Stockholm university
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Mathematics III - Abstract algebra

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. When the course is given as a distance course instruction is digital, e.g., recorded videos and/or live sessions over Zoom.


    The course is assessed through written and oral examination.

    Assessment when the course is given as a distance course

    Even when the course is given as a distance course, the exam is on campus. If you cannot come to Stockholm for the exam, you may be able to arrange to take the exam elsewhere, e.g. at another university or (if you are not in Sweden) at a Swedish embassy or consulate.

    More information about taking exams off campus


    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.

    Dummit & Foote: Abstract Algebra. John Wiley & Sons Inc.

    List of course literature Department of Mathematics

  • Course reports

  • 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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