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York University

AS/SC/AK/MATH 4430 3.0AF/6602 3.0AF (Fall 2008)

Course Outline


Elementary Probability - MATH 2030 3.0; An additional prerequisite or corequisite is any mathematics course at the 3000 level or higher, without 2nd digit 5. The material on elementary probability is essential. The other requirement is intended to ensure sufficient mathematical maturity to handle the course content, rather than covering specific topics.

Instructor/Contact Information:

Tom Salisbury Department of Mathematics and Statistics


MWF 10:30-11:20 in Curtis Lecture Hall J
This is an integrated course. In other words, an undergraduate course and a graduate course meeting at the same time and place, with the same lectures. The graduate and undergraduate versions differ in terms of the readings and assignments, and are using different textbooks (by the same authors however).

Course Webpage:

Office hours:

Monday 1:00-2:00, Wednesday 12:00-1:00 (subject to change).
If you need to see me outside these hours, you are welcome to try dropping by my office. If I am able to talk to you then, I will; if not we can arrange another time. Or you can e-mail me to arrange an appointment.


MATH 4430: An introduction to stochastic modeling by Taylor and Karlin; Academic Press, 3rd edition The basic course material is found in chapters 3, 4, 6, and 8. But we will pull additional topics from the other chapters as needed.

MATH 6602: A first course in stochastic processes by Karlin and Taylor; Academic Press, 2nd edition The basic course material is found in chapters 2, 3, 4, and 7. But we will pull additional topics from the other chapters as needed.


To be announced


There will be, two 50 minute midterm test, and a 3 hour final exam (during the university examination period). Homework will be assigned for credit. Other information about grading:

Course description:

This course continues the study of probability theory, started in elementary courses such as MATH 2030. In elementary courses one studies individual random variables X, and then sums S(n) of independent random variables X(n) through results such as the law of large numbers and the central limit theorem. Courses such as MATH 2131 go further into the study of dependencies between small numbers of random variables. In MATH 4430/6602 or its companion course MATH 4431/6604 we go on to study more general sequences of random variables Z(n) , now called discrete-time stochastic processes. We also study continuous-time stochastic processes Z(t), that is, families of random variables indexed by a continuously varying time parameter t.

The idea is that we are looking at how random quantities change over time. As such, stochastic processes form a key modeling tool, as most random physical quantities do indeed evolve over time. Examples include the weather, positions of particles (eg in physics), credit ratings, stock prices, mortality, reliability, etc. The particular class of stochastic processes studied most intensively in MATH 4430/6602 are Markov chains both discrete and continuous. We will also study a related process, known as Brownian motion. All these stochastic processes have the property that in predicting the future evolution of the process, all we need to know is the present state of the process, not its whole history. This is commonly the case in physics or economics (in economics it is known as the efficient markets hypothesis). Under this assumption we can in fact calculate many interesting properties of the processes, and we will focus on developing the tools to carry out these calculations.

Students may take both MATH 4430/6602 and MATH 4431/6604, in any order. They are normally given in alternate years. Both courses are relevant to a variety of other mathematical topics, including actuarial science, operations research, economics and finance.

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