% use [nosolutions] flag to hide solutions.
% use [solutions] flag to show solutions.
\documentclass[
	solutions,
	singlenumbering,
	shortwarning,
	unfinished
]{../../resources/ormc_handout}
\usepackage{../../resources/macros}

\usepackage{units}

\uptitlel{Advanced 2}
\uptitler{Fall 2023}
\title{Quotient Groups}
\subtitle{Prepared by \githref{Mark} on \today{}}


\def\znz#1{\nicefrac{\mathbb{Z}}{#1\mathbb{Z}}}

\begin{document}

	\maketitle

	\input{parts/0 mod}
	\input{parts/1 groups}
	\input{parts/2 subgroups}


	% Rough outline:
	%
	% Part 1: (DONE)
	% mod, eqrel, eqclass.
	%
	% Part 2: (IN PROGRESS)
	% groups, Z/nZx, graphs, isomorphism.
	%   generators, generating sets.
	%
	% Part 3: (IN PROGRESS)
	% subgroups, isomorphic subgroups,

	% TODO:
	%
	% cosets
	% normal subgroups
	% quotient groups
	% Understand Z/nZ
	% Functions as objects (groups of functions)
	% Q/Z problems (mod generalization)
	% isomorphism groups (which are iso to symmetric group)


	% Another handout:
	%
	% symmetric group, number of permutations,
	% cycle notation, type and sign,
	% proofs about generators, alternating group
	% alternating group generators, fun problems.

\end{document}
