(Created 2011-09-01.)

ALGEBRA | FMA190 |

**Aim**

The aim of the course is to give an introduction to the basic concepts of abstract algebra, with particular regard to subjects of importance in applications in, e.g., computer science, information theory, physics and chemistry. The course also aims to give a deeper understanding of the basic concepts in other areas of mathematics. Furthermore, the course should develop the student's problemsolving ability and her/his ability to understand mathematical text.

*Knowledge and understanding*

For a passing grade the student must

be able to describe basic properties of the important concepts in abstract algebra; ring, ideal, quotient ring, group and field.

in writing and orally be able to explain the contents of some central definitions and proofs.

be able to give examples of and illustrate some important applications of the course content.

*Skills and abilities*

For a passing grade the student must

be able to show a good ability to independently, in writing and orally, explain mathematical reasoning in a well structured way, with clear logic.

**Contents***Rings:* Polynomial rings. Ideals and quotient rings. Ring homomorphisms and isomorphisms.

*Groups*: Lagrange's theorem. Permutation groups. Normal subgroups and quotient groups. Group homomorphisms and isomorphisms.

*Fields*: Characteristic. Finite fields. Field extensions.

**Literature**

Hungerford: Abstract Algebra, an introduction, 2nd ed. Brooks/Cole 1996. ISBN 0-03-010559-5