TAU:0366-3098
| Probability for mathematicians
| Semester 2, 2010/2011
|
- Lecturer
- Prof. Boris Tsirelson
(School of Mathematical Sciences).
- Time and place
- Monday 12-14 Holcblat 007 (Melamed);
Wednesday 15-16 Ornstein 103.
- Instructor
- Boaz Slomka
- Prerequisites
- Functions of a real variable; calculus 3 (in parallel); introduction to
probability theory.
- Grading policy
- The final exam.
LECTURE NOTES
RESULTS FORMULATED
- Part A: Independence
(long independent sequences; central limit theorem; infinite independent sequences).
- Part B: Stopping
(random walks; Markov chains).
- Part C: Dependence
(martingales; conditioning).
PROOFS AND MORE
TEXTBOOKS
- KORALOV Leonid, SINAI Yakov,
"Theory of probability and random processes"
(second edition, Springer, 2007).
- DURRETT Richard,
"Probability: theory and examples"
(second edition, Cornell/Wadsworth 1996).
- WILLIAMS David,
"Probability with martingales"
(Cambridge 1991-2008).
- POLLARD David,
"A user's guide to measure theoretic probability"
(Cambridge 2002).
EXAMS (in Hebrew)
Some quotes:
Probability theory has a right and a left hand.
On the left is the rigorous foundational work using the tools of measure
theory.
The right hand `thinks probabilistically'.
DURRETT, page xii (after Breiman).
...measure theory, that most arid of subjects when done for its own sake,
becomes amazingly more alive when used in probability, not only because it is
then applied, but also because it is immensely enriched.
...
But what really enriches and enlivens things is that we deal with lots of
sigma-algebras, not just the one sigma-algebra which is the concern of measure
theory.
WILLIAMS, page xi.
Of course, intuition is much more important than knowledge of measure theory.
WILLIAMS, page xii.
♦ signifies something important, ♦♦ something very important,
and ♦♦♦ the Martingale Convergence Theorem.
WILLIAMS, page xiv.