% Use this file as a template for your reports.
%

\documentclass{article}

% Load these packages to help with mathematics and graphics.
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{graphicx}
\usepackage{setspace}
\usepackage{url}
\usepackage[paperheight=11in,paperwidth=8.5in,margin=0.75in]{geometry}

\onehalfspacing    %Only if you want to double space.

\newtheorem{thm}{Theorem}
\newtheorem{cor}[thm]{Corollary}
\newtheorem{lem}[thm]{Lemma}
\newtheorem{prop}[thm]{Proposition}
\theoremstyle{definition}
\newtheorem{defn}[thm]{Definition}

\title{My First \LaTeX~Document}
\author{Ima R.E.U. Student}
\date{}

\begin{document}

\maketitle

\section{Introduction}

This is my first \LaTeX~document.  Perhaps I could use this section
to list some interesting things about myself.  For instance,

\begin{itemize}
\item I am seven feet tall.
\item I own a llama.
\item Bob Barker is my uncle.
\end{itemize}

\section{Pictures}

I like to include pictures in my documents.  Here is one that I
found in ``My Pictures'' subdirectory on my computer:

\begin{figure}[ht]      %h = here, t=top of page, b=bottom of page; not
                       %always reliable.
\begin{center}
\includegraphics[width= 4 in, height=2 in]{c:/images/Sunset}
\caption{Very  beautiful sunset at unknown location.}\label{fig:a}
\end{center}
\end{figure}

\section{Some mathematics}

I am very excited about my research this summer.  I'm sure that it
will involve lots of interesting mathematics.  I hope to discover a
short proof of the following theorem, which I conjectured last
summer:

\begin{thm}\label{thm:a} Let $n \geq 3$ be an integer.  Then there are no
nonzero integers $x$, $y$, and $z$ such that $x^n + y^n = z^n$.
\end{thm}

To prove Theorem \ref{thm:a}, I plan to use one of my favorite
formulas:

\begin{equation}
\frac{\pi^2}{6} = \sum_{k=1}^{\infty} \frac{1}{k^2}
\label{eq:favorite}
\end{equation}

When I type up my results in \LaTeX, I should probably use codes
like \verb!\label{...}! and \verb!\ref{...}! to refer to things like
Theorem \ref{thm:a} and Equation \ref{eq:favorite}.

\section{Conclusion}

Wow, I am so special now that I have made my first \LaTeX~document.
I think that I will go read my favorite book.  (See \cite{bib1}.)

\begin{thebibliography}{99}
\bibitem{bib1} Author, Ann.  \emph{Mathematics Research for Dummies}.  REU
Press, Allendale, 2007.
\end{thebibliography}

\end{document}
