Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

Algebra 3 (Alg3)

Practical information
Study year 2016/2017
Block 1
Programme level Full Degree Master
Course responsible
  • Ian Kiming (6-716f736f746d4673677a6e34717b346a71)
Phone +35 32 07 58, office 04.2.21
  • Department of Mathematical Sciences
Course number: NMAA05014U

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 and nilpotent groups, radical extensions and solvability via root extractions, constructions with straightedge and compass, finite fields, quadratic reciprocity.

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.

Recommended prerequisites

Algebra 2 (Alg2)

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MSc programme in Mathematics


Study Board of Mathematics and Computer Science

Course type

Single subject courses (day)


1 block


---- SKEMA LINK ----

Teaching and learning methods

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

Final part of the evaluation in week 8.


No limit




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


Type of assessment

Continuous assessment
Two one week exercises and a final one hour quiz in week 8 of the course. The three elements count a third of the grade each.


All aids allowed

Marking scale

7-point grading scale

Criteria for exam assessment

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

Censorship form

External censorship


30 minute oral examination without preparation

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