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AS/SC/AK/MATH 4430 3.0AF/6602 3.0AF (Fall 2008)
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.
Department of Mathematics and Statistics
- 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
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).
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.
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.
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:
- 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.
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.