diff --git a/template/mat-thesis-template.tex b/template/mat-thesis-template.tex new file mode 100644 index 0000000..0f50272 --- /dev/null +++ b/template/mat-thesis-template.tex @@ -0,0 +1,400 @@ +% University of Helsinki +% Department of Mathematics and Statistics +% Template for Bachelor's or Master's thesis +% +% This template is intended as a starting point for a thesis; +% feel free to customize it or use your own template. +% See the comments for hints and customization. +% +% Initial version: 29 August 2024 / Petri Laarne + + +% Add the 'twoside, openright' options when producing a proper printed version +\documentclass[a4paper, 11pt]{report} + +\usepackage[hidelinks]{hyperref} % Always load this: clickable links and PDF reader navigation bar +\usepackage{lastpage} % Used to determine the total page count +\usepackage{calc} % For layout calculations involving TeX length units (template title page) +\usepackage{graphicx} % For embedding image files (JPEG, PNG, PDF) +\usepackage{subcaption} % For subfigures +\usepackage{tikz} % For drawing diagrams and other complex vector graphics + +% If you use the LuaLaTeX or XeLaTeX compiler, comment out the following line. +% These compilers offer better support for Unicode, so you should use them if possible. +\usepackage[T1]{fontenc} + +% Pass the language of the thesis as the LAST option in the list below. +% This changes the language used for dates and words like 'Chapter' or 'Bibliography'. +% You can remove the languages that do not appear in your work. +\usepackage[finnish,swedish,english]{babel} + +\usepackage{csquotes} % This package is suggested by 'babel' + +% Bibliography. Change the latter command if you modify the .bib file name. +\usepackage{biblatex} +\addbibresource{thesis-refs.bib} + +\usepackage{mathtools} % Extended mathematics support (this package extends amsmath) +\usepackage{amssymb} % More mathematical symbols +\usepackage{amsfonts} % Blackboard bold mathematics font + +% Theorem environments +\usepackage{amsthm} +\theoremstyle{plain} +\newtheorem{theorem}{Theorem}[section] % Theorems are numbered within chapter and section +\newtheorem{lemma}[theorem]{Lemma} % Lemmas etc. follow the same numbering as theorems +\theoremstyle{definition} +\newtheorem{definition}[theorem]{Definition} +\theoremstyle{remark} +\newtheorem{remark}[theorem]{Remark} + +% Some examples of custom mathematical commands +\newcommand{\ZZ}{\mathbb Z} % Blackboard bold Z +\newcommand{\dx}{\mathop{}\!\mathrm d x} % Nice spacing (and upright d) for dx in integrals + +% Finnish notation for evaluating integrals +% Instead of \int_a^b syntax you must use it as \sij{a}{b} +% (To enable the sub-/superscript syntax would require some more complicated TeX wizardry.) +\newcommand{\sij}[2]{\mathop{\bigg/}\nolimits_{\hspace{-0.65em}#1}^{\hspace{0.05em}#2}\hspace{-0.2em}} + + +\begin{document} + +% +% TITLE PAGE +% +\begin{titlepage} + +\noindent +\begin{minipage}[b]{\textwidth-45pt} +University of Helsinki\\ +Faculty of Science\\ +Insert DEGREE PROGRAMME name here +% Helsingin yliopisto\\ +% Matemaattis-luonnontieteellinen tiedekunta\\ +% Helsingfors universitet\\ +% Matematisk-naturvetenskapliga fakulteten\\ +\end{minipage} +\hfill\includegraphics[width=45pt]{HYlogo.pdf} + +\vspace{4pt}\hrule\vfill + +\begin{center} +Bachelor's thesis / Master's thesis\\[8pt] +% Kandidaatintutkielma / Maisterintutkielma\\[8pt] +% Kandidatavhandlingen / Magisteravhandlingen\\[8pt] + +{\huge\bfseries Title of the thesis}\\[8pt] + +Firstname Lastname +\end{center} + +\vfill\hrule\vspace{4pt} + +\noindent +Supervisor:\hfill Month and year of submission\\ +Firstname Lastname\\ +Possible Other Supervisor +\end{titlepage} + +% +% ABSTRACT +% +% This command starts a new page. +% In a print version ('twoside' option passed to \documentclass), the page is on the right side +\pagenumbering{gobble} +\cleardoublepage + +\noindent\textbf{Title:} Repeat the title here\\ % Otsikko / Titel +\textbf{Author:} Your name here\\ % Tekijä / Författare +\textbf{Month and year:} Month and year of submission\\ % Aika / Datum +\textbf{Page count:} \pageref*{LastPage}~pp.\\[1em] % Sivumäärä: XX~s. / Sidoantal: XX~s. +% The page count is updated automatically, but it might require two compilations to be correct. +% If you customize the backmatter, this might become incorrect - check and correct manually if needed. + +% If you include an abstract in a different language, wrap it in a foreignlanguage block +\begin{foreignlanguage}{english} +\noindent\textbf{Abstract:}\\ % Tiivistelmä / Referat +The abstract should be about one page long. +It also doubles as the maturity test. +Do not use mathematical notation in the abstract, +since it will also be displayed on the electronic thesis repository. + +For the publication date, put in the month and year of submission of the finished thesis. +Also include 3~to 5~keywords that support searching for your thesis. +They are also shown one the repository page. + +You can include the abstract in more than one language by copying and modifying +this code between comment blocks. +To get correct hyphenation for the language (and not with the rules of the main language), +put the text in a \verb|foreignlanguage| block as shown in the code +(just modify the language parameter to match the abstract). +\end{foreignlanguage} + + +\vfill + +\noindent\textbf{Keywords:} Fill in some keywords, Separated by commas % Avainsanat / Nyckelord + + + + +% +% TABLE OF CONTENTS +% +\cleardoublepage +\tableofcontents + + +% +% MAIN TEXT STARTS HERE +% + +% The \pagenumbering{arabic} command must be immediately after the first chapter title. +% Do not repeat it for other chapters. +\chapter{Introduction} +\pagenumbering{arabic} + +\section{Compiling the document} + +Depending on the language of your thesis, pass the correct option to the +\verb|\usepackage{babel}| command in the preamble. +This package changes all the built-in words (like \emph{Bibliography}) to the specified language. + +If possible, you should use either the LuaLaTeX or XeLaTeX compiler to produce the PDF file. +You can change the compiler in the settings of your \LaTeX{} editor. +(In Overleaf, this setting is in the menu at the upper-left corner of screen.) + +These compilers have better Unicode support than the old pdfLaTeX compiler, +and any future accessibility improvements will depend on these compilers. +If you use them, comment out the \verb|\usepackage{fontenc}| line +from the beginning of the document. + + +The bibliography is produced by a program called Biber. +Overleaf handles this automatically. +You can edit the \verb|.bib| source file for bibliography entries either manually% +\footnote{See Section~2 of the biblatex documentation at \url{https://ctan.org/pkg/biblatex} +for more information on the syntax. +The documentation also explains customization of the bibliography and citation styles.} +or export the file from a reference management program like Zotero. + + + +\section{Figures and tables} + +\LaTeX{} automatically ``floats'' figures and tables into a suitable position, +usually at the top of current or next page. +It is usually best to let the algorithm do its thing; +any manual tweaks are likely to break if the layout changes even by a tiny bit. + +To create a figure, you can use the \verb|figure| environment. +You can create a cross-reference point (like Figure~\ref{fig:university logo}) +by adding a label after the caption. +Note that the cross-reference above is clickable +-- this feature is provided by the `hyperref' package. + +\begin{figure} +\centering +\includegraphics[width=0.4\textwidth]{HYlogo.pdf} +\caption{The emblem of University of Helsinki. +As it is a trademark of the university, its use is governed by some restrictions.} +\label{fig:university logo} +\end{figure} + +To create subfigures as in Figure~\ref{fig:subfigures}, +you can use the `subcaption' package. +It is possible to create subfigure references like Figure~\ref{sub} +by placing the label inside the subcaption definition. +(You can also create automatic, clickable references to the subfigure letter, like (\subref{sub})). + +\begin{figure} +\centering + +\subcaptionbox{The university logo.\label{sub}}{\includegraphics[width=0.3\textwidth]{HYlogo.pdf}} +\subcaptionbox{Made a bit bigger.}{\includegraphics[width=0.4\textwidth]{HYlogo.pdf}} +\subcaptionbox{And a bit smaller.}{\includegraphics[width=0.2\textwidth]{HYlogo.pdf}} +\subcaptionbox{This goes on a new row.}{\includegraphics[width=0.2\textwidth]{HYlogo.pdf}} + +\caption{The subfigures are automatically placed in a grid. +Manual break points can be created with empty lines.} +\label{fig:subfigures} +\end{figure} + +If you need to place a picture inline with text, +you can also do so, but then the picture is not numbered (and it might cause ugly page breaking). +Here the feature is illustrated with a simple diagram using the 'tikz' package. +TikZ is an extremely powerful package for making diagrams. +You can find a lot of examples online. + +\begin{center} +\begin{tikzpicture} + +\node[draw] (A) at (0,0) {Find supervisor}; +\node[draw] (B) at (4,0) {Write thesis}; +\node[draw] (C) at (7.5,0) {Profit!}; + +\draw[->] (A.east) -- (B.west); +\draw[->] (B.east) -- (C.west); + +\end{tikzpicture} +\end{center} + + +Like figures, there are also floating environments for tables. +Tables are numbered in their own sequence (like Table~\ref{tbl:theses}) by default. +Table contents are set with a \verb|tabular| environment. + +\begin{table} +\centering +\begin{tabular}{r|lcc} +Dissertation & Shorthand & Typical length & Credits\\ +\hline +Bachelor's & BSc & 10--20 pages & 6~cr\\ +Master's & MSc & 30--50 pages & 30~cr\\ +Doctoral & PhD & 3 articles + intro & N/A +\end{tabular} +\caption{Various academic dissertations in mathematics.} +\label{tbl:theses} +\end{table} + +For better automatic handling of cross-references (although only in English-language text), +you can look at the `cleveref' package\footnote{\url{https://ctan.org/pkg/cleveref}}. + + + +\section{Mathematics} + +This example equation illustrates some custom commands defined in the document preamble: +\begin{equation}\label{eq:example} +\int_0^{2\pi} \sin(x + k\pi) \dx = -\sij{0}{2\pi} \cos(x) = 0, +\quad k \in \ZZ. +\end{equation} +In particular, the \verb|\dx| command ensures good spacing (and upright `d') of $\dx$ within the integral. +(The middle notation is only used in Finland.) + +To create an unnumbered display equation like +\[ +a^2 + b^2 = c^2, +\] +use the \verb|\[ \]| syntax or \verb|equation*| environment. +The old \TeX{} syntax \verb|$$ $$| is not fully compatible +with modern \LaTeX{} enhancements. + +Remember that equations are part of text, +so you should put punctuation (like \verb|.| and \verb|,|) +inside equation environments if necessary. +For inline mathematics like $a^2 + b^2$, keep the punctuation outside the dollar signs. +Do not put empty lines around equation environments unless +there is supposed to be a paragraph break. + +\bigskip + +To find a particular mathematical symbol, +the Detexify tool\footnote{\url{https://detexify.kirelabs.org/}} is super useful. +It lets you draw a symbol, and suggests similar symbols from base \LaTeX{} and common packages. +Common symbols are also listed in the mathematics section of +\LaTeX{} Wikibook\footnote{\url{https://en.wikibooks.org/wiki/LaTeX/Mathematics}}. + +Equations are numbered within chapter by default. +They too can be cross-referenced, like \eqref{eq:example}. +There are several other equation environments, like the one that aligns lines +(each line is numbered except for one, and one of them has a special name): +\begin{align} +\left( \sum_{k=0}^2 a^{2-k} b^k \right) (a-b) +&= (a^2 + ab + b^2) (a - b) \label{eq:second}\\ +&= a^3 - a^2 b + a^2 b - ab^2 + b^2 a - b^3 \label{eq:third}\\ +&= a^3 - (a^2 b - a^2 b) - (ab^2 - a b^2) - b^3 \notag\\ +&= a^3 - b^3. \tag{AB}\label{eq:AB} +\end{align} +The lines can be referred to as \eqref{eq:second}, \eqref{eq:third}, and \eqref{eq:AB}. + + +\section{Theorems, definitions, and proofs} + +The preamble defines some theorem-like environments with different styles. +You can create more such environments and change their names by modifying the code there. + +These environments are numbered within chapter and section. +If you'd prefer to not reset the numbering in each section +(that is, Definition~1.1 instead of Definition~1.4.1), +you can change the indicated line in the preamble. + +\begin{definition} +A triple $(a, b, c)$ of positive integers is called \emph{Pythagorean} if $a^2 + b^2 = c^2$. +\end{definition} + +It is possible to give a name to such a block. + +\begin{lemma}[A very silly lemma] +There exists at least one Pythagorean triple. +\end{lemma} +\begin{proof} +Pick $(a, b, c) = (3, 4, 5)$. +\end{proof} + +If you want the block name to refer to a result in a published work, +you need to wrap the citation command in \verb|{{}}|. +This is due to some unfortunate \TeX nical details. + +\begin{theorem}[{{\cite[Theorem~0.5]{wiles}}}] +There does not exist a triple $(a, b, c)$ of positive integers such that $a^3 + b^3 = c^3$. +\end{theorem} +\begin{proof} +Left as an exercise to the reader. +\end{proof} + +\begin{remark} +The last proof was a joke. +\end{remark} + + + +\section{Citing literature} + +Use the \verb|\cite| command to cite entries from the \verb|.bib| file, +like \cite{analyysia}. +You can also use an optional argument to cite a specific part, like \cite[p.~20]{analyysia}. + +Only cited entries are included in the final bibliography. +To force the inclusion of all entries (for testing purposes!), +you can add \verb|\nocite{*}| somewhere in the code. +\nocite{*} + +Refer to the biblatex documentation \cite{biblatex} +for changing the appearance of citations and the bibliography. +The \verb|.bib| file attached to this template shows the basic elements +of various entry types. + +Reference management programs like Zotero support exporting \verb|.bib| files. +You can also download citations from \mbox{zbMATH}, Google~Scholar, and most journals +directly in \verb|.bib| format. + +One more note: Some bibliography styles may change the capitalization of words. +Use \verb|{}| to protect specific words from this behaviour, +like \verb|{Fermat's}| in the entry for \cite{wiles}. + + + + +% +% BIBLIOGRAPHY +% +% The [heading=bibintoc] option adds the bibliography to table of contents +\printbibliography[heading=bibintoc] + + + + +% +% APPENDICES (if necessary) +% +\appendix + +\chapter{Some more information} + +If you need to have appendices in your thesis, +you can write them as usual chapters after the \verb|\appendix| command. +Appendices are numbered alphabetically. + +\end{document} diff --git a/template/thesis-refs.bib b/template/thesis-refs.bib new file mode 100644 index 0000000..902fe56 --- /dev/null +++ b/template/thesis-refs.bib @@ -0,0 +1,45 @@ +@article{wiles, + author = {Wiles, Andrew}, + title = {Modular Elliptic Curves and {Fermat's} Last Theorem}, + journal = {Annals of Mathematics}, + year = {1995}, + volume = {141}, + issue = {3}, + pages = {443--551}, + doi = {10.2307/2118559} +} + +@book{analyysia, + author = {Harjulehto, Petteri and Klèn, Riku and Koskenoja, Mika}, + title = {Analyysiä reaaliluvuilla}, + publisher = {Gaudeamus}, + year = {2023}, + edition = {Sixth, revised edition}, + note = {Previously published by Unigrafia} +} + +@unpublished{some-preprint, + author = {Aizenman, Michael and Duminil-Copin, Hugo}, + title = {Marginal triviality of the scaling limits of critical 4D {Ising} and {$\phi^4_4$} models}, + year = {2019}, + note = {arXiv preprint 1912.07973}, +} + +@inbook{book-chapter, + author = {Nonexistent, Nana}, + title = {A 3-page solution to the {Riemann} hypothesis}, + pages = {14--16}, + booktitle = {A compendium of invalid proofs}, + bookauthor = {Lastname, Firstname von}, + publisher = {Puuhamaa University Press}, + year = {2024}, +} + +@manual{biblatex, + author = {Kime, Philip and Wemheuer, Moritz and Lehman, Philipp}, + title = {The {\texttt{biblatex}} package}, + year = {2024}, + urldate = {2024-08-22}, + url = {https://ctan.org/pkg/biblatex}, + note = {Version~3.20}, +}