Its aim is to introduce students to algebraic structures and to axiomatic methods in pure mathematics. Its main topic is Group Theory. It will introduce the principal notions of groups, subgroups, homomorphisms and factor groups. While it can be taken on its own, this unit in conjunction with Algebra II is the prerequisite for several third year Pure Mathematics courses. The course is a 10 UCU unit of 20 lectures with three support classes.
Modern algebra bases itself on axiomatic systems where theories are developed from axioms.
This is true particularly for Group Theory. One of its roots and influential in its development has been the study of geometrical transformations and symmetry. Group Theory is therefore very close to these fundamental mathematical notions. It is also a subject where theory and axiomatics interacts with intuition and insight in fascinating ways. Axiomatic methods are not always easy to get used to.