% Open this file in any TeX software and process it twice.
% Then look carefully at the typeset document along with the
% TeX code in this file.  That should get you started with TeX
% fairly quickly.

\documentclass[11pt]{article}

\usepackage{amsmath,amsfonts,amssymb,amsthm,amsrefs}
\usepackage{graphicx, float}
\textwidth=6.5in
\textheight=9in
\topmargin=0in
\headheight=0in
\headsep=0in
\oddsidemargin=0in
\evensidemargin=0in
\parskip = 0.2in
\parindent = 0.0in

\title{{\bf PROJECT TITLE}}  %PUT YOUR TITLE IN THESE BRACES
\author{
Directed Research in Mathematics\\
submitted in partial fulfillment \\
of the requirements for \\
the Master of Arts in Mathematics\\
by\\ \\
{\bf Student Name}\\ \\  % PUT YOUR NAME HERE
Mentor: Name
}


\begin{document}

\maketitle

\subsection*{Abstract}
This paragraph contains redundant sentences.
This paragraph contains redundant sentences.
This paragraph contains redundant sentences.

\subsection*{Introduction}  % section title the star suppresses numbering.
This paragraph contains redundant sentences.
This paragraph contains redundant sentences.
This paragraph contains redundant sentences.

This (new) paragraph contains redundant sentences. We created a new
paragraph by skipping a line in the TeX code.
This paragraph contains redundant sentences.
This paragraph contains redundant sentences.

Here is a centered equation with an equation number:
\begin{equation}
\int_0^1 x^2 ~dx = \frac{1}{3}
\label{eqn-int}
\end{equation}

If you don't want numbered equations, you can just use double dollar signs. Then you 
will see just the centered equation with no numbering, such as this matrix equation:
$$\det \begin{bmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8  & 9 \end{bmatrix} = 0$$

The advantage to numbering is that you can reference the equation later by number,
like referring back to ``Equation \ref{eqn-int}.'' That is what the label command in the
equation environment in TeX allows. 
A style tip: Only number crucial equations you need
to refer to again later in your document.

Also notice that there are double quotes around the expression; to get nice double quotes 
use two back ticks (upper left of your keyboard) to open and two apostrophes to close.
Here are some more redundant sentences.
This redundant sentence includes an in-line equation: 
$\sin(3 \theta) - 1 = 10$.

\subsection*{Background Section}

Here are some more redundant sentences.
This paragraph contains redundant sentences.
This paragraph contains redundant sentences. Here is some code:

\begin{verbatim} 
for i from 1 by 1 to 10 do 
     print(evalf(sin(i)^2-1)) 
end do
\end{verbatim}

\subsection*{Another Section}

Here are some more redundant sentences.
This paragraph contains redundant sentences and citations for two references \cite{mathy, web1}.
This paragraph contains redundant sentences.  
We end with a nice figure that includes a caption and a label, which can be referenced in a way similar to the numbered
equation: Figure \ref{img-quad}.

\begin{figure}[H]  % The H specifier indicates to put the figure precisely at this point in the doc.
\caption{Quadratics}
\centering 
%\includegraphics[width=3in]{put the file name for the image here}
\label{img-quad}
\end{figure}

The figure is placed exactly at the point in the document where you type the figure environment when using the [H] position specifier; however, as long as you number and caption figures, you can let them float to a spot so that you can eliminate excess white space in your document. Just use [h] instead to have this placement occur.

\begin{bibsection}[Bibliography] % These will be numbered in the order cited in the text.
\begin{biblist}

\bib{Church}{book}{  % Use this for books
    author={Church, Alonzo},
     title={Introduction to mathematical logic},
 publisher={Princeton University Press},
     place={Princeton, NJ},
      year={1996},
}

\bib{mathy}{article}{  % Use this for articles
author = {Mathy, Clever},
author = {Adams, John},
author = {Gump, Forrest}
title = {An amazing paper in a journal},
journal = {Journal Name},
year = {2013},
volume = {1},
pages = {5-6},
}

\bib{web1}{article}{  % Use this for websites
   author={Websites R Us Inc.},
   title={My website as I like it},
   year={2010},
   eprint={http://www.some.site.com/},

 }

\end{biblist}
\end{bibsection}


\end{document}               % End of document.