

\subsection{\bf Why Use Monte Carlo}
\subsection{\bf for Summations?}

\begin{slide}
\begin{itemize}
\item This can have important consequences.  Suppose our integral
involves
$$
S = \sum^{1000}_{l=1} f_l \left( x_a, x_b, x_c \right)
$$
\item Then if we direct calculate the sum, it has computational cost,
which is 1000 times that of calculating $f_l$.

\item Suppose we generate $r$ and set $l_r = 1 + \hbox{INT}(1000\times
r)$ ($\hbox{INT}(y)$ gives you integer part of floating point number
$y$). 

\item And then let $S=1000\times f_{l_r}\,\left( x_a, x_b, x_c \right)$
where $x_a, x_b, x_c$ chosen by continuous Monte Carlo procedure.
\end{itemize}
\end{slide}

