MAT 1301 Euclidean and Non-Euclidean Geometries
Development of the mathematical way of thinking through firsthand experience. Emphasis on the student’s strengthening of his or her imagination, deductive powers and ability to use language precisely and efficiently. Study of Euclid’s geometry; Hilbert’s axioms; neutral geometry; hyperbolic geometry (non-Euclidean geometry of Gauss, Bolyai, Lobachevsky); the axiomatic method; and consistency, independence and completeness of axiom systems. Historical perspective and philosophical implications are included. Students must prove a significant number of theorems on their own.
Offered
Fall and Spring