\documentclass{amsart}
\usepackage{
  amsmath,
  amsfonts,
  amscd,
  amsthm,
  amssymb,
  color,
  enumerate    % Use [wide] option for non-indented lists
}

\usepackage[colorlinks=true, pdfstartview=FitH, bookmarks=false, linkcolor=blue, citecolor=blue, urlcolor=blue, breaklinks=true]{hyperref}

%=============
% Heading info
%=============

\newcommand\name{Mathy McMatherson}
\newcommand\studentnumber{123456789}
\newcommand\course{MAT 1362}
\newcommand\semester{Fall 2020}
\newcommand\heading{Assignment 1}

%=================
% Question counter
%=================

\newcounter{question}
\setcounter{question}{0}
\newcommand{\question}{\addtocounter{question}{1}
\paragraph{\textsc{Question} \arabic{question}}}

%================
% Margin settings
%================

\setlength{\voffset}{-1cm}
\setlength{\textwidth}{17cm}
\addtolength{\textheight}{2cm}
\setlength{\footskip}{1cm}
\addtolength{\oddsidemargin}{-2cm}
\addtolength{\evensidemargin}{-2cm}

%==============
% List behavior
%==============

\renewcommand{\theenumi}{\alph{enumi}}
\renewcommand{\theenumii}{\roman{enumii}}

%========================
% Math symbol definitions
%========================

\newcommand\C{\mathbb{C}}
\newcommand\N{\mathbb{N}}
\newcommand\Q{\mathbb{Q}}
\newcommand\R{\mathbb{R}}
\newcommand\Z{\mathbb{Z}}

\DeclareMathOperator{\Image}{Im}
\DeclareMathOperator{\Ker}{Ker}

%======
% Other
%======

\allowdisplaybreaks

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{document} \thispagestyle{empty}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\setlength{\parskip}{1ex}

\begin{center}
{\Large \course\ -- \semester}

\medskip

{\large \heading}

\medskip

{\large \name\ (\studentnumber)}

\end{center}

\bigskip


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%---------
% Question
%---------

\question Write your solution to the first question here.  You can write in-line mathematics like this: $x^2 + a_1^4 + b' = 2$.  Write centered mathematics like this:
\[
  \begin{bmatrix}
    a & -1 & 2 \\
    0 & * & \sin z \\
    2 & \frac{2}{3} & -\infty
  \end{bmatrix}.
\]
Refer to an equation such as
\begin{equation} \label{eq:pythag}
  x^2 + y^2 = z^2,\quad x,y,z \in \Z,\ x \ge 0,
\end{equation}
like this: Check out \eqref{eq:pythag}.

%---------
% Question
%---------

\question Here's another question.  This is fun.  If you have a long series of equations that take more than one line, you can use the \texttt{multline*} environment like this:
\begin{multline*}
  \left( \frac{1+x}{y + \frac{2}{z+\cos y}} \right)^{-1}
  = \int_1^2 f(x), dx + y''(t) + X^\R + \left( 1+x^2+y^{3^2} \right)^{2+z}
  = \prod_{i=1}^\infty (x^i + iyz)
  = e^{e^{|x|}}
  \\
  = \{(x,y) : x^5 + y^t \in \C \text{ for all } t\}
  = \R \times \C \oplus \R \otimes \Z \cap \Q \cup \langle 2 \rangle
  = \mathcal{A} \backslash \mathcal{B}
  \\
  = \alpha + \beta + \gamma + \delta + \pi + \Omega + \zeta + \Xi
  = \Delta + \nabla.
\end{multline*}
Use \texttt{multline} (without the *) if you want it to be numbered.  This goes for other types of equation environments too.  If you want to align some expressions, you can use the \texttt{align} environment:
\begin{align*}
  A \cup B
  &= C \cap D \\
  &= \bar x + \overline{z+2y} \\
  &= \sqrt{2+5} \\
  &\ne \sqrt[4]{y+8} \\
  &\ge \gamma^2 \\
  &\le \omega \\
  &\in A \\
  &\notin B \\
  &\subseteq C \\
  &\subsetneq D.
\end{align*}

%---------
% Question
%---------

\question It must be terrible to have a sore throat if you're a giraffe.  Here's a sum:
\[
  \sum_{n=1}^\infty x^n = \frac{1}{1-x}.
\]
If you want to add explanations to the side of a series of equalities or implications, do this:
\begin{align*}
  A &\implies B & \text{by Axiom 1} \\
  &\implies C & \text{by Proposition 2} \\
  &\implies D & \text{because I said so}
\end{align*}
Note that we use the \texttt{text} command to write text within a math environment.  Otherwise, \LaTeX\ will think your text is mathematics and the formatting won't be appropriate for text.

%---------
% Question
%---------

\question Let's have fun with math fonts in an itemized list:
\begin{itemize}
  \item mathcal: $\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
  \item mathbb: $\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
  \item mathbf: $\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz}$
  \item mathfrak: $\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz}$
  \item mathrm: $\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz}$
  \item mathit: $\mathit{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz}$
  \item mathsf: $\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz}$
  \item mathtt: $\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz}$
\end{itemize}

We can also do enumerated lists:
\begin{enumerate}
  \item This is the first item.
  \item This is the second item.
  \begin{enumerate}
    \item This a subitem in the second item.
    \item You can nest \texttt{enumerate}/\texttt{itemize} environments inside each other like this.
  \end{enumerate}
\end{enumerate}

To find the \LaTeX\ code for a symbol, this website is helpful:
\begin{center}
  \url{http://detexify.kirelabs.org/classify.html}
\end{center}
You can add a hyperlink to some text \href{https://alistairsavage.ca/}{like this}.

\end{document}
