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

• Academic Integrity Code is Strictly Enforced
• Prerequisites Requirements are Enforced
• Attendance is Required in Lower-Division Courses
• Exam Policies (No Make Up Exams and More)
• Cell Phone and Pager Use Prohibited in Class
• Drop Date (Nov. 12, 2018) is Strictly Observed
• Complete DMS Course Policies (math.njit.edu/students/undergraduate/policies_math)

Prepared by Prof. Wenge Guo, August 18, 2018