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 Euclid'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.