Course Description
Advanced elementary geometry for prospective teachers of secondary school mathematics: axiom systems and models; the parallel postulate; neutral, Euclidean, and non-Euclidean geometries.
Additional Requirements for Graduate Students:
Extra problems on weekly homework.
Athena Title
Foundations of Geometry I
Equivalent Courses
Not open to students with credit in MATH 5200W or MATH 7200W
Undergraduate Pre or Corequisite
MATH 3000 or [(MATH 3200 or MATH 3200W) and (MATH 3300 or MATH 3300E)] or [(MATH 3500 or MATH 3500H) and (MATH 3510 or MATH 3510H)]
Semester Course Offered
Offered fall and spring
Grading System
A - F (Traditional)
Course Objectives
Students should be able to write proofs of basic propositions in classical geometry, and they should understand the role of axioms and definitions. They should also know how to perform experiments in geometry--with pencil and paper, ruler and compass, or computer software--to test hypotheses and form conjectures. They should become familiar with the relations of geometry to other subjects in the high school mathematics curriculum, such as algebra, trigonometry, and precalculus.
Topical Outline
1. Straightedge and compass constructions 2. The parallel axiom and Euclidean geometry 3. Geometry in Cartesian coordinates 4. Vectors and geometry 5. Perspective 6. Linear transformations
Syllabus
Public CV