%% ----------------------------------------
%%
%% NYU PhD thesis template.
%% Created by José Koiller 2007--2008.
%% Modified by Siddharth Krishna, 2019.
%%
%% ----------------------------------------
%% Use the first of the following lines during production to
%% easily spot "overfull boxes" in the output. Use the second
%% line for the final version.
%\documentclass[12pt,draft,letterpaper]{report}
\documentclass[12pt,oneside,letterpaper]{report}
% ----------------------------------------
% Macro to switch between draft version and final version
% ----------------------------------------
% Use or comment this to enable/disable draft version
% \def\draftversion{}
\newcommand{\draftfinal}[2]{\ifdefined\draftversion#1\else#2\fi}
\newcommand{\draftonly}[1]{\draftfinal{#1}{}}
\newcommand{\finalonly}[1]{\draftfinal{}{#1}}
% ----------------------------------------
% Thesis metadata
% ----------------------------------------
%% Replace the title, name, advisor name, graduation date and dedication below
%% with your own. Graduation months must be January, May or September.
\newcommand{\thesistitle}{On Complete Systems of Invariants for Ternary Biquadratic Forms}
\newcommand{\thesisauthor}{Amalie Emmy Noether}
\newcommand{\thesisadvisor}{Professor Paul Gordan}
\newcommand{\thesisdept}{Mathematics}
\newcommand{\gradmonth}{September}
\newcommand{\gradyear}{2019}
%% If you do not want a dedication, scroll down and comment out
%% the appropriate lines in this file.
\newcommand{\thesisdedication}{To my dog Weierstra\ss, with affection.}
% ----------------------------------------
% Layout and formatting
% ----------------------------------------
% Uncomment to get a big black box to spot "overfull hboxes"
% \setlength{\overfullrule}{5pt}
%% Page layout (customized to letter paper and NYU requirements):
\RequirePackage[margin=1in, includefoot, letterpaper]{geometry}
%% Color definitions:
\RequirePackage[prologue]{xcolor}
\definecolor[named]{ThesisBlue}{cmyk}{1,0.1,0,0.1}
\definecolor[named]{ThesisYellow}{cmyk}{0,0.16,1,0}
\definecolor[named]{ThesisOrange}{cmyk}{0,0.42,1,0.01}
\definecolor[named]{ThesisRed}{cmyk}{0,0.90,0.86,0}
\definecolor[named]{ThesisLightBlue}{cmyk}{0.49,0.01,0,0}
\definecolor[named]{ThesisGreen}{cmyk}{0.20,0,1,0.19}
\definecolor[named]{ThesisPurple}{cmyk}{0.55,1,0,0.15}
\definecolor[named]{ThesisDarkBlue}{cmyk}{1,0.58,0,0.21}
% School color found from university's graphic identity site:
% http://www.nyu.edu/employees/resources-and-services/media-and-communications/styleguide.html
\definecolor{SchoolColor}{rgb}{0.3412, 0.0235, 0.5490} % purple
\definecolor{chaptergrey}{rgb}{0.2600, 0.0200, 0.4600} % dialed back a little
\definecolor{midgrey}{rgb}{0.4, 0.4, 0.4}
\usepackage{hyperref}
\hypersetup{colorlinks,
linkcolor=ThesisDarkBlue,
citecolor=ThesisPurple,
urlcolor=ThesisDarkBlue,
filecolor=ThesisDarkBlue}
%% Captions of Figures, tables
\RequirePackage[labelfont={bf,sf,small,singlespacing},
textfont={sf,small,singlespacing},
% justification={justified,RaggedRight},
% singlelinecheck=false,
margin=0pt,
figurewithin=chapter,
tablewithin=chapter]{caption}
%% Chapter headings, captions
\usepackage{fix-cm}
\RequirePackage[raggedright,sc]{titlesec}
\definecolor{gray75}{gray}{0.75}
\newcommand{\hsp}{\hspace{20pt}}
\titleformat{\chapter}[hang]
{\Huge\sc}
{\textcolor{SchoolColor}{\thechapter}\hsp\textcolor{gray75}{|}\hsp}
{0pt}{\Huge\sc\raggedright}
% [\textcolor{gray75}{|}\hsp\textcolor{SchoolColor}{\thechapter}]
%% The following makes chapters and sections, but not subsections,
%% appear in the TOC (table of contents). Increase to 2 or 3 to
%% make subsections or subsubsections appear, respectively. It seems
%% to be usual to use the "1" setting, however.
\setcounter{tocdepth}{2}
%% Sectional units up to subsubsections are numbered. To number
%% subsections, but not subsubsections, decrease this counter to 2.
\setcounter{secnumdepth}{3}
%% Use the following commands, if desired, during production.
%% Comment them out for final version.
%\usepackage{layout} % defines the \layout command, see below
%\setlength{\hoffset}{-.75in} % creates a large right margin for notes and \showlabels
%% Controls spacing between lines (\doublespacing, \onehalfspacing, etc.):
\usepackage{setspace}
%% Use the line below for official NYU version, which requires
%% double line spacing. For all other uses, this is unnecessary,
%% so the line can be commented out.
\finalonly{
\doublespacing % requires package setspace, invoked above
}
%% For generating sample text.
%% Can be removed when you've replaced all \lipsum commands with your text.
\usepackage{lipsum}
% ----------------------------------------
% Comments and TODOs:
% ----------------------------------------
% Uncomment this to remove all comments
\newcommand{\nocomments}{}
% Uncomment this to remove all TODOs
\newcommand{\notodos}{}
% Comments and TODOs
\newcommand{\fcomment}[2]{\ifdefined\nocomments{}\else\footnote{\textcolor{red}{#1:} #2}\fi}
\newcommand{\todo}[1]{\ifdefined\notodos{}\else\textcolor{red}{TODO\ifstrempty{#1}{}{: #1}}\fi}
\newcommand{\ftodo}[1]{\ifdefined\notodos{}\else\fcomment{TODO}{#1}\fi}
% Author comments:
\newcommand{\aen}[1]{\fcomment{Emmy}{#1}}
% ----------------------------------------
% User-specific packages and macros
% ----------------------------------------
%% This inputs your auxiliary file with \usepackage's and \newcommand's:
%% It is assumed that that file is called "defs.tex".
\input{defs}
% ----------------------------------------
% Document header
% ----------------------------------------
%% Cross-referencing utilities. Use one or the other--whichever you prefer--
%% but comment out both lines for final version.
%\usepackage{showlabels}
%\usepackage{showkeys}
\begin{document}
%% Produces a test "layout" page, for "debugging" purposes only.
%% Comment out for final version.
%\layout % requires package layout (see above, on this same file)
%%%%%% Title page %%%%%%%%%%%
%% Sets page numbering to "roman style" i, ii, iii, iv, etc:
\pagenumbering{roman}
%
%% No numbering in the title page:
\thispagestyle{empty}
%
\vspace*{25pt}
\begin{center}
{\Large
\begin{doublespace}
{\textcolor{SchoolColor}{\textsc{\thesistitle}}}
\end{doublespace}
}
\vspace{.7in}
by
\vspace{.7in}
\thesisauthor
\vfill
\begin{doublespace}
\textsc{
A dissertation submitted in partial fulfillment\\
of the requirements for the degree of\\
Doctor of Philosophy\\
Department of \thesisdept\\
New York University\\
\gradmonth, \gradyear}
\end{doublespace}
\end{center}
\vfill
\noindent\makebox[\textwidth]{\hfill\makebox[2.5in]{\hrulefill}}\\
\makebox[\textwidth]{\hfill\makebox[2.5in]{\hfill\thesisadvisor}}
\newpage
%%%%%%%%%%%%% Copyright page %%%%%%%%%%%%%%%%%%
\thispagestyle{empty}
\vspace*{25pt}
\begin{center}
\scshape \noindent \small \copyright \ \small \thesisauthor \\
all rights reserved, \gradyear
\end{center}
\vspace*{0in}
\newpage
%%%%%%%%%%%%%% Dedication %%%%%%%%%%%%%%%%%
%% Comment out the following lines if you do not want to dedicate
%% this to anyone...
\cleardoublepage
\phantomsection
\addcontentsline{toc}{chapter}{Dedication}
\vspace*{\fill}
\begin{center}
\thesisdedication
\end{center}
\vfill
\newpage
%%%%%%%%%%%%%% Acknowledgements %%%%%%%%%%%%
%% Comment out the following lines if you do not want to acknowledge
%% anyone's help...
\chapter*{Acknowledgements}
\addcontentsline{toc}{chapter}{Acknowledgments}
% \input{acknowledge}
\lipsum[1-2]
\newpage
%%%% Abstract %%%%%%%%%%%%%%%%%%
\chapter*{Abstract}
\addcontentsline{toc}{chapter}{Abstract}
\input{abstract}
\newpage
%%%% Table of Contents %%%%%%%%%%%%
\tableofcontents
%%%%% List of Figures %%%%%%%%%%%%%
%% Comment out the following two lines if your thesis does not
%% contain any figures. The list of figures contains only
%% those figures included within the "figure" environment.
\cleardoublepage
\phantomsection
\addcontentsline{toc}{chapter}{List of Figures}
\listoffigures
\newpage
%%%%% List of Tables %%%%%%%%%%%%%
%% Comment out the following two lines if your thesis does not
%% contain any tables. The list of tables contains only
%% those tables included within the "table" environment.
\cleardoublepage
\phantomsection
\addcontentsline{toc}{chapter}{List of Tables}
\listoftables
\newpage
%%%%% Body of thesis starts %%%%%%%%%%%%
\pagenumbering{arabic} % switches page numbering to arabic: 1, 2, 3, etc.
% ----------------------------------------
% Body of Thesis
% ----------------------------------------
\chapter{Introduction}
\label{chp-introduction}
% \input{introduction}
% Sample content:
\lipsum[1-2]
\begin{figure}
\centering
\begin{tikzpicture}[scale=3]
\draw[step=.5cm, gray, very thin] (-1.2,-1.2) grid (1.2,1.2);
\filldraw[fill=green!20,draw=green!50!black] (0,0) -- (3mm,0mm) arc (0:30:3mm) -- cycle;
\draw[->] (-1.25,0) -- (1.25,0) coordinate (x axis);
\draw[->] (0,-1.25) -- (0,1.25) coordinate (y axis);
\draw (0,0) circle (1cm);
\draw[very thick,red] (30:1cm) -- node[left,fill=white] {$\sin \alpha$} (30:1cm |- x axis);
\draw[very thick,blue] (30:1cm |- x axis) -- node[below=2pt,fill=white] {$\cos \alpha$} (0,0);
\draw (0,0) -- (30:1cm);
\foreach \x/\xtext in {-1, -0.5/-\frac{1}{2}, 1}
\draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north,fill=white] {$\xtext$};
\foreach \y/\ytext in {-1, -0.5/-\frac{1}{2}, 0.5/\frac{1}{2}, 1}
\draw (1pt,\y cm) -- (-1pt,\y cm) node[anchor=east,fill=white] {$\ytext$};
\end{tikzpicture}
\caption{A pictorial view of \refThm{thm-pythagorean}.}
\label{fig-pythagorean}
\end{figure}
\begin{definition}
A function $f$ is said to be \emph{continuous} if its derivative exists at every point.
\end{definition}
\begin{lemma}
Let $f$ be a function whose derivative exists in every point, then $f$ is
a continuous function.
\end{lemma}
\begin{theorem}[Pythagorean theorem]
\label{thm-pythagorean}
This is a theorema about right triangles and can be summarised in the next
equation
\[ x^2 + y^2 = z^2 \]
\end{theorem}
\begin{proof}
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
\end{proof}
And a consequence of \refThm{thm-pythagorean} is the statement in the next
corollary~\cite{lamport94}.
\begin{corollary}
There's no right rectangle whose sides measure 3cm, 4cm, and 6cm.
\end{corollary}
\lipsum[3-5]
\begin{table}
\centering
\caption{Predicted final standings of Group B.}
\begin{tabular}{l*{6}{c}r}
Team & P & W & D & L & F & A & Pts \\
\hline
Manchester United & 6 & 4 & 0 & 2 & 10 & 5 & 12 \\
Celtic & 6 & 3 & 0 & 3 & 8 & 9 & 9 \\
Benfica & 6 & 2 & 1 & 3 & 7 & 8 & 7 \\
FC Copenhagen & 6 & 2 & 1 & 3 & 5 & 8 & 7 \\
\end{tabular}
\label{tab-forecast}
\end{table}
\lipsum[5-7]
\chapter{Preliminaries}
\label{chp-preliminaries}
% \input{preliminaries}
\lipsum
\chapter{Proof of the Reimann Hypothesis}
\label{chp-proof}
% \input{proof}
\lipsum
\chapter{Conclusion}
\label{chp-conclusion}
% \input{conclusion}
\lipsum
%% If your thesis has different "Parts", use commands such as the following:
%\part{First Part\label{part:one}}%
% \input{chap1}
%\input{chap2} % further chapters -- change file names to meaningful things...
%\input{chap3}
%\part{Second Part\label{part:two}}%
%\input{chap4}
%\input{chap5}
%\input{chap6}
%%%%% Appendices start %%%%%%%%%%%%%%%%
%% Comment out the following if your thesis has no appendix
\appendix
\chapter{Appendix}
% \input{appendix}
\lipsum
%% Note: If your thesis has more than one appendix, NYU requires a "list of
%% appendices" page before the body of the thesis. I don't provide the tools
%% to create that here, so you're on your own for that one... Sorry.
%%%% Input bibliography file %%%%%%%%%%%%%%%
%% For computer science dissertations, I'd recommend using the bibly package
%% to automatically create the .bib file from your citations:
%% https://github.com/michael-emmi/bibly
\cleardoublepage
\phantomsection
\bibliographystyle{apalike}
\addcontentsline{toc}{chapter}{Bibliography}
% \bibliography{dblp,references}
% The following is just for the sample template,
% I'd recommend deleting this and using the \bibliography command above
\begin{thebibliography}{99}
\bibitem[Lamport, 1994]{lamport94}
Leslie Lamport,
\textit{\LaTeX: a document preparation system},
Addison Wesley, Massachusetts,
2nd edition,
1994.
\end{thebibliography}
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End: