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\section*{Topics for Week of October 18th 1999}

\subsection*{State Machine -- Termination 
\\(Reading: F97 Lec Notes 7)}

\begin{itemize}

\item

Derived variables of state machines and related notions (decreasing,
non-increasing, and non-skipping derived variables).

\item 

Proving termination of algorithms by state machine modeling \\
(Main Example: the mating problem).
\end{itemize}


\subsection*{Well-Orderings \\
(Reading: S99 H18)}

\begin{itemize}
\item Well founded posets
\end{itemize}

\subsection*{Sums and Series\\
(Reading: F97 Lec Notes 8)}

\begin{itemize}
\item Sum of a geometric series with a finite number of terms
\item Sum of a geometric series with an infinite number of terms
\item Evaluating sums by reduction 
to related sums which have already been solved.
(Reduction techniques: variable substitution, differentiation) 
\item Harmonic Numbers
\end{itemize}

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