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.
Final quiz in week 8 of the course.
- 7,5 ECTS
- Type of assessment
- Continuous assessmentEvaluation via two sets of written assignments and a quiz at the end of the course.
The part-examinations are not weighted but assessed individually; an overall assessment is then applied.
- 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.
- Theory exercises