MM825: Algebra (5 ECTS)

STADS: 13000001

Level
Master's level course approved as PhD course

Teaching period
The course is offered when needed.

Teacher responsible
Email: hillary@imada.sdu.dk

Timetable
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Comment:
Ubegrænset deltagerantal. 4.kvartal.

Prerequisites:
None

Academic preconditions:
Basic notions of linear algebra should be known or the student should be familiar with concepts of groups and rings.

Course introduction
The course introduces basic concepts of field extensions and Galois theory and applications thereof.

Expected learning outcome
At the end of the course, the student will be able to:

• reproduce definitions and results within the syllabus of the course 
• apply the theory to solve problems within the socpe of the syllabus of the course 
• argue in a mathematically correct and stringent way the steps in the solution of given problems 
• supply stringent and complete proofs for statements within the syllabus of the course 
• identify and descirbe mathematical structures within the scope of the syllabus of the course in specific examples

Subject overview
Algebraic extensions, factorization, polynomial rings as field extensions, Galois extensions, finite fields, cyclic groups,  group actions.

Literature

• Meddeles ved kursets start.: .

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
Mandatory assignments. Must be pasted to participate in the oral exam (13000012)

Assessment and marking:
Oral exam, Danish 7 mark scale, internal examiner (5 ECTS). (13000002)

Reexam in the same exam period or immediately thereafter. The reexam may differ from the ordinary exam.

Expected working hours
The teaching method is based on three phase model.
Intro phase: 28 hours
Skills training phase: 20 hours, hereof:
 - Tutorials: 20 hours

Educational activities

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.