1st degree (Bachelor)
Coordinator Office Hours:
Prof Benjamin Weiss
A second course in probability theory, from the standpoint of measure theory. The course revolves around stochastic processes, their invariants and convergence. These topics are studies via classical tools such as characteristic function, and modern tools such as martingales.
Same as in learning outcomes.
Learning outcomes - On successful completion of this module, students should be able to:
Establishing probability theory on the shoulders of measure thoery.
Ability to prove the fundamental theorems in that theory in a general form.
Relating probability theory and harmonic analysis via characteristic functions.
Understanding discrete stochastic processes through the notion of a martingale.
familiarity with the wiener process (Brownian motion), and deriving its basic properties from simple random walks.
Teaching arrangement and method of instruction:
Convergence of random variables
Law of large numbers
Central limit theorem
Additional Reading Material:
Probability with martinagles / Williams
End of year written/oral examination 0 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 100 %
Assignments 0 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %