MAT2200 – Groups, Rings and Fields
Course description
Schedule, syllabus and examination date
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.
Admission to the course
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.
Special admission requirements
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
Overlapping courses
- 9 credits overlap with MA131.
- 9 credits overlap with MA220.
- 9 credits overlap with MA120.
Teaching
4 hours of lectures and 2 hours of exercise sessions 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 written 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.
Grading scale
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.
Resit an examination
This course offers both postponed and resit of examination. Read more:
More about examinations at UiO
- Use of sources and citations
- Special exam arrangements due to individual needs
- Withdrawal from an exam
- Illness at exams / postponed exams
- Explanation of grades and appeals
- Resitting an exam
- Cheating/attempted cheating
You will find further guides and resources at the web page on examinations at UiO.