# Mathematics in LaTeX¶

LaTeX has a math mode designed to format mathematics. It can be invoked on the
same line as text by enclosing the mathematics in dollar signs: `$your
math here$`. This is called “inline” math.

`The positive real root of $x^4-16=0$ is $x=2$.`

The positive real root of \(x^4-16=0\) is \(x=2\).

## Basic Typesetting¶

The most common typesetting needs in mathematics is the superscript and the
subscript. These can be accessed using the caret `^` and the underscore
`_`.

`Consider the sequence $(x_i)$ where $x_i = 2^x$.`

Consider the sequence \((x_i)\) where \(x_i = 2^x\).

These only work for a single character, so

`A gigabyte contains $2^30$ bytes. Let $x_ij=x_ji$.`

actually returns: A gigabyte contains \(2^30\) bytes. Let \(x_ij=x_ji\)

To tell LaTeX that more than one character should be typeset as a superscript or subscript, enclose the desired text in braces.

```
A gigabyte contains $2^{30}$ bytes. Consider a matrix $A$ where
$a_{ij}=a_{ji}$.
```

This gives the desired result: A gigabyte contains \(2^{30}\) bytes. Let \(a_{ij}=a_{ji}\).

There is a native equation environment, displaymath, which can be invoked by
encasing math inside double dollar signs or `\[`, and `\]`. It can
typeset up to one line of math at a time.

```
\begin{document}
$$e=\sum_{i=0}^\infty \frac{1}{i!}$$
\[
\sum_{i=0}^\infty x^i = \frac{1}{1-x}
\]
```

Both invoke the displaymath environment, and so are nearly identical. The only
difference is that `$$` math `$$` makes a call to TeX and
`\[` stuff `\]` makes a call to LaTeX. It is not recommended to use
these environments except when minimal control is needed. The environments
provided by the `amsmath` package are much more robust and flexible. The
most common replacement environment from `amsmath` is `align`, or
`align*` if you do not want individual lines to be numbered. As with all
environments, these are opened and closed with `\begin{}` and
`\end{}`. Just place the desired environment name between the braces. For
example:

```
\begin{align*}
e&=\sum_{i=0}^\infty \frac{1}{i!}\\
&=\lim_{n\rightarrow\infty}\left(1+\frac{1}{n}\right)^n
\end{align*}
```

produces:

Everything that works in `displaymath` works in `align`. The main
advantage of `align` is that it can display many lines of mathematics at
once, aligning them based on the location of the `&` in each line.

## Advanced Mathematics¶

The `amsmath` package is essential whenever more than just the
basics are required. As mentioned above, most people use `amsmath` for
the `align*` environment. Since `amsmath` is not natively included
in LaTeX, you must include the line `\usepackage{amsmath}` in the
preamble in order to use any of its functionality.

### Equation Line Numbering¶

The `align` environment allows