\documentclass{article}
\usepackage{2130,amsmath,amssymb,graphicx}

\begin{document}

\section{My first \LaTeX\ experience}

This is my {\it first} document.

This is the second paragraph.

My grocery list includes:
\begin{enumerate}
\item milk

\item liquor

\item potato chips

\begin{itemize}

\item ketchup

\item salt and vinegar

\end{itemize}

\item vegetables

\end{enumerate}

My hockey pool can be found in Table \ref{Hockey}.

\begin{table}[htbp]
\begin{center}
\begin{tabular}{|l|c|c|}
\hline
Participant's Name & Winner & Loser\\
\hline
Nicole & Toronto & Montreal\\
Jennifer & Tampa Bay & Edmonton\\
Amanda & Calgary & Boston\\
\hline
\end{tabular}
\end{center}
\caption{Participants in my hockey pool}\label{Hockey}
\end{table}

\section{Mathematics}

Let's consider the function $\displaystyle f_{\alpha}(x) = 
\sin\left(\frac{x^{20}}{2x + 1}\right)$ and the function $$f_{\beta}(x) 
= x^4 - 9x^3 + 5x^2 + 7x - 2,$$ which we will investigate further. Most 
important is the product
\begin{equation}
P(x) = f_{\alpha}(x)\cdot f_{\beta}(x). \label{ProdFunc}
\end{equation}
We will refer frequently to Equation~\eqref{ProdFunc}.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=2in]{tardis}
\end{center}
\caption{The TARDIS from {\it Doctor Who}.}
\end{figure}

Now we need the derivative of $f_{\beta}(x)$:
\begin{align}
\nonumber \frac{d}{dx}[f_{\beta}(x)] & = \frac{d}{dx}[x^4] - 
\frac{d}{dx}[9x^3] + \frac{d}{dx}[5x^2] + \frac{d}{dx}[7x] - 
\frac{d}{dx}[2]\\
\nonumber & = \frac{d}{dx}[x^4] - 9\frac{d}{dx}[x^3] + 
5\frac{d}{dx}[x^2] + 7\frac{d}{dx}[x] - \frac{d}{dx}[2]\\
\nonumber & = 4x^3 - 9\cdot 3x^2 + 5\cdot 2x + 7\cdot 1 - 0\\
& = 4x^3 - 27x^2 + 10x + 7. \label{MyDeriv}
\end{align}

\end{document}
