Course overview
The algebraic notions of groups, rings and fields are inherently interesting, while their practical applications extend across numerous areas. This course will provide students with a comprehensive understanding of the fundamental structures and concepts in abstract algebra. The course begins with definitions and examples of groups, rings and fields. It then advances to examining and proving key theorems, culminating in establishing the connection between solving polynomials and the procedure of field extensions.
Course learning outcomes
- Apply techniques of algebraic manipulation and reasoning to evaluate properties of an algebraic structure
- Prove the basic results of groups, rings and field theory
- Apply more advanced results such as Burnside's theorem and the Sylow theorems
- Develop proficiency in constructing rigorous mathematical proofs within abstract algebra, employing various proof techniques
- Demonstrate skills in communicating algebraic concepts and arguments effectively
Degree list
The following degrees include this course