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
**

**--------------------------------------------------------------------**

**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**