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.
- Symmetric group.
- Transformation groups. Burnside’s formula.
- Groups, subgroups, and quotient groups.
- Free groups. Groups presented by generators and relators.
- Rings and ideals.
- Divisibility theory in Euclidean rings.
- Fields. Complex numbers. Finite fields.
- Algebras. Quaternions.
- Matrix algebra. Vector spaces. Basis. Dimension.
- Grassmann algebra. Determinant.
- D.S.Dummit, R.M.Foote, Abstract Algebra.
- Robert B.Ash, Abstract Algebra: The Basic Graduate Year.