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MATH 691 Course Syllabus
NJIT HONOR CODE: All Students should be aware that the Department of Mathematical Sciences takes the NJIT Honor Code 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 Honor Code, students are obligated to report any such activities to the Instructor.
Math 691-101: Stochastic Processes with Applications
FALL 2009
Instructor: Prof. Bhattacharjee
Textbook: Introduction to Probability Models, 9th Edition by S. M. Ross. Academic Press © 2007; ISBN: 0-12-598062-0.
Prerequisites: Math 662.
Grading Policy: The final grade in this course will be determined using the following weight distributions over the performance components: (H),(M),(F). The weight distribution is subject to marginal modification.
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▪ Homework (H): |
35% |
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▪ Midterm Examination (M): |
30% |
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▪ Final Examination (F): |
35% |
Drop Date: Please note that the University Drop Date November 2, 2009 deadline will be strictly enforced.
Attendance Policy: Students must attend all classes. Absences from class will inhibit your ability to fully participate in class discussions. Tardiness to class is very disruptive to the instructor and students and will not be tolerated.
Examinations: One in-class midterm examination and one final examination will be given on the following days:
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Midterm Examination: |
October 15, 2009 |
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Final Examination: |
December 17, 2009 |
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.
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.
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Labor Day Holiday ~ University Closed |
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| M |
Last Day to Withdraw from this course |
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Classes follow a Thursday Schedule |
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November 25, 2009 |
W |
Classes follow a Friday Schedule |
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November 26-29, 2009 |
R-Su |
Thanksgiving Recess ~ University Closed |
Course Outline:
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Week |
Topics |
Notes |
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Week 1 |
Poisson Processes - I |
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Introductory examples, definitions, properties Typical applications |
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Week 2 |
Poisson Processes - II |
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Relationship to exponential distribution Interarrival and waiting times |
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Week 3 |
Poisson Processes - III |
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Nonhomogenious Poisson processes Compound and mixed Poisson processes |
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Week 4 |
Renewal Processes - I |
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The Renewal function Examples and Applications Associated renewal theorems |
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Week 5 |
Renewal Processes - II |
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The Poisson process as a renewal process Computing the renewal function Renewal reward processes |
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Week 6 |
Renewal Processes - III |
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Alternating renewal processes Replacement problems |
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Week 7 |
└► MIDTERM EXAM: Thursday ~ October 15, 2009 |
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Week 8 |
Discrete Time Finite / Countable Markov Chains - I |
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Introductory examples, definitions, time homogeneous chains Transition probability, probability matrix Communicating classes, classification of states |
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Week 9 |
Discrete Time Finite / Countable Markov Chains - II |
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Recurrence and Transience Return times |
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(Mon. Nov. 2) Last Day to Withdraw from this course |
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Week 10 |
Discrete Time Finite / Countable Markov Chains - III |
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Long run behavior, Stationary distribution Absorbing chains, time to absorption |
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Week 11 |
Continuous Time Markov Chains - I |
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Definitions, Motivating examples, Application: Poisson process Applications: special cases of Birth and death processes |
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Week 12 |
Continuous Time Markov Chains - II |
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Finite time transition probabilities Backward and forward Kolmoroff differential equations Infinitesimal generators, the embedded Markov chain and classification of states |
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(Tues. Nov. 24) Classes Follow A Thursday Schedule |
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Week 13 |
Continuous Time Markov Chains - III |
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Basic limit theorem for continuous time Markov chains General Birth and Death Processes Applications: queues, epidemic models |
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(Thurs.-Sun. Nov. 26-29) Thanksgiving Recess ~ University Closed |
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Week 14 |
Final Review |
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└► Review for Final |
└► Study for Final |
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Final |
Final EXAM: Thursday ~ December 17, 2009 |
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Prepared By: Prof. Manish Bhattacharjee
Last revised: August 3, 2009