The Hebrew University Logo
Syllabus Seminar in analysis: Irrational numbers - 80808
close window close
PDF version
Last update 12-08-2020
HU Credits: 2

Degree/Cycle: 2nd degree (Master)

Responsible Department: Mathematics

Semester: 1st Semester

Teaching Languages: Hebrew

Campus: E. Safra

Course/Module Coordinator: Dan Mangoubi

Coordinator Email:

Coordinator Office Hours:

Teaching Staff:
Prof Dan Mangoubi

Course/Module description:
We follow the book Irrational numbers by I. Niven:
1) e is transcendental (Hermite, 1873)
2) pi is transcendental (Lindemann, 1882)
3) Liouville numbers
4) Continued franctions
5) Hilbert's seventh problem and Gelfond-Schneider's Theorem (1934) If a, b are algebraic then a^b is transcendental (unless a&eq;0 or 1).

Course/Module aims:

Learning outcomes - On successful completion of this module, students should be able to:
Acquaintance with ideas of Diophantine approximation and Transcendental Number Theory.

Attendance requirements(%):

Teaching arrangement and method of instruction: Lectures by students

Course/Module Content:
See course description.

Required Reading:

Additional Reading Material:
Irrational Numbers, Niven.
Transcendental Numbers, Siegel.
The Theory of Numbers, Hardy and Wright.

Course/Module evaluation:
End of year written/oral examination 0 %
Presentation 80 %
Participation in Tutorials 20 %
Project work 0 %
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.