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NJIT Academic Integrity CODE:  All Students should be aware that the Department of Mathematical Sciences takes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly.  This means that there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams.  Under the University Code on Academic Integrity, students are obligated to report any such activities to the Instructor.

 

 

Number of Credits:  3

 

Course Description:  An introduction in the use of computer simulation to study stochastic models. Topics include the generation of samples of continuous and discrete random variables and processes with applications to stochastic models, statistical analysis of the results, and variance reduction techniques. Effective From: Spring 2009.

 

Prerequisites:  Math 333 or Math 244 and Math 340 with a grade of C or better.

Textbook:  Simulation, Fourth Edition by Sheldon Ross. ISBN-13: 978-0-12-598063-0, ISBN-10: 0-12-598063-9. Publisher: Academic Press.

Instructor:   (for specific course-related information, follow the link below)

 

Math 448-001

Prof. Subramanian

 

 

Grading Policy:  The final grade in this course will be determined as follows: 

▪ Homework/Quizzes:	20%
▪ Midterm Exam 1:	25%
▪ Midterm Exam 2:	25%
▪ Final Exam:	30%

Your final letter grade will be based on the following tentative curve. This curve may be adjusted slightly at the end of the semester.

A	90-100	C	68-74
B+	85-89	D	50-67
B	80-84	F	0-49
C+	75-79

 

Drop Date:  Please note that the University Drop Date November 6, 2012 deadline will be strictly enforced.

Homework Policy:  All assignments must be turned in on time. Late assignments are NOT accepted. Even though not every problem in an assignment may be graded, you are expected to attempt all of them. As a standing assignment, you should read the relevant sections of the textbook prior to lecture.

Additional Policies: Bring a scientific calculator to all the lectures and exams. Attendance at all classes and tests is mandatory. Instructor will maintain a detailed record of attendance as the administration needs to know dates the classes were missed. Grading complaints need to be sorted at the earliest available opportunity with the instructor. This may mean in-class or immediately after the class in which the graded homework or exam was handed out.

Attendance:  Attendance at all classes will be recorded and is mandatory. Please make sure you read and fully understand the Department’s Attendance Policy. This policy will be strictly enforced.

Examinations:  There will be two midterm examinations and a final examination. The final examination date, time, and location will be determined by the university during the final exam week. Exams are held on the following days:

Exam 1:	September 27, 2012
Exam 2:	October 29, 2011
Final Exam Week:	December 14-20, 2012

 

Makeup Exam Policy:  There will be No make-up EXAMS during the semester. In the event the Final Exam is not taken, under rare circumstances where the student has a legitimate reason for missing the final exam, a makeup exam will be administered by the math department. In any case the student must notify the Math Department Office and the Instructor that the exam will be missed and present written verifiable proof of the reason for missing the exam, e.g., a doctors note, police report, court notice, etc., clearly stating the date AND time of the mitigating problem.

Further Assistance:  For further questions, students should contact their Instructor. All Instructors have regular office hours during the week. These office hours are listed at the link above by clicking on the Instructor’s name. Teaching Assistants are also available in the math learning center.

Cellular Phones:  All cellular phones and beepers must be switched off during all class times.

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MATH DEPARTMENT CLASS POLICIES LINK 

All DMS students must familiarize themselves with and adhere to the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policies very seriously and enforces them strictly. For DMS Course Policies, please click here.

September 3, 2012	M	Labor Day ~ No classes
November 6, 2012	T	Last Day to Withdraw from this course
November 20, 2012	T	Classes follow a Thursday Schedule
November 21, 2012	W	Classes follow a Friday Schedule
November 22-25, 2012	R-Su	Thanksgiving Recess
December 13, 2012	R	Reading Day
December  14-20, 2012	F- R	Final Exams

 

Course Topics & assignments*:

 

*For assignments, see course webpage. Below is a tentative distribution of topics

 

Week	Date	Topics
1	9/6 (R)	Elements of probability Conditional probability, independence, random variables, expectation, variance, Chebyshev’s inequality, law of large numbers
2	9/10 (M)	Elements of probability   Discrete random variables: binomial, Poisson, geometric, negative binomial, and hypergeometric Continuous random variables: uniform, normal, and exponential. Conditional expectation and variance
3	9/17 (M)	Probability and stochastic processes The Poisson process and gamma random variables The nonhomogeneous Poisson process
4	9/24 (M)	Review for midterm exam 1
		└►	MID TERM EXAM 1: Thursday ~ September 27, 2012
5	10/1 (M)	Generating discrete random variables   The inverse transform method, acceptance-rejection technique, the composition approach
6	10/8 (M)	Generating continuous random variables Inverse transform, rejection method, polar method for generating normal random variables
7	10/15(M)	Generating processes (continued) Generating a Poisson process Generating a nonhomogeneous Poisson process
8	10/22(M)	Generating processes (continued) Generating a nonhomogeneous Poisson process (continued) Review for mid term exam 2
9	10/29(M)	└►	MID TERM EXAM 2: Monday ~ October 29, 2012
		Variance reduction techniques Antithetic variates
10	11/5 (M)	Variance reduction techniques (continued) Control variates Variance reduction by conditioning
11	11/12(M)	Variance reduction techniques (continued) Stratified sampling Importance sampling
12	11/19(M)	Variance reduction techniques (continued) Importance sampling
13	11/26(M)	Statistical analysis of simulated data   Sample mean and sample variance Interval estimates of  a population mean The bootstrap
14	12/3 (M)	Discrete event simulation approach Queueing systems
15	12/10(M)	Review for final exam
	12/14-12/20	FINAL EXAM WEEK

Prepared By:  Prof. Sundar Subramanian

Last revised:  May 15, 2012