FOUNDATIONS OF PROBABILITY THEORY
autumn 2007

The course covers, i.a.,

* Basics:
events and probabilities, measures, random variables and their distributions,
expectations with a view towards the Lebesgue integral, the first Borel-Cantelli lemma.

* Independence and Conditioning:
conditional probabilities, the second Borel-Cantelli lemma, the strong law
of large numbers, random walk and the Markov property.

* Transforms:
    probability generating functions, moment generating functions, Laplace
    transforms, Characteristic functions, Poisson approximation, the central
    limit theorem.

Now when we have entered a new century, it seems appropriate that
we have a course at the Master level that covers the foundations of
probability theory that were laid after the year 1900!

The book to be used is
Williams: Weighing the Odds (Cambridge University Press 2001).
It is available in paperback; the preliminary plan is to take
Chapters 1-5 as a base for the course.

The book shall be available at local book-stores in due time. If you like to
have a copy of the book right away: please order from your
favorite book-shop on the net.
To check it, click here: the book
If you like to know more about the author, click here: Williams

The course takes place in the second quarter of the academic year,
i.e., essentially November-December (until the Christmas break).

There will be three sessions à 2x45 minutes a week:
two of them for lectures, and one for classes, with exercises, examples, etc.

The preliminary schedule looks as follows:

lectures: Mondays and Wendesdays, 10.00-11.45
classes: Mondays, 13.15-15.00

See you!

Torgny Lindvall

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Clich here for some very influential people!

Two poineers of measure and integration theory:
H. Lebesgue E. Borel

and four dedicated to probability theory:
A. Khinchin A. Kolmogorov P. Lévy J. Doob