This course will provide the students with the basis of group and field theory in modern algebra.
The course consists of a presentation of the foundations of modern algebra. It aims both to provide a knowledge base for disciplines as part of the traditional mathematics and secondly to identify universal principles.
Group theory (subgroup - quotient group - action group on a set) - rings and skew fields - polynomial rings - field extension - Galois theory.
1. The concept of group - 2. Subgroups - 3. Normal subgroups - 4. Action of a group - 5. Rings and skew fields - 6. Polynomial rings and field extension - 7. Galois theory.
Oral exam consisting of: (1) complete proof of a theorem; (2) synthesis of a concept; (3) one or several exercises; (4) possibly, several small questions on theory (without preparation).
Group project (oral presentation and final report).
Final mark: oral exam (85%) - group project (15%)