\documentclass[12pt]{amsart}
\usepackage[margin=3cm]{geometry}
%\graphicspath{ {desktop/Analysis} }

\usepackage{graphicx}
\usepackage{hyperref}
\usepackage{adjustbox}
\usepackage[shortlabels]{enumitem}
\usepackage{xcolor}
\usepackage{tabularx}
\usepackage{amsmath,amssymb,amsthm,amscd}

%\usepackage{exercise}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem*{corollary*}{Corollary}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem*{proposition*}{Proposition}
\newtheorem*{theorem*}{Theorem}
\theoremstyle{definition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{exercise}{Exercise}
\newtheorem{remark}{Remark}

\newcommand{\Z}{\mathbb{Z}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\F}{\mathbb{F}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\PP}{\mathbb{P}}
\newcommand{\lfl}{\left \lfloor}
\newcommand{\rfl}{\right \rfloor}

\usepackage{mathrsfs}
\usepackage{url}
\date{April 19, 2024}
\author{Your name(s) here}
\title{MATH 4573: Course Project on [Your project here]}
\begin{document}
\maketitle

\section{Introduction}
Here's your {\color{red}I}{\color{blue}n}{\color{green}t}{\color{purple}r}{\color{orange}o}{\color{cyan}!} An example of a reference: \cite{NZM91}. More specific reference: \cite[Theorem 1.1]{NZM91}.

Here's the itemize command:
\begin{itemize}
\item First;
\item second;
\item third!
\end{itemize}
Or maybe you'd prefer numbering:
\begin{enumerate}[1.]
\item First;
\item second;
\item third.
\end{enumerate}

To write math, we put dollar signs around the math to create a ``math environment." For example, define $f(x):=5x+1$. Sometimes, we also like starting math on its own line, like
\[
\lfl\frac{a}{b}\rfl=0.
\]

You can include pictures using the graphicx package, with a command such as the one commented out below (see LaTeX file). However, you'll also need to include the png file in your Overleaf document (or in an appropriate location with the correct path, see ``graphicspath" in the preamble). 
%\begin{figure}
%    \centering
%    \includegraphics[width=1\textwidth]{p-adic1.png}
%    \caption{Some open sets in an ultrametric space, \cite{blah}}
%\end{figure}

If you're using a math symbol frequently, you might create a ``new command" to save you time re-using it. See for example the ``newcommand" options I've added in the preamble of this LaTeX file.

When referencing a site, you can use the ``href" command to make a clickable hyperlink. For example, the Overleaf site is \href{https://www.overleaf.com/}{https://www.overleaf.com/}. You can also make a clickable phrase \href{https://www.overleaf.com/}{like this.}
\section{Section}
You should divide your paper into logical parts using the section command.
\section{Conclusion}
Don't forget to take a look at the project description and rubric. One final piece of advice: have fun while working on your project. Make it look fancy, pretty and interesting!

\section{Acknowledgments}
In this section, you can give thanks or acknowledge any book, paper, person or site that helped you write this project. 
\begin{thebibliography}{GMGS1111}
%\bibitem[Gou20]{Gou20}
%F.Q. Gouv\^{e}a,
%\emph{{$p$}-adic numbers},
%3rd ed.,
%Springer (2020).
%\bibitem[IR90]{IR90}
%K. Ireland and M. Rosen,
%\emph{A classical introduction to modern number theory},
%2nd ed., Springer-Verlag, New York (1990).
%\bibitem[LR11]{LR11}
%\'{A}. Lozano-Robledo,
%\emph{Elliptic curves, modular forms, and their {$L$}-functions},
%American Mathematical Society, Providence, RI; Institute for Advanced Study (IAS), Princeton, NJ (2011).
\bibitem[NZM91]{NZM91}
I. Niven, H.S. Zuckerman and H.L. Montgomery, 
\emph{An introduction to the theory of numbers},
5th ed., John Wiley \& Sons, Inc., New York (1991).
\end{thebibliography}
\end{document}
