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My Mathematics 504 Simulation Modeling and Analysis, CSU Fullerton

Nasser M. Abbasi

April 23, 2008   Compiled on October 26, 2018 at 8:25am  [public]

Contents

1 Introduction
 1.1 Instructor
 1.2 Class description handout/flyer
2 Handouts given during the course
3 study notes,lecture notes
4 HWs
5 Challenge Problems
6 Links

1 Introduction

This course part of my Masters degree in Applied Mathematics at California State University, Fullerton

Course description (from CSUF catalogue)

MATH 504A Simulation Modeling and: Prerequisites: Math 501A,B; 502A,B; 503A,B. Corequisite: Math 504B. Advanced techniques of simulation modeling, including the design of Monte Carlo, discrete event, and continuous simulations. Topics may include output data analysis, comparing alternative system configurations, variance-reduction techniques, and experimental design and optimization.Units: (3)

MATH 504B Applications of Simulation Modeling Techniques

Description: Prerequisites: Math 501A,B; 502A,B; 503A,B. Corequisite: Math 504A. Introduction to a modern simulation language, and its application to simulation modeling. Topics will include development of computer models to demonstrate the techniques of simulation modeling, model verification, model validation, and methods of error analysis.Units: (3)

1.1 Instructor

Professor Gearhart, W. B. CSUF Math department.

1.2 Class description handout/flyer

PDF

2 Handouts given during the course

We followed mostly the instructor class notes pdf

These are additional handouts given





#

date

description

link





1

Monday 1/22/200

Course description

pdf





2

Monday 1/22/08

A problem in conditional probability (the first simulation HW, confidence interval, histogram)

pdf





3

Monday 1/28/08

Computing project guideline

image





4

Monday 1/28/08

Continuous approximation to random walks

pdf





5

Monday 2/25/08

Problems to practice solving first order pde using the characteristics method

pdf





6

Monday

Craps game and inventory problem. Markov chain computing assignment

image





7

Monday 3/10/2008

Handout on convergent finite markov chains

pdf





8

Monday 3/17/2008

Key solution to problem 5.7 (HW 8)

pdf





9

Monday 3/19/08

Key solution to problem 6.3,6.5 (HW 9)

pdf





10

Wed 4/23/20088

Key solution to problem 10.4 to practice on

pdf





11

Monday 4/28/2008

Chapter 10 supplement. Kolmogorov equations with worked examples showing how to make the Q matrix

pdf





12

Wed 5/7/08

Key solutions to Poisson chapter from lecture notes, chapter 9

pdf





13

Wed 5/7/088

Key solutions to continuous time Markov chains, chapter from lecture notes, chapter 10

pdf





14

Hastings metropolis algorithm lecture 11

pdf





3 study notes,lecture notes

Some notes I did during the course HTML

4 HWs







#

date

description

solution

code

score







1

Wed 2/7/08

Computing Assignment #1

A problem in conditional probability (the first simulation HW, confidence interval, histogram) see first hand out PDF for more details

PDF

HTML

Matlab source code file.m

5/5







2

Mon 2/5/08

Derive PDF of Y from an experiment where we switch boxes, uses probability decision tree

PDF

HTML

2/2







3

Wed 2/20/2008

The long analytical problem. Problem #4 from handout #3 above. Solving Einstein-Weiner pde using fourier transform

PDF

HTML

2/2







4

Wed 2/27/2008

Computing Assignment #2

The limiting process simulation. Show that random walk final position is normally distributed in the limit under the Einstein-Weiner process (see problem 2 in this handout PDF

HTML

2/2







5

Wed 2/27/2008

Problem 3.9 from handouts (probability distribution related to record time distribution)

PDF

HTML

2/2







6

Monday 3/3/2008

Computing Assignment #3

Craps game and inventory problem. Markov chain Problem description is here

report

PDF

HTML

Mathematica notebooks

inventory.nb

code listing HTML







7

Practice problems

These are 5 problems to practice using method of characteristics to solve first order liner pde. The problems are listed in the handout above. PDF

PDF

HTML

2/2







8

Monday 3/10/2008

Problem 5.7 from lecture notes (Irreducible matrix, analytical problem)

Problem description here

Key solution is PDF

PDF

HTML

2/2







9

Monday 3/17/08

Problems 6.3 and 6.5 from the handout

Description here

Solution key PDF

PDF

HTML

2/2







10

Wed 4/16/2008

These problem related to Hastings-Meropolis algorithm. And Proofing a Markov chain is irreducible, regular and time inverse. Implemented the simulation using Mathematica

PDF

HTML

Graded solution. (Entered some data wrong for the numerical problem. corrected) PDF

Key solution PDF

  1. 8.5 part (a) code Hastings simulation. notebook    PDF
  2. 8.5 part(b): direct construction of p matrix from q and \(\pi \).    notebook    PDF

4/4







11

Wed 5/7/2008

Problems 10.5 and 10.6 These deal with continues time markov chains. To determine rate of arrival and departure for birth/death process

PDF    HTML







12

Wed 5/7/2008

Computer problem, problem 12.3 in lecture notes. Simulation of problem 10.5 in above HW. Repair shop problem

PDF

key Matlab code given file.m

Matlab function file.m

4/4







13

Wed 5/7/2008

Problems 9.3 and 9.5 (On Poisson process)

PDF    HTML

Small Mathematica function for problem 9.5 to plot \(P(X=n)\) notebook







5 Challenge Problems

These are extra problems relating to first midterm the instructor gave the class to try to work out. Here are the questions image    image

This is my solution so far HTML

6 Links

  1. Mathworks SimEvents http://www.mathworks.com/products/simevents/description2.html
  2. Free demo of extend http://www.extendsim.com/prods_demo.html
  3. Started to make comparison between some simulation packages. Here is a link. This is not complete HTML