English

Every spring semester

The course is established in order to give the doctoral students knowledge about basic concepts of abstract algebra, which is useful for further studies in mathematics as well as within digital technology and coding theory.

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.

be able to describe basic properties of integers and polynomials, and be able to compute with congruences modulo these objects.

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

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

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

have acquired basic knowledge for further studies in algebra or subjects based on algebraic methods.

For a passing grade the student must

be able to independently construct proofs of simple statements within the framework of the course.

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

Lectures

Exercises

Written exam

Oral exam

Failed, pass

In terms of content, basic courses in calculus (in one and several variables) and linear algebra are sufficient. However, the mathematical maturity provided by one or more further courses in mathematics is helpful .

Hungerford, T.: Abstract Algebra: An Introduction. Cengage Learning, 2012. ISBN 9781111573331.

FMAN10F

 -01-27

FN1/Anders Gustafsson