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Mathematics III - Abstract algebra

  • 7.5 credits

In this course, you will study the algebraic structures groups, rings, fields and vector spaces, and learn to use methods in abstract algebra to solve mathematical and applied problems.

This course is one of the requirements for eligibility to our Master's Programme in Mathematics.

The course covers: Group theory: sub groups, cosets, Lagrange's theorem, homomorphisms, normal subgroups and quotient groups, permutation groups, simple groups. Rings and fields: matrix rings, quaternions, ideals and homomorphisms, quotient rings, polynomial rings, principal ideal rings, Euclidean rings and unique factorization. Fields and vector spaces: finite-dimensional vector spaces, algebraic field extensions, finite fields.

  • Course structure

    The course consists of one element.

    Teaching format

    Instruction is given in the form of lectures and exercises.


    The course is assessed through written and oral examination.


    A list of examiners can be found on

    Exam information

  • Schedule

    The schedule will be available no later than one month before the start of the course. We do not recommend print-outs as changes can occur. At the start of the course, your department will advise where you can find your schedule during the course.
  • Course literature

    Note that the course literature can be changed up to two months before the start of the course.

    Course literature Department of Mathematics

  • More information

    New student
    During your studies

    Course web

    We do not use Athena, you can find our course webpages on

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