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+\begin{frame}{Contents}
+ \tableofcontents
+\end{frame}
+
+\section{Motivation}
+
+\subsection{The Basic Problem That We Studied}
+
+\begin{frame}{Make Titles Informative. Use Uppercase Letters. Long Titles
+ are Split Automatically.}{Subtitles are optional.}
+ \begin{itemize}
+ \item
+ Use \texttt{itemize} a lot.
+ \item
+ Use very short sentences or short phrases.
+ \end{itemize}
+\end{frame}
+
+\begin{frame}{Make Titles Informative.}
+
+ You can create overlays\dots
+ \begin{itemize}
+ \item using the \texttt{pause} command:
+ \begin{itemize}
+ \item
+ First item.
+ \pause
+ \item
+ Second item.
+ \end{itemize}
+ \item
+ using overlay specifications:
+ \begin{itemize}
+ \item<3->
+ First item.
+ \item<4->
+ Second item.
+ \end{itemize}
+ \item
+ using the general \texttt{uncover} command:
+ \begin{itemize}
+ \uncover<5->{\item
+ First item.}
+ \uncover<6->{\item
+ Second item.}
+ \end{itemize}
+ \end{itemize}
+\end{frame}
+
+
+\subsection{Previous Work}
+
+\begin{frame}[fragile]{An old algorithm}
+% NB. listings is quite powerful, but not well suited to be used with beamer
+% consider using semiverbatim or the like, see below
+\begin{semiverbatim}
+int main (void)
+{
+ std::vector<bool> is_prime (100, true);
+ for (int i = 2; i < 100; i++)
+ if (is_prime[i])
+ {
+ std::cout << i << " ";
+ for (int j = i; j < 100;
+ is_prime [j] = false, j+=i);
+ }
+ return 0;
+}
+\end{semiverbatim}
+\end{frame}
+
+\begin{frame}[fragile]{An Algorithm For Finding Primes Numbers.}
+\begin{semiverbatim}
+\uncover<1->{\alert<0>{int main (void)}}
+\uncover<1->{\alert<0>{\{}}
+\uncover<1->{\alert<1>{ \alert<4>{std::}vector<bool> is_prime (100, true);}}
+\uncover<1->{\alert<1>{ for (int i = 2; i < 100; i++)}}
+\uncover<2->{\alert<2>{ if (is_prime[i])}}
+\uncover<2->{\alert<0>{ \{}}
+\uncover<3->{\alert<3>{ \alert<4>{std::}cout << i << " ";}}
+\uncover<3->{\alert<3>{ for (int j = i; j < 100;}}
+\uncover<3->{\alert<3>{ is_prime [j] = false, j+=i);}}
+\uncover<2->{\alert<0>{ \}}}
+\uncover<1->{\alert<0>{ return 0;}}
+\uncover<1->{\alert<0>{\}}}
+\end{semiverbatim}
+ \visible<4->{Note the use of \alert{\texttt{std::}}.}
+\end{frame}
+
+\section{Our Results/Contribution}
+
+\subsection{Main Results}
+
+\begin{frame}{Make Titles Informative.}
+ \begin{example}
+ \begin{itemize}
+ \item 2 is prime (two divisors: 1 and 2).
+ \item 3 is prime (two divisors: 1 and 3).
+ \item 4 is not prime (\alert{three} divisors: 1, 2, and 4).
+ \end{itemize}
+ \end{example}
+\end{frame}
+
+\begin{frame}{Make Titles Informative.}
+\begin{theorem}
+ There is no largest prime number and, in addition, $$\int_\Omega \nabla u \cdot \nabla v = - \int_\Omega u \Delta v + \int_{\partial\Omega} u v n$$
+ \end{theorem}
+ \begin{proof}
+ \begin{enumerate}
+ \item<1-> Suppose $p$ were the largest prime number.
+ \item<2-> Let $q$ be the product of the first $p$ numbers.
+ \item<3-> Then $q + 1$ is not divisible by any of them.
+ \item<1-> Thus $q + 1$ is also prime and greater than $p$.\qedhere
+ \end{enumerate}
+ \end{proof}
+ \uncover<4->{The proof used \textit{reductio ad absurdum}.}
+\end{frame}
+
+\begin{frame}{Make Titles Informative.}
+\end{frame}
+
+
+\subsection{Basic Ideas for Proofs/Implementation}
+
+\begin{frame}{Make Titles Informative.}
+\end{frame}
+
+\begin{frame}{Make Titles Informative.}
+\end{frame}
+
+\begin{frame}{Make Titles Informative.}
+\end{frame}
+
+
+
+\section*{Summary}
+
+\begin{frame}{Summary}
+
+ % Keep the summary *very short*.
+ \begin{itemize}
+ \item
+ The \alert{first main message} of your talk in one or two lines.
+ \item
+ The \alert{second main message} of your talk in one or two lines.
+ \item
+ Perhaps a \alert{third message}, but not more than that.
+ \end{itemize}
+
+ % The following outlook is optional.
+ \vskip0pt plus.5fill
+ \begin{itemize}
+ \item
+ Outlook
+ \begin{itemize}
+ \item
+ Something you haven't solved.
+ \item
+ Something else you haven't solved.
+ \end{itemize}
+ \end{itemize}
+\end{frame}
+
+
+
+% All of the following is optional and typically not needed.
+\appendix
+\section<presentation>*{\appendixname}
+\subsection<presentation>*{For Further Reading}
+
+\begin{frame}[allowframebreaks]
+ \frametitle<presentation>{For Further Reading}
+
+ \begin{thebibliography}{10}
+
+ \beamertemplatebookbibitems
+ % Start with overview books.
+
+ \bibitem{Author1990}
+ A.~Author.
+ \newblock {\em Handbook of Everything}.
+ \newblock Some Press, 1990.
+
+
+ \beamertemplatearticlebibitems
+ % Followed by interesting articles. Keep the list short.
+
+ \bibitem{Someone2000}
+ S.~Someone.
+ \newblock On this and that.
+ \newblock {\em Journal of This and That}, 2(1):50--100,
+ 2000.
+ \end{thebibliography}
+\end{frame}
+