Request Information

Please complete the form below, and an admissions advisor will contact you shortly.


Apply Now

Ready to take the next step?

The application process is easy. We accept and review applications year-round, and qualified applicants can begin classes any month of the year, depending on your program and location.

Click Apply Now to get started on the next exciting chapter of your life!

Apply Now

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.