NMAK17011U Algebraic Number Theory (AlgNT)
MSc Programme in Mathematics
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.
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.
Academic qualifications equivalent to a BSc degree is recommended.
Final quiz in week 8 of the course.
- Theory exercises
- 7,5 ECTS
- Type of assessment
- Continuous assessmentTwo one week exercises and a final one hour quiz in week 8 of the course. The final quiz must be passed with at least 40 points out of 100 as a prerequisite for passing the course. If this requirement is fulfilled, the final grade will be determined from an overall evaluation of the three elements. The three elements will be considered as having equal weight in the final evaluation.
- Only certain aids allowed
The quiz at the end of the course must be done without the use of textbook and notes.
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner.
30 minutes oral examination without preparation. One internal examiner.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.