\documentclass[12pt]{article}

\usepackage[table,xcdraw]{xcolor}
\setlength{\headheight}{15pt}

\usepackage{multicol}

%% Flag 'syntax' causes the compiler to not render ANYTHING but just check syntax
\usepackage{syntonly}

\usepackage{enumitem} % for custom labels on enumerate (WARNING: plays badly with beamer)

%% Create an environment similar to choices in the exam document class.
\newenvironment{choices}
  {\begin{enumerate}[label=\Alph*), leftmargin=*, itemsep=0pt]}
  {\end{enumerate}}

%% For multiple choice questions
\newcommand{\choice}{\item}
\newcommand{\correctchoice}{\item}
\newcommand{\CorrectChoice}{\item}

\usepackage[top=1in, bottom=1in, left=0.5in, right=0.5in]{geometry}

\usepackage[utf8]{inputenc}
\usepackage[english]{babel}

\usepackage{caption}

\usepackage{luatex85} %% magic needed to get tikz to work: https://tex.stackexchange.com/a/501706
\usepackage[color,matrix,arrow]{xy}
\usepackage{tikz} %% for drawing circles

\usepackage[absolute,overlay]{textpos}
\usepackage{graphics,graphicx}
\usepackage{graphbox}
\usepackage{multirow}
\usepackage{amsmath,amssymb,amsthm}

\usepackage{pifont}
\newcommand{\xmark}{\ding{55}} %% to complement amssymb's \checkmark

\newcommand{\define}[1]{\textbf{#1}}

\DeclareMathOperator{\lcm}{lcm}

\usepackage{manfnt} %% for the dangerous bend symbol
\usepackage{bbding} %% for the \FiveStarConvex symbol
\usepackage{booktabs} %% for \midrule and invigilation

\usepackage{siunitx} %% for scientific units (needs texlive-science)

\usepackage{qrcode} %% for creating QR codes %% for creating QR codes
%% https://www.ctan.org/tex-archive/macros/latex/contrib/qrcode?lang=en
\newcommand{\qrurl}[1]{\qrcode{#1}\\\url{#1}}

\usepackage{systeme} %% for typesetting systems of linear equations 
%% https://ctan.org/pkg/systeme?lang=en

\usepackage{listings} %% for typesetting code listing
%% https://ctan.org/pkg/listings?lang=en

\usepackage{mathtools} %% for extenible long arrows (xlong arrows)
%% https://ctan.org/pkg/mathtools?lang=en

\usepackage{caption} %% for complicated figure
\usepackage{subcaption} %% with subfigures

\usepackage{cancel} %% for cancelling fraction

\usepackage{mathdots} %% for top-left to bottom-right dots \iddots

\usepackage{lipsum} %% provides lorem ipsum filler

\usepackage{tcolorbox}
\usepackage{color,soul}

\usepackage{hyperref}
\hypersetup{colorlinks=true,
linkcolor=blue,
urlcolor=blue,
hyperfootnotes=false
}

\usepackage{typed-checklist} %% for check lists

\usepackage{dashrule} %% for dashed and dotted rules



%% tk: shrink the emoji graphic
\newcommand{\EmojiRunner}{
\includegraphics[scale=0.02]{runner.png}
}

\usepackage{tcolorbox}
\usepackage{enumitem}

\newtcolorbox{activity}[1]{
colback=green!10!white,
colbacktitle=green!50,
coltitle=black,
fonttitle=\bfseries\Huge,
title=\EmojiRunner Activity: #1
}

\newtcolorbox{activebox}[1]{
colback=green!10!white,
colbacktitle=green!50,
coltitle=black,
fonttitle=\bfseries\Huge,
title=\EmojiRunner Activity: #1
}

\newtcolorbox{example}[1]{
colframe=black!50,
colback=red!10!white,
colbacktitle=red!50,
coltitle=black,
fonttitle=\bfseries\large,
title=Example: #1
}

\newtcolorbox{examplebox}[1]{
colframe=black!50,
colback=red!10!white,
colbacktitle=red!50,
coltitle=black,
fonttitle=\bfseries\large,
title=Example: #1
}

%% box-testing
\newtcolorbox{question}[1]{
colframe=black!50,
colback=red!10!white,
colbacktitle=red!50,
coltitle=black,
fonttitle=\bfseries\large,
title=Question: #1
}

\newtcolorbox{theorembox}[1]{
colframe=black!50,
colback=blue!10!white,
colbacktitle=blue!40,
coltitle=black,
fonttitle=\bfseries\large,
title=Theorem: #1
}

\newtcolorbox{defnbox}[1]{
colframe=black!50,
colback=blue!10!white,
colbacktitle=blue!40,
coltitle=black,
fonttitle=\bfseries\large,
title=Definition: #1
}

%% box-testing
\newtcolorbox{definition}[1]{
colframe=black!50,
colback=blue!10!white,
colbacktitle=blue!40,
coltitle=black,
fonttitle=\bfseries\large,
title=Definition: #1
}

\newtcolorbox{generalbox}[1]{
colframe=black!50,
colback=blue!10!white,
colbacktitle=blue!40,
coltitle=black,
fonttitle=\bfseries\large,
title=#1
}

\newtcolorbox{remarkbox}[1]{
colframe=black!20,
colback=black!10,
coltitle=black,
fonttitle=\bfseries\large,
title=Remark: #1
}

\usepackage{fancyhdr}

\newcommand{\DocumentVersion}{Version: 1.0}
\newcommand{\CourseTerm}{Winter 2025}
\newcommand{\ClassSection}{LEC 01}
\newcommand{\CourseTitle}{MAT XYZ}
\newcommand{\CourseAuthor}{Felix Clousseau}

\pagestyle{fancy}

\fancyhf{}
%% RE = right on even pages
\fancyhead[RE,RO]{\CourseTerm\ \ClassSection}
\fancyhead[LE,LO]{\CourseTitle : Week \thesection}
\fancyfoot[CE,CO]{p. \thepage}
\fancyfoot[RE,RO]{\DocumentVersion}
\fancyfoot[LE,LO]{
\copyright\ \CourseAuthor\ (\CourseTerm)\\
}
\renewcommand{\headrulewidth}{2pt}
\renewcommand{\footrulewidth}{1pt}

%% Use a hack to make sections in to weeks
\usepackage{titlesec}

\titleformat{\section}{\normalfont\large\bfseries}{Week \thesection:}{1em}{}

\renewcommand{\thesubsection}{\thesection \Alph{subsection}:}

\begin{document}

\section{Welcome to the Course}
\begin{remarkbox}{What's The Point of This Course?}
	This course is supposed to be \emph{fun} and \emph{magical}.
	The purpose of this class is to expose you to some cool mathematics,
	make math less scary,
	and develop your ability to present ideas in public.
\end{remarkbox}

\begin{activebox}{The Birthday Circle}
	Everyone arrange yourselves in a big circle
	according to your date of birth.
\end{activebox}

\newpage
\begin{defnbox}{Sets}
	A \define{set} is a collection of elements.
	For example,
	\[
	S = \{1, 2, 3\}
	\]
	contains the numbers $1,2,3$.
	The \define{empty set} contains nothing $\emptyset = \{ \}$.
	We write $x \in S$ to denote \define{$x$ is an element of $S$}.
	We can write some sets explicitly by listing all their elements.
	We can also use \define{set builder notation} such as:
	\[
	S = \{ n : \text{$n$ is even} \} = \{\dots, -4, -2, 0, 2, 4, \dots \}.
	\]
\end{defnbox}

\begin{examplebox}{Operations on Sets}
	Suppose that $S = \{1, 2, 3, 4\}$ and $T = \{3, 4, 5, 6\}$.\\
	Write $S \cap T$, $S \cup T$, and $S \setminus T$ explicitly as lists of elements.
\end{examplebox}

\newpage
\begin{remarkbox}{Multiple Choice Questions}
	Our term tests and final exam will be entirely multiple choice.
	Answering multiple choice questions (MCQs) is a skill.
	We're going to do a bunch of practice of answering MCQs in class.
\end{remarkbox}

\begin{examplebox}{Multiple Choice Questions}
	Let $A = \{2,4,6\}$. Which statement is true?
	\begin{choices}
		\choice $3 \in A$
		\choice $\{2\} \in A$
		\correctchoice $4 \in A$
		\choice $A \in 4$
	\end{choices}
\end{examplebox}

\newpage
\begin{theorembox}{$\sqrt{2}$ Is Irrational}
	The square root of two is irrational. 
	Formally, there is no rational number $a/b$ so that $(a/b)^2 = 2$.
\end{theorembox}

\end{document}
\endinput
