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Algebraic Number Theory (AlgNT)
Provider: Faculty of Science

Activity no.: 5584-23-07-31 
Enrollment deadline: 24/04/2023
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time24.04.2023, at: 08:00 - 23.06.2023, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserIan Kiming    E-mail address: kiming@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 4
Scheme groupA (Tues 8-12 + Thurs 8-17)
Exam formContinuous assessment
Exam formEvaluation via two sets of written assignments and a quiz at the end of the course
Exam detailsThe part-examinations are not weighted but assessed individually; an overall assessment is then applied. Aid: Only certain aids allowed. The quiz at the end of the course must be done without the use of textbook and notes.
Grading scalePassed / Not passed
Course workload
Course workload categoryHours
Lectures42.00
Preparation73.00
Theory exercises21.00
Exam70.00

Sum206.00


Content
Algebraic number fields and their rings of integers, trace, norm, and discriminants, prime decomposition in Dedekind domains and rings of integers, prime decomposition in quadratic and cyclotomic number fields, decomposition theory in Galois extensions, decomposition- and inertia groups and fields, quadratic reciprocity via decomposition theory, Frobenius automorphisms, the prime divisors of the discriminant and ramification, finiteness of class numbers, Dirichlet's unit theorem, the first case of Fermat's last theorem for regular primes.

Learning outcome
Knowledge: After completing the course the student will know the subjects mentioned in the description of the content.

Skills: At the end of the course the student is expected to be able to follow and reproduce arguments at a high, abstract level corresponding to the contents of the course.

Competencies: At the end of the course the student is expected to be able to apply abstract results from the curriculum to the solution of concrete problems of moderate difficulty.

Literature
See Absalon.

Teaching and learning methods
3 + 3 hours of lectures and 3 hours of exercises per week for 7 weeks.

Final quiz in week 8 of the course.

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