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\mode<presentation>{
%\usetheme[numbers]{Warsaw} %Rebordes y n\'{u}meros
\usetheme{Frankfurt} %Rebordes y n\'{u}meros indice con puntos
%\usecolortheme{seahorse} % Rebordes malvas
%\usecolortheme{rose} %Reborde azules m\'{a}s claros en bloques
%\usefonttheme[onlylarge]{structuresmallcapsserif} %\sc en t\'{\i}tulos
%\usefonttheme[onlysmall]{structurebold} % t\'{\i}tulo de arriba en negrita ??
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%fondo rojiblanco
}







\title[Math and Myth]{Communicating in English for a University Context}


\author[F. Chamizo]{\includegraphics[scale=1.0]{./images/m_m.jpg}\\ Fernando Chamizo}
\date{\footnotesize\url{http://www.uam.es/fernando.chamizo}}
\institute{Universidad Aut\'{o}noma de Madrid
\\
\
\\
{\small March 13th, 2012}}

\begin{document}

\setbeamertemplate{headline}
{%
\begin{beamercolorbox}{section in head/foot}
%\alert{\ \insertframenumber\ de \inserttotalframenumber}
\ \vskip6.5pt\par \insertnavigation{\paperwidth}\vskip2pt
\end{beamercolorbox}%
}

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% SLIDE 0  %
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%tITLE
\begin{frame}
\titlepage
\end{frame}


%%%%%%%%%%%%
% SLIDE 0+ %
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%Index
%\section*{\'{I}ndice}
%\begin{frame}
%\frametitle{\'{I}ndice}
%%\tableofcontents[pausesections]
%\tableofcontents
%\end{frame}






%%%%%%%%%%
% SLIDE  %
%%%%%%%%%%
\begin{frame}
\frametitle{Main objective}


\begin{center}
\includegraphics[scale=1.0]{./images/m_m.jpg}
\end{center}

\begin{block}{}
The primary purpose of this talk is that
\begin{center}
\begin{huge}
You enjoy it!\raisebox{10pt}{\begin{small}$^*$\end{small}}
\end{huge}
\end{center}
\end{block}


\vspace{35pt}

\begin{footnotesize}$^*$ \underline{Disclaimer}: This slide is not a contract. No money
refund if you learn something.\end{footnotesize}

\end{frame}







%%%%%%%%%%
% SLIDE  %
%%%%%%%%%%
\begin{frame}
\frametitle{\only<1>{Sentences that every mathematician has heard many times}\only<2->{The Myths}}


\begin{itemize}
 \item {\color{red}\only<1>{\bf\large} So, you're mathematician... Can you check the bill?}
 

 
\uncover<2->{ \hspace{-23pt}\begin{tabular}{l}
          \includegraphics[scale=0.18]{./images/myth1.png}
         \end{tabular} 
\fbox{\textbf{\large Math is the ability to do long calculations}}
}



\


 \item
{\color{red}\only<-2>{\bf\large} Is there any unsolved problem in Mathematics?}
 
 
% 
 
 \uncover<3->{  \hspace{-23pt}\begin{tabular}{l}
          \includegraphics[scale=0.18]{./images/myth2.png}
         \end{tabular}
\fbox{\textbf{\large Math is finished since ancient times}}
}


\


 \item
{\color{red}\only<-3>{\bf\large\hspace{-1pt}}What is this for?
Why didn't you study engineering?}


 
 \uncover<4->{  \hspace{-23pt}\begin{tabular}{l}
          \includegraphics[scale=0.18]{./images/myth3.png}
         \end{tabular} 
\fbox{\textbf{\large Math has no real-world applications}}
}


\



\end{itemize}



\end{frame}


%%%%%%%%%%
% SLIDE  %
%%%%%%%%%%
\begin{frame}


\begin{center}
\includegraphics[scale=0.4]{./images/hands_m_m.jpg}
\end{center}


\lq\lq You take the blue pill and [\dots ] you believe whatever you want
to believe [\dots ] You take the red pill and you stay in Wonderland''


\end{frame}



%%%%%%%%%%
% SLIDE  %
%%%%%%%%%%
\section[1. Calculations]{Myth 1}
\begin{frame}
\frametitle{Myth 1: Mathematics and calculations}



\begin{center}
\begin{tabular}{cl}
\begin{tabular}{l}
          \raise-14pt\hbox{\includegraphics[scale=0.2]{./images/myth1.png}}
         \end{tabular} 
&\fbox{Math requires ability with mental calculations}
\end{tabular}
\end{center}


\begin{center}
\begin{tabular}{c}
\includegraphics[scale=0.6]{./images/matrixcode.jpg}
\\
\small \sl \lq\lq Why don't we start something a little fun?''
\end{tabular}
\end{center}


\end{frame}



%%%%%%%%%%
% SLIDE  %
%%%%%%%%%%
\begin{frame}
\frametitle{Myth 1: Mathematics and calculations}


\begin{block}{Math does \textbf{not} requires ability with mental calculations}
In fact  mathematicians use very
frequently symbols and  tricks to avoid calculations.
\end{block}

\


\textbf{Example:} 

\[
 1+2+3+4+\dots +97+98+99+100 = ?
\]


\end{frame}



%%%%%%%%%%
% SLIDE  %
%%%%%%%%%%
\begin{frame}


\begin{center}

\begin{tabular}{c}
\ 
\\
\includegraphics[scale=0.4]{./images/triang_f.png}
\end{tabular}
\qquad
\begin{tabular}{c}
\ 
\\
\animategraphics[controls, scale=0.4]{5}{./images/rota/rota}{01}{17}
\end{tabular}


\end{center}




\pause

{\setbeamercolor{block title}{bg=green}
\begin{block}{}
A rectangular pattern is simpler than a triangular one for counting
\[
 1+2+3+4+\dots +97+98+99+100=\frac{100\cdot 101}{2}=5050
\]
\end{block}
}



\[
1+2+3+4+\dots + N=\frac{N(N+1)}{2}
\]


\end{frame}




%%%%%%%%%%
% SLIDE  %
%%%%%%%%%%
\section[2. Progress]{Myth 2}
\begin{frame}
\frametitle{Myth 2: Mathematics and progress}


\begin{center}
\begin{tabular}{cl}
\begin{tabular}{l}
          \raise-24pt\hbox{\includegraphics[scale=0.2]{./images/myth2.png}}
         \end{tabular} 
&\fbox{Math is exhausted}
\end{tabular}
\end{center}


\begin{center}
\begin{tabular}{c}
\includegraphics[scale=0.3]{./images/neo_arc.jpg}
\\
\small \sl \lq\lq Flawless. Sublime. A triumph only equaled by its monumental failure.''
\end{tabular}
\end{center}


\end{frame}



%%%%%%%%%%
% SLIDE  %
%%%%%%%%%%
\begin{frame}
\frametitle{Myth 2:  Mathematics and progress}


\begin{block}{Math is a \textbf{living science}}
Mathematics advances continuously
and there are breakthroughs from time to time, as in any other Science.
\end{block}


\

{\setbeamercolor{block title}{bg=green}
\begin{block}{}
There are many open problems in Mathematics, some of them very old, some of them brand new.
\end{block}
}




\end{frame}



%%%%%%%%%%
% SLIDE  %
%%%%%%%%%%
\begin{frame}
\frametitle{{\bf\Large A dirt simple unsolved problem}}




{\setbeamercolor{block title}{bg=red}
\begin{block}{}
{\color{blue}
Can an odd number equal the sum of its divisors excepting itself?}
\end{block}
}

\

Even numbers with this property are rather well-known and they are related to certain prime numbers
through one of the oldest theorems in pure Mathematics (c. 300 B.C.)

\

\textbf{Examples:}
\[
28=1+2+4+7+14
\]
\[
496=1+2+4+8+16+31+62+124+248
\]

\end{frame}




%%%%%%%%%%
% SLIDE  %
%%%%%%%%%%
\section[3. Real world]{Myth 3}
\begin{frame}
\frametitle{Myth 3: Mathematics and applications}

\begin{center}
\begin{tabular}{cl}
\begin{tabular}{l}
          \raise-24pt\hbox{\includegraphics[scale=0.2]{./images/myth3.png}}
         \end{tabular} 
&\fbox{Math is not applicable}
\end{tabular}
\end{center}


\begin{center}
\begin{tabular}{c}
\includegraphics[scale=0.3]{./images/room.jpg}
\\
\small \sl \lq\lq It is all around us, even now in this very room.''
\end{tabular}
\end{center}


\end{frame}



%%%%%%%%%%
% SLIDE  %
%%%%%%%%%%
\begin{frame}
\frametitle{Myth 3: Mathematics and applications}


\begin{block}{}
Most people are unaware that Mathematics is essential in very common technological applications.
\end{block}


\

{\setbeamercolor{block title}{bg=green}
\begin{block}{\color{blue}Reversed Ockham's razor?}
When something is hidden one tends to assume that it does not exist or that it is less important.
\end{block}
}

\end{frame}



%%%%%%%%%%
% SLIDE  %
%%%%%%%%%%
\begin{frame}
\frametitle{\bf\Large Welcome to the real world!}


J. Radon 1917 

\begin{center}
\begin{tabular}{c}
Is it possible to recover a the shape of\hspace{20pt}
\\
a translucent  object from its shadows?\hspace{20pt}
\\[6pt]
\begin{tabular}{c}
\includegraphics[scale=0.3]{./images/n_3tubs_1.jpg}
\end{tabular}
{\small\color{blue} Objects}
\\
\uncover<2->{$\Big\downarrow\Big\downarrow$\hspace{30pt}}
\\[6pt]
\uncover<2->{\begin{tabular}{c}
\includegraphics[scale=0.3]{./images/n_3tubs_2.jpg}
\end{tabular}
{\small\color{blue} Shadows}}
\end{tabular}
\end{center}


\uncover<3->{\[
\rho(x,y)={\int_0^\pi\int_{-\infty}^\infty}
|r|\widehat{P_\theta}(r)\; 
e^{2\pi i(xr\cos\theta+yr\sin\theta)}\; dr
d\theta.
\]}


\end{frame}


%%%%%%%%%%
% SLIDE  %
%%%%%%%%%%
\begin{frame}
\frametitle{\bf\Large Welcome to the real world!}

The first CAT (Computed axial tomography) scanners were installed in 1974 and they are very common
nowadays

\begin{center}
\begin{tabular}{c}
\includegraphics[scale=0.5]{./images/CAT.jpg}
\end{tabular}
\end{center}

\end{frame}



%%%%%%%%%%
% SLIDE  %
%%%%%%%%%%
\begin{frame}
\frametitle{\bf\Large Welcome to the real world!}


R.W. Hamming 1947

\vspace{10pt}

Redundancy allows error correction

{\setbeamercolor{block title}{bg=green}
\begin{block}{}
\begin{center}
\small
\begin{tabular}{cl}
University Context &
\\
$\downarrow$ & {\color{blue} encode}
\\
UUUnnniiivvveeerrrsssiiitttyyy CCCooonnnttteeex{\color{red}s}xttt &
\\
$\downarrow$ & {\color{blue} decode}
\\
University Context &
\end{tabular}
\end{center}\end{block}
}

It is possible to reduce largely the redundancy.

$X=\text{words}$,
$n=\#\text{letters/word}$,
$q=\text{alphabet size}$,
$t=\text{error correction capability}$
\[
|X|\sum_{i=1}^t\binom{n}{i}(q-1)^i\le q^n
\]
The first CD players were released in 1983.
\end{frame}




%%%%%%%%%%
% SLIDE  %
%%%%%%%%%%
\begin{frame}
\frametitle{To sum up}



\begin{block}{}
\begin{itemize}
 \item 
In Math \textsc{intuition} and \textsc{creativity} are more important than calculations
\item
Math is a \textsc{living} science
\item
Math is hidden inside of \textsc{everyday technologies} 
\end{itemize}
\end{block}


\end{frame}




%%%%%%%%%%
% SLIDE  %
%%%%%%%%%%
\begin{frame}

\begin{block}{{\footnotesize\url{http://www.uam.es/fernando.chamizo}}}
\begin{itemize}
\item
T. Gowers. Mathematics. A very short introduction. Oxford University Press, Oxford, 2002. 
\item
G.H. Hardy. A mathematician's apology.  Cambridge University Press, Cambridge, 1992. 
\item
S. Lang. The beauty of doing mathematics. Three public dialogues. Translated from the French.
Springer-Verlag, New York, 1985.
 \item 
M. Liebeck. A concise introduction to pure mathematics.  Chapman \& Hall/CRC Mathematics. CRC Press, Boca Raton, FL, 2011.
\item
I. Stewart. Letters to a young mathematician. Basic Books, New York, 2006. 
\item
I. Stewart. From here to infinity. The Clarendon Press, Oxford University Press, New York, 1996.
\end{itemize}

\end{block}


\end{frame}



%%%%%%%%%%
% SLIDE  %
%%%%%%%%%%
\begin{frame}
\frametitle{Myth 4: Mathematicians are weirdos}



\begin{itemize}
 \item \begin{tabular}{l}
          \includegraphics[scale=0.2]{./images/myth4.png}
         \end{tabular} 
{\color{red}\sf  [Censored]}
{\color{blue}\sf  [Not qualified to enter into it]}
\end{itemize}

In popular culture mathematicians are male, bald or with too much hair, wearing thick glasses, poorly dressed, boring, lacking social abilities\dots 




{\setbeamercolor{block title}{bg=green}
\begin{block}{}
\textbf{Fact:} In Spain more than the one half of the people with a degree in mathematics are women.
\end{block}
}

\pause

You are more likely to find 

\begin{center}
\begin{tabular}{ccc}
    \begin{tabular}{c}
    \includegraphics[scale=0.25]{./images/p_41.jpg}
    \end{tabular}
&instead of&
    \begin{tabular}{c}
    \includegraphics[scale=0.25]{./images/p_42.jpg}
    \end{tabular}
\end{tabular}
\end{center}

\end{frame}


%%%%%%%%%%
% SLIDE  %
%%%%%%%%%%
\begin{frame}


\vspace{30pt}

\begin{center}
\LARGE
Thank you
\end{center}

\vspace{30pt}

\begin{block}{}
\large
A copy of this presentation will be posted in:
\begin{center}
\url{http://www.uam.es/fernando.chamizo}

\end{center}\end{block}
\end{frame}


\end{document}


