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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.