4 hours of lectures and exercise sessions per week.
Lecturer: Jens Carsten Jantzen
Content:
This is a general introduction to modern algebra. It builds on the linear algebra from Mat 10 and the topics on groups, rings, and fields treated in Algebra 1.
Subjects to be discussed in this course include:
An extension of the factorisation theory from Algebra 1. In particular the factorisation of polynomials with integer coefficients will be discussed.
The theory of field extensions leading to Galois's theory on the (in)solvability of polynomial equations.
The theory of modules over principal ideal domains leading to a classification of all finite commutative groups and to the Jordan normal form for matrices.
Prerequisites: Algebra 1.
Literature: Notes.