Fall 2017 Course Syllabus: Math 448
|
Course Title: |
Stochastic Simulation |
|
Textbook: |
Simulation, by Ross, Sheldon,
M.
|
|
Reference
Book: |
Introductory Statistics with R, by Peter Dalgaard (2008, 2nd edition). |
|
Prerequisites: |
Math 333 with a grade of C or better or Math 340 with a grade of C or better. |
|
Course
Outline |
||||
|
Date |
Lecture |
Chapter |
Topic |
Assignment |
|
Week 1 9/5 |
1 |
Chapter 1
Chapter 2 |
Course Introduction
Elements of Probability (I): Conditional probability, independence, random variables, expectation, variance, Chebyshev’s inequality, law of large numbers |
|
|
Week 2 9/12 |
3 |
Chapter 2 |
Elements of Probability (II): Discrete random variables -- binomial, Poisson, geometric, negative binomial, and hypergeometric Continuous random variables -- uniform, normal, and exponential. Conditional expectation and variance |
Homework 1 |
|
Week 3 9/19 |
5 |
Chapter 2
Chapter 3 |
Elements of Probability (III): The Poisson process and gamma random variables, The nonhomogeneous Poisson process
Random Numbers |
|
|
Week 4 9/26 |
7 |
Chapter 4 |
Generating Discrete Random Variables: The inverse transform method, acceptance-rejection technique, the composition approach |
Homework 2 |
|
Week 5 10/3 |
9 |
Chapter 5 |
Generating Continuous Random Variables (I): Inverse transform and Rejection method |
|
|
Week 6 10/10 |
11 |
Chapter 5 |
Generating Continuous Random Variables (II): Polar method and Generating a Poisson process |
Homework 3 |
|
Week 7 10/17 |
13 |
Chapter 5 |
Generating Continuous Random Variables (III): Generating a nonhomogeneous Poisson process |
|
|
Week 8 10/24 |
|
|
Variance Reduction Techniques (I): Antithetic variates |
|
|
|
MIDTERM EXAM: Thursday ~ Oct. 26, 2017 |
|||
|
Week 9 10/31 |
16 |
Chapter 9 |
Variance Reduction Techniques (II): Control variates |
|
|
Week 10 11/7 |
18 |
Chapter 9 |
Variance Reduction Techniques (III): Variance reduction by conditioning, Stratified sampling |
Homework 5 |
|
Week 11 11/14 |
20 |
Chapter 9 |
Variance Reduction Techniques (IV): Importance sampling |
|
|
Week 12 11/21 |
22 |
Chapter 9 |
Variance Reduction Techniques (V): Importance sampling (Cont.) |
|
|
|
Thanksgiving Recess |
|||
|
Week 13 11/28 |
23 |
Chapter 8 |
Statistical Analysis of Simulated Data: Sample mean and sample variance, Interval estimates of a population mean, Bootstrap |
Homework 6 |
|
Week 14 12/5 |
25 |
Chapter 7 |
The Discrete Event Simulation Approach: Queuing systems |
Homework 7 |
|
Week 15 12/12 |
27 |
|
Review for Final Exam |
|
|
|
Thursday: Reading Day |
|||
|
Week 16 12/19 |
|
|
FINAL EXAM: Tuesday ~ December 19, 2017 |
|
|
IMPORTANT
DATES |
|
|
FIRST DAY OF SEMESTER |
September 5, 2017 |
|
LAST DAY TO WITHDRAW |
November 6, 2017 |
|
LAST DAY OF CLASSES |
December 13, 2017 |
|
FINAL EXAM PERIOD |
December 15 – 21, 2017 |
Grading Policy
|
Assignment Weighting |
|
Tentative Grading Scale |
||
| Attendance | 5% |
|
A |
90 -- 100 |
|
Homework |
25 % |
|
B+ |
85 -- 90 |
|
Midterm Exam |
30 % |
|
B |
80 -- 85 |
|
Final Exam |
40 % |
|
C+ |
75 -- 80 |
|
|
|
|
C |
70 -- 75 |
|
|
|
|
|
62 -- 70 |
|
|
0 -- 62 |
|||
Important Departmental and University
Policies
Prepared by Prof. Wenge Guo, August 28, 2017