Prerequisite and degree relevance: The prerequisite is one of 408D,  M408L, M408S or upper-division standing and consent of the instructor. These requirements are set to ensure the mathematical maturity, rather than for content knowledge. They may be 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.