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\begin{document}

\lecture{NUMBER --- DATE, 2014}{Fall 2014}{Prof.\ Eric Price}{YOUR NAME}

\section{Overview}

In the last lecture we \ldots.

In this lecture we \ldots.

\section{Math things}
Here is an equation:
\begin{equation*}
a^2 + b^2 = c^2 ,
\end{equation*}
or
$$
a^2 + b^2 = c^2 .
$$

Here's the same equation but that can be referenced:
\begin{equation}
a^2 + b^2 + c^2 \label{eqn:pythagoras}
\end{equation}
Equation~\ref{eqn:pythagoras} has been known for a long
time. Sometimes you might want to align equations:
\begin{align*}
(x+y)^2 - (x-y)^2 &= (x^2 + 2xy + y^2) - (x^2 - 2xy - y^2) \\
{}&= 4xy
\end{align*}
or align them with numbers to be referenced:
\begin{align}
(x+y)^2 - (x-y)^2 &= (x^2 + 2xy + y^2) - (x^2 - 2xy - y^2) \label{eqn:1}\\
{}&= 4xy \label{eqn:2}
\end{align}
or where only some of them can be easily referenced:
\begin{align}
\nonumber (x+y)^2 - (x-y)^2 &= (x^2 + 2xy + y^2) - (x^2 - 2xy - y^2) \\
{}&= 4xy \label{eqn:3}
\end{align}

Here are some other math goodies: $\binom{n}{k}$, $\frac{n}{k}$, $x\gg
y$, $x\ll y$, $x\lesssim y$, $x\gtrsim y$, $\inprod{x,y}$, $x\in\R^n$,
$x\in S$, $S\ni x$, $x\notin S$, $x\neq y$, $x\oplus y$, $x\pm y$,
$\sqrt{x}$, $x\equiv y$, $S\cap T$, $\S\cup T$, $S\subset T$,
$S\subseteq T$, $S\supset T$, $\gamma$, $\Gamma$, $\R$, $\mathbb{F}$
$$\sum_{i=1}^n i,\ \sum_{\substack{i=1\\i\ odd}}^n i, \prod_{i=1}^n i$$

\section{Main Section}

We begin by describing the problem \ldots.
Make sure to use sections and subsections.

\subsection{Blah blah blah}
Here is a subsection.

\subsubsection{Blah blah blah}
Here is a subsubsection. You can use these as well.

\subsection{Using Boldface}
Make sure to use \textbf{lots} of {\bf boldface}.

\paragraph{Question:}
How would you use boldface?

\paragraph{Example:}
This is an example showing how to use boldface to help organize your
lectures.


\paragraph{Some Formatting.}
Here is some formatting that you can use in your notes:
\begin{itemize}
\item {\em Item One} -- This is the first item.
\item {\em Item Two} -- This is the second item.
\item \dots and here are other items.
\end{itemize}

If you need to number things, you can use this style:
\begin{enumerate}
\item {\em Item One} -- Again, this is the first item.
\item {\em Item Two} -- Again, this is the second item.
\item \dots and here are other items.
\end{enumerate}

\paragraph{Bibliography.}
Please give real bibliographical citations for the papers that we
mention in class. See below for how to include a bibliography section.
If you use BibTeX, integrate the .bbl file into your .tex source. You
should reference papers like this: ``The tug of war sketch originates
in a paper by Alon, Matias and Szegedy \cite{AMS99}.''  In general,
the name of the authors should appear in text at most once (for the
first citation); further citations look like: ``Our proof follows that
of \cite{AMS99}''.

Take a look at previous lectures (TeX files are available) to see the
details. A excellent source for bibliographical citations is
DBLP. Just Google DBLP and an author's name.



\bibliographystyle{alpha}

\begin{thebibliography}{42}

\bibitem[AMS99]{AMS99}
Noga~Alon, Yossi~Matias, Mario~Szegedy.
\newblock The Space Complexity of Approximating the Frequency Moments.
\newblock {\em J. Comput. Syst. Sci.}, 58(1):137--147, 1999.

\end{thebibliography}

\end{document}