\documentclass[12pt,letterpaper,oneside]{article}
\usepackage[margin=1.25in]{geometry} %easy way to set the page dimensions
\usepackage{amssymb, enumerate, amsthm, amsmath, graphicx} %symbols, graphics, and a better enumerate environment
\usepackage{hyperref} %this will cause links to be clickable in some PDF viewers
\usepackage[alphabetic]{amsrefs} %package for the bibliography
%% some handy shortcuts
%% you can make your own, but this can get out of control if you do to many
%% and too many can make your code very very hard to read!
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Q}{\mathbb{Q}}
%% determines the numbering behavior of theorems, etc.
\numberwithin{equation}{section}
\numberwithin{figure}{section}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{question}[theorem]{Question}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{example}[theorem]{Example}
\newtheorem{goal}[theorem]{Goal}
\numberwithin{theorem}{section}
\newcommand{\define}[1]{\emph{#1}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% your document begins here
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%% paper details
\begin{document}
\title{A, perhaps very long, title, which accurately describes your project; you may use mathematical symbols such as $\R$ here if you must}
\author{{\small senior project of}\\
Adam G. Weyhaupt\\
Advisor: Dr.\ Karl Gauss\\
Southern Illinois University Edwardsville}
%\contrib[Advisor]{blah}
\date{\today}
\maketitle %causes the title to be generated
\section{Introduction}
An introduction should introduce your topic. In particular, you should give a brief review of the literature. This ensures that the reader is aware of the context of your problem \cite{saari}. Throughout your project you will need to type mathematics. Mathematics that runs with the text can be written like $f(x) = \sin(x^2)$. You should only number your equations
\begin{equation}\label{eqn:stokes}
\int_\Omega d\omega = \int_{\partial\Omega} \omega
\end{equation}
if you are going to refer to them, as in Equation \ref{eqn:stokes}, but never number them otherwise. To typeset an unnumbered equation, try \[\sup \left\{\frac{1}{n} ~|~ n \in \N\right\} =1.\]
\section{Other sections}
The other sections of your paper will vary depending on your project. I'm going to use this section to give you some examples of typesetting some mathematics that you might use.
\subsection{Roses are red}
It is possible to make subsections. It is possible to include graphics in your paper by doing the following
\begin{figure}[h!] %h! means "put it here -- and I mean it!"
\begin{center}
\includegraphics[width=4in]{graphic1.png}
\end{center}
\caption{Wow, look at those Riemann sums}
\end{figure}
\begin{theorem}[\cite{taylor}] If a social choice procedure for 3 or more alternatives satisfies Pareto, IIA, and montonicity, then it is a dictatorship.
\end{theorem}
\begin{proof}
We leave the proof to the reader.
\end{proof}
\begin{definition}Let $A, B \subseteq \R$. $A$ is called \emph{dense in $B$} if for every $\epsilon > 0$ and for every $x \in B$, there is some $y \in A$ so that $|x-y| < \epsilon$.
\end{definition}
\begin{lemma}The set $\Q$ is dense in $\R$.
\end{lemma}
\begin{proposition}
You can write propositions in a similar way. There are more of these types of things; have a look at the preamble. You can also make your own!
\end{proposition}
\[\left(\begin{array}{ccc}1 & 2 & 3 \\4 & 5 & 6 \\7 & 8 & \pi\end{array}\right)\]
When you type a complicated expression, you'll want to make sure that the parentheses ``self-size'' themselves. Compare
\[ (\frac12 \cdot \int_0^1 f(x) dx)\] to \[ \left(\frac12 \cdot \int_0^1 f(x) dx\right).\]
Note that the period above is placed in the displayed equation, and not orphaned on the next line.
Lots of different types of math characters are possible:
\[ \mathbf{R}, \mathbb{R}, \mathcal{R}.\]
You can decorate above and below expressions, like \[ \underbrace{n \cdot n \dots n}_{k\text{ times}}\]
\subsubsection{Violets are blue}
And even sub-subsections.
\subsection{Sugar is sweet}
You can use these to identify natural divisions in your paper.
\subsection{And \LaTeX\ is too}
By using sections, subsections, and theorems/definitions, you can clearly illustrate the organization of your paper. This makes a poorly organized paper really stand out, so \emph{think} about your organization.
You can use lists as well, by doing:
\begin{enumerate}[i) ]
\item Hello
\item World!
\end{enumerate}
but these are rarely used in a senior project.
\section{Conclusion}
Your brief conclusion should summarize your results and indicate if they have any applicability to applications or to other areas of mathematics. If there are natural further directions for (you or someone else) to investigate, this would be a good place to mention them.
I'm probably missing some important information in here, so it would help alot if you could tell me what I should include!
To conclude, I want to say a few words about references. Using MathSciNet, you can find your article. Then, in the drop down box at the top, choose ``AMSRefs'', and then copy and paste the result you get into the file below. Voil\`a, you have references!
\begin{bibdiv}
\begin{biblist}
\bib{saari}{book}{
author={Saari, Donald G.},
title={Chaotic elections!},
subtitle={A mathematician looks at voting},
publisher={American Mathematical Society},
place={Providence, RI},
date={2001},
pages={xiv+159},
isbn={0-8218-2847-9},
review={\MR{1822218 (2002g:91001)}},
}
\bib{taylor}{book}{
author={Taylor, Alan D.},
title={Mathematics and politics},
series={Textbooks in Mathematical Sciences},
subtitle={Strategy, voting, power and proof},
publisher={Springer-Verlag},
place={New York},
date={1995},
pages={xiv+284},
isbn={0-387-94500-8},
review={\MR{1344686 (96j:90013)}},
}
\end{biblist}
\end{bibdiv}
%\closegraphsfile
\end{document}