\documentclass[12pt]{article}
\newcommand{\real}{\mbox{${\mathbb R}$}}
\usepackage{amssymb}

\begin{document}

\begin{center}
{\bf \large LaTeX Demonstration Document}\\
\end{center}

This document shows you some of the more commonly used sorts of
things that LaTeX can do.  First of all, it is sometimes
convenient to include a bit of mathematics in the narrative.  For
instance, if we want to tell our reader that $f: \real \rightarrow
\real$ is a function and is given by $f(x) = x^{3y}$, we can do
that by moving in and out of {\em in-line} math mode. I only
recommend in-line math mode for smaller things.  As you can see,
if we ask LaTeX  to typeset $f(x) = \frac{\sin(x)}{1+x^{2}}$, it
will, but it will be hard to read. If we want to force LaTeX to
give this expression enough room by spreading the lines apart, we
can do it by using the ``displaystyle'' command, $\displaystyle
f(x) = \frac{\sin(x)}{1+x^{2}}$; it will look pretty weird,
though.  In general, if you need to include mathematics that takes
up more room than an ordinary line will accommodate, you should
use displayed mathematics.

With this in mind, also notice how to write set notation.
\begin{displaymath}
A = \{ (x,y) \in \real^{2} : x^2 + y^2 = 16 \}.
\end{displaymath}
Since LaTeX  uses the curly brace as a special symbol, in order to
get the special symbol, you have to put a $\backslash$ in front of
it to cue LaTeX. (Otherwise, it will ignore the curly brace.) The
same thing goes for other special symbols, like \$.

\bigskip

 \noindent {\bf Left and Right Delimiters:}

If you need ``larger than usual'' left or right parentheses (or
other things like braces or brackets) you have to let LaTeX know.
For instance, this looks weird:
\begin{displaymath}
f(x) = ( \frac{x}{1+\exp(x)} )^{2x}.
\end{displaymath}
But this is much better!
\begin{displaymath}
f(x) = \left ( \frac{x}{1+\exp(x)} \right )^{2x}.
\end{displaymath}
With the \begin{verbatim} \left and \right \end{verbatim}
commands, LaTeX   senses how large the delimiters should be and
makes the whole thing look good. If you only need one delimiter
instead of a pair, you can make LaTeX  do it.  Look it up or ask
Carol.

\bigskip

 \noindent{\bf Final Comments:}
\begin{itemize}

\item A single carriage return is treated exactly like a space by
LaTeX.  A double carriage return is a paragraph break.  If you
really {\em must} force a carriage return otherwise, you can use a
double backslash, but ordinarily, just give LaTeX the logic of
your choice and it will typeset it correctly.

\item  If you want to learn how to include graphics in your
document, wait until there is something specific you want to do
and then come see me.
\end{itemize}

\begin{center}
{\bf \huge Enough for Now!}
\end{center}



\end{document}
