Multilinear algebra and group theory [ LMAT1231 ]

A first course in linear algebra

Elements of the theory of groups: quotients groups and the isomorphism theorems, abelianisation, cyclic groups, group actions and symmetric groups. Complements of linear algebra: quotient spaces, duality of finite-dimensional vector spaces. Multilinear algebra: basic properties of the tensor product of vector spaces and of linear maps.

This course is an introduction to group theory and to multilinear algebra. In this context we consider some universal constructions which are important in algebra and geometry. The course aims to develop reasoning and calculating skills in the context of algebraic structures.