Course overview
Projective geometry is one of the important modern geometries introduced in the 19th century. Projective geometry is more general than our usual Euclidean geometry, and it has useful applications in Information Security, Statistics, Computer Graphics and Computer Vision. The majority of this course will be on projective planes. Topics covered are: projective planes, homogeneous coordinates, field planes, collineations of projective planes, conics in field planes, k-arcs in projective planes, projective geometry of general dimension, quadrics and ovoids in 3-dimensional projective space.
Course learning outcomes
- Demonstrate a deep understanding of the axiomatic approach to projective spaces.
- Be able to perform calculations in Desarguesian planes and projective 3-spaces.
- Classify the structure of collineations of projective planes.
- Demonstrate an understanding of the theory of conics in field planes.
- Apply the theory to solve problems of varying levels of difficulty.
- Demonstrate skills in communicating mathematics orally and in writing.