Special Topics in Geometry and Topology Course Objectives

Upon successful completion, students should be able to:

1. Describe the logical development of Euclidean and non-Euclidean plane Geometry. 
2. Develop geometric intuition through the use of figures, models, and dynamic geometric software. 
3. Demonstrate facility in making good arguments in a mathematical context. 
4. Prove substantive Euclidean results in a context where they already have comfortable intuition. 
5. Explain hyperbolic geometry as an axiomatic system. 
6. Develop intuition in non-Euclidean axiomatic systems by carefully employing the axioms. 
7. Prove theorems in non-Euclidean axiomatic systems by carefully employing the axioms. 
8. Communicate ideas clearly and concisely both orally and in writing. 

 

Description

Includes manifolds, fundamental group, and classification of surfaces, covering spaces, homotopy types, differential geometry, Riemannian geometry, algebraic geometry, projective geometry, and algebraic topology.

 

Prerequisite

Licensed Secondary Teacher Mathematics Endorsement Level 4 State of Utah and/or permission of instructor.