Probability theory, or Introduction to random processes.
Grading policy
Based on oral reports and written abstracts.
Topics (for your choice)
More than 300 proofs of Pythagorean theorem are collected.
(Hint.)
What about the Central Limit Theorem (CLT)?
Let us collect and compare as many proofs of CLT as we can.
(Hint.)
In addition, we may consider (a) lacunary trigonometric series
(Hint.)
and (b) moderate deviations.
Random walk is recurrent in dimension 2 (and 1), but transient in dimension 3
(and more).
Let us collect and compare as many proofs of this fact as we can.
(Hint.)