Algebra II - groups
Summary
This course deals with group theory, with particular emphasis on group actions and notions of category theory.
Content
Topics covered include quotient groups, the isomorphism theorems, abelian groups, Sylow subgroups, group actions and representations, basic notions of category theory.
Keywords
Group, quotient, isomorphism, Sylow subgroup, action, representation, category.
Learning Prerequisites
Required courses
MATH-110(a) Advanced linear algebra I
MATH-115(a) Advanced linear algebra II
MATH-113 Algebraic structures
Important concepts to start the course
Definitions of groups and basic examples: symmetric groups, reflection groups, dihedral groups.
Learning Outcomes
- Prove basic results of group theory
- Construct examples of groups and their actions
- Systematize groups, homomorphisms and categories
- Formulate the main theorems of the course
Teaching methods
Lectures and exercise sessions
Expected student activities
Students are expected to attend all lectures and participate in all problem sessions.
Assessment methods
Written exam
Supervision
| Office hours | No |
| Assistants | Yes |
| Forum | Yes |
Resources
Bibliography
J. J. Rotman, "An introduction to the Theory of Groups"
D. S. Dummit, R. M. Foote, "Abstract algebra, 3rd edition"
Moodle Link
In the programs
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Algebra II - groups
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: mandatory