The Hebrew University Logo
Syllabus PROBABILITY THEORY (2) - 80421
עברית
Print
 
close window close
PDF version
Last update 27-07-2020
HU Credits: 3

Degree/Cycle: 1st degree (Bachelor)

Responsible Department: Mathematics

Semester: 2nd Semester

Teaching Languages: Hebrew

Campus: E. Safra

Course/Module Coordinator: Benjamin Weiss

Coordinator Email: weiss@math.huji.ac.il

Coordinator Office Hours: By appointment

Teaching Staff:
Prof Benjamin Weiss

Course/Module description:
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.

Course/Module aims:
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.

Attendance requirements(%):
0

Teaching arrangement and method of instruction: Lecture

Course/Module Content:
Convergence of random variables
Law of large numbers
Characteristic functions
Central limit theorem
Martingales

Required Reading:
Lecture notes

Additional Reading Material:
Probability with martinagles / Williams

Course/Module evaluation:
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 %

Additional information:
none
 
Students needing academic accommodations based on a disability should contact the Center for Diagnosis and Support of Students with Learning Disabilities, or the Office for Students with Disabilities, as early as possible, to discuss and coordinate accommodations, based on relevant documentation.
For further information, please visit the site of the Dean of Students Office.
Print