Skip to Main Content


Master Syllabus

Print this Syllabus « Return to Previous Page

Administrative Unit: Computer and Mathematical Sciences Department
Course Prefix and Number: MATH 331
Course Title: Foundations of Geometry
Number of:
Credit Hours 3
Lecture Hours 3
Lab Hours 0
Catalog Description: This course provides students with the opportunity to broaden and deepen their understanding of Euclidean Geometry usually encountered in a high school geometry course. The course extends the geometric experience to non-Euclidean topics and serves to unify the study of geometry as the result of a system of axioms. Prerequisite: Grade of C or higher in MATH 222.
Prerequisite(s) / Corequisite(s): Grade of C or higher in MATH 222.
Course Rotation for Day Program: Offered odd Spring.
Text(s): Most current editions of the following:

College Geometry
By Kay (Addison Wesley/Longman)
Foundations of Geometry
By Venema (Pearson)
Course Objectives
  • To learn about the axiomatic nature of geometry.
  • To read, write, and critique geometric proofs.
  • To explore the similarities and differences between Euclidean and Non-Euclidean geometry
  • To use technology as an integral part of the process of formulation, solution and communication of geometric ideas.
    Measurable Learning
  • Determine whether a set of axioms is consistent and independent.
  • Solve problems and complete proofs involving the axioms for points, lines, lanes and angles in 3-dimensional space.
  • Solve problems and complete proofs involving triangles, quadrilaterals and circles based on triangle congruencies.
  • Adapt the Parallel Postulate for Euclidean Geometry to develop the basic concepts of classical geometry, including concepts related to rectangles, regular polygons and circles.
  • Solve problems and complete proofs involving transformations (reflections, rotations and translations).
  • Describe the development of non-Euclidean geometry.
  • Perform various standard constructions by classical compass and straight edge and via technology.
  • Outline the surprising consequences of replacing Euclid’s parallel axiom with axioms that contradict it.
    Topical Outline:

  • Euclid's Elements 
  • Axiomatic Systems 
  • Incidence Geometrics 
  • Axioms for Plane Geometry 
  • Neutral Geometry 
  • Euclidean Geometry 
  • Circles
  • Transformations 
  • Introduction to Hyperbolic Geometry 
  • Poincare's Disc 
  • Introduction to Elliptic Geometry (Spherical Geometry)


    Recommended maximum class size for this course: 20

    Library Resources:

    Online databases are available at You may access them using your CougarTrack login and password when prompted.

    Prepared by: Ann Schlemper Date: November 7, 2013
    NOTE: The intention of this master course syllabus is to provide an outline of the contents of this course, as specified by the faculty of Columbia College, regardless of who teaches the course, when it is taught, or where it is taught. Faculty members teaching this course for Columbia College are expected to facilitate learning pursuant to the course objectives and cover the subjects listed in the topical outline. However, instructors are also encouraged to cover additional topics of interest so long as those topics are relevant to the course's subject. The master syllabus is, therefore, prescriptive in nature but also allows for a diversity of individual approaches to course material.

    Office of Academic Affairs