NMAK17011U  Algebraic Number Theory (AlgNT)

Volume 2017/2018
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 of the course.
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.
The 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.

Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner.
Re-exam

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.

  • Category
  • Hours
  • Lectures
  • 42
  • Theory exercises
  • 21
  • Exam
  • 70
  • Preparation
  • 73
  • Total
  • 206