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 allfinite commutative groups and to the Jordan normal form for matrices.
Prerequisites
Algebra 1
Literature
Notes
Evaluation
Students who do not intend to take a degree in Mathematics or Statistics from the University of Aarhus, but wish to earn credits for a 2.dels course from the Department of Mathematics, should indicate at the beginning of the course that they wish to be examined.
The form of examination for these students will be active participation together with oral or written contributions.
Credits
10 ECTS
Semester
Spring 2003