A beamer template for use at the Technical University of Denmark (DTU) following the DTU design guide at DTU design guide.
For any suggestions, problems or bug fixes, please contact latex-support@student.dtu.dk or https://www.facebook.com/dtulatex
\begin
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\documentclass[aspectratio=169,hyperref={pdfpagelabels=false}]{beamer}
\input{preamble.tex}
\subtitle{DTU \LaTeX~Support Group - latex.dtu.dk DTU}
\title{Beamer template}
\setdepartment{DTU Compute}
\setcolor{blue}
\begin{document}
\inserttitlepage
\begin{frame}{Colors}
\begin{testcolors}[rgb,cmyk]
\testcolor{dtured}
\testcolor{white}
\testcolor{black}
\testcolor{blue}
\testcolor{brightgreen}
\testcolor{navyblue}
\testcolor{yellow}
\testcolor{orange}
\testcolor{pink}
\testcolor{red}
\testcolor{green}
\testcolor{purple}
\end{testcolors}
\end{frame}
\begin{frame}{Graphs and figures}
\section{Tables and figures}
\begin{table}[H]
\centering
\label{tab:tableExample}
\begin{tabular}{@{}llS@{}}
\toprule
\multicolumn{2}{c}{Item} & \\ \cmidrule(r){1-2}
Animal & Description & Price (\$) \\ \midrule
Gnat & per gram & 13.65 \\
& each & 0.01 \\
Gnu & stuffed & 92.50 \\
Emu & stuffed & 33.33 \\
Armadillo & frozen & 8.99 \\ \bottomrule
\end{tabular}
\end{table}
\end{frame}
\begin{frame}{Equations}
The ideal gas law is shown in .
\begin{equation}
p \cdot V = n \cdot R \cdot T
\end{equation}
\begin{equation} \label{eq:IME}
\frac{\partial}{\partial t} \int_{0}^{\delta} U dy = - \delta \frac{1}{\rho}\frac{\partial P}{\partial x}-U_f(t)^2
\end{equation}
\end{frame}
\begin{frame}{More equations}
\begin{equation}
\begin{aligned}
CH_3COOH + OH^{-} &\rightleftharpoons CH_3COO^{-} + H_2O \\
H_2O &\rightleftharpoons H^{+}_{(aq)} + OH^{-}_{(aq)}
\end{aligned}
\end{equation}
\begin{align}
\label{eq:align1}
f(x) &= 1 + x - 3 x^2 \\
\label{eq:align2}
g(x) + y &= 3x - \frac{1}{2} x^3
\end{align}
\end{frame}
\begin{frame}[allowframebreaks]{Probability}
\begin{block}{Law of total probability for random variables}
Let \(X,Y\) be random variables where \(x,y\) represent possible values, it holds that:
\[
P(x) = \sum_y P(x,y) = \sum_y P(x|y)\cdot P(y)
\]
\end{block}
\framebreak
\begin{block}{Bayes' theorem}
\begin{itemize}
\item For any two events \(A\) and \(B\) in the sample space \(S\), where \(\mathds{P}(B) \neq 0\), it holds that
\[\mathds{P}(A|B) = \frac{\mathds{P}(P|A) \cdot \mathds{P}(A)}{\mathds{P}(B)}\]
\item Let \(A_1, A_2, \dots , A_K\) be a \textit{partition} of the sample space \(S\). Using the \textit{law of total probability} for \(\mathds{P}(B)\), it then holds that:
\[
\mathds{P}(A_j | B) = \frac{\mathds{P}(B|A_j) \cdot \mathds{(A_j)}}{\sum_k \mathds{P}(B|A_k) \cdot \mathds{P}(A_k)}
\]
\end{itemize}
\end{block}
\end{frame}
\begin{frame}{Generalising problem-solving by searching}
So far we have only considered search problems in environments that are:
\begin{itemize}
\item \textbf{Single agent.} There is a single agent acting, the one we control.
\item \textbf{Static.} When the agent is not acting, the world doesn't change.
\item \textbf{Deterministic.} Every action has a unique outcome.
\item \textbf{Fully observable.} The full state description is accessible to the agent.
\end{itemize}
Problem solving in the real world rarely satisfies these assumptions.
Today, we will drop the assumption that the environment is deterministic and fully observable. We will also shortly consider generalising beyond single-agent and static environments.
\end{frame}
\end{document}