Algebra and Geometry

The module will offer an approach to linear algebra through various geometric problems in two, three, and even higher dimensions. Starting with classical coordinate geometry in two and three dimensions, we will describe the geometric transformations of various kinds. We will introduce and study the complex numbers and their useful properties that come in handy when describing certain planar transformations. We will investigate a possible generalisation of the known techniques in coordinate geometry called linear algebra.
Linear algebra is an important field of study in Mathematics with a wide range of applications in many fields, such as analysis, probability, or differential equations. This course will cover the following topics in linear algebra: vectors, matrix algebra, linear systems, and determinants. This module will be especially useful for students interested in mathematics, physics, and engineering.