YAlg3.tex

%!TEX TS-program = xelatex
%!TEX encoding = UTF-8

% To be compiled by XeLaTeX, preferably under TeX Live.
% LaTeX source for ``Yanqi Lake Lectures on Algebra'' Part III.
% Copyright 2019  李文威 (Wen-Wei Li).
% Permission is granted to copy, distribute and/or modify this
% document under the terms of the Creative Commons
% Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)
% https://creativecommons.org/licenses/by-nc/4.0/

% The document is based on the standard book class.
\documentclass[a4paper,12pt]{book}
\usepackage[backend=biber, hyperref=auto, backref=true]{biblatex}

\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}

% Indexing via imakeidx + xindy
\usepackage[xindy]{imakeidx}
\makeindex[columns=2, program=truexindy, intoc=true, options=-M texindy -I xelatex -C utf8, title={Index}]

% Hyperref set-up
\usepackage[unicode, colorlinks]{hyperref}
\hypersetup{
	linkcolor = blue,
	citecolor = red,
	urlcolor = teal,
	bookmarksnumbered = true,
	pdfauthor = {Wen-Wei Li},
	pdftitle = {Yanqi Lake Lectures on Algebra: Part 3}
}

% Overall font set-up
\usepackage{fontspec}
\usepackage{unicode-math}
\setromanfont{TeX Gyre Pagella}
\setsansfont{TeX Gyre Heros Cn}
\setmathfont[math-style=ISO, bold-style=ISO]{texgyrepagella-math.otf}

% Make \today print yyyy-mm-dd
\usepackage[iso, english]{isodate}

\def\CoverPage{Cover-page.pdf}	% Cover page to be included (here: a PDF file)


% Change the geometry if need be
\usepackage{geometry}
\geometry{
	paper=a4paper,
	top=3cm,
	inner=2.54cm,
	outer=2.54cm,
	bottom=3cm,
	headheight=6ex,
	headsep=6ex,
}

\usepackage{stmaryrd}
\usepackage{bbding}
\usepackage[nottoc]{tocbibind}
\usepackage{mathrsfs}
\usepackage[centercolon]{mathtools}
\usepackage[dvipsnames]{xcolor}
\usepackage{tikz-cd}
\usetikzlibrary{positioning, shapes.geometric, patterns, matrix, knots}

\usepackage{paralist}
\usepackage[figurewithin=none]{caption}
\usepackage{graphicx}

% Environments for theorems etc.
% I prefer linear ordering within sections.
\theoremstyle{plain}
\newtheorem{proposition}{Proposition}[section]
\newtheorem{lemma}[proposition]{Lemma}
\newtheorem{theorem}[proposition]{Theorem}
\newtheorem{corollary}[proposition]{Corollary}
\newtheorem{fact}[proposition]{Fact}
\theoremstyle{definition}
\newtheorem{definition}[proposition]{Definition}
\newtheorem{definition-theorem}[proposition]{Definition-Theorem}
\newtheorem{definition-proposition}[proposition]{Definition-Proposition}
\newtheorem{hypothesis}[proposition]{Hypothesis}
\newtheorem{example}[proposition]{Example}
\newtheorem{exercise}[proposition]{Exercise}
\theoremstyle{remark}
\newtheorem{remark}[proposition]{Remark}
\newtheorem{note}[proposition]{Note}
\newtheorem{notation}[proposition]{Notation}
\newtheorem{convention}[proposition]{Convention}
\newtheorem{conjecture}[proposition]{Conjecture}

% Customize the numbering of equations
\numberwithin{equation}{chapter}
\renewcommand{\theequation}{\thechapter--\arabic{equation}}

% Use the usual symbols for real and imaginary parts of a complex number
\renewcommand{\Re}{\operatorname{Re}}
\renewcommand{\Im}{\operatorname{Im}}

\renewcommand*\arraystretch{1.5} % Extra spacing in a table environment.

% Load custom commands
\usepackage{mycommand}
\usepackage{myarrows}

\usepackage{xstring}
\usepackage{pdfpages}

\usepackage{fancyhdr}
\newcommand\sectionname{\arabic{chapter}.\arabic{section}}
\pagestyle{fancy}
	\renewcommand{\chaptermark}[1]{\markboth{\scshape #1}{}}
	\renewcommand{\sectionmark}[1]{\markright{\S\sectionname\quad \scshape #1}}
	\fancyhf{} % delete current setting for header and footer
	\fancyhead[EC]{\footnotesize{\leftmark}\vspace{1mm}}
	\fancyhead[OC]{\footnotesize{\rightmark}\vspace{1mm}}
	\fancyhead[LE,RO]{$\cdot\;${\footnotesize \thepage}$\;\cdot$\vspace{1mm}} %
	\fancyhead[RE,LO]{}
	\renewcommand{\headrulewidth}{0.5pt}
	\renewcommand{\footrulewidth}{0pt}
	\addtolength{\headheight}{0.5pt}

\fancypagestyle{plain}{%
	\fancyhead{} % get rid of headers on plain pages
	\renewcommand{\headrulewidth}{0pt} % and the line
}

% Set up the chapter titles
\usepackage{titlesec}
\titleformat{\chapter}[display]
	{\filleft\normalfont\fontspec[Scale=2.5]{League Spartan}}
	{Lecture \thechapter}
	{10mm}
	{}[]

% Customize biblatex
\DeclareFieldFormat{postnote}{#1}	% Disable pagination in postnote for biblatex
\addbibresource{YAlg3.bib}

\begin{document}
	\frontmatter
	% Make the cover page by reading the file \CoverPage if it exists.
	\ifdefempty{\CoverPage}{%
		\relax
	}{%
		\pagestyle{empty}%	Clean-up the page style
		\renewcommand{\thepage}{C\arabic{page}}%	The page numbers here should start with "C" (PDF: logical page numbers)
		\IfEndWith{\CoverPage}{.pdf}{% If the file name ends with .pdf or .PDF, we include the PDF file directly.
			\includepdf{\CoverPage}
		}{%
			\IfEndWith{\CoverPage}{.PDF}{%
				\includepdf{\CoverPage}
			}{%
				\input{\CoverPage}		% Otherwise we import the TeX source
			}
		}%
		\pagestyle{fancy}		% Resume the page style to "fancy".
		\pagenumbering{roman}	% Resume the page numbers to roman style.
	}
	
	\begin{titlepage}
		\vspace*{\stretch{1}}
		\noindent\begin{center}\rule{\linewidth}{2pt}\end{center}	% Draw a rule
		\begin{center}
			\Huge \textbf{Yanqi Lake Lectures on Algebra}  \\ \vspace{1em}
			\Huge Part 3
		\end{center}
		\noindent\begin{center}\rule{\linewidth}{2pt}\end{center}	% Draw a rule
		\vspace{1em}
		\begin{center}
			{\Large Wen-Wei Li} \\ \vspace{1em}
			{\Large Chinese Academy of Sciences} \\ \vspace{1.5em}
		\end{center}
		\vfill
%		\begin{center} \href{http://www.ucas.edu.cn}{\includegraphics[height=40pt]{logo-UCAS.png}} \end{center}
	\end{titlepage}
	
	\newpage
	\thispagestyle{empty}
	\begin{center}
		\Large Version: \today
	\end{center}
	\vfill
	\begin{tabular}{p{.9\textwidth}}
		The cover page uses the fonts \textit{Bebas Neue} and \textit{League Gothique}, both licensed under the \href{https://opensource.org/licenses/OFL-1.1}{SIL Open Font License}. \\  \vspace{\baselineskip}
		This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. To view a copy of this license, visit \url{http://creativecommons.org/licenses/by-nc/4.0/}. \\
		\vspace{\baselineskip}
		\begin{center}
			\includegraphics[scale=1]{by-nc.eps}
		\end{center}\\
	\end{tabular}

	\tableofcontents

	\mainmatter
	\include{YAlg3-intro}
	\include{YAlg3-1}
	\include{YAlg3-2}
	\include{YAlg3-3}
	\include{YAlg3-4}
	\include{YAlg3-5}
	\include{YAlg3-6}
	\include{YAlg3-7}
	\include{YAlg3-8}

	\backmatter
	\printbibliography[heading=bibintoc]	% For Biber
	\printindex

\end{document}