Polytechnic University,
Department of CIS
Computer Simulation
Spring 2003, CS 909 (1025), Tue., 6:00  8:15 pm, RH 702
Instructor: K. Ming Leung
In many areas of science and engineering, computer simulation and
other computational methods now have a role
equal in importance to the traditional theoretical and experimental approaches.
Even in disciplines, such as finance, management, and social sciences,
which traditionally have not been considered as highly computational in nature,
the use of simulation and other numerical methods have been steadily
growing.
The ability to compute by simulation has now become a part of the
essential repertoire of many researchers in these areas.
The course CS 909 deals with basic computer simulation techniques,
such as Monte Carlo, genetic algorithms and artificial life,
random walks and diffusion, cellular automata, neural networks, and
molecular dynamics.
Students must have at least taken the complete sequence of
introductory level mathematics courses, and have the ability
to
write computer programs in a high level computer language.
Prior knowledge in numerical analysis is not required.
Although there is no
required textbook for this course, you will find the following 2 books useful.
They have been placed on course reserve in our library.
 Simulation Modeling and Analysis, 3rd edition,
Averill M. Law and W. David Kelton (McGrawHill, 2000).
 A Primer for the Monte Carlo Method, by Ilya
M. Sobol (CRC Press, 1994).
The following is a tentative schedule:.

Portable Pseudorandom Number Generators (2 weeks)
 Linear Congruential Method
 Generalized Feedback Shift Register Method
 Mersenne Twister
 Usage of Random Numbers in Simulation  A Simple
HitOrMiss Monte Carlo Method

Discrete Random Variables (1 week)

Continuous Random Variables (1 week)

Monte Carlo Simulations (3 weeks)
 The HitOrMiss Method with Error Analysis
 The Sample Mean Method
 Nonuniform Probability Distributions
 Importance Sampling & Other Variance Reduction Techniques
 Application: Neutron Transport through Materials

QuasiMonte Carlo Simulations (1 week)
 The van der Corput sequence
 The Hammersley point set
 The Halton sequence
 The skipped Halton sequence
 The randomstart Halton sequence
 Genetic Algorithms & Artificial Life (2 weeks)
 Reproduction, Crossover, and Mutation
 Similarity Templates  Schemata
 Optimization via Simulation  Use of Hilbert and other
SpaceFilling Curves in GA

Cellular Automata (2 weeks)
 OneDimensional CA
 Modeling Traffic Flow
 HighDimensional CA, Game of Life

DiscreteEvent System Simulation (2 weeks)
 Simulation of Queueing Systems
 Simulation of Inventory Systems
Homework Assignments

Assignment 1

Assignment 2

Assignment 3

Assignment 4

Assignment 5

Assignment 6
25 numbers from the Halton sequence in s=5 dimensions
Lecture Notes

Pseudorandom Number Generators and Introduction to Computer Simulation

Discrete and Continuous Random Variables

Basic Monte Carlo Method

Generating Nonuniformly Distributed Random Numbers

Use of Variance Reduction and Importance Sampling techniques in Monte Carlo Simulation

Metropolis Rule in Monte Carlo Simulation

Use of QuasiRandom (Low Discrepancy) Sequences in Simulation

Cellular Automata

One Dimensional Cellular Automata

Two Dimensional Celluar Automata

Genetic Algorithm
Matlab program

SampleMean Monte Carlo Method to Evaluate a 5Dimensional Integral (Assignment #4)