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HU Credits:
3
Degree/Cycle:
2nd degree (Master)
Responsible Department:
Mathematics
Semester:
1st Semester
Teaching Languages:
English and Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Ari Shnidman
Coordinator Office Hours:
By appointment
Teaching Staff:
Dr. Schneidman Ari
Course/Module description:
Introduction to the basic properties of algebraic numbers.
Course/Module aims:
Getting acquainted with the basic properties of the rings of integers in number fields, decomposition of prime ideals in extensions, p-adic numbers, Hensel's lemma, finiteness of the class number, finite generation of the group of units.
Learning outcomes - On successful completion of this module, students should be able to:
- to compute rings of integers in algebraic number fields of low degree
- to decompose an ideal to a product of primes
- to evaluate the ramification indices and inertial degrees of primes in extensions of low degree
- to compute units of number fields
- to prove simple properties of algebraic number fields.
Attendance requirements(%):
Teaching arrangement and method of instruction:
Lecture
Course/Module Content:
Traces and norms, discriminants, integral ring extensions, Number fields, integer rings, Dedekind rings, ramification and inertia, cyclotomic fields, the geometric embedding, p-adic fields, Hensel's lemma, finiteness of the class group, the structure of the group of units.
Required Reading:
None
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:
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