\documentclass[12pt]{report} % sometimes it's necessary to use [psamsfonts]
%\documentclass[psamsfonts]{amsart}

\usepackage{amsmath} % already loaded, but doesn't hurt
\usepackage{amsthm} % already loaded, but doesn't hurt
\usepackage{amsfonts} % already loaded, but doesn't hurt
\usepackage{amssymb} % extra symbols not included in amsfonts
\usepackage{bbold} % good for those double-struck NUMBERS using \mathbb{}
%\usepackage{mathbbol} % alternative to bbold package... slightly better?
\usepackage{mathrsfs} % provides better \mathscr{} font than standard
\usepackage{setspace} % allows you to set 1.5x spacing, 2x spacing, etc
\usepackage{natbib} % expands bibliography citation considerably
\usepackage{hyperref} % references get hyperlinks in PDF file
\hypersetup{colorlinks,bookmarksopen,bookmarksnumbered,citecolor=blue,
        pdfstartview=FitH}
\usepackage{tocbibind} % expanded table of contents
\usepackage[usenames,dvipsnames]{color} % color text
\usepackage{graphicx} % obvious
\usepackage{verbatim} % gives \begin{verbatim} environment
\usepackage[all]{xy} % commutative diagrams
\usepackage{tabularx} % for better tables
%\usepackage{fullpage} % much smaller margins

\date{November 15, 2006}
\title{A Brief Guide to Ordinary K-Theory}
\author{Spencer Stirling}
\email{}
\address{Department of Mathematics, University of Texas at Austin}

\begin{document}

%\doublespacing
%\onehalfspacing

% set up a new command macro
\newcommand{\id}{\text{id}}

% this controls equation numbering within sections - CUSTOMIZE ME
\setcounter{secnumdepth}{2}
\numberwithin{equation}{section}

% set up some amsthm theorem environments
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}
\newtheorem{proposition}{Proposition}
\newtheorem{lemma}{Lemma}
\newtheorem{fact}{Fact}
\theoremstyle{definition}
\newtheorem{definition}{Definition}
\theoremstyle{remark}
\newtheorem{remark}{Remark}

\maketitle
\pagenumbering{roman}
\tableofcontents
%\listoffigures
%\listoftables


\chapter*{Acknowledgements}

\begin{abstract}
In this paper we describe some basic notions behind ordinary K-theory.
\end{abstract}

\pagenumbering{arabic}



\chapter{Vector Bundles}

\section{Introduction}
Here is my introduction \cite{bakalov_kirillov:book}
\begin{equation*}
\xymatrix{ % sample XY-Pic command
  f:\mathbb{1}\ar[r]^-{A}_-{B} & H \\
}
\end{equation*}
That was a very simple commutative diagram, huh?  Notice that I used
the special "double-struck 1" in the above commutative diagram... THIS
REQUIRED THE "bbold" package.

Here are more examples (except I don't think that you need bbold for these)
$\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$, $\mathbb{RP}^2$. 

Now I'll include a random figure.  See figure \ref{pairofpants}.  Note
that I used the MetaPost "mps" format.  This should work in both
PDFLaTex and plain LaTex.
\begin{figure}[ht]
	\centering
	\includegraphics{pairofpants.mps}
	\caption{A manifold with some primitive notion of causality}
        \label{pairofpants}
\end{figure}


Now I think that I'll put a random empty axis in... this is how some
simple pictures can be drawn using native LaTex commands
\setlength{\unitlength}{1mm}
\begin{picture}(60,60)
  % The horizontal axis
  \put(0,30){\line(1,0){60}}
  % On the horizontal axis, a tick mark every 10 milimeters
  \multiput(0,30)(5,0){13}{\line(0,-1){1}}
  % The vertical axis
  \put(30,0){\line(0,1){60}}
  % On the vertical axis, a tick mark every 10 milimeters
  \multiput(30,0)(0,5){13}{\line(-1,0){1}}
\end{picture}

\section{Conclusion}
In conclusion, this paper sucks.


\appendix

\chapter{Appendix A}


\bibliographystyle{amsalpha}
\bibliography{mybib,yourbib}

\end{document}