\documentclass{beamer}

\usetheme{Madrid}
\title[Bare Bones Beamer]{A Bare Bones Beamer Presentation}
\subtitle{A Demonstration for a Simple Talk}

\author[ERS]{Edward Scheinerman}
\institute[JHU]{Johns Hopkins University}

\date{January 1, 2009}

\begin{document}

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


\begin{frame}
  \frametitle{Core ideas}
  \begin{definition}
    An integer $n$ is called \alert{even} provided $n=2a$ where $a$ is
    an integer.
  \end{definition}

  \bigbreak
  \pause

  \begin{block}{Example}
    $20$ is even because $20 = 2 \times 10$ and $10$ is an integer.
  \end{block}
  \bigbreak
  \pause
  More examples: $0$, $-12$, $100$.

  \pause
  Nonexamples: $1$, $-3$, $\sqrt{2}$, $\pi$
\end{frame}

\begin{frame}
  \frametitle{Our main result}
  \begin{theorem}
    The sum of two even integers is even.
  \end{theorem}

  \pause

  \begin{proof}
    Suppose $n$ and $m$ are even. Then there exist integers $a$ and
    $b$ such that $n=2a$ and $m=2b$.

    Therefore
    $$
    n+m = 2a + 2b = 2(a+b) 
    $$
    and since $a+b$ is an integer, $n+m$ is even.
  \end{proof}
\end{frame}

\begin{frame}
  \Huge
  \begin{center}
    Questions?
  \end{center}
\end{frame}


\end{document}