Basic Algebra

We present a course giving an overview of basic algebraic structures. It is an essential part of mathematical education in general; besides, our experience shows that it also provides motivation to specialize in algebra.


  1. Symmetric group.
  2. Transformation groups. Burnside’s formula.
  3. Groups, subgroups, and quotient groups.
  4. Free groups. Groups presented by generators and relators.
  5. Rings and ideals.
  6. Divisibility theory in Euclidean rings.
  7. Fields. Complex numbers. Finite fields.
  8. Algebras. Quaternions.
  9. Matrix algebra. Vector spaces. Basis. Dimension.
  10. Grassmann algebra. Determinant.


  • D.S.Dummit, R.M.Foote, Abstract Algebra.
  • Robert B.Ash, Abstract Algebra: The Basic Graduate Year.