13-4-1en.tex

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% 13-4-1en.tex 用 pdfLaTeX 处理

\documentclass{beamer}

\mode<presentation>
{
  \usetheme{Warsaw}
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  % 无导航条的主题: Bergen, Boadilla, Madrid, Pittsburgh, Rochester;
  % 有树形导航条的主题: Antibes, JuanLesPins, Montpellier;
  % 有目录竖条的主题: Berkeley, PaloAlto, Goettingen, Marburg, Hannover;
  % 有圆点导航条的主题: Berlin, Dresden, Darmstadt, Frankfurt, Singapore, Szeged;
  % 有节与小节导航条的主题: Copenhagen, Luebeck, Malmos, Warsaw

%  \setbeamercovered{transparent}
  % 如果取消上一行的注解 %, 就会使得被覆盖部分变得透明(依稀可见)
}

\usepackage{times}

\title{There Is No Largest Prime Number}

%\subtitle{}

\author[Euclid]{Euclid of Alexandria \\ \texttt{[e-mail]}}
\date[ISPN '80]{27th International Symposium of Prime Numbers}

%\institute[]{}

\begin{document}

\begin{frame}
  \titlepage
\end{frame}

\begin{frame}
  \frametitle{Outline}
  \tableofcontents
\end{frame}

\section{Motivation}
\subsection{The Basic Problem That We Studied}

\begin{frame}
  \frametitle{What Are Prime Numbers?}
  \begin{definition}
    A \alert{prime number} is a number that has exactly two divisors.
  \end{definition}
\end{frame}

\begin{frame}
  \frametitle{What Are Prime Numbers?}
  \begin{definition}
    A \alert{prime number} is a number that has exactly two divisors.
  \end{definition}
  \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}
  \frametitle{There Is No Largest Prime Number}
  \framesubtitle{The proof uses \textit{reductio ad absurdum}.}

  \begin{theorem}
    There is no largest prime number.
  \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}
  \frametitle{What's Still To Do?}
  \begin{block}{Answered Questions}
    How many primes are there?
  \end{block}
  \begin{block}{Open Questions}
    Is every even number the sum of two primes?
    \cite{Goldback1742}
  \end{block}
\end{frame}

%\begin{frame}
%  \frametitle{What's Still To Do?}
%  \begin{columns}
%    \column{.5\textwidth}
%      \begin{block}{Answered Questions}
%        How many primes are there?
%      \end{block}
%
%    \column{.5\textwidth}
%      \begin{block}{Open Questions}
%        Is every even number the sum of two primes?
%        \cite{Goldback1742}
%      \end{block}
%  \end{columns}
%\end{frame}

\begin{frame}
  \begin{thebibliography}{10}
  \bibitem{Goldback1742}[Goldback, 1742]
    Christian Goldback.
    \newblock A problem we should try to solve before the ISPN '43 deadline,
    \newblock \emph{Letter to Leonhard Euler}, 1742.
  \end{thebibliography}
\end{frame}

\begin{frame}[fragile]
  \frametitle{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}

\end{document}