%\usepackage{psfig}

\setlength{\oddsidemargin}{0 in}
\setlength{\evensidemargin}{0 in}
\setlength{\topmargin}{-0.6 in}
\setlength{\textwidth}{6.5 in}
\setlength{\textheight}{9 in}
\setlength{\headsep}{0.5 in}
\setlength{\parindent}{0 in}
\setlength{\parskip}{0.1 in}

\newcommand{\lecture}[3]{
   \pagestyle{myheadings}
   \thispagestyle{plain}
   \newpage
   \setcounter{page}{1}
   \noindent
   \begin{center}
   \framebox{
      \vbox{\vspace{1mm}
    \hbox to 6.28in { #1 \hfill {\it #3} }
       \vspace{2mm}
       \hbox to 6.28in { {\Large \hfill #2 \hfill} }
      \vspace{1mm}}
   }
   \end{center}
   \markboth{#1}{#2}
}

\renewcommand{\i}{\item}
\newcommand{\bee}{\begin{enumerate}}
\newcommand{\ene}{\end{enumerate}}
\newcommand{\bei}{\begin{itemize}}
\newcommand{\eni}{\end{itemize}}
\newcommand{\tto}{~$\longrightarrow$~}
\newcommand{\tfr}{~$\longleftarrow$~}
\newcommand{\br}{\begin{tabular}{@{}p{6.5in}@{}}\\\hline\\\end{tabular}}

\newcommand{\leftright}[2]{\vspace{-2mm}\contentsline {section}{\large #1}{\textnormal{#2}}\vspace{-0mm}}

\newenvironment{solution}
  {\linespread{1}\center%
   \begin{tabular}{|p{5.8in}|}%
     \hline\vspace{+0.02in}%
     \begin{sffamily}%
     }
  {\end{sffamily} \vspace{+0.05in}\\\hline%
   \end{tabular}\vspace{+0.1in}\\}