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Syllabus Topics in Analysis - 80612
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Last update 15-09-2015
HU Credits: 2

Degree/Cycle: 2nd degree (Master)

Responsible Department: Mathematics

Semester: 1st Semester

Teaching Languages: Hebrew

Campus: E. Safra

Course/Module Coordinator: Prof. Jonathan Breuer

Coordinator Email:

Coordinator Office Hours: Wednesday, 12:00--13:00

Teaching Staff:
Prof Yoram Last

Course/Module description:
Szego's Theorems deal with the asymptotics of Toeplitz determinants and are of central importance in various areas of analysis. The course will survey several proofs of the two theorems and in particular various applications in random matrix theory, statistical mechanics, orthogonal polynomials and spectral theory.

Course/Module aims:
To study Szego's Theorems, their proofs and some of their applications.

Learning outcomes - On successful completion of this module, students should be able to:
to quote Szego's Theorems, to prove them and to describe applications.

Attendance requirements(%):

Teaching arrangement and method of instruction: Lecture

Course/Module Content:
1) Szego's Theorems and orthogonal polynomials.
2) The Law of Large Numbers and Central Limit Theorem in Random Matrix Theory.
3) Szego's Theorem and spectral stability.
4) Szego's Theorem and the Ising model.

Required Reading:

Additional Reading Material:

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:
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.