NMAK17011U Algebraic Number Theory (AlgNT)
MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject
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.
Advanced Vector Spaces (AdVec).
Academic qualifications equivalent to a BSc degree is recommended.
- Category
- Hours
- Lectures
- 35
- Preparation
- 140
- Theory exercises
- 28
- Exam
- 3
- Total
- 206
- Credit
- 7,5 ECTS
- Type of assessment
- On-site written exam, 3 hours under invigilation
- Type of assessment details
- Three hours written on-site exam
- Aid
- All aids allowed except Generative AI and internet access
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner
- Re-exam
30 minute oral examination with no preparation time.
Criteria for exam assesment
The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.
Course information
- Language
- English
- Course code
- NMAK17011U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 4
- Schedule
- A
- Course capacity
- No limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinators
- Ian Kiming (6-6e6c706c716a437064776b316e7831676e)