This course goes beyond the Euclidean Geometry typically taught in high schools. This is a modern approach to geometry based on the systematic use of transformations. It includes a study of some advanced concepts from Euclidean Geometry and then proceeds to examine a wide variety of other geometries, including Non-Euclidean and Projective Geometry. A working knowledge of vectors, matrices, and multivariable calculus is assumed.
- Compare/contrast the development, axioms and/or postulates and theorems of Euclidean and Non-Euclidean geometries.
- Define and understand mathematical axiomatic systems and their properties.
- Present concepts of Euclidean geometry from a transformational viewpoint.
- Use hypotheses to draw valid conclusions and to avoid making invalid arguments.