### Mathematics Mode

In order to obtain a mathematical formula using LaTeX, one must
enter *mathematics mode* before the formula and leave it
afterwards. Mathematical formulae can occur either embedded in text
or else displayed between lines of text. When a formula occurs within
the text of a paragraph one should place a `$`

sign before and
after the formula, in order to enter and leave mathematics mode.
Thus to obtain a sentence like

one should type
Let $f$ be the function defined by $f(x) = 3x + 7$, and
let $a$ be a positive real number.

In particular, note that even mathematical expressions consisting
of a single character, like *f* and *a* in the example above,
are placed within `$`

signs. This is to ensure that they are set
in italic type, as is customary in mathematical typesetting.
LaTeX also allows you to use `\(`

and `\)`

to mark
the beginning and the end respectively of a mathematical formula
embedded in text. Thus

may be produced by typing
Let \( f \) be the function defined by \( f(x) = 3x + 7 \).

However this use of `\(`

... `\)`

is only
permitted in LaTeX: other dialects of TeX such as
Plain TeX and AmSTeX use `$`

... `$`

.
In order to obtain an mathematical formula or equation which
is displayed on a line by itself, one places `\[`

before and
`\]`

after the formula. Thus to obtain

one would type
If $f(x) = 3x + 7$ and $g(x) = x + 4$ then
\[ f(x) + g(x) = 4x + 11 \]
and
\[ f(x)g(x) = 3x^2 + 19x +28. \]

(Here the character `^`

is used to obtain a superscript.)
LaTeX provides facilities for the automatic numbering of
displayed equations. If you want an numbered equation then you
use `\begin{equation}`

and `\end{equation}`

instead
of using `\[`

and `\]`

. Thus

If $f(x) = 3x + 7$ and $g(x) = x + 4$ then
\begin{equation}
f(x) + g(x) = 4x + 11
\end{equation}
and
\begin{equation}
f(x)g(x) = 3x^2 + 19x +28.
\end{equation}

produces