# MAT2200 – Groups, Rings and Fields

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## Changes in the course due to coronavirus

Autumn 2020 and Spring 2021 the exams of most courses at the MN Faculty will be conducted as digital home exams or oral exams, using the normal grading scale. The semester page for your course will be updated with any changes in the form of examination.

Please note that there may be changes in the form of examination for some courses taught Spring 2021. We aim to bring both the course description and the semester page of all courses up to date with correct information by 1 February 2021.

## Course content

The course gives an introduction to group and ring theory with emphasis on finite groups, polynomial rings, and field extensions.

## Learning outcome

After completing the course you:

• know the fundamental definitions and results in group theory, including the Lagrange Theorem, group homomorphisms, the relation between normal subgroups and quotient groups, and the isomorphism theorems;
• will have detailed knowledge of the structure of finitely generated abelian groups and permutation groups, and you will have learned about cyclic, dihedral, symmetric, and alternating groups;
• have learned about group actions, orbits and stabilizer groups, and the symmetry groups of certain geometric figures
• know the fundamental concepts and results in ring theory, including the concepts of an ideal, quotient ring, integral domain, and field, and you will have seen examples of finite rings and fields
• will have learned about principal ideal domains and in more detail about polynomial rings in one variable, and you will know the fundamental properties of finite field extensions
• will know the proofs and applications of central theorems in one or more of the subjects:
• elementary number theory
• Burnside’s Theorem
• the Sylow Theorems
• Galois theory
• classical results on constructibility.

Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

In addition to fulfilling the Higher Education Entrance Qualification, applicants have to meet the following special admission requirements:

• Mathematics R1 (or Mathematics S1 and S2) + R2

And in addition one of these:

• Physics (1+2)
• Chemistry (1+2)
• Biology (1+2)
• Information technology (1+2)
• Geosciences (1+2)
• Technology and theories of research (1+2)

The special admission requirements may also be covered by equivalent studies from Norwegian upper secondary school or by other equivalent studies (in Norwegian).

## Overlapping courses

• 9 credits overlap with MA131.
• 9 credits overlap with MA220.
• 9 credits overlap with MA120.

## Teaching

4 hours of lectures/exercises per week throughout the semester.

The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.

## Examination

Final oral exam which counts 100 % towards the final grade.

This course has 1 mandatory assignment that must be approved before you can sit the final exam.

### Examination support material

No examination support material is allowed.

### Language of examination

Courses taught in English will only offer the exam paper in English. You may write your examination paper in Norwegian, Swedish, Danish or English.

### Resit an examination

This course offers both postponed and resit of examination. Read more:

### Special examination arrangements, use of sources, explanations and appeals

See more about examinations at UiO

Last updated from FS (Common Student System) Jan. 16, 2021 4:19:34 PM

Credits
10
Level
Bachelor
Teaching
Spring
Examination
Spring
Teaching language
English

## Contact

Department of Mathematics