Department of CIS
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
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
Students must have at least taken the complete sequence of
introductory level mathematics courses, and have the ability
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 (McGraw-Hill, 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
Hit-Or-Miss Monte Carlo Method
Discrete Random Variables (1 week)
Continuous Random Variables (1 week)
Monte Carlo Simulations (3 weeks)
- The Hit-Or-Miss Method with Error Analysis
- The Sample Mean Method
- Nonuniform Probability Distributions
- Importance Sampling & Other Variance Reduction Techniques
- Application: Neutron Transport through Materials
Quasi-Monte Carlo Simulations (1 week)
- The van der Corput sequence
- The Hammersley point set
- The Halton sequence
- The skipped Halton sequence
- The random-start Halton sequence
Genetic Algorithms & Artificial Life (2 weeks)
- Reproduction, Crossover, and Mutation
- Similarity Templates - Schemata
- Optimization via Simulation - Use of Hilbert and other
Space-Filling Curves in GA
Cellular Automata (2 weeks)
- One-Dimensional CA
- Modeling Traffic Flow
- High-Dimensional CA, Game of Life
Discrete-Event System Simulation (2 weeks)
- Simulation of Queueing Systems
- Simulation of Inventory Systems
25 numbers from the Halton sequence in s=5 dimensions
Pseudorandom Number Generators and Introduction to Computer Simulation
Discrete and Continuous Random Variables
Basic Monte Carlo Method
Generating Non-uniformly Distributed Random Numbers
Use of Variance Reduction and Importance Sampling techniques in Monte Carlo Simulation
Metropolis Rule in Monte Carlo Simulation
Use of Quasi-Random (Low Discrepancy) Sequences in Simulation
One Dimensional Cellular Automata
Two Dimensional Celluar Automata
Sample-Mean Monte Carlo Method to Evaluate a 5-Dimensional Integral (Assignment #4)