MATH 3021 - Geometry

(3) Credit Hours
Prerequisite: MATH 2500
This course is a modern treatment of geometry primarily from the metric approach, but with some reference to the Euclidean Synthetic approach. Topics include parallelism, similarity, area, constructions, non-Euclidean and finite geometries. After successfully completing this course, students will be prepared to teach geometry by being able to: (1) Demonstrate an understanding of the historical development of geometry from its Euclidean foundations on through the formulation of hyperbolic and elliptical non-Euclidean geometries. (2) Demonstrate an understanding of the axiomatic foundations of various geometries and skill in formulating conjectures, proving theorems, disproving non-theorems and solving problems in these geometries. (3) Demonstrate an understanding and skill in comparing and contrasting geometries - finite, non-finite, affine, projective, elliptic, hyperbolic, parabolic and such. (4) Demonstrate an understanding and skill in proving theorems and solving problems in two and three-dimensional Euclidean geometry whether through synthetic, vector, matrix and/or transformational approaches. (5) Demonstrate an understanding and skill with Geometric and other appropriate software as it relates to different approaches and the study of different geometries.