Transformation Geometry

Geometry as the study of properties deduced from a set of axioms. Brief introduction to non-Euclidean geometries, synthetic projective geometry. Geometry as the study of invariants of a transformation group: analytic projective geometry and its sub-geometries. Methods from complex analysis, including linear fractional transformations and the Riemann sphere.
Note. A course in Linear Algebra is required and must be completed before taking this course.