%Begin single space.
\def\singlespace{\setlength{\baselineskip}{12pt}}

%Begin double space.
\def\doublespace{\setlength{\baselineskip}{24pt}}


%make page a little bigger - use topmargin 0in when compiling on gauss
%\topmargin 0.5in %use this one on gauss
\topmargin 0.75in %hammath1  actual margin is topmargin+1
%\topmargin 0.5in %actual margin is topmargin+1
\headheight 12pt
\headsep 12pt
%24pt = 1/3 inch
%%%%%%%%%%%%%%%%%%%%%%%%%%% I don't know why 9.0 doesn't work ???
%\textheight9.0in % 9in - headheight - headsep
\textheight 8.5in % 9in - headheight - headsep
\textwidth 5.9in


\oddsidemargin 0.5in %actual margin is oddsidemargin+1 

\textfloatsep 36pt plus 2pt minus 2pt
\intextsep 36pt plus 2pt minus 2pt

\pagestyle{myheadings}{\markright{}}
%Definition Section
%%%%%%%%%%%%%%%%% A FEW Newcommands %%%%%%%%%%%%%%%%%%%%%
\newcommand{\ra}{\rightarrow}
\newcommand{\Ra}{\Rightarrow}
\newcommand{\ds}{\displaystyle}         %% \newcommand{\ds}[1]{\displaystyle{#1}}
\def\beq{\begin{equation}}
\def\eeq{\end{equation}}
\def\beqa{\begin{eqnarray}}
\def\eeqa{\end{eqnarray}}
\def\reals{{{\rm I}\kern - .15em{\rm R}}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%********* BLACKBOARD BOLD FONT ************
\font\msbmHuge=msbm10 at 30pt
\font\msbmhuge=msbm10 at 25pt
\font\msbmLARGE=msbm10 at 22pt
\font\msbmLarge=msbm10 at 18pt
\font\msbmlarge=msbm10 at 14pt
\font\msbmnormal=msbm10 at 12pt
\font\msbmsmall=msbm7 at 9.5pt
\font\msbmfootnotesize=msbm7 at 9.5pt
\font\msbmscriptsize=msbm5 at 3pt
\font\msbmtiny=msbm5 at 3pt
\newfam\BlackBoard
\textfont\BlackBoard=\msbmnormal
\scriptfont\BlackBoard=\msbmsmall
\scriptscriptfont\BlackBoard=\msbmtiny
\def\BB{\fam\BlackBoard\msbmnormal}
%\def\BBT{{\BB T}}
%\def\R{{\BB R}}

\def\HB{\hbox{\tiny HB}}
\def\HC{\hbox{\tiny HC}}
\def\LP{\hbox{\tiny LP}}
\def\LB{\hbox{\tiny LB}}
\def\SS{\hbox{\tiny SS}}

\font\Bbb=msbm10 at 11pt
\def\R{\hbox{\Bbb R}}
\font\BBb=msbm10 at 24pt
%\def\LIM{\mathop{\rm LIM}\limits}
%\def\To{\mathop{\longrightarrow}\limits}
%\def\liminf{\mathop{\rm lim\,inf}\limits}
%\def\TT{\hbox{\BBb T}}
%\def\qed{\quad \vrule height7.5pt width5.17pt depth0pt}
%\def\max{\mathop{\rm max}\limits}
%\def\filbreak{\vfil\penalty-200\vfilneg}
%\newcommand{\no}{\noindent}
\newcommand{\pf}{ {\noindent {\em Proof:}\hspace{.1in} }}
\newtheorem{thm}{\sc  Theorem}[chapter] %include chapter in numbering scheme
\newtheorem{lemma}[thm]{\sc  Lemma} %use the thm counter 
\newtheorem{definition}[thm]{\sc Definition}
\newtheorem{prop}[thm]{\sc Proposition}
\newtheorem{cor}[thm]{\sc  Corollary}
\newtheorem{claim}[thm]{\sc Claim}
% Make a counter to consecutively number tables throughout the thesis
\newcounter{tablectr}

% Make a counter to consecutively number figures throughout the thesis
\newcounter{figurectr}

\newif\ifinputpicture \inputpicturetrue
  
% Use this command to input pictures, then control whether that
% happens or not by saying \inputpicturetrue or \inputpicturefalse
% in the preamble
\newcommand{\inputpicture}[1]{%
   \ifinputpicture \input{#1} \else \input{box.tex} \fi }