Fall 2018 Course Syllabus:  Math 448

 

Course Title:

Stochastic Simulation

Textbook:

Simulation, by Ross, Sheldon, M.
Publisher: Academic Press; 5 edition (2013); ISBN: 978-0125980630.

 

Reference Book:

MATLAB Prime, by Timothy Davis and Kermit Sigmon (2005, 7th 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

9/4

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

9/11

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

9/18

5

Chapter 2

 

 

 

Chapter 3

Elements of Probability (III):

The Poisson process and gamma random variables, The nonhomogeneous Poisson process

 

Random Numbers

Week 4

9/25

7

Chapter 4

 

Generating Discrete Random Variables:

The inverse transform method, acceptance-rejection technique, the composition approach

Homework 2

Week 5

10/2

9

Chapter 5

Generating Continuous Random Variables (I): Inverse transform and Rejection method

 

Week 6

10/9

11

Chapter 5

Generating Continuous Random Variables (II):  Polar method and Generating a Poisson process

Homework 3

Week 7

10/16

13

Chapter 5

Generating Continuous Random Variables (III): Generating a nonhomogeneous Poisson process

 

Week 8

10/23

 15

 Chapter 9

Variance Reduction Techniques (I): Antithetic variates

 Homework 4

 

MIDTERM EXAM:

Thursday ~ Oct. 25, 2018

 

Week 9

10/30

16

Chapter 9

Variance Reduction Techniques (II): Control variates

 

Week 10

11/6

18

Chapter 9

Variance Reduction Techniques (III): Variance reduction by conditioning, Stratified sampling

Homework 5

Week 11

11/13

20

Chapter 9

Variance Reduction Techniques (IV): Importance sampling

 

Week 12

11/20

22

Chapter 9

Variance Reduction Techniques (V): Importance sampling (Cont.)

 Homework 6

 

Thanksgiving Recess

 

Week 13

11/27

23

Chapter 8

 Statistical Analysis of Simulated Data: Sample mean and sample variance, Interval estimates of a population mean, Bootstrap

 

Week 14

12/4

25

Chapter 7

The Discrete Event Simulation Approach: Queuing systems

Homework 7

Week 15

12/11

27

 

Review for Final Exam

 

 

Thursday: Reading Day

 

Week 16

12/18

 

 

FINAL EXAM:

Tuesday ~ December 18, 2018

 

 

 

IMPORTANT DATES

FIRST DAY OF SEMESTER

September 4, 2018

LAST DAY TO WITHDRAW

November 12, 2018

LAST DAY OF CLASSES

December 12, 2018

FINAL EXAM PERIOD

December 15 – 21, 2018

 

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

 

 

 

 D

62 -- 70

F

0 -- 62

 

 

 

Important Departmental and University Policies

 

 

Prepared by Prof. Wenge Guo, August 18, 2018