Course syllabus

Algebraiska strukturer
Algebraic Structures

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

Valid for: 2020/21
Decided by: PLED F/Pi
Date of Decision: 2020-04-01

General Information

Elective for: C4-ks, C4-sec, D4-ns, F4, 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

Competences and skills
For a passing grade the student must

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 - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Written examination followed, for those who pass, by an oral examination.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Admission

Assumed 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, MATM11

Reading list

Contact and other information

Course coordinator: Studierektor Anders Holst, Studierektor@math.lth.se
Teacher: Victor Ufnarovski, ufn@maths.lth.se
Course coordinator: Studerandeexpeditionen, expedition@math.lth.se
Course homepage: http://www.maths.lth.se/course/fman10/