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%  Sample presentation slides - beamer.tex                                     %
%  By Elana Hashman for CUMC -- CCEM 2013, July 2013                           %
%                                                                              %
%  Commercial use prohibited. For personal or non-commercial use only.         %
%  See additional licensing information below.                                 %
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% Heavily modified LaTeX code under non-commercial use as per license below.
%
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% This text is proprietary.                                                    %
% It's a part of presentation made by myself.                                  %
% It may not used commercial.                                                  %
% The noncommercial use such as private and study is free                      %
% Dec 2007                                                                     %
% Author: Sascha Frank                                                         %
% University Freiburg                                                          %
% www.informatik.uni-freiburg.de/~frank/                                       %
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\documentclass{beamer}
\setbeamertemplate{navigation symbols}{}
\beamersetuncovermixins{\opaqueness<1>{25}}{\opaqueness<2->{15}}
\DeclareFontShape{OT1}{cmtt}{bx}{n}{
<5><6><7><8><9><10><10.95><12><14.4><17.28><20.74><24.88>cmttb10}{}
\usepackage{ragged2e}
\usepackage{tikz}

\begin{document}
\title{Title Here}
\subtitle{Subtitle here}  
\author{Author here \thanks{the author is thankful!}}
\institute{\large Your university?}
\date{\today} 

%%% Title
\frame{\titlepage}

%%% ToC
\begin{frame}
\frametitle{Table of contents}
\tableofcontents
\end{frame} 


%%% History
\section{Basic} 
\subsection{A slide}
\begin{frame}
\frametitle{This slide has a title.}
Here is the body of the slide.
\end{frame}

\begin{frame}
Note that this slide does not have a title.
\end{frame}

\begin{frame}
\frametitle{Blocks}
\begin{block}{Block title}
Some text in a block.
\end{block}
\begin{block}{Block 2}
The second block.
\end{block}
\end{frame}

\section{Lists}
\subsection{Unordered Lists}
\begin{frame}
\frametitle{Unordered list}
\begin{itemize}
\item Thing one
\item Thing two
\item Thing red
\item Thing blue
\end{itemize}
\end{frame}

\subsection{Ordered lists}
\begin{frame}
\frametitle{Ordered list}
\begin{enumerate}
\item Thing one
\item Thing two
\item Thing three
\item Thing four
\end{enumerate}
\end{frame}

\section{Other fancy things}
\begin{frame}
\frametitle{Pausing}
\begin{itemize}
\item Sometimes if you have a list... \pause
\item You might only want to focus on one item at a time. \pause
\item So you can use a pause!
\end{itemize}
\end{frame}

\begin{frame}[fragile]
\begin{verbatim}
If you use the verbatim environment, you must
ensure that you declare your frame as 'fragile.'

   // Note to self:
   // Verbatim is awesome...
\end{verbatim}
\end{frame}

%%% Proof and code
\subsection{Proof environment}
\begin{frame}
\frametitle{\tt \textbackslash begin\{document\} }
{\bf Squeeze Theorem.}\\[1mm]
{\justifying Let $(x_n)$, $(y_n)$ and $(z_n)$ be sequences in $\mathbb{R}$.  
Suppose $(x_n)\to L$, $(z_n)\to L$, and for all $n \ge n_0$, we have $x_n \le 
y_n \le z_n$; then $(y_n)\to L$.\\[1mm]
\begin{proof}
Let $\varepsilon > 0$. Since $(x_n)\to L$, there is some integer $n_1$ such 
that $\forall\ n \ge n_1$, we have $|x_n - L| < \varepsilon$.\\[2mm]

Similarly, for the same $\varepsilon$, since $(z_n)$ converges, $\exists\ n_2 
\in \mathbb{N}$ such that $\forall\ n \ge n_2$, we have $|z_n - L| < 
\varepsilon$.\\[2mm]

Then take $N = \max(n_0, n_1, n_2)$, and let $n \ge N$. For all $n \ge N$, we 
must have
\[ L-\varepsilon < x_n \le y_n \le z_n < L+\varepsilon \]
which implies $|y_n - L| < \varepsilon$. So $(y_n)$ converges to $L$.
\end{proof}
}
\end{frame}

\subsection{Graphics}
\begin{frame}
\frametitle{TiKZ and Other Graphics Packages}
\begin{center}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% This file is part of the book
%%
%% Algorithmic Graph Theory
%% http://code.google.com/p/graph-theory-algorithms-book/
%%
%% Copyright (C) 2009--2011 Minh Van Nguyen <nguyenminh2@gmail.com>
%%
%% See the file COPYING for copying conditions.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%% from http://code.google.com/r/isabelindarj-graph/source/browse/image/distance-connectivity/petersen-graph.tex?r=6b8618b651eb5af51b726d688de6acad9ff931a1
%% Copying permitted under the GPL v1.3.
\begin{block}{Pretty graph}
\begin{tikzpicture}
[nodeDecorate/.style={shape=circle,inner sep=2pt,draw,thick},%
  lineDecorate/.style={-,thick},scale=1.5]
%% nodes or vertices
\foreach \nodename/\x/\y in {
  %% outer pentagon
  0/0/2, 1/-1.9021/0.6180, 2/-1.1755/-1.6180, 3/1.1755/-1.6180,
  4/1.9021/0.6180,
  %% inner pentagon
  5/0/1, 6/-0.9510/0.3090, 7/-0.5877/-0.8090, 8/0.5877/-0.8090,
  9/0.9510/0.3090}
{
  \node (\nodename) at (\x,\y) [nodeDecorate] {};
}
%% edges or lines
\path
\foreach \startnode/\endnode in {0/1, 0/4, 0/5, 1/2, 1/6, 2/3, 2/7,
  3/4, 3/8, 4/9, 5/7, 5/8, 6/8, 6/9, 7/9}
{
  (\startnode) edge[lineDecorate] node {} (\endnode)
};
\end{tikzpicture}
\end{block}
\end{center}
\end{frame}

%%% Conclusion
\section{Web links}

\begin{frame}
\frametitle{URL command}
My website:\\ {\small \url{http://hashman.ca/tex}}
\end{frame}

\end{document}