The course will also be a training for analytic thinking and students will see several applications and learn problem solving techniques.
Syllabus: Groups: Direct and semi-direct products. Finite abelian groups. Sylow theorems. Series of subgroups, Solvable groups. Nilpotent groups. Free groups. Generators and relations. Fields: Algebraic extensions, Splitting fields, algebraic closures and normal extensions. Roots of unity and finite fields. separable and inseparable extensions. The Galois group and the fundamental theorem. Solubility of equations by radicals.
