\documentclass[12pt]{article}
\newenvironment{problem}[2][Problem]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}\hskip \labelsep {\bfseries #2.}]}{\end{trivlist}}
\usepackage{amssymb}
\usepackage{amsmath}
\begin{document}
\title{Problem Set 6}
\author{Author}
\date{October 18, 2014}
\maketitle
\begin{problem}{1}
\renewcommand{\labelenumi}{(\alph{enumi})}
\begin{enumerate}
\item
\end{enumerate}
\end{problem}
\end{document}