% Copyright 2019 Clara Eleonore Pavillet
% Author: Clara Eleonore Pavillet
% Description: This is an unofficial Oxford University Beamer Template I made from scratch. Feel free to use it, modify it, share it.
% Version: 1.0
\documentclass{beamer}
\input{Theme/Packages.tex}
\usetheme{oxonian}
\title{Mathematical and Computational Modelling}
\titlegraphic{\includegraphics[width=2cm]{Theme/Logos/OxfordLogoV1.png}}
\author{Clara El{\'e}onore Pavillet}
\institute{University of Oxford}
\date{} %\today
\begin{document}
{\setbeamertemplate{footline}{}
\frame{\titlepage}}
\section*{Outline}\begin{frame}{Outline}\tableofcontents\end{frame}
\section{Text}
\begin{frame}[plain]
\vfill
\centering
\begin{beamercolorbox}[sep=8pt,center,shadow=true,rounded=true]{title}
\usebeamerfont{title}\insertsectionhead\par%
\color{oxfordblue}\noindent\rule{10cm}{1pt} \\
\LARGE{\faFileTextO}
\end{beamercolorbox}
\vfill
\end{frame}
\subsection{Welcome}
\begin{frame}{Welcome}
Feel free to contact me if you have any suggestions! \href{https://github.com/CEPav}{\faGithub}
\begin{enumerate}
\item Simple
\item Clean
\item Oxford University Colours
\end{enumerate}
\vspace{1cm}
\begin{center}
Enjoy! \faSmileO
\end{center}
\end{frame}
\section{Equations}
\begin{frame}[plain]
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\centering
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\subsection{Example}
\begin{frame}{Example}
\only<1>{
Let \(p(x)=\mathcal{N}(\mu\textsubscript{1},\,\sigma^{2}\textsubscript{1})\) and \(q(x)=\mathcal{N}(\mu\textsubscript{2},\,\sigma^{2}\textsubscript{2})\): \\
\begin{equation}
\mathcal{N}=\frac{1}{\sigma\,\sqrt{2\,\pi}}\,\E^{-\frac{\left(x-\mu\right)^2}{2\,\sigma^2} }
\end{equation}}
\only<2>{
Kullback-Leibler divergence for continuous probabilities:
\begin{align*}
D(p,q)=&\int p(x) \log \frac{p(x)}{q(x)}\ud x\\
=& \int p(x) \,\ln p(x) \ud x -\int p(x) \,\ln q(x) \ud x\\
=&\,\frac{1}{2} \ln\left(2\,\pi\,\sigma_2^{2}\right) +\frac{\sigma_1^{2}+\left(\mu_1-\mu_2 \right)^2 }{2\,\sigma_2^2}-\frac{1}{2}\left( 1+\ln 2\,\pi\,\sigma_1^2\right) \\
=&\,\ln\frac{\sigma_2}{\sigma_1} +\frac{\sigma_1^{2}+\left(\mu_1-\mu_2 \right)^2 }{2\,\sigma_2^2}-\frac{1}{2}
\end{align*}
}
\end{frame}
\section{Code}
\begin{frame}[plain]
\vfill
\centering
\begin{beamercolorbox}[sep=8pt,center,shadow=true,rounded=true]{title}
\usebeamerfont{title}\insertsectionhead\par%
\color{oxfordblue}\noindent\rule{10cm}{1pt} \\
\LARGE{\faFileCodeO}
\end{beamercolorbox}
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\end{frame}
\subsection{Example}
\begin{frame}[fragile]{Example}
\begin{block}{Greatest Common Divisor}
\begin{lstlisting}[firstnumber=1, label=glabels, xleftmargin=10pt]
def greatest_c_remainder(a,b):
'''Greatest common divisor of a and b'''
r = a % b
if r == 0:
return b
else:
m = b
n = r
return greatest_c_remainder(m,n)
\end{lstlisting}
\end{block}
\end{frame}
\end{document}