\documentclass[11pt]{article}
\usepackage[utf8]{inputenc}

\usepackage[margin=1in]{geometry}
\usepackage{enumitem}
\usepackage{amsmath, amssymb, amsthm}
\usepackage{tikz, tikz-cd}
\usetikzlibrary{decorations.markings}
\usepackage{xcolor}
\usepackage{verbatim}
\usepackage{graphicx}
\usepackage{hyperref}
\hypersetup{
    colorlinks=true,
    linkcolor=blue,
    filecolor=magenta,      
    urlcolor=blue,
    pdftitle={Knot Theory},
    pdfpagemode=FullScreen,
    }
% \usepackage{ulem}

% THEOREM ENVIRONMENTS
\theoremstyle{definition}
\newtheorem*{theorem}{{Theorem}}
\newtheorem*{lemma}{{Lemma}}
\newtheorem*{proposition}{{Proposition}}
\newtheorem*{definition}{{Definition}}
\newtheorem*{corollary}{{Corollary}}
\newtheorem*{example}{{Example}}
\newtheorem*{remark}{{Remark}}
\newtheorem*{claim}{{Claim}}
\newtheorem*{question}{{Question}}

\theoremstyle{plain}
\newtheorem*{reminder}{{\textit{Reminder}}}
\newtheorem*{hint}{{\textit{Hint}}}



% COMMANDS
\newcommand{\solution}{{\color{blue} \textsc{\ \\ Solution.\ \ }}}
\newcommand{\Z}{\mathbb{Z}} % the integers
\newcommand{\N}{\mathbb{N}} % natural numbers
\newcommand{\R}{\mathbb{R}} % real nubers
\newcommand{\Q}{\mathbb{Q}} % rational numbers
\newcommand{\st}{ \ : \ } % such that
\newcommand{\inv}{^{-1}} % inverse
\newcommand{\img}{\mathrm{im}} % image
\newcommand{\into}{\hookrightarrow} % injection
\newcommand{\onto}{\twoheadrightarrow} % surjection
\newcommand{\map}[1]{\xrightarrow{#1}} % named map
\newcommand{\id}{\mathrm{id}} % identity map
\newcommand{\ind}{\mathrm{index}} % index of crit pt in Morse theory
\newcommand{\ord}{\mathrm{ord}} % order of element in group
\newcommand{\CC}{\mathcal{C}} % category, or chain complex
\newcommand{\Ob}{\mathrm{Ob}} % objects
\newcommand{\Mor}{\mathrm{Mor}} % morphisms
\newcommand{\Mat}{\mathrm{Mat}} % additive closure


% knot theory
\newcommand{\lk}{\mathrm{lk}} % linking number


% SOME ENVIRONMENTS

\newcommand{\exheading}[1]{\section*{Exercise #1}}
\newcounter{exnum}
% \setcounter{exnum}{1} % default 0 start
\newcommand{\exercise}{
    \stepcounter{exnum} 
    \exheading{\theexnum}
    }

\newcommand{\bea}{\begin{enumerate}[label={(\alph*)}]}
\newcommand{\ee}{\end{enumerate}}




\title{MAT180 HW08}
\author{(ADD NAME)}
\date{Due 5/26/23 at 11:59 pm on Gradescope}

\begin{document}

\maketitle

The purpose of this homework is to get you started on your final project.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\exercise

We went through the final project guidelines on Friday. If you weren't in class, read through the \href{https://www.melissa-zhang.com/Teaching/SQ2023/MAT180.html#final}{Final Project PDF}. 

You should spend a bit of time looking at potential topics before choosing your project topic. 
After you've chosen your project topic, answer the following questions.
\begin{itemize}
\item What will you study for your final project?
\item What materials have you already found / will you use to write your article? (E.g. the textbook, articles you found online, etc.)
\end{itemize}

As soon as you're done with this Exercise, send me an email with subject line "180 Project Topic" and your answer to this exercise (in plaintext; LaTeX code is fine) in the body of the email. 

Also submit your answer as your solution for Exercise 1.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\exercise

Write a \emph{first draft} of your expository article. \textbf{I am not looking for perfectly crafted sentences.} This can even just be an outline of the paper, e.g. containing the definitions, theorems, and examples you want to fill in later, and maybe an idea of what your figures should be. 

The length of this draft should be at least 1 page without the figures. If you write more of your expository article, that's even better!
The purpose of this draft is for us to potentially give you feedback on the trajectory of the article.

Recall that I will be posting the Lecture 22 notes in the form of an expository article so that you can get a sense of what the article should look like. You can also look at what other articles in the geometric topology look like, by checking out the \href{https://arxiv.org/list/math.GT/recent}{arXiv page for math.GT}.


\end{document}
