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\def\ppa{-- ++(10pt,0pt) -- ++(0pt,10pt) ++(5pt,-10pt)}
\def\ppb{-- ++(10pt,0pt) -- ++(0pt,10pt) ++(-10pt,0pt) -- ++(0pt,-10pt) ++(15pt,0pt)}
\def\ppc{-- ++(10pt,0pt) ++(-10pt,0pt) -- ++(0pt,10pt) ++(15pt,-10pt)}
\def\ppd{-- ++(10pt,0pt) -- ++(0pt,10pt) -- ++(-10pt,0pt) ++(15pt,-10pt)}
\def\ppe{-- ++(10pt,0pt) -- ++(0pt,10pt) -- ++(-10pt,0pt) -- ++(0pt,-10pt) ++(15pt,0pt)}
\def\ppf{-- ++(10pt,0pt) ++(0pt,10pt) -- ++(-10pt,0pt) -- ++(0pt,-10pt) ++(15pt,0pt)}
\def\ppg{ ++(10pt,0pt) -- ++(0pt,10pt) -- ++(-10pt,0pt) ++(15pt,-10pt)}
\def\pph{ ++(10pt,0pt) -- ++(0pt,10pt) -- ++(-10pt,0pt) -- ++(0pt,-10pt) ++(15pt,0pt)}
\def\ppi{ ++(10pt,0pt) ++(0pt,10pt) -- ++(-10pt,0pt) -- ++(0pt,-10pt) ++(15pt,0pt)}
\def\ppj{-- ++(10pt,0pt) -- ++(0pt,10pt) ++(-5pt,-5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppk{-- ++(10pt,0pt) -- ++(0pt,10pt) ++(-10pt,0pt) -- ++(0pt,-10pt) ++(5pt,5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppl{-- ++(10pt,0pt) ++(-10pt,0pt) -- ++(0pt,10pt) ++(5pt,-5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppm{-- ++(10pt,0pt) -- ++(0pt,10pt) -- ++(-10pt,0pt) ++(5pt,-5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppn{-- ++(10pt,0pt) -- ++(0pt,10pt) -- ++(-10pt,0pt) -- ++(0pt,-10pt) ++(5pt,5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppo{-- ++(10pt,0pt) ++(0pt,10pt) -- ++(-10pt,0pt) -- ++(0pt,-10pt) ++(5pt,5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppp{ ++(10pt,0pt) -- ++(0pt,10pt) -- ++(-10pt,0pt) ++(5pt,-5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppq{ ++(10pt,0pt) -- ++(0pt,10pt) -- ++(-10pt,0pt) -- ++(0pt,-10pt) ++(5pt,5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppr{ ++(10pt,0pt) ++(0pt,10pt) -- ++(-10pt,0pt) -- ++(0pt,-10pt) ++(5pt,5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\pps{ ++(0pt,10pt) -- ++(5pt,-10pt) -- ++(5pt,10pt) ++(5pt,-10pt)}
\def\ppt{ ++(0pt,10pt) -- ++(10pt,-5pt) -- ++(-10pt,-5pt) ++(15pt,0pt)}
\def\ppu{ ++(10pt,10pt) -- ++(-10pt,-5pt) -- ++(10pt,-5pt) ++(5pt,0pt)}
\def\ppv{-- ++(5pt,10pt) -- ++(5pt,-10pt) ++(5pt,0pt)}
\def\ppw{ ++(0pt,10pt) -- ++(5pt,-10pt) -- ++(5pt,10pt) ++(-5pt,-5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppx{ ++(0pt,10pt) -- ++(10pt,-5pt) -- ++(-10pt,-5pt) ++(5pt,5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppy{ ++(10pt,10pt) -- ++(-10pt,-5pt) -- ++(10pt,-5pt) ++(-5pt,5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppz{-- ++(5pt,10pt) -- ++(5pt,-10pt) ++(-5pt,5pt) node {$\cdot$} ++(10pt,-5pt)}
\newcommand \sboxOne{
\mbox{
$
\begin{array}{|c|c|c|c|c|}\hline
\amp 00 \amp 01 \amp 10 \amp 11 \\ \hline
00 \amp 01 \amp 11 \amp 10 \amp 11 \\ \hline
01 \amp 11 \amp 10 \amp 01 \amp 00 \\ \hline
10 \amp 00 \amp 10 \amp 01 \amp 11 \\ \hline
11 \amp 11 \amp 01 \amp 11 \amp 10 \\ \hline
\end{array}
$
}
}
\newcommand \sboxTwo{
\mbox{
$
\begin{array}{|c|c|c|c|c|}\hline
\amp 00 \amp 01 \amp 10 \amp 11 \\ \hline
00 \amp 00 \amp 01 \amp 10 \amp 11 \\ \hline
01 \amp 10 \amp 00 \amp 01 \amp 11 \\ \hline
10 \amp 11 \amp 00 \amp 01 \amp 00 \\ \hline
11 \amp 10 \amp 01 \amp 10 \amp 11 \\ \hline
\end{array}
$
}
}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\)
Chapter 4 Triumphs of Logic and Statistics
In this chapter discuss the emerging roll of mathematics in analysis:
- Falconer's Attacks
- Babbage's attack
- Friedman and Statistics
- Sukhotin's Algorithm