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.
- Groups
- Rings
- Fields
Course learning outcomes
- Explain and apply advanced concepts in group theory, including group actions and Sylow theorems.
- Analyse the structure and properties of rings and ideals, with applications to divisibility and factorisation in integral domains.
- Apply the theory of field extensions to problems including the classification and arithmetic of finite fields.
- Construct rigorous mathematical proofs within abstract algebra employing various proof techniques
- Communicate algebraic ideas and arguments effectively using mathematical language
Degree list
The following degrees include this course