%--------------
%% preamble.tex
%% this should be included with a command like
%% \input{preamble.tex}
%% \lecture{1}{September 4, 1996 }{Daniel A. Spielman}{name
%%  of poor scribe}

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   %\renewcommand{\thepage}{#1-\arabic{page}}
   \noindent
   \begin{center}
   \framebox{
      \vbox{
    \hbox to 5.78in { {\bf 6.5420 Randomness and Computation}
     	 \hfill #2 }
       \vspace{4mm}
       \hbox to 5.78in { {\Large \hfill #5  \hfill} }
       \vspace{2mm}
       \hbox to 5.78in { {\it #3 \hfill #4} }
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   \vspace*{4mm}
}
\newcommand{\syllabusstyle}[3]{
   %\renewcommand{\thepage}{#1-\arabic{page}}
   \noindent
   \begin{center}
   \framebox{
      \vbox{
    \hbox to 5.78in { {\bf 6.5420 Randomness and Computation}
     	 \hfill #1 }
       \vspace{4mm}
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       \vspace{2mm}
       \hbox to 5.78in { {\Large \hfill #2  \hfill} }
      }
   }
   \end{center}
   \vspace*{4mm}
}
%% \syllabus{September 8, 2004}{Ronitt A. Rubinfeld}
\newcommand{\syllabus}[2]{\syllabusstyle{#1}{Lecturer:
#2}{Course Information}}
%% usage:
%% \syllabus{September 8, 2004}{Ronitt A. Rubinfeld}

\newcommand{\lecture}[4]{\handout{#1}{#2}{Lecturer:
#3}{Scribe: #4}{Lecture #1}}
%% usage:
%% \lecture{1}{September 4, 1996 }{Daniel A. Spielman}{name
%%  of poor scribe}

\usepackage{amsmath,amssymb,amsthm}

\newtheorem{theorem}{Theorem}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{observation}[theorem]{Observation}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{fact}[theorem]{Fact}
\newtheorem{assumption}[theorem]{Assumption}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{example}[theorem]{Example}

\newenvironment{remark}{\noindent{\bf Remark.}\hspace*{1em}}{\bigskip}

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\newcommand{\E}{{\mathbf E}}
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\newcommand{\F}{{\mathbb F}}
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\newcommand{\Q}{{\mathbb Q}}
\newcommand{\eqdef}{{\stackrel{\rm def}{=}}}
\newcommand{\poly}{{\mathsf poly}}
