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.

Education

MSc Programme in Mathematics

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.

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

Final quiz in week 8 of the course.

Algebra 3 or similar.

Academic qualifications equivalent to a BSc degree is recommended.

Continuous feedback during the course of the semester
ECTS
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.
Criteria for exam assessment

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

Single subject courses (day)

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

Kursusinformation

Language
English
Course number
NMAK17011U
ECTS
7,5 ECTS
Programme level
Full Degree Master
Duration

1 block

Schedulegroup
A
Capacity
No limit
Studyboard
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Mathematical Sciences
Contracting faculty
  • Faculty of Science
Course Coordinator
  • Ian Kiming   (6-6f6d716d726b447165786c326f7932686f)
Phone +45 35 32 07 58, office 04.2.21
Saved on the 12-06-2019

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