NMAK17011U Algebraic Number Theory (AlgNT)

Volume 2024/2025
Education

MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject

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.
Advanced Vector Spaces (AdVec).

Academic qualifications equivalent to a BSc degree is recommended.
2 + 3 hours of lectures and 2+2 hours of exercises per week for 7 weeks.
  • Category
  • Hours
  • Lectures
  • 35
  • Preparation
  • 73
  • Theory exercises
  • 28
  • Exam
  • 70
  • Total
  • 206
Written
Oral
Individual
Continuous feedback during the course of the semester
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Type of assessment details
Two 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.
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-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.