<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\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&lt;3-&gt;
      First item.
    \item&lt;4-&gt;
      Second item.
    \end{itemize}
  \item
    using the general \texttt{uncover} command:
    \begin{itemize}
      \uncover&lt;5-&gt;{\item
        First item.}
      \uncover&lt;6-&gt;{\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&lt;bool&gt; is_prime (100, true);
  for (int i = 2; i &lt; 100; i++)
    if (is_prime[i])
      {
        std::cout &lt;&lt; i &lt;&lt; " ";
        for (int j = i; j &lt; 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&lt;1-&gt;{\alert&lt;0&gt;{int main (void)}}
\uncover&lt;1-&gt;{\alert&lt;0&gt;{\{}}
\uncover&lt;1-&gt;{\alert&lt;1&gt;{ \alert&lt;4&gt;{std::}vector&lt;bool&gt; is_prime (100, true);}}
\uncover&lt;1-&gt;{\alert&lt;1&gt;{ for (int i = 2; i &lt; 100; i++)}}
\uncover&lt;2-&gt;{\alert&lt;2&gt;{    if (is_prime[i])}}
\uncover&lt;2-&gt;{\alert&lt;0&gt;{      \{}}
\uncover&lt;3-&gt;{\alert&lt;3&gt;{        \alert&lt;4&gt;{std::}cout &lt;&lt; i &lt;&lt; " ";}}
\uncover&lt;3-&gt;{\alert&lt;3&gt;{        for (int j = i; j &lt; 100;}}
\uncover&lt;3-&gt;{\alert&lt;3&gt;{             is_prime [j] = false, j+=i);}}
\uncover&lt;2-&gt;{\alert&lt;0&gt;{      \}}}
\uncover&lt;1-&gt;{\alert&lt;0&gt;{ return 0;}}
\uncover&lt;1-&gt;{\alert&lt;0&gt;{\}}}
\end{semiverbatim}
  \visible&lt;4-&gt;{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&lt;1-&gt; Suppose $p$ were the largest prime number.
 \item&lt;2-&gt; Let $q$ be the product of the first $p$ numbers.
 \item&lt;3-&gt; Then $q + 1$ is not divisible by any of them.
 \item&lt;1-&gt; Thus $q + 1$ is also prime and greater than $p$.\qedhere
 \end{enumerate} 
 \end{proof}
 \uncover&lt;4-&gt;{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&lt;presentation&gt;*{\appendixname}
\subsection&lt;presentation&gt;*{For Further Reading}

\begin{frame}[allowframebreaks]
  \frametitle&lt;presentation&gt;{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}

</pre></body></html>