Group and Ring Theory

MATP33 Group and Ring Theory, 7.5 credits, is an alternative-compulsory course at advanced level for a Master of Science degree in mathematics. The course can be taken as an stand-alone course.  The course is given at half study pace in the first half of the autumn semester. The language of instruction in English.

Course Content
The course treats

• Groups: Permutation groups. Burnside's lemma with application to Pólya arithmetic. Sylow's theorems. Symmetric and alternating groups. The structure of finitely generated Abelian groups.
• Rings: Noetherian and Artinian rings and modules. Artin-Wedderburn's theorem. Finitely generated modules over a principal ideal domain with application to the Jordan normal form of matrices.
• Linear algebra: Multilinear mappings. Tensor products.

Teaching
The teaching consists of lectures and some seminars.

Assessment
The examination consists of a written examination (5 credits) followed by an oral examination (2.5 credits) at the end of the course. The oral examination may only be taken by those students who passed the written examination.

Course Literature

• Bhattacharya P.B., Jain S.K., Nagpaul S.R., Basic Abstract Algebra, 2nd ed., 1994, ISBN: 0-521-46629-6
• Lecture notes and supplementary reading is provided during teh course

Official Course Description

• Syllabus in English
• Kursplan på svenska