Simulation

At the end of the course, the students shall be able to:

• Execute discrete simulations using computational methods

• Optimize simulation processes

• Analyze simulation results

Chapter 01 REVIEW OF PROBABILITY AND RANDOM VARIABLES

• Lecture 01 - Sample Spaces and Events

• Lecture 02 - Axiomatic Probability Theory and Other Approaches

• Lecture 03 - Conditional Probability, Independence, and Baye's Rule

• Lecture 04 - Random Variables and Distributions

• Lecture 05 - Special Distributions

Chapter 02 RANDOM NUMBERS

• Lecture 06 - Pseudo Random Number Generation

• Lecture 07 - Examples of Simulation Applications

Chapter 03 GENERATING DISCRETE RANDOM NUMBERS

• Lecture 08 - Inverse Transform Method

• Lecture 09 - Acceptance Rejection Technique

• Lecture 10 - Composition Approach

• Lecture 11 - Generating Poisson and Binomial Random Variables

Chapter 04 GENERATING CONTINUOUS RANDOM NUMBERS

• Lecture 12 - Inverse Transform

• Lecture 13 - Rejection Technique

• Lecture 14 - Generating Normal Random Variables

• Lecture 15 - Generating Poisson Process

• Lecture 16 - Generating a Nonhomogeneous Poisson Process

Chapter 05 DISCRETE EVENT SIMULATION

• Lecture 17 - Simulation via Discrete Events

• Lecture 18 - Single Server Queues

• Lecture 19 - More Complicated Queues

Chapter 06 VARIANCE REDUCTION TECHNIQUES

• Lecture 20 - Use of Antithetic Variables

• Lecture 21 - Use of Control Variables

• Lccture 22 - Stratified Sampling

• Lecture 23 - Importance Sampling

Chapter 07 ANALYSIS OF SIMULATED DATA

• Lecture 24 - Sample Mean and Sample Variance

• Lecture 25 - Confidence Interval for the Mean

• Lecture 26 - Bootstrapping for Estimating Mean Squared Errors

• Lecture 27 - Goodness of Fit

A good background of Probability Theory will be important especially in the earlier part of the course. Since simulations will be executed using computers throughout the semester, experience in coding or programming will be helpful such as in C++ or Java, Mathematica, Matlab, or Python, and at least, Microsoft Excel or other similar programs.

• 27 Lecture Exercises

• 9 Quizzes

• 4 Major Examinations

• 2 Projects

Cut-off score is 50% for all course requirements.

Answers to lecture exercises and quizzes shall be written in sheets of 1/4 of short-sized bond paper. Take a photo of each page and send them as attachment to my e-mail address julius.selle@ctu.edu.ph or jdselle@up.edu.ph with subject properly indicating which course requirement is being submitted (for example "Math-C 228 Quiz No. 1"). Then, in the body of the mail, write your full name, course, year, and block section (I encourage you to do this in formal and complete sentences). The reason why it is required to write in 1/4 sheets is to enhance visibility. (Photos of whole-sized paper are sometimes difficult to read). You are allowed to use as many 1/4 sheets as you would need.

• Ross (2012). Simulation. Academic Press.

• Kelton & Law. Simulation Modeling and Analysis. McGraw Hill.

• Guerrero (2019). Excel Data Analysis: Modeling and Simulation. Springer.