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HU Credits:
2
Degree/Cycle:
2nd degree (Master)
Responsible Department:
Mathematics
Semester:
2nd Semester
Teaching Languages:
Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Dan Mangoubi
Coordinator Office Hours:
Teaching Staff:
Prof. Dan Mangoubi
Course/Module description:
Classical proofs in transcendental number theory.
Lectures are given by students.
Possible topics include:
Hermite's proof on the transcendence of e,
Lindemann's proof on the transcendence of π.
Padé approximations,
Hilbert 7th problem: 2^{sqrt{2}} is transcendental,
Baker's theorem on linear forms in logarithms of algebraic numbers.
Diophantine approximations: Dirichlet's theorem, Liouville Theorem, Thue's theorem.
Continued fractions,
Siegel's theory on values of E-functions.
Course/Module aims:
Exposure to fascinating theorem of transcendental number theory, with methods bridging analysis and number theory.
Learning outcomes - On successful completion of this module, students should be able to:
Understanding ideas in transcendental Number Theory with a view towards Spectral Geometry.
Attendance requirements(%):
100
Teaching arrangement and method of instruction:
Course/Module Content:
See course description
Required Reading:
-
Additional Reading Material:
Siegel - Transcendental Numbers
Lang-Introduction to transcendental numbers
Niven, Irrational numbers
Waldschmidt, introduction to Diophantine methods
Sound- Transcendental Number Theory
Grading Scheme :
Presentation / Poster Presentation / Lecture 100 %
Additional information:
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