Abstract Algebra (MAT250)

Introduction to the axiomatic approach to algebraic objects, such as groups, rings and fields, with applications to modular arithmetic and symmetries of geometric shapes.

Course description for study year 2023-2024. Please note that changes may occur.


Course code




Credits (ECTS)


Semester tution start


Number of semesters


Exam semester


Language of instruction

English, Norwegian


Groups, rings and fields; subgroups and ideals; factor groups and factor rings, homomorphisms. Examples and applications.

Learning outcome

After completion of the course, the student is be able to:

  • Reproduce and exemplify the axioms and elementary properties of an abstract group, ring and field
  • Reproduce and exemplify definitions of central algebraic notions such as subgroup, factor group, ideal, factor ring and homomorphism.
  • Explain and apply the notions of finite and finitely generated group.
  • Identify subgroups, residue classes and factor groups in manageable examples.
  • Identify ideals and quotient rings in manageable examples.
  • Carry out and convey reasoning with abstract algebraic objects.

Required prerequisite knowledge


Recommended prerequisites

MAT120 Discrete Mathematics


Form of assessment Weight Duration Marks Aid
Written exam 1/1 4 Hours Letter grades Basic calculator

Course teacher(s)

Head of Department:

Bjørn Henrik Auestad

Method of work

4 hours lectures, 2 hours tutorials and home work.

Overlapping courses

Course Reduction (SP)
Groups and Symmetry, Groups and symmetry ( MAT230_1 ÅMA230_1 ) 16
Groups and symmetry (ÅMA230_1) 6
Groups and Symmetry (MAT230_1) 6

Open for

Admission to Single Courses at the Faculty of Science and Technology
Mathematics and Physics - Five Year Integrated Master's Degree Programme

Course assessment

There must be an early dialogue between the course supervisor, the student union representative and the students. The purpose is feedback from the students for changes and adjustments in the course for the current semester.In addition, a digital subject evaluation must be carried out at least every three years. Its purpose is to gather the students experiences with the course.


The syllabus can be found in Leganto