematical expressions: inline math mode and display math mode.

Inline math mode is used to write formulas that belong within a paragraph.
Display math mode is used to write expressions that are not part of a paragraph and are therefore placed on separate lines.

Inline Math Mode

You can use any of these "delimiters" to typeset your mathematics in inline mode.

$...$
$...$
\begin{math}...\end{math}

They are all valid, and the choice is a matter of taste, so let's look at some examples:

home/new.tex
\documentclass{article}
\begin{document}

\noindent Standard \LaTeX{} practice is to write inline math by enclosing it between \verb|\(...\)|:

\begin{quote}
In physics, the mass-energy equivalence is stated 
by the equation \(E=mc^2\), discovered in 1905 by Albert Einstein.
\end{quote}

\noindent Instead if writing (enclosing) inline math between \verb|\(...\)| you can use \texttt{\$...\$} to achieve the same result:

\begin{quote}
In physics, the mass-energy equivalence is stated 
by the equation $E=mc^2$, discovered in 1905 by Albert Einstein.
\end{quote}

\noindent Or, you can use \verb|\begin{math}...\end{math}|:

\begin{quote}
In physics, the mass-energy equivalence is stated 
by the equation \begin{math}E=mc^2\end{math}, discovered in 1905 by Albert Einstein.
\end{quote}
\end{document}

Display Math Mode

Use one of these structures to typeset mathematics in display mode.

\[...\]
\begin{displaymath}...\end{displaymath}
\begin{equation}...\end{equation}

Display math mode has two versions that can produce numbered or unnumbered equations. Let's look at a basic example:

home/new.tex
\documentclass{article}
\begin{document}
The mass-energy equivalence is described by the famous equation

\[E=mc^2\]

discovered in 1905 by Albert Einstein. 
In natural units ($c$ = 1), the formula expresses the identity

\begin{equation}
E=m
\end{equation}
\end{document}

Another Example

The following example uses the equation* environment provided by the amsmath package—see the amsmath article for more information:

home/new.tex
\documentclass{article}
\usepackage{amsmath} % for the equation* environment
\begin{document}

This is a simple math expression \(\sqrt{x^2+1}\) inside text. 
And this is also the same: 
\begin{math}
\sqrt{x^2+1}
\end{math}
but by using another command.

This is a simple math expression without numbering
\[\sqrt{x^2+1}\] 
separated from text.

This is also the same:
\begin{displaymath}
\sqrt{x^2+1}
\end{displaymath}

\ldots and this:
\begin{equation*}
\sqrt{x^2+1}
\end{equation*}

\end{document}

Reference Guide

Below is a table containing some common mathematical symbols. For a more complete list, see the list of Greek letters and mathematical symbols.

Description	Code
Greek Letters	`\alpha` `\beta` `\gamma` `\rho` `\sigma` `\delta` `\epsilon`
Binary Operators	`\times` `\otimes` `\oplus` `\cup` `\cap`
Relation Operators	`<` `>` `\subset` `\supset` `\subseteq` `\supseteq`
Others	`\int` `\oint` `\sum` `\prod`

Different categories of mathematical symbols have different formatting characteristics (e.g., variables are italicized, but operators are not) and different spacing.

Introduction​

Mathematical Modes​

Inline Math Mode​

Display Math Mode​

Another Example​

Reference Guide​

Further Reading​