Module Title
Symmetries In Geometry

Module Level
Level 2

Module Credits
5.00

Academic Year
2024/25

Semester
SEM2

This module is a mathematical treatment of symmetries as the transformation groups of geometric spaces. This will provide students a geometric viewpoint for algebraic concepts such as group theory. Students will become familiarised with interesting non-Euclidean geometries such as spherical, hyperbolic, affine, and projective geometry. Furthermore, students will gain proficiency in using transformation groups to simplify problems in geometry. This module synergises well with metric spaces and provides a foundation for further study in topology, differential geometry, and algebra.

A. Recognise the similarities and differences between Euclidean and non-Euclidean geometries. B. Work effectively with explicit models of the hyperbolic plane to perform calculations. C. Solve problems using isometries of Euclidean, spherical, or hyperbolic space. D. Apply knowledge of linear algebra and group theory to problems arising in geometry.

This module will be delivered mainly through a combination of formal lectures and tutorials.