\documentclass[11pt]{book}
\usepackage{fancybox,amssymb,amsmath,array,pifont}

\textheight 7.5in
\textwidth 4.5in
\evensidemargin 0.5in
\oddsidemargin 1.5in

\pagestyle{myheadings}

\def\a{\mathbf{a}}
\def\b{\mathbf{b}}
\def\S{\mathcal{S}}
\def\ds{\displaystyle}
\def\important{{\ding{74}}}

\renewcommand{\chaptername}{Lecture}
\renewcommand{\equiv}{\overset{\text{def}}{=}}
\renewcommand{\figurename}{{\bf Fig.}}
\renewcommand{\thefigure}{{\bf \arabic{figure}}}

\newcounter{dummy}[chapter]
\newtheorem{example}[dummy]{Example}

\newenvironment{problems}[1]%
        {\begin{list}%
          {\hskip\labelsep \textbf{\theproblem}.}%
          {\usecounter{problem} \labelwidth 0pt \leftmargin 0pt}%
           \small #1}%
        {\end{list}}
\newcounter{problem}
\def\theproblem{P\thesection.\arabic{problem}}

\newenvironment{proof}[2]%
        {\begin{list}%
           {\small \textsc{#1}:}%
           \small #2}%
        {$\blacksquare$ \end{list}}

\begin{document}

\reversemarginpar

\input{lecture}


\end{document}