APMA 120 - Operational Research: Probabilistic Methods-Spring 2012


Instructor: Konstantinos Spiliopoulos

Office: 37 Manning, Room 101
Office Hours: Thursdays 10:30-11:30 unless otherwise specified in class
Email: kspiliop_at_dam.brown.edu
to send me an email replace _at_ by @.

Meets:

TuTh... 9:00-10:20AM at Watson (CIT) Center 165


T.A.: Dane Johnson, email: Dane_Johnson_at_Brown.edu ; Yufei Liu, email: Yufei_Liu_at_Brown.edu


Office hours: Tuesdays 12:00-2:00 and Fridays 3:00-5:00 in room 104, 37 Manning Street
Recitation Session: Wedensdays 3-4:50 in CIT 227


Required Text: An Introduction to Stochastic Modeling, Mark Pinsky, Samuel Karlin, 4th Edition, Academic Press
Recommended Texts:

The class will be based mostly on the required text. However, we will use both of the recommended texts for certain parts of the course and for homework problems.


Course Description: Basic probabilistic problems and methods in operations research and management science. Methods of problem formulation and solution. The course will cover basic stochastic processes such as simple random walk, Markov chains, Martingales, Poisson processes, and Brownian motion. It will also offer introductory level treatment to stochastic optimization problems, such as optimal stopping and optimal control, based on dynamic programming principle.


Prerequisites: APMA 1650 or MATH 1610 or equivalent. The students are required to have a solid understanding of basic probability and calculus.



Syllabus (tentative)


I will try to follow the syllabus as closely as possible. However it may change depending on our progress. Any changes will be announced in class and posted here.


Homework assingments:
AssingmentDue DateAssignmentMaterial Covered
Homework 1 Tuesday Feb 7th Chapter 1: Ex 2.3,Pr 5.2, Chapter 2: Ex 1.5,3.5, Pr 1.4,1.7,2.1, 3.3(part (a) only). NOTE: Ex. 3.5 and Pr. 1.7 and 2.1 from Chapter 2 are optional Chapter 1: review, Chapter 2: Sections 1-3
Homework 2 Thursday Feb 9th Chapter 2: Ex 4.2, 4.5, Pr 4.3, 5.1, 5.3 Chapter 2: Sections 4-5
Homework 3 Thursday Feb 16th Ex: 3.5, 4.3, 4.7 Pr: 2.4,3.4, 3.8, 4.1,4.6,4.17 Chapter 3: Sections 1-4
Homework 4 Thursday Feb 23th Ex:5.2,6.4, 8.1,9.1,9.2 and Pr: 6.2,8.4,9.3,9.8 Chapter 3: Sections 5-9
Homework 5 Thursday March 1st Ex: 1.3, 1.4, 1.10, Pr. 1.5,1.6, 1.10, 2.3 Chapter 4: Sections 1-2
Homework 6 Thursday March 8th Ex: 3.1, 3.2, 4.2, Pr. 3.2, 4.2, 4.5 Chapter 4: Sections 3-4
Homework 7 Thursday March 15th Ex: 1.1,1.4,1.6,2.2 and Pr.1.5,1.6,2.1,2.4 Chapter 5: Sections 1-2
Homework 8 Thursday March 22th Ex: 3.8,4.5,6.2 and Pr. 3.3,3.8,3.10,4.4,4.6,4.7,6.3 Chapter 5: Sections 3,4,5,6
Homework 9 Thursday April 5th Ex. 1.3, 1.5, 3.1 Pr. 1.3,1.4,1.13, 2.2, 3.1, 3.2 Chapters 6, Sections 1, 2, 3
Homework 10 Thursday April 12th Ex. 4.1, 4.5 Pr. 3.3 (use the result of exercise 3.3), 4.2,4.5, 5.2, 6.2, Chapters 6, Sections 4,5,6
Homework 11 Thursday April 19th Ex. 1.4,2.2,4.6 Pr. 1.2,1.3,3.2,3.5,4.1 Chapter 7, Sections 1,2,3,4
Homework 12 Thursday April 26th Ex. 1.2, 1.5a), 4.2, 4.5 Pr. 1.3, 2.4, 4.7, 4.9 Chapter 8,Sections, 1,2,3,4


Currently the Exam schedule is as follows:
DateAssignmentMaterial Covered
Thursday, March 8th, 9am, regular class time Midterm Chapters I,II,III (excluding section 7),IV (excluding section 5) from the book
May, 15th at 02:00 PM Final


Tentative grading policy: Your grade will be based on :(a) Homework (35%), (b) midterm exam (35%) and final exam (30%). The grading policy may change depending on the progress of the class.


Exam & Homeworks:
Exams: There will be one midterm exam and one final exam. The exam material for each one of the two exams will be announced in class and posted on the webpage of the course. The final exam will concentrate on the material that was taught from the previous test and then. However, I reserve the right to include a couple of questions from the material of the previous exam. Hence, make sure that you have learned from your mistakes.
Homeworks: There will be several homeworks, both theoretical and more of applied flavor. The due date of each homework will be announced in class and it will usually be 7-10 days after. Needless to say, you should work on the homework on your own, unless otherwise instructed by me. Late homeworks will be heavily penalized.


Make-up policy: Make up exams will be given only in extreme circumstances, and only when accompanied by appropriate documentation. Any student with a valid reason to be given a make up exam must contact me prior to the exam, either by email or in person, and present documentation at the next class session attended.