2.  Monte Carlo method is very general.  use random numbers to approximate solutions to problems.  especially useful for simulating systems with many coupled degrees of freedom  simulate procedures with a large number of inputs.  We can apply the method in everything from economics to nuclear physics to regulating the flow of traffic.

3.  Traffic flow  Financial analysis  Computer Graphics  Nuclear reactor design  Molecular dynamics  Radiation cancer therapy

4.  Define a domain of possible inputs.  Generate inputs randomly from a probability distribution over the domain.  Perform a deterministic computation on the inputs.  Aggregate the results.

6. for i=1:N; x=rand; y=rand; F(i,1)=x; F(i,2)=y; if(x<=y) count=count+1; end sol = count/N;

10.  So Generally, the more iterations of the Monte Carlo simulation, the better the approximation will be.  The problem: It requires an intensive computing

11. Can we parallelize ?

15.  Monte Carlo Algorithms are very easy to convert to parallel algorithms.  When scaling to larger numbers of parallel CPU’s we see a smooth decrease in the time spent per timestep for a given simulation.