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\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm}

%%%%%%%%%% Fill out the the definitions %%%%%%%%%
\def \name {Valentin Brandl}					%
\def \matrikel {108018274494}				%
\def \pname {Marvin Herrmann}				%
\def \pmatrikel {108018265436}				%
\def \qname {Pascal Brackmann}
\def \qmatrikel {108017113834}				%
\def \gruppe {2 (Mi 10-12 Andre)}
\def \uebung {3}								%
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\newcommand{\hwsol}{
\vspace*{-2cm}
\noindent \matrikel \quad \name \hfill \"Ubungsgruppe: \gruppe \\
\noindent \pmatrikel \quad \pname \\
\noindent \qmatrikel \quad \qname \\
\begin{center}{\Large \bf L\"osung f\"ur \"Ubung \# \uebung}\end{center}
}

\begin{document}
%Import header
\hwsol

\section*{Aufgabe 3.4}

% \begin{itemize}

% 	\item $o$ impliziert $O$

% 	\item $\omega$ impliziert $\Omega$

% 	\item $f = \Theta(g) \Rightarrow f = \Omega(g) \text{ und } f = O(g)$

% 	\item $f = O(g) \Rightarrow g = \Omega(f)$

% 	\item $f = o(g) \Rightarrow g = \omega(f)$

% \end{itemize}

\begin{tabular}{|l||l|l|l|l|l|l|l|l|}
	\hline
	\backslashbox{f}{g} & $4^n$ & $e^{2n}$ & $\sum\limits_{k=1}^n k$ & $n \ln n$ & $2^{(2^{n+1})}$ & $51^{\ln n}$ & $2^{(2^n)}$ &
	$2^{\sqrt{\ln n}}$ \\\hline
	$4^n$ & $\Theta$ & $o$ & $o$ & $\omega$  & $O$ & $\omega$  & $O$ & $\omega$ \\\hline
	$e^{2n}$ & $\omega$ & $\Theta$ & $o$ & $\omega$ & $\omega$ & $\omega$ & $\omega$ & $\omega$ \\\hline
	$\sum\limits_{k=1}^n k$ & $\omega$ & $\omega$ & $\Theta$ & $\omega$ & $\omega$ & $\omega$  & $\omega$ & $\omega$ \\\hline
	$n \ln n$ & $o$ & $o$ & $o$ & $\Theta$ & $o$ & $o$  & $o$ & $\omega$ \\\hline
	$2^{(2^n)}$ & $\Omega$ & $o$ & $o$ & $\omega$ & $\Theta$ & $\Omega$  & $\Omega$ & $\omega$ \\\hline
	$51^{\ln n}$ & $o$ & $o$ & $o$ & $\omega$ & $O$ &  $\Theta$ & $O$ & $\omega$ \\\hline
	$2^{(2n)}$ & $\Omega$ & $o$ & $o$ & $\omega$ & $O$ & $\Omega$  & $\Theta$ & $\omega$ \\\hline
	$2^{\sqrt{\ln n}}$ & $o$ & $o$ & $o$ & $o$ & $o$  & $o$  & $o$  & $\Theta$ \\\hline
\end{tabular}

\end{document}