Course syllabus

Algebraiska strukturer
Algebraic Structures

FMAN10, 7,5 credits, A (Second Cycle)

Valid for: 2012/13
Decided by: Education Board 1
Date of Decision: 2011-03-23

General Information

Elective for: C4, C4-ks, D4, D4-ks, F3, Pi2, Pi2-ssr, Pi2-pv
Language of instruction: The course will be given in English on demand

Aim

The aim of the course is to give an introduction to the fundamental concepts and structures 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 students ability to solve problems and to understand mathematical text.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

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.

Competences and skills
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.

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.

Examination details

Grading scale: TH
Assessment: Compulsory assignments that must be approved before the exam. Written examination followed, for those who pass, by an oral examination.

Admission

Required prior knowledge: In terms of content, the courses in Calculus and Linear algebra are sufficient. However, the greater mathematical maturity provided by one or more further courses in mathematics is helpful .
The number of participants is limited to: No
The course overlaps following course/s: FMA190

Reading list

Contact and other information

Course coordinator: Studierektor Anders Holst, Studierektor@math.lth.se
Teacher: Arne Meurman, Arne.Meurman@math.lu.se
Course homepage: http://www.maths.lth.se/education/lth/courses/algebraicstruct/