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.

The following is a tentative schedule:.

  1. Portable Pseudorandom Number Generators (2 weeks)

  2. Discrete Random Variables (1 week)

  3. Continuous Random Variables (1 week)

  4. Monte Carlo Simulations (3 weeks)

  5. Quasi-Monte Carlo Simulations (1 week)

  6. Genetic Algorithms & Artificial Life (2 weeks)

  7. Cellular Automata (2 weeks)

  8. Discrete-Event System Simulation (2 weeks)

Homework Assignments

  1. Assignment 1
  2. Assignment 2
  3. Assignment 3
  4. Assignment 4
  5. Assignment 5
  6. Assignment 6
    25 numbers from the Halton sequence in s=5 dimensions

Lecture Notes

  1. Pseudorandom Number Generators and Introduction to Computer Simulation
  2. Discrete and Continuous Random Variables
  3. Basic Monte Carlo Method
  4. Generating Non-uniformly Distributed Random Numbers
  5. Use of Variance Reduction and Importance Sampling techniques in Monte Carlo Simulation
  6. Metropolis Rule in Monte Carlo Simulation
  7. Use of Quasi-Random (Low Discrepancy) Sequences in Simulation
  8. Cellular Automata
  9. One Dimensional Cellular Automata
  10. Two Dimensional Celluar Automata
  11. Genetic Algorithm

Matlab program

  1. Sample-Mean Monte Carlo Method to Evaluate a 5-Dimensional Integral (Assignment #4)