PROBABILITES AND EXPECTATIONS, 7.5 credit points autumn 2011 
Teacher: Torgny Lindvall, office MVH3015, phone connection: 3574,  e-mail:
The fundaments of modern probability theory were laid in the first decades of the 20:th century, following the development of measure and integration theory. In this course, we will carefully study the connections between
- measures and probabilities,
- integrals and expectations, and
- product spaces and independence.
A crucial role here is played by  Dynkin's lemma, using so called  pi-systems, which are very convenient and effecient to use in probability theory.
The last main topic of the course is characteristic functions (= Fourier transforms of probability measures) and their use to prove  the central limit theorem.
Among other topics, we notice Kolmogorov's 0-1 law, and a probabilistic proof
of Weierstrass' approximation theorem.

The book
to be used is:
David Williams: Probability with Martingales, Cambridge University Press.
It is available in paperback.

If you are curious about the author, you may click here :  Williams.

And you may consult the excellent site MacTutor archive to learn about the  pioneers of measure and integration theory,  and  probability theory:  Borel, Lebesgue, Kolmogorov, Khinchin, Levy...

The preliminary schedule is that we meet on Mondays and Wendesdays,  10-12.
However, if that is not suitable, then we find other hours.  The first session is on

Monday, 29 August, 10.00-11.45 in MVL15.

See you then!
Torgny Lindvall