\documentclass[10pt]{article}
\usepackage{fullpage}
\usepackage{amsmath, amsfonts}

\author{John Doe}
\title{6.897 Problem 1 -- Solutions}

% these are compressed lists to help fit into a 1 page limit
\newenvironment{enumerate*}%
  {\vspace{-2ex} \begin{enumerate} %
     \setlength{\itemsep}{-1ex} \setlength{\parsep}{0pt}}%
  {\end{enumerate}}
 
\newenvironment{itemize*}%
  {\vspace{-2ex} \begin{itemize} %
     \setlength{\itemsep}{-1ex} \setlength{\parsep}{0pt}}%
  {\end{itemize}}
 
\newenvironment{description*}%
  {\vspace{-2ex} \begin{description} %
     \setlength{\itemsep}{-1ex} \setlength{\parsep}{0pt}}%
  {\end{description}}


\begin{document}

\maketitle

I'm writing something.

A paragraph is started by a blank line. Now, let's include a formula: 
$a^2 + b^2 = c^2$. Another way to include formulas is this:

\[ \binom{n}{k} \le \binom{n}{\lfloor n/2 \rfloor}, (\forall) 1 \le k \le n \]

Making a compact list now:

\begin{itemize*}
\item abc
\item def
\end{itemize*}

The end.

\end{document}