Radboud University - Mathematics Thesis template EN
% Deze template is gemaakt door Fons van der Plas (f.vanderplas@student.ru.nl) voor het publiek domein en mag gebruikt worden **zonder vermelding van zijn naam**.
% This template was created by Fons van der Plas (f.vanderplas@student.ru.nl) for the public domain, and may be used **without attribution**.
\documentclass{article}
\usepackage[utf8]{inputenc} % for éô
\usepackage[english]{babel} % for proper word breaking at line ends
\usepackage[a4paper, left=1.5in, right=1.5in, top=1.5in, bottom=1.5in]{geometry}
% for page size and margin settings
\usepackage{graphicx} % for ?
\usepackage{amsmath,amssymb} % for better equations
\usepackage{amsthm} % for better theorem styles
\usepackage{mathtools} % for greek math symbol formatting
\usepackage{enumitem} % for control of 'enumerate' numbering
\usepackage{listings} % for control of 'itemize' spacing
\usepackage{todonotes} % for clear TODO notes
\usepackage{hyperref} % page numbers and '\ref's become clickable
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\def\thesistitle{Interesting Theorems}
\def\thesissubtitle{Why I Definitely Deserve a Fields Medal}
\def\thesisauthorfirst{Huey}
\def\thesisauthorsecond{Duck}
\def\thesissupervisorfirst{dr. Dewey}
\def\thesissupervisorsecond{Duck}
\def\thesissecondreaderfirst{prof. dr. Louie}
\def\thesissecondreadersecond{Duck}
\def\thesisdate{February 2049}
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%% FOR PDF METADATA
\title{\thesistitle}
\author{\thesisauthorfirst\space\thesisauthorsecond}
\date{\thesisdate}
%% TODO PACKAGE
\newcommand{\towrite}[1]{\todo[inline,color=yellow!10]{TO WRITE: #1}}
%% THEOREM STYLES
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}{Corollary}[theorem]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\theoremstyle{remark}
\newtheorem*{remark}{Remark}
%% MATH OPERATORS
\DeclareMathOperator{\supersine}{supersin}
\DeclareMathOperator{\supercosine}{supercos}
%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\begin{titlepage}
\thispagestyle{empty}
\newcommand{\HRule}{\rule{\linewidth}{0.5mm}}
\center
\textsc{\Large Radboud University Nijmegen}\\[.7cm]
\includegraphics[width=25mm]{img/in_dei_nomine_feliciter.eps}\\[.5cm]
\textsc{Faculty of Science}\\[0.5cm]
\HRule \\[0.4cm]
{ \huge \bfseries \thesistitle}\\[0.1cm]
\textsc{\thesissubtitle}\\
\HRule \\[.5cm]
\textsc{\large Thesis BSc Mathematics}\\[.5cm]
\begin{minipage}{0.4\textwidth}
\begin{flushleft} \large
\emph{Author:}\\
\thesisauthorfirst\space \textsc{\thesisauthorsecond}
\end{flushleft}
\end{minipage}
~
\begin{minipage}{0.4\textwidth}
\begin{flushright} \large
\emph{Supervisor:} \\
\thesissupervisorfirst\space \textsc{\thesissupervisorsecond} \\[1em]
\emph{Second reader:} \\
\thesissecondreaderfirst\space \textsc{\thesissecondreadersecond}
\end{flushright}
\end{minipage}\\[4cm]
\vfill
{\large \thesisdate}\\
\clearpage
\end{titlepage}
\tableofcontents
\newpage
\section{Complex stuff}
\subsection{Domains}
Let's start with the following definition:
\begin{definition}\label{def:domain}
A set $U \subseteq \mathbb{C}$ is a \emph{domain} if:
\begin{itemize}
\item $U$ is open in $\mathbb{C}$, and
\item $U$ is connected.
\end{itemize}
\end{definition}
\subsection{Yumyumyumyum}
\towrite{an introduction and some examples}
\begin{theorem}[]
Suppose $n \in \mathbb{Z}$, then the following are equivalent:
\begin{enumerate}[label=\roman*.]
\item $n > 5$.
\item $5 > 5$.\todo{This doesn't seem right...}
\item For each $n \in n$, we have:
\begin{align}\label{eq:truth}
n > n+1 > n+1^2 > \dots > n+7.
\end{align}
where $7$ is an arbitrary element of
\begin{align*}
\oint_{a}^{b} \supersine \alpha + i \supercosine \beta db(a).
\end{align*}
\end{enumerate}
\end{theorem}
\begin{remark}
Interesting!
\end{remark}
\begin{proof}
See \cite{Rynne2008LinearAnalysis}.
\end{proof}
\begin{figure}[h]
\centering
\includegraphics[width=.3\textwidth]{img/in_dei_nomine_feliciter.eps}
\caption{Motivational illustration. Similar to \cite{Oort1958,Reed1960}.}
\label{fig:logo}
\end{figure}
\begin{corollary}
Suppose $U \subseteq \mathbb{C}$ is a domain (see Definition \ref{def:domain}), and $f: \overline{U} \rightarrow \mathbb{C}$ is continuous on $\overline{U}$ and holomorphic on $U$. If $z \mapsto |f(z)|$ is constant on $\partial U$, then $f$ has a zero in $U$.
\end{corollary}
\begin{proof}
If not, consider $\frac{1}{f}$.
\end{proof}
The proof of this theorem is illustrated in Figure \ref{fig:logo}.
\begin{figure}
\centering
\includegraphics[width=.7\textwidth]{img/cat.jpg}
\caption{A cute dog.}
\label{fig:my_label}
\end{figure}
\newpage
% You can choose a citation style, 'plain' is the default
% See:
% https://www.overleaf.com/learn/latex/Bibtex_bibliography_styles
\bibliographystyle{plain}
\bibliography{references.bib}
\end{document}
% Have fun!
% -fons
% http://www2.washjeff.edu/users/rhigginbottom/latex/resources/symbols.pdf