\documentclass[12pt,letterpaper]{amsart}
\setlength{\oddsidemargin}{.0in}
\setlength{\evensidemargin}{.0in}
\setlength{\textwidth}{6.5in}
\setlength{\topmargin}{-.3in}
\setlength{\headsep}{.20in}
\setlength{\textheight}{9.in}
\usepackage[leqno]{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage[all]{xy}
\usepackage{graphicx}


%Here are some user-defined notations
\newcommand{\RR}{\mathbf R}
\newcommand{\CC}{\mathbf C}
\newcommand{\ZZ}{\mathbf Z}
\newcommand{\ZZn}[1]{\ZZ/{#1}\ZZ}
\newcommand{\QQ}{\mathbf Q}
\newcommand{\rr}{\mathbb R}
\newcommand{\cc}{\mathbb C}
\newcommand{\zz}{\mathbb Z}
\newcommand{\zzn}[1]{\zz/{#1}\zz}
\newcommand{\qq}{\mathbb Q}
\newcommand{\calM}{\mathcal M}
\newcommand{\latex}{\LaTeX}
\newcommand{\tex}{\TeX}
\newcommand{\sm}{\setminus} 


%improving spacing in tables (space above and below characters in a row)
\newcommand{\tfix}{\rule{0pt}{2.6ex}}
\newcommand{\bfix}{\rule[-1.2ex]{0pt}{0pt}}



%Here are commands with variable inputs 
\newcommand{\intf}[1]{\int_a^b{#1}\,dx}
\newcommand{\intfb}[3]{\int_{#1}^{#2}{#3}\,dx}
\newcommand{\marginalfootnote}[1]{%
        \footnote{#1}
        \marginpar[\hfill{\sf\thefootnote}]{{\sf\thefootnote}}}
\newcommand{\edit}[1]{\marginalfootnote{#1}}


%Here are some user-defined operators
\newcommand{\Tr}{\operatorname {Tr}}
\newcommand{\GL}{\operatorname {GL}}
\newcommand{\SL}{\operatorname {SL}}
\newcommand{\Prob}{\operatorname {Prob}}
\newcommand{\re}{\operatorname {Re}}
\newcommand{\im}{\operatorname {Im}}


%These commands deal with theorem-like environments (i.e., italic)
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{conjecture}[theorem]{Conjecture}

%These deal with definition-like environments (i.e., non-italic)
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{remark}[theorem]{Remark}

%This numbers equations by section
\numberwithin{equation}{section}


\begin{document}


\begin{titlepage}
\title{Title Here}
\author{Your Name}
\date{Date Here}
\maketitle

\centerline{\Large Math 2784 (or 2794W)}


\thispagestyle{empty}
\end{titlepage}


\pagebreak



%%%Start your work here. 

\section{Introduction}\label{intro}


In this file, edit the information between  
\verb1\begin{titlepage}1 and \verb1\end{titlepage}1.
Do {\it not} change the typesetting commands such as 
\verb1\setlength1 at the top of the file, which 
affect the size of the output.

Write your paper between  
\verb1\section{Introduction}\label{intro}1 and \verb1\end{document}1.
In this section you should put an introduction.  
Tell us what your topic is about, roughly, 
and what you are going to do with it. 



If you need any \latex{} command, see if you can find a similar one in one of the \latex{} files you have and then 
copy, paste and edit.  Or ask a math professor (most know \latex).


\section{The Next Section}\label{sec1}





The function $\sin x$ can be defined as an infinite series
\begin{equation}\label{sineseries}
\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots = \sum_{k \geq 0} \frac{x^{2k+1}}{(2k+1)!}.
\end{equation}
Here is another way to characterize it, using differential equations and initial conditions.

\begin{theorem}\label{diffthm}
The function $\sin x$ is the unique solution of the differential equation
\begin{equation}\label{sine-eqn}
\frac{d^2y}{dx^2} + y = 0
\end{equation}
satisfying the initial conditions $y(0) = 0$ and $y'(0) = 1$.
\end{theorem}

Notice in the code for this file that the number for the theorem, \ref{diffthm}, is {\it not} hard-coded, and that 
if you need to manually enter parentheses if you want the equation number to appear in text as (\ref{sine-eqn}).


\section{The Section After That}\label{sec2}

There is nothing here.

\appendix

\section{Some More Stuff}


There are four references below: \cite{irros}, \cite{unabomber}, \cite{roquette}, and \cite{sloane}. 



\begin{thebibliography}{4}


\bibitem{irros}
K. Ireland and M. Rosen, ``A Classical Introduction to Modern 
Number Theory,'' 2nd ed., Springer-Verlag, New York, 1990.

\bibitem{unabomber}
T. J. Kaczynski, Another proof of Wedderburn's theorem, 
{\it Amer. Math. Monthly} {\bf 71} (1964), 652--653.


\bibitem{roquette}
P. Roquette, Class field theory in characteristic $p$, its origin 
and development, pp.~549--631 in: ``Class field theory -- its centenary 
and prospect,'' Math. Soc. Japan, Tokyo, 2001.

\bibitem{sloane}
N. J. A. Sloane, On-line Encyclopedia of Integer Sequences, 
{\tt http://www.research.att.com/$\sim$njas/ sequence\underline{ }page/}.

\end{thebibliography}

\end{document}