Mathematics BA (C), Algebra

Abstract algebra is about the study of algebraic structures and their properties. We shall in this course see that well-known principles and properties of sets of matrices, polynomials, vector spaces and the integers modulo n and their associated operations are a consequence of the underlying algebraic structure of these sets. The course gives a classic first introduction to groups, rings, and fields, where concepts and ideas from topics such as number theory and geometry are generalised. Some highlights are permutation groups, symmetry groups and the construction of all finite fields. The course forms a solid basis for more advanced courses in algebra, discrete mathematics and also subjects like coding theory and cryptology.