Algebra 3 (Alg3)

Course content

Field extensions, algebraic extensions, splitting fields, separable polynomials and extensions, cyclotomic polynomials and extensions, Galois theory, composite fields, Galois groups of polynomials, abelian extensions over Q, solvable groups, radical extensions and solvability via root extractions, finite fields, quadratic reciprocity.

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 part of the evaluation in week 8.

Algebra 2 (Alg2)

Academic qualifications equivalent to a BSc degree is recommended. Additionally it is recommended that students have written their Bachelor project before taking the course.

Continuous feedback during the course of the semester
ECTS
7,5 ECTS
Type of assessment
Continuous assessment
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 35 points out of 100 as a prerequisite for passing the course. If this requirement is fulfilled, the final grade will be determinded from an overall evaluation of the three elements. The three elements will be considered as having equal weight in the final evaluation.
Aid
Written aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship
Criteria for exam assessment

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

Single subject courses (day)

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