%%
%%	This is 5024lectures.sty, a LaTeX package just for CS 5024 lecture
%%	notes created with the slides document class.
%%
%%	Created:  8/23/96	By:  Lenwood S. Heath
%%	Modified: 8/21/97	By:  Lenwood S. Heath
%%

\usepackage{array}
\usepackage{slidepagestyles}
\usepackage{xspace}

%%	These macros should be constants for this course

\newcommand{\coursenumber}{CS 5024}
\newcommand{\coursetitle}{Models and Analysis}
\newcommand{\doctitle}{Lecture \lecturenumber}
\newcommand{\instructor}{Lenwood S. Heath}

%%	\docdate is the date of this lecture

\newcommand{\docdate}{}

%%	\lecturenumber is the number of this lecture

\newcommand{\lecturenumber}{}

%%	\lecturetitlestring is a phrase that identifies which lecture this is

\newcommand{\lecturetitlestring}{}

%%	These macros determine the headers and footers on slides.  They
%%	are tied to the use of package slidepagestyles.

\renewcommand{\oddfoot}{\coursenumber\hfill\docdate\hfill}
\renewcommand{\oddhead}{\framebox{\doctitle}\hfill\lecturetitlestring}

%%	\firstslidenumber provides a crude method for breaking up the series
%%	of lecture notes into multiple LaTeX files

\newcommand{\firstslidenumber}[1]{\setcounter{slide}{#1}%
\addtocounter{slide}{-1}}

%%	These macros provide standard ways to insert a slide title, a
%%	topic title, or a subtitle

\newcommand{\slidetitle}[1]{\begin{center}\Large\bfseries #1\end{center}}
\newcommand{\topictitle}[1]{\textbf{#1}}
\newcommand{\subtitle}[1]{\begin{center}\bfseries #1\end{center}}

%%	\answerbox is a way to emphasize a question that needs to be
%%	answered in the ensuing discussion.

\addtolength{\fboxrule}{2pt}
\addtolength{\fboxsep}{3pt}
\newcommand{\answerbox}[1][40pt]{%
\rule{0pt}{28pt}\fbox{\rule[-4pt]{0pt}{18pt}\rule{#1}{0pt} ?}}

%%	These macros are special symbols, etc., for 5024

\newcommand{\diff}[1]{\frac{d}{d#1}}
\newcommand{\egf}{\displaystyle%
\stackrel{\mathrm{egf}}{\longleftrightarrow}}
\newcommand{\ogf}{\displaystyle%
\stackrel{\mathrm{ogf}}{\longleftrightarrow}}
\newcommand{\ogfinverse}{\displaystyle%
\stackrel{\mathrm{ogf}^{-1}}{\longleftrightarrow}}
\newcommand{\pgf}{\displaystyle%
\stackrel{\mathrm{pgf}}{\longleftrightarrow}}
\newcommand{\coefficient}[1]{\left[#1\right]}
\newcommand{\expect}[1]{\mathrm{E}\left[#1\right]}
\newcommand{\variance}[1]{\mathrm{Var}\left[#1\right]}
\newcommand{\prob}[1]{\mathrm{P}\left[#1\right]}
\newcommand{\probname}{\mathrm{P}}
\newcommand{\given}{\mid}
\newcommand{\reliability}[1]{R_{#1}}
\newcommand{\stirling}[2]{S\left(#1,#2\right)}
\newcommand{\select}[1]{{\langle#1\rangle}}
\newcommand{\I}{\mathrm{I}}
\newcommand{\R}{\mathrm{R}}
\newcommand{\M}{\mathrm{M}}
\newcommand{\N}{\mathrm{N}}
\newcommand{\X}{\mathrm{X}}
\newcommand{\Rplus}{R^+}
\newcommand{\Zplus}{Z^+}

\newcommand{\mgf}[2]{{\psi_{#1}\left[#2\right]}}
\newcommand{\lst}[2]{{#1^*\left[#2\right]}}
\newcommand{\zt}[2]{{g_{#1}\left[#2\right]}}
\newcommand{\ztp}[2]{{g'_{#1}\left[#2\right]}}
\newcommand{\ztpp}[2]{{g''_{#1}\left[#2\right]}}

\newlength{\evalheight}
\setlength{\evalheight}{50pt}
\newcommand{\evaluated}[1][10pt]{\mbox{$\ \rule[-20pt]{2pt}{\evalheight}\ $}}

\newcommand{\elementary}{\omega}
\newcommand{\family}{{\mathcal F}}
\newcommand{\sample}{\Omega}

\newcommand{\complement}[1]{\bar{#1}}
\newcommand{\intersect}{\cap}
\newcommand{\union}{\cup}

\newcommand{\ABox}[1][6]{\raisebox{3pt}%
{\fbox{\rule{0pt}{#1pt}\rule{#1pt}{0pt}}}}

\newcommand{\tabularskip}{\\[8pt]}
\newcommand{\tabularstrut}{\rule{0pt}{24pt}}

%% 3 variants of the \binom command `n choose k'
%% each has an optional argument for additional vertical space
%% between the `n' and the `k'
\newcommand\binom[3][0pt]{{%
\renewcommand{\arraystretch}{1.0}\setlength{\arraycolsep}{0pt}%
\left(\begin{array}{c} #2\\[#1] #3\end{array}\right)}}
\newcommand{\textbinom}[3][0pt]{%
\left(\vcenter{\vskip 4pt%
\hbox{$\textstyle #2$}\vskip 8pt\vskip #1%
\hbox{$\textstyle #3$}\vskip 4pt}\right)%
}
\newcommand{\scriptbinom}[3][0pt]{%
\left(\vcenter{\vskip 2pt%
\hbox{$\scriptscriptstyle #2$}\vskip -12pt\vskip #1%
\hbox{$\scriptscriptstyle #3$}\vskip 2pt}\right)%
}

\newcommand{\binomial}[3]{b\left(#1;#2,#3\right)}

\newcommand{\dollar}{\$}

%	KENDALL NOTATION
\newcommand{\MMone}{$M$/$M$/1}
\newcommand{\MMtwo}{$M$/$M$/2}
\newcommand{\MMc}{$M$/$M$/$c$}
\newcommand{\MMinfty}{$M$/$M$/$\infty$}
\newcommand{\MMcc}{$M$/$M$/$c$/$c$}
\newcommand{\MMoneK}{$M$/$M$/1/$K$}
\newcommand{\MMoneKK}{$M$/$M$/1/$K$/$K$}

%       Erlang formulas
\newcommand{\erlangC}[2]{C[#1,#2]}
\newcommand{\erlangB}[2]{B[#1,#2]}

%%	Here are some standardized environments for examples, etc.

\newenvironment{application}{\textbf{APPLICATION. }}{\par}
\newenvironment{example}{\textbf{EXAMPLE. }}{\par}
\newenvironment{exercise}[ 1][]{\textbf{EXERCISE#1. }}{}
\newenvironment{solution}[ 1][]{\textbf{SOLUTION. }}{}
\newenvironment{notation}{\textbf{NOTATION. }}{}
\newenvironment{proof}{\textbf{PROOF. }}{\hspace{20pt}$\ABox$}
\newenvironment{shapes}{\begin{minipage}{4.0in}\rule{0pt}{25pt}\raggedright}%
{\rule[-15pt]{0pt}{20pt}\end{minipage}}

%%	These macros support pseudocode formatting in a tabbing environment

\newcounter{pseudocode}
\newcommand{\firstline}{\setcounter{pseudocode}{0}\linenumber}
\newcommand{\linenumber}{\refstepcounter{pseudocode}\thepseudocode}
\newcommand{\comment}{\%}	% comment indicator; may never be used
\newcommand{\var}[1]{\mbox{\textit{#1}}}	% a variable
\newcommand{\IF}{\textbf{if}\xspace}
\newcommand{\THEN}{\textbf{then}\xspace}
\newcommand{\ELSE}{\textbf{else}\xspace}
\newcommand{\SWITCH}{\textbf{switch}\xspace}
\newcommand{\CASE}{\textbf{case}\xspace}
\newcommand{\CALL}{\textbf{call}\xspace}
\newcommand{\FOR}{\textbf{for}\xspace}
\newcommand{\TO}{\textbf{to}\xspace}
\newcommand{\REPEAT}{\textbf{repeat}\xspace}
\newcommand{\UNTIL}{\textbf{until}\xspace}
\newcommand{\WHILE}{\textbf{while}\xspace}
\newcommand{\DO}{\textbf{do}\xspace}
\newcommand{\RETURN}{\textbf{return}\xspace}
\newcommand{\STOP}{\textbf{stop}\xspace}
\newcommand{\READ}{\textbf{read}\xspace}
\newcommand{\WRITE}{\textbf{write}\xspace}
\newcommand{\ASSIGN}{\longleftarrow}

%%	Font/shape undefined, therefore substituted.  Other substitutions
%%	may be necessary.

\DeclareFontShape{OT1}{lcmss}{m}{sc}{<->sub*cmr/m/sc}{}

%%	The remainder of this package consists of adjustments to various
%%	spacing parameters.

\newlength{\somespace}
\setlength{\somespace}{12pt}

\newlength{\lineheight}
\setlength{\lineheight}{1.0in}

\addtolength{\jot}{8pt}

\addtolength{\headheight}{8pt}

\newlength{\headshift}
\setlength{\headshift}{60pt}
\addtolength{\headsep}{\headshift}
\addtolength{\voffset}{-\headshift}

\newlength{\footshift}
\setlength{\footshift}{40pt}
\addtolength{\footskip}{\footshift}

\raggedright

