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SF2729 Groups and Rings 7.5 credits

Grupper och ringar

  • Educational level

    Second cycle

  • Academic level (A-D)

    C

  • Subject area

    Mathematics

  • Grade scale

    A, B, C, D, E, FX, F

Course offerings

Autumn 12 for programme students

Autumn 13 for programme students

Learning outcomes

After the course, the student shall be able to pursue abstract reasoning about algebraic structures. The student shall be trained in logical thinking and in constructions of mathematical proofs. Algebraic structures appear in many disciplines within Science and Technology. The student shall be able to recognize and use such structures in his or her forthcoming work. Concretely, this means that the student shall be able to:

  • Identify and describe fundamental algebraic structures such as groups, rings and fields,
  • Identify algebraic substructures such as subgroups, subrings and ideals,
  • Identify and describe relations between algebraic structures, such as homomorphisms and group actions,
  • Define and use bijective functions between algebraic structures, with special attention to permutations,
  • Use classical results in basic group theory and ring theory, such as Lagrange's theorem or Cauchy's theorem, to describe the structure of the group or the ring,
  • Explain relations using mathematical proofs and logical reasoning,
  • Formulate certain practical problems by means of algebraic structures.

Course main content

Groups, permutations, homomorphisms, group actions, rings, ideals, modules, fields and field extensions.

Eligibility

SF1604 Linear algebra and SF1204 Discrete mathematics or corresponding courses are required prerequisites.

Literature

{A First Course on Abstract Algebra, 7th Edition} by John B. Fraleigh.

Examination

  • TEN1 - Examination, 7.5 credits, grade scale: A, B, C, D, E, FX, F

One written exam which can partly be replaced by homework assignments and one mid term exam.

Grade scale A, B , C, D, E, Fx, F.

Offered by

SCI/Mathematics

Contact

Carel Faber

Examiner

Carel Faber <faber@kth.se>

Version

Course plan valid from: Spring 10.
Examination information valid from: Autumn 08.