MTH630 Fundamentals of Geometry
Lead Faculty: Dr. Igor Ya Subbotin
Course Description
Considers areas of Euclidean and non-Euclidean geometries, axiomatic systems, synthetic and analytic representations, relationships with algebra, and selected topics and applications
Learning Outcomes
- Evaluate and contrast projective geometry as generalizations of Euclidean geometry
- Evaluate projective geometry as developed from a set of axioms or from groups of transformations
- Analyze the various attempts to prove the Fifth Postulate and the social climate of the times and countries
- Analyze Euclidean, hyperbolic geometry and elliptic geometry
- Elaborate straightedge and compass constructions and the geometric constructions of arithmetic operations
- Discuss the concepts in Euclidandapos;s elements, Euclidean geometry and proofs of the theorems of Thales and Pythagoras
- Elaborate definition of geometry as study of invariants of groups of transformation, introduction to transformation groups, quaternion field, and operations on spherical spaces
- Elaborate the concept of parallax and describe how modern scientists use non-Euclidean geometry to attempt to describe the physical nature of the universe
