Algebraic Number Theory (AlgNT)

Course 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.


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

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.

2+3 hours of lectures and 2+2 hours of exercises per week for 7 weeks.

Algebra 3 or similar.

Academic qualifications equivalent to a BSc degree is recommended.

Continuous feedback during the course of the semester
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.
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 minute oral examination without preparation.

Criteria for exam assessment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 35
  • Preparation
  • 73
  • Theory exercises
  • 28
  • Exam
  • 70
  • English
  • 206


Course number
7,5 ECTS
Programme level
Full Degree Master

1 block

Block 4
No limit
The number of seats may be reduced in the late registration period
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Mathematical Sciences
Contracting faculty
  • Faculty of Science
Course Coordinator
  • Ian Kiming   (6-6d6b6f6b7069426f63766a306d7730666d)
Phone +45 35 32 07 58, office 04.2.21
Saved on the 11-10-2023

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