Algebra and Geometry

Module Leader:
Pál Galicza
2017-2018 Summer
Numerical Sciences

Some people claim that our 3-dimensional perception of the surrounding world is only a simple (yet very complex) anomaly; the universe in truth is embedded in a 10 (or 26 depending on the prophet) dimensional space. While the module neither intends to support nor disprove the above claim, it offers the students a well- (or better) grounded definition and understanding of dimension and many related concepts such as spaces and linear maps.

The module will offer an approach to linear algebra through various geometric problems in two, three, and even higher dimensions (including 10 and 26, apparently). Starting with classical coordinate geometry in two and three dimensions, we will describe 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 system, and determinants. This module will be especially useful for students interested in mathematics, physics, and engineering.