M333L STRUCTURE OF MODERN GEOMETRY

Prerequisite and degree relevance:

The prerequisite is 408D or upper-division standing and consent of the instructor, this is

for the development of mathematical maturity rather than direct utilization of concepts

and is waived by the instructor in some cases—most notably a specialization in

mathematics. M333L is required for students seeking certification to teach secondary

school mathematics.

Course description:

The course is designed to familiarize prospective mathematics teachers with the

geometrical concepts which relate to two and three dimensional geometry and the

mathematical techniques used in the study of geometry. The emphasis is both on the

development of understanding of the concepts and the ability to use the concepts in

proving theorems. The course includes study of axiom systems, transformational

geometry, and an introduction to non-Euclidean geometries, supplemented by other

topics as determined by the instructor. While the course is primarily designed for

teachers, its content and approach may be of interest to other students of mathematics.