University of Galway

Course Module Information

Course Modules

Semester 1 | Credits: 5

This course is an introduction to non-Euclidean, projective and Riemannian geometry. Topics covered include Riemannian metrics, their isometries, geodesics, curvature and the Gauss-Bonnet theroem.
(Language of instruction: English)

Learning Outcomes
  1. Give examples of geometries that violate the parallel postulate.
  2. Identify isometries and geodesics in Euclidean and standard non-Euclidean geometries.
  3. Calculate distance in Euclidean and non-Euclidean geometries.
  4. Manipulate homogeneous coordinates in projective spaces.
  5. Perform rotations using Quaternions.
  6. Calculate the Gaussian and the mean curvature of a surface.
  7. Prove the Gauss-Bonnet theorem.
Assessments
  • Written Assessment (67%)
  • Continuous Assessment (33%)
Teachers
Reading List
  1. "Geometry and Topology" by M. Reid and B. Szendroi, C.U.P.
  2. "Naïve Lie Theory, Undergraduate Texts in Mathematics" by J. Stillwell, Springer
The above information outlines module MA3101: "Euclidean and Non-Euclidean Geometry" and is valid from 2018 onwards.
Note: Module offerings and details may be subject to change.