Course Outline

- email: salt@yorku.ca
- Office: N536 Ross Building
- Personal homepage: www.math.yorku.ca/~salt/
- Phone: (416) 736-2100 extension 33921

- Departmental office: N520 Ross Building, (416) 736-5250, FAX: (416) 736-5757
- Undergraduate Program office: N502/503 Ross Building, (416) 736-5902
- Graduate Program office: N519 Ross Building, (416) 736-2100, ext. 33974

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).

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 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.

- 20% Midterm test (Tentative date: Friday October 17)
- 20% Midterm test (Tentative date: Monday November 10)
- 15% Assignments
- 45% Final exam

- I will mark the midterm and finals. Our TA will mark the assignments. Restrictions on TA hours mean that only a selection of the assignment problems will be marked.
- No late assignments will normally be accepted, but I will drop everybody's worst assignment mark.
- Assignments may be handed in in class or dropped in the course mailbox (one of the brown boxes by the north elevator of the 5th floor of Ross will soon have our course number on it).
- All assignment, quizz, and exam marks should be interpreted as raw scores and not 'percentages'. Cutoffs will be announced for converting midterm scores into letter grades. The distribution of scores will be announced for both the midterms.
- There will be no makeup midterm examinations. If you miss a midterm exam due to illness, and can supply an acceptable note from your doctor, then I will give more weight to your final examination results. This will be done by calculating an equivalent midterm score based on your ranking on the final.

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.

- Students with disabilities may obtain advice from the disability services office, including alternate exams and test accommodation services. See www.yorku.ca/altexams for further information.
- Students are expected to be familiar with York's policies on academic integrity. See www.yorku.ca/academicintegrity/students/index.htm for details.