UVU Math 6100 Objectives
Special Topics in Geometry and Topology Course Objectives
Upon successful completion, students should be able to:
- Describe the logical development of Euclidean and non-Euclidean plane Geometry.
- Develop geometric intuition through the use of figures, models, and dynamic geometric
- Demonstrate facility in making good arguments in a mathematical context.
- Prove substantive Euclidean results in a context where they already have comfortable
- Explain hyperbolic geometry as an axiomatic system.
- Develop intuition in non-Euclidean axiomatic systems by carefully employing the axioms.
- Prove theorems in non-Euclidean axiomatic systems by carefully employing the axioms.
- Communicate ideas clearly and concisely both orally and in writing.
Includes manifolds, fundamental group, and classification of surfaces, covering spaces,
homotopy types, differential geometry, Riemannian geometry, algebraic geometry, projective
geometry, and algebraic topology.
Licensed Secondary Teacher Mathematics Endorsement Level 4 State of Utah and/or permission