\documentclass[a4paper,DIV8,10pt]{scrartcl}
  
	% additional packages
	\usepackage[latin1]{inputenc} % useful for Umlauts
	\usepackage{amsmath}   % useful math macros
	\usepackage{amsthm}    % for theorems, definitions, proofs, etc.
	\usepackage{amsfonts}  % special AMS math fonts
	\usepackage[headinclude]{scrpage2}  % for page headings


	% math macros
	\newcommand{\N}{\ensuremath{\mathbb{N}}}   % natural numbers
	\newcommand{\Z}{\ensuremath{\mathbb{Z}}}   % integers
	\newcommand{\Q}{\ensuremath{\mathbb{Q}}}   % rational numbers
	\newcommand{\R}{\ensuremath{\mathbb{R}}}   % real numbers


	% declaration of theorem/definition/etc environments, based on amsthm
	\newtheorem{theorem}{Theorem}[section]
	\newtheorem{proposition}[theorem]{Proposition}
	\newtheorem{lemma}[theorem]{Lemma}
	\newtheorem{corollary}[theorem]{Corollary}
	\theoremstyle{definition}
	\newtheorem{definition}[theorem]{Definition}
	\newtheorem{remark}[theorem]{Remark}
	\newtheorem{exercise}[theorem]{Exercise}
	\newtheorem{example}[theorem]{Example}


	% further macros
	\makeatletter                    % footnotes without labels
	\def\blfootnote{\xdef\@thefnmark{}\@footnotetext}
	\renewcommand{\sectfont}{\normalfont} % changes section font
	\renewcommand{\labelitemi}{--} 


	% title of handout
	%   #1 name of speaker
	%   #2 email address
	%   #3 date of talk
	%   #4 title of talk
	\newcommand{\handouttitle}[4]
	{\begin{center}
	  \Large #4
	\end{center}

	\bigskip

	\noindent
	#1 (\textsf{#2})
	\hfill
	#3%
	\blfootnote{Seminar ``Variational Methods in Numerical Mathematics'',
		SS~2016, Freie~Universit\"at~Berlin}

	\noindent
	\rule{\linewidth}{.5pt}

	\bigskip

	\@afterindentfalse\@afterheading
	}
	\makeatother


% Beginning of the content part of the document.
\begin{document}

	% The handout's header.
	\handouttitle{Your Name}
		{your@mail.address}
		{March 14, 1592}
		{The Title of your Talk}


	% New section.
	\section{Introduction to functions}

	\begin{definition}[function]
		\label{def:function}
		Suppose $A$ and $B$ are sets.
		A subset $f \subseteq A \times B$ is called a \emph{function from $A$ into $B$} if and only if
		\begin{align*}
			\forall{a \in A} \ \exists{b \in B} \colon \ (a,b) \in f
		\end{align*}
		and
		\begin{align*}
			\forall{a \in A} \ \forall{b,b'\in B} \colon \ (a,b) \in f \wedge (a,b') \in f \ \Longrightarrow \ b = b'\text{.}
		\end{align*}
	\end{definition}
  
	\begin{remark}
		See for example https://en.wikibooks.org/wiki/LaTeX/Mathematics for more mathematical commands.
		Also try to not overuse quantifiers in formulas -- they usually have a negative impact on readability.
	\end{remark}


	% New section.
	\section{Properties of functions}

	\begin{theorem}[union of functions]
		Suppose that $A$, $B$ and $C$ are sets and $f \subseteq A \times C$ is a function from $A$ into $C$ and $g \subseteq B \times C$ is a function from $B$ into $C$.
		If $A \cap B = \emptyset$ then $f \cup g$ is a function from $A \cup B$ into $C$.
	\end{theorem}

	\begin{proof}
		We verify that $f \cup g$ fulfills the properties from Definition~\ref{def:function}. \dots
	\end{proof}
	
	\begin{remark}
		Above result is a special case of \cite[Theorem 1.23]{theLabel}.
	\end{remark}


	% And another section.
	\section{Examples}

	\begin{example}
		\hfil
		\begin{itemize}
			\item Try to find some (counter-)examples!
			\item They help to illustrate new concepts.
			\item And thus make it easier to understand those concepts.
		\end{itemize}
	\end{example}

	\begin{exercise}
		Also put in some exercises if possible.
		This allows the other participants to test their understanding of the new subject.
	\end{exercise}


	% Literature
	\begin{thebibliography}{99}
		\bibitem{theLabel} M.~Mustermann. \emph{Title of the Paper/Book}, further information, 2016.
	\end{thebibliography}

% end of the document 
\end{document}
