MATH 477-002 Stochastic Processes Course Syllabus - SPRING 2014
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: This course introduces the theory and applications of random processes needed in
various disciplines such as mathematical biology, finance, and engineering. Topics include discrete and
continuous Markov chains, Poisson processes, as well as topics selected from Brownian motion, renewal
theory, and simulation.
Prerequisites: Math 244 with a grade of C or better or Math 333 with a grade of C or better and Math
337 with a grade of C or better.
Textbook: Introduction to Probability Models, Tenth Edition by S. Ross, Academic Press, ISBN: 978-012-375686-2
Additional References:
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S. Karlin and H. Taylor, A First Course in Stochastic Processes, contains a more theoretical
treatment of many of the topics of this course.
P. Hoel, S. Port, and C. Stone, Introduction to Stochastic Processes, is a classical introduction to
stochastic processes.
H. Taylor and S. Karlin, An Introduction to Stochastic Modeling, is similar in breadth and depth as
our textbook.
Student Learning Outcomes: On successful completion of this course, a student will be able to
demonstrate understanding of discrete and continuous Markov chains, Poisson processes, as well as
topics selected from Brownian motion, renewal theory, and simulation.
Assessment: Will be based on regular homework assignments, a mid-term exam, and a final exam.
Instructor: (for specific course-related information, follow the link below)
MATH 477-002 (TR)
S. Subramanian
Grading Policy: The final grade in this course will be determined as follows:
▪ Homework
30%
▪ Midterm Exam
35%
▪ Final Exam
35%
Final letter grade will be based on the following tentative curve.
A
90-100
C
65-74
B+
85-89
D
50-64
B
80-84
F
0-49
C+
75-79
Drop Date: Please note that the University Drop Date March 31, 2014 deadline will be strictly enforced.
Homework and Quiz Policy: Homework will be assigned in class and will be due on the date specified
by the instructor. No late homework will be accepted.
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.
Exams and Exam Policy: There will be a midterm exam during the semester and a final exam during
the final exam week. Exams will be held on the following days:
Mid Term exam
March 13, 2014
Final Exam Week
May 8 - 14, 2014
Make sure you read and fully understand the department's Examination Policy . This policy will be
strictly enforced. Please note that electronic devices (such as programmable calculators, CD players,
etc.) are not allowed during any exam.
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.
Cellular Phones: All cellular phones and beepers must be switched off during all class times and exams.
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.
January 20, 2014
March 16 - 23, 2014
March 31, 2014
April 18, 2014
May 6, 2014
May 7, 2014
May 8 -14, 2014
M
F
M
F
T
W
R- W
Martin Luther King, Jr. Day ~ No classes
Spring recess ~ No Classes
Last Day to withdraw from this course
Good Friday-No Classes
Classes follow a Friday Schedule
Reading Day
Final Exams
COURSE OUTLINE:
Week
Topic
Week 1
1/21 (T)
Week 2
1/28 (T)
Week 3
2/4 (T)
Week 4
2/11 (T)
Week 5
2/18 (T)
Week 6
2/25 (T)
Week 7
3/4 (T)
Week 8
3/11 (T)
Week 9
3/16 to
3/23
Week 10
3/25 (T)
Week 11
4/1 (T)
Week 12
4/8 (T)
Week 13
4/15 (T)
Week 14
4/22 (T)
Week 15
5/7 (W)
5/8 5/14
Review of Basic Probability
Common Discrete and Continuous Distributions
Common Discrete and Continuous Distributions
Moment Generating Functions
Conditional Probability
Discrete-Time Markov Chains
Chapman--Kolmogorov Equations
Classification of States
Limiting Probabilities
Mean Time in Transient States
Poisson Processes
Poisson Processes
Poisson Processes
REVIEW FOR EXAM #1
MIDTERM EXAM: THURSDAY ~ MARCH 13, 2014
SPRING RECESS ( NO CLASSES)
Continuous--Time Markov Chains
Birth and Death Processes
Transition Probabilities
Time Reversibility
Stationary Processes
Brownian Motion
Gaussian Processes
White Noise
Pricing Stock Options
REVIEW FOR FINAL EXAM
Reading Day
FINAL EXAM WEEK
Prepared by Sundar Subramanian