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)
Professor Gearhart, W. B. CSUF Math department.
We followed mostly the instructor class notes pdf
These are additional handouts given
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# |
date |
description |
link |
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1 |
Monday 1/22/200 |
Course description |
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2 |
Monday 1/22/08 |
A problem in conditional probability (the first simulation HW, confidence interval, histogram) |
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3 |
Monday 1/28/08 |
Computing project guideline |
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4 |
Monday 1/28/08 |
Continuous approximation to random walks |
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5 |
Monday 2/25/08 |
Problems to practice solving first order pde using the characteristics method |
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6 |
Monday |
Craps game and inventory problem. Markov chain computing assignment |
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7 |
Monday 3/10/2008 |
Handout on convergent finite markov chains |
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8 |
Monday 3/17/2008 |
Key solution to problem 5.7 (HW 8) |
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9 |
Monday 3/19/08 |
Key solution to problem 6.3,6.5 (HW 9) |
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10 |
Wed 4/23/20088 |
Key solution to problem 10.4 to practice on |
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11 |
Monday 4/28/2008 |
Chapter 10 supplement. Kolmogorov equations with worked examples showing how to make the Q matrix |
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12 |
Wed 5/7/08 |
Key solutions to Poisson chapter from lecture notes, chapter 9 |
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13 |
Wed 5/7/088 |
Key solutions to continuous time Markov chains, chapter from lecture notes, chapter 10 |
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14 |
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Hastings metropolis algorithm lecture 11 |
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Some notes I did during the course HTML
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# |
date |
description |
solution |
code |
score |
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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 |
Matlab source code file.m |
5/5 |
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2 |
Mon 2/5/08 |
Derive PDF of Y from an experiment where we switch boxes, uses probability decision tree |
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2/2 |
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3 |
Wed 2/20/2008 |
The long analytical problem. Problem #4 from handout #3 above. Solving Einstein-Weiner pde using fourier transform |
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2/2 |
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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 |
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2/2 |
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5 |
Wed 2/27/2008 |
Problem 3.9 from handouts (probability distribution related to record time distribution) |
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2/2 |
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6 |
Monday 3/3/2008 |
Computing Assignment #3 Craps game and inventory problem. Markov chain Problem description is here |
report |
Mathematica notebooks code listing HTML |
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7 |
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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 |
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2/2 |
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8 |
Monday 3/10/2008 |
Problem 5.7 from lecture notes (Irreducible matrix, analytical problem) Problem description here Key solution is PDF |
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2/2 |
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9 |
Monday 3/17/08 |
Problems 6.3 and 6.5 from the handout Description here Solution key PDF |
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2/2 |
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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 |
Graded solution. (Entered some data wrong for the numerical problem. corrected) PDF Key solution PDF |
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4/4 |
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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 |
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12 |
Wed 5/7/2008 |
Computer problem, problem 12.3 in lecture notes. Simulation of problem 10.5 in above HW. Repair shop problem |
key Matlab code given file.m |
Matlab function file.m |
4/4 |
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13 |
Wed 5/7/2008 |
Problems 9.3 and 9.5 (On Poisson process) |
Small Mathematica function for problem 9.5 to plot \(P(X=n)\) notebook |
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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
