\documentclass[12pt]{article}

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\usepackage{fancyhdr,lastpage}

\usepackage{amsmath,amsfonts,amssymb,amsthm}

% We'll define several "theorem" environments.
\newtheorem{prop}{Proposition}
\newtheorem{lem}{Lemma}
\newtheorem{thm}{Theorem}

\pagestyle{fancy}

\lhead{MATH 311-01}
\chead{Problem of the Day}
\rhead{YOUR NAME HERE}
\lfoot{}
\cfoot{Page \thepage\ of \pageref{LastPage}}
\rfoot{\textbf{due September 20, 2013}}
\begin{document}
\begin{enumerate}
\item \emph{Prove that for integers $a$ and $b$, if either $a$ or $b$ is
  odd, then $a+b$ and $ab$ have different parities.}

\begin{proof}
  We may address this premise in two different cases.

  % Here's how you can describe cases. Obviously, these aren't the
  % right cases.
  \textbf{Case I: The gostak distims the doshes.} From our case
  premise, we may assume the gostak distims the doshes. And flippety
  floppety blah.

  \textbf{Case I: The gostak does not distim the doshes.}
  Contrariwise, here we assume the gostak does not distim the
  doshes. Babble on until you're convincing!

\end{proof}

\item \emph{Prove that for integers $m$ and $n$, if $m$ and $n$ have
    opposite parities, then $4\mid(m^2+n^2-1)$.}
\end{enumerate}
\end{document}
