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MATH 6605 3.00AF (Fall 2010)
Probability Theory
Description:
The course will cover the probabilistic techniques required for
rigorous work in probability and statistics at the graduate level. We
will start by studying notions of convergence in probability theory,
such as the weak law of large numbers, the Borel-Cantelli lemma, the
strong law of large numbers, the law of the iterated logarithm, characteristic
functions, weak convergence, and the central limit theorem.
If time permits, we will go on to other topics, which may be chosen with
the interests of the class in mind. For example, we could look at weak
convergence of stochastic processes and Donsker's theorem (topics
essential for the study of empirical processes in statistics, or for
constructing Brownian motion).
Prerequisites:
Undergraduate probability and mathematical analysis. Measure theory
is an asset, but is not required.
Course Webpage:
www.math.yorku.ca/~salt/courses/6605f10/6605.html
Instructor/Contact Information:
Tom Salisbury
Department of Mathematics and Statistics
- Departmental office: N520 Ross Building, (416) 736-5250,
FAX: (416) 736-5757
- Graduate Program office: N519 Ross Building, (416) 736-3974
Lectures:
MWF 9:30-10:20, in BC 228
Office hours:
Wed 2-3, Fri 11-12
I will try to post a notice on the course webpage if other commitments make
it necessary to reschedule one or more office hour.
If you need to see me outside these hours, you are welcome to e-mail or call
me to try to arrange an appointment.
Text:
- A first look at rigorous probability theory by Jeff Rosenthal,
2nd edition, World Scientific 2006
Grading:
- 25% Assignments
- 25% Midterm exam (Friday October 22)
- 50% Final exam
Other information:
- There will be no makeup midterm assignments.
If you miss one due to illness (with an
acceptable note from your doctor), or some other valid reason then I
will simply count your final exam for more.
- Students are responsible for reviewing the
Student Information Sheet maintained by the university, which outlines
policies on academic honesty, access and disability, religious observance
accommodation, and student conduct.