\documentclass[titlepage]{book}
% PACKAGES
\usepackage[fontsize=13pt]{fontsize}
\usepackage{afterpage}
\usepackage{amsmath}
\usepackage[utf8]{inputenc}
\usepackage{chngcntr}
\usepackage{blindtext}
\usepackage[labelsep=space]{caption}
\usepackage{enumitem}
\usepackage{fancyhdr}
\usepackage[T1]{fontenc}
\usepackage[bottom=6.5em]{geometry}
\usepackage{graphicx}
\usepackage{gensymb}
\usepackage[hyperfootnotes=false,linktoc=page,pdfpagelayout=TwoPageRight]{hyperref}
\usepackage{lettrine}
\usepackage{cfr-lm}
\usepackage{makecell}
\usepackage{mathtools}
\usepackage{multicol}
\usepackage[defaultlines=4,all]{nowidow}
\usepackage{titlesec}
\usepackage{tocloft}
\usepackage{wrapfig}
\usepackage{lipsum}
\input{math_preamble}
% PAGE HEADERS
\let\Sectionmark\sectionmark
\def\sectionmark#1{\def\Sectionname{#1}\Sectionmark{#1}}
\let\Subsectionmark\subsectionmark
\def\subsectionmark#1{\def\Subsectionname{#1}\Subsectionmark{#1}}
\pagestyle{fancy}
\fancyhf{}
\fancyhead[LE]{\thepage}
\fancyhead[RE]{\Sectionname}
\fancyhead[LO]{\MakeUppercase{\Subsectionname}}
\fancyhead[RO]{\thepage}
\renewcommand{\headrulewidth}{0pt}
% GRAPHICS
\graphicspath{ {./images/} }
% SECTION FORMAT
\counterwithout{subsection}{section}
\renewcommand{\thesection}{PART \Roman{section}}
\renewcommand{\thesubsection}{\Roman{subsection}}
\renewcommand{\thesubsubsection}{\Roman{subsubsection}}
\newcommand{\subsectionbreak}{\newpage}
\titleformat{\section}[display]{\Large\bfseries\filcenter}{\thesection}{.5em}{}
\titleformat{\subsection}[display]{\large\bfseries\filcenter}{\thesubsection}{0em}{\uppercase}
\counterwithin*{footnote}{page}
% FIGURES
\renewcommand{\thefigure}{\roman{figure}}
\renewcommand{\figurename}{\textsc{Fig.}}
\newcommand{\fig}[3]{
\begin{figure}[h]
\centering
\includegraphics[width=\linewidth]{#1}
\textbf{\caption{#2}}
\label{fig:#3}
\end{figure}
}
% EQUATIONS
\newcommand{\eq}[1]{
\begin{equation*}
\begin{split}
#1
\end{split}
\end{equation*}
}
\newcommand{\eqnum}[1]{
\begin{equation}
\begin{split}
#1
\end{split}
\end{equation}
}
% OLDSTYLENUMS
\DeclareMathSymbol{0}{\mathalpha}{letters}{`0}
\DeclareMathSymbol{1}{\mathalpha}{letters}{`1}
\DeclareMathSymbol{2}{\mathalpha}{letters}{`2}
\DeclareMathSymbol{3}{\mathalpha}{letters}{`3}
\DeclareMathSymbol{4}{\mathalpha}{letters}{`4}
\DeclareMathSymbol{5}{\mathalpha}{letters}{`5}
\DeclareMathSymbol{6}{\mathalpha}{letters}{`6}
\DeclareMathSymbol{7}{\mathalpha}{letters}{`7}
\DeclareMathSymbol{8}{\mathalpha}{letters}{`8}
\DeclareMathSymbol{9}{\mathalpha}{letters}{`9}
% REFERENCES
\hypersetup{
colorlinks=false,
linkbordercolor={0 0 0},
pdfborderstyle={/S/U/W 0.0}
}
\newcommand{\secref}[1]{\hyperref[sec:#1]{Section #1}}
\newcommand{\figref}[1]{\hyperref[fig:#1]{Fig. #1}}
% LARGE FIRST LETTER OF SECTION
\newcommand{\firstword}[2]{
\lettrine[lines=3,nindent=0em,findent=0.5em,realheight]{#1}{#2}
}
% TABLE OF CONTENTS FORMAT
\renewcommand{\contentsname}{CONTENTS}
\renewcommand{\cfttoctitlefont}{\hfil\bfseries\fontsize{15pt}{0pt}\selectfont}
\renewcommand{\cftaftertoctitleskip}{0.5\baselineskip}
\renewcommand{\cftsecfont}{\bfseries}
\addtolength{\cftsecnumwidth}{40pt}
\addtolength{\cftsubsecnumwidth}{10pt}
\setlength{\cftbeforetoctitleskip}{-3em}
\setcounter{tocdepth}{4}
\setcounter{secnumdepth}{4}
% TITLE SETUP
\title{\textbf{\huge{Title}\\\Large{Primary Author}}}
\author{
Secondary Author
\and
Tertiary Author
}
\date{}
% MISC
\newcommand{\aether}[0]{\ae ther}
\newcommand{\letlist}[1]{
\begin{enumerate}[label=(\emph{\alph*})]
#1
\end{enumerate}
}
% DOCUMENT
\begin{document}
% TITLE
\maketitle
% PREFACE
\begin{center}
\textbf{\Large{PREFACE}}
\end{center}
\firstword{T}{his} is a preface! \lipsum[1]
\vspace{\baselineskip}
\textit{Some Left Text, (Maybe a Date)} \hfill PREFACE AUTHOR
% TABLE OF CONTENTS
\pagenumbering{gobble}
\pagestyle{empty}
\newgeometry{bottom=6em}
\renewcommand{\baselinestretch}{0.94}\normalsize
\tableofcontents
\renewcommand{\baselinestretch}{1.0}\normalsize
\restoregeometry
\pagestyle{fancy}
\clearpage
% CONTENTS
\pagenumbering{arabic}
\section{PART TITLE}
\subsection{CHAPTER TITLE} \label{sec:I}
\firstword{M}{ore} big letter text. \lipsum[5]
Lettered List:
\letlist{
\item \lipsum[1]
\item \lipsum[2-2]
\item \lipsum[3-3]
}
\subsection{NEXT CHAPTER TITLE}
\firstword{H}{ere} is an example of a chapter reference: \secref{I}. \lipsum[1]
\lipsum[2-2] \textbf{An example of a centered equation:} \[
t' = \frac{t - \frac{v}{c^2}x}{\sqrt{1 - \frac{v^2}{c^2}}}
\]
\lipsum[3-3] \textbf{An example of an inline equation:} $x = -\frac{\pm \sqrt{b^2 - 4ac}}{2a}$ \lipsum[4-4]. \textbf{Now we have a footnote}\footnote{Hello! Example equations down here also: $\ham \psi = \hat{E}\psi$.}.
An example figure: \fig{fig1}{An Example Figure Caption}{i}
If I want to reference it, \figref{i}.
Unnumbered equations:\eq{
x = y \\
y = z \\
x = z \\
}
Numbered group of equations:\eqnum{
a = b \\
b = c \\
a = c \\
}
\end{document}