NMAK13002U Algebraic Number Theory (AlgNT)

Volume 2013/2014
Education
MSc Programme in Mathematics
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.
Algebra 3 or similar.
3 + 3 hours of lectures and 3 hours of exercises per week for 7 weeks.

Final quiz in week 8 or 9 of the course.
  • Category
  • Hours
  • Exam
  • 70
  • Lectures
  • 42
  • Preparation
  • 73
  • Theory exercises
  • 21
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Evaluation via two sets of written assignments and a quiz at the end of the course
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner.
Re-exam
30 minute oral examination without preparation. Several internal examiners.
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.