MAT2200 – Groups, Rings and Fields
Schedule, syllabus and examination date
MAT2200 gives an introduction to group and ring theory with emphasis on finite groups, polynomial rings, and field extensions.
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.
If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.
Formal prerequisite knowledge
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).
Recommended previous knowledge
*The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department.
4 hours of lectures/exercises every week for the duration of the semester.
Final written examination.
Examination support material
No examination support material is allowed.
Language of examination
Subjects taught in English will only offer the exam paper in English.
You may write your examination paper in Norwegian, Swedish, Danish or English.
Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.
Explanations and appeals
Resit an examination
This course offers both postponed and resit of examination. Read more:
Withdrawal from an examination
It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.
Special examination arrangements
Application form, deadline and requirements for special examination arrangements.
The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.