MAST30001 - Stochastic Modelling

  Lecturer: Nathan Ross Office: 147 Richard Berry Office Hours: Wed 2-4 and by appt
  Tutor: Kevin Vo SSLC Rep: Justin Smallwood
  Lecture Schedule:
Mon 9-10, Richard Berry - Russell Love Theatre
Wed 9-10, Old Geology - Theatre 2
Thurs 10-11, Old Engineering - A1 Theatre
Wed 1-2, Richard Berry - 213
Thurs 2:15-3:15, Richard Berry - Russel Love Theatre
  Prerequisites: Calculus (derivatives, sequences, series, integrals, etc), epsilon-delta style proofs and a first course in probability. See the handbook for more details.
  Subject Overview (from the handbook): Stochastic processes occur in finance as models for asset prices, in telecommunications as models for data traffic, in computational biology as hidden Markov models for gene structure, in chemistry as models for reactions, in manufacturing as models for assembly and inventory processes, in biology as models for the growth and dispersion of plant and animal populations, in speech pathology and speech recognition and many other areas.

This course introduces the theory of stochastic processes including Poisson processes, Markov chains in discrete and continuous time, and renewal processes. These processes are illustrated using examples from real-life situations. It then considers in more detail important applications in areas such as queues and networks (the foundation of telecommunication models), finance, and genetics.

  Assessment: As per the handbook, there will be two written homework assignments (due dates below) and a final examination. All assignments must be handed in by the due date and the exam must be taken at the time it's given (unless you qualify for special consideration; and please contact me if that is the case). Problems for the assignments and additional "recommended" problems will be given as material is covered and it will greatly help your understanding of lectures to do problems soon after they are posted. (Doing this will also help you to not have to do all of the problems the night before the assignment is due!)  
  Assessment dates:
Assignment 1: Due Mon, 9 Sept in lecture
Assignment 2: Due Mon, 21 Oct in lecture
Final Exam: Check Exam Timetable
Grading Distribution:
Assignment 1: 10%
Assignment 2: 10%
Final Exam: 80%
Prescribed Text:
Title: Elements of Stochastic Modelling
Author: K. Borovkov
ISBN: 981-238-301-8
  The text: There are copies of the book on reserve in the ERC Library (overnight loan) and the Giblin Eunson Library (overnight and two hour loan). We will be following the book closely, so it is a good resource for the course.
  Plagiarism: All students are required to to fill out and sign one plagiarism declaration form and hand it in with the first assignment. No assignment feedback or marks will be given until the form has been filled out and signed. You may consult with others regarding homework solutions, but must write your own solutions. Any further level of collaboration in the course (such as copying a solution verbatim or reading another student's solution during an exam) constitutes cheating and is strictly prohibited.  
  Some general remarks about the course: I will be using LMS to make announcements and also to keep your grades so that you can check that no mistakes have been made (something I recommend that you do). I will only answer emails that have questions of a timely nature - other questions can be asked directly to me in lecture, practicals or office hours. It is extremely important that you keep up on the homework; it not only affects your grade directly, but also largely determines your success on the exam.
  Assignment Problems:
  Assignment 1: PDF
Assignment 2: PDF
  Recommended Problems:
  Chapter 2: 1 - 9, 14, 32, 33, 38
Chapter 2 Additional: PDF
Chapter 3 (Part I): 1, 3, 11, 12
Chapter 3 Additional (Part I): PDF
Chapter 3 Additional (Part II): PDF
Chapter 3 (Part II): 5, 8, 15, 18
Chapter 3 Additional (Part III): PDF
Chapter 4: 2
Chapter 4 Additional: PDF
Chapter 5: 1, 3, 5, 6, 8, 9
Chapter 5 Additional: PDF
Chapter 6: 4, 6, 8, 9
Chapter 6 Additional: PDF
Chapter 7: 1 - 6, 10, 11, 13
Chapter 7 Additional: PDF
Chapter 8: 2
  Rough Course Outline:
Chapter 2: 6 lectures
Chapter 3: 8 lectures
Chapter 4: 2 lectures
Chapter 5: 4 lectures
Chapter 6: 5 lectures
Chapter 7: 5 lectures
Chapter 8: 3 lectures
Application: 1 lecture
Review: 2 lectures