Course Description
This course is an introduction to group theory. We will mainly study the following topics.
Definition and examples of groups. Our goal is to understand how groups "encode symmetry" by studying many examples of groups arising from algebra, geometry and combinatorics.
Basic notions of group theory such as subgroups, cosets, conjugation and group homomorphisms. Lagrange's theorem. The isomorphism theorems.
Group actions on sets. The orbit-stabilizer theorem. The Sylow theorems.
At least one topic from the following list: classification of finitely generated abelian groups, finite subgroups of SO(3), group presentations.
I will post a short lecture summary after each class here.
(Note: we ended up discussing group presentations before group actions.)
The final exam is comprehensive.
You can check your grades on our onQ course page.
Special Accommodations
Students with disabilities who will be taking this course and may need disability-related accommodations are encouraged to make an appointment to see the instructor as soon as possible. Also, please contact Disability Services to register for support services.
Academic Integrity
It is the obligation of each student to understand the university's policies regarding academic intergrity and to uphold these standards. Departures from academic integrity include plagiarism, use of unauthorized materials, facilitation, forgery, and falsification. Actions that contravene the regulations on academic integrity carry sanctions that can range from a warning to the loss of grades on an assignment to the failure of a course to a requirement to withdraw from the university.