University Mathematics
Abstract Algebra
Groups, rings and fields: the structures behind symmetry, number systems and polynomial equations.
Curriculum / Syllabus
- Groups, Subgroups and Cyclic Groups
- Permutation Groups
- Cosets and Lagrange's Theorem
- Normal Subgroups, Quotient Groups and Homomorphisms
- Group Actions and the Sylow Theorems
- Rings, Ideals and Quotient Rings
- Polynomial Rings and Field Extensions
Exam & Course Strategy
Questions ask both for proofs and for concrete computations in specific groups and rings. Working through small examples such as S3, Z_n and D4 until they are second nature is the core of the preparation.