\chapter{Some Introduction and Examples}
You can freely use the present template for your final thesis (i.e.~master or
bachelor or project thesis).

This template was made from the following theses:
\begin{itemize}
\item \url{http://thorsten-wissmann.de/theses/ma-wissmann.pdf}
\item \url{http://thorsten-wissmann.de/theses/project-wissmann.pdf}
\item \url{http://thorsten-wissmann.de/theses/bachelor-thesis-wissmann.pdf}
\end{itemize}

\section{Meaning}
It is not mandatory at all to use this template for your final thesis. It is
just a suggestion! You are also allowed to change anything you would like to
change in order to fit your needs/taste/$\ldots$.

Of course, you should adjust some places when using it for your final thesis:
\begin{enumerate}
\item In the parameters to the \texttt{hyperref}-package, you should adjust the
fields \texttt{pdfauthor} and \texttt{pdftitle} to your name and the title of
your thesis.

\item In \texttt{src/titlepage.tex} you should adjust the title and (possibly
the) subtitle of your thesis, the degree of your thesis (Masters degree?
Bachelor?), your name and the name of your advisors.

\end{enumerate}

\section{Some hints}
\subsection{Macros}

% some macros only needed for these hints here
\newcommand{\C}{\ensuremath{\mathcal{C}}\xspace}
\newcommand{\preview}[2]{
\begin{center}
\fbox{\begin{minipage}[t]{.47\textwidth}
#1
\end{minipage}}%
\hspace{.02\textwidth}%
\fbox{\begin{minipage}[t]{.47\textwidth}
#2
\end{minipage}}%
\end{center}}

When using certain mathematical symbols very often, it makes sense to define
macros for them, e.g.~
\begin{verbatim}
\newcommand{\C}{\ensuremath{\mathcal{C}}\xspace}
\end{verbatim}
The \texttt{ensuremath} enforces mathmode and the \texttt{xspace} inserts a
space if necessary:
\preview{
\Verb|Some \textbackslash C in the midle of the sentence|
\Verb|and at the end: \textbackslash C.|
}{
Some \C in the midle of the sentence
and at the end: \C.
}

\subsection{UTF-8}

I strongly recommend exploiting the utf8 capability of \LaTeX:

\begin{verbatim}
\usepackage{newunicodechar}
\newunicodechar{∀}{\ensuremath{\forall}}
\newunicodechar{∃}{\ensuremath{\exists}}
\newunicodechar{×}{\ensuremath{\times}}
\newunicodechar{ø}{\ensuremath{\emptyset}}
\newunicodechar{≤}{\ensuremath{\le}}
\newunicodechar{∈}{\ensuremath{\in}}
\newunicodechar{→}{\ensuremath{\to}}
\newunicodechar{⊆}{\ensuremath{\subseteq}}
\newunicodechar{⊗}{\ensuremath{\otimes}}
\newunicodechar{∧}{\ensuremath{\wedge}}
\end{verbatim}

with that, you can write:
\begin{verbatim}
    \begin{definition}[Transitivity]
    A relation $\text{``}≤\text{''} ⊆ X×X$ has upper bounds if
    \[
        ∀a,b ∈ X\ ∃ c ∈ X: a ≤ c ∧ b ≤ c
    \]
    \end{definition}
\end{verbatim}

It will result in the following:

    \begin{definition}[Transitivity]
    A relation $\text{``}≤\text{''} ⊆ X×X$ has upper bounds if
    \[
        ∀a,b ∈ X\ ∃ c ∈ X: a ≤ c ∧ b ≤ c
    \]
    \end{definition}

In order to input unicode characters, just configure a compose key, e.g.:
\begin{itemize}
\item \url{https://en.wikipedia.org/wiki/Compose_key}
\item
\url{https://wiki.archlinux.org/index.php/Keyboard_configuration_in_Xorg#Configuring_compose_key}

\end{itemize}

\subsection{Autoref}

Let \LaTeX~include whether something references is a definition or what else
using the \texttt{\textbackslash autoref} command:

\begin{verbatim}
    \begin{definition}[label={relation},name={Relation}]
    A relation $R$ between sets $X$ and $Y$ is just a subset of $X×Y$.
    \end{definition}
    We have just seen \autoref{relation}.
\end{verbatim}

This results in:


    \begin{definition}[label={relation},name={Relation}]
    A relation $R$ between sets $X$ and $Y$ is just a subset of $X×Y$.
    \end{definition}
    We have just seen \autoref{relation}.

\subsection{Further Comments}
For even more convenience while writing, you should look at the following:
synctex, git (for managing your \TeX-sources).

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