MATH 7395:Non-Euclidean Geometry

3 Class Hours 0 Laboratory Hours 3 Credit Hours
Prerequisite: MATH 3395 or MATH 7714 or consent of the instructor.
This course examines the development of the axiomatic basis for non-Euclidean geometry and its relationship to Euclidean geometry, and analyzes proofs of important theorems in hyperbolic geometry. Topics will include Hilbert’s axioms, finite and infinite affine and projective planes, neutral geometry, Hilbert planes, Euclidean planes, and hyperbolic planes. Special emphasis will be given to the nature of geometric proof and historical attempts to prove the Euclidean parallel postulate.