\newcommand{\thetop}[5]{
   \renewcommand{\thepage}{\arabic{page}}
   \noindent
   \begin{center}
   \framebox{
      \vbox{
    \hbox to 5.78in { Spectral Graph Theory \hfill #2 }
       \vspace{4mm}
       \hbox to 5.78in { {\Large \hfill #5  \hfill} }
       \vspace{2mm}
       \hbox to 5.78in { {\it #3 \hfill #4} }
      }
   }
   \end{center}
   \vspace*{4mm}
}

\newcommand{\lecture}[2]{\thetop{#1}{Instructor: Padraic Bartlett}{#2}{Mathcamp 2011}{Lecture #1}}

\newcommand{\recitation}[2]{\thetop{#1}{Instructor: Padraic Bartlett}{#2}{Mathcamp 2011}{Recitation #1}}

\newcommand{\handout}[2]{\thetop{#1}{Instructor: Padraic Bartlett}{#2}{Mathcamp 2011}{Handout #1}}

\newcommand{\homework}[2]{\thetop{#1}{Instructor: Padraic Bartlett}{#2}{Mathcamp 2011}{Homework #1}}

\newcommand{\solutionset}[2]{\thetop{#1}{Instructor: Padraic Bartlett}{#2}{Mathcamp 2011}{Solution Set #1}}

\newcommand{\blank}[2]{\thetop{#1}{Instructor: Padraic Bartlett}{#2}{Mathcamp 2011}{#1}}


\def\squarebox#1{\hbox to #1{\hfill\vbox to #1{\vfill}}}
\def\qed{\hspace*{\fill}
        \vbox{\hrule\hbox{\vrule\squarebox{.667em}\vrule}\hrule}}

\newtheorem{theorem}{Theorem}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{fact}[theorem]{Fact}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{question}[theorem]{Question}
\newtheorem{claim}[theorem]{Claim}

\newenvironment{proof}[1][Proof.]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
\newenvironment{solution}[1][Solution.]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
\newenvironment{definition}[1][Definition.]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
\newenvironment{example}[1][Example.]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
\newenvironment{remark}[1][Remark.]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}


\def\QQ{\mathbb Q}
\def\ZZ{\mathbb Z}
\def\RR{\mathbb R}
\def\CC{\mathbb C}
\def\NN{\mathbb N}

\def\from{\gets}
\def\isin{\subseteq}
\def\iso{\cong}
\def\st{\ |\ }