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MATHEMATICS
300
GEOMETRY
I. Introduction
A. Catalog Description
The course
will present a rigorous treatment of the foundations of Euclidean geometry and
an introduction to a non-Euclidean geometry.
The course will emphasize the axiomatic method and students will be
expected to do proofs. Students will be
introduced to the history of the discovery of non-Euclidean geometry. This course is especially recommended for
prospective mathematics teachers. Prerequisite: Math 122. Satisfies the proof-based requirement in
major contracts.
B. Objectives
This course is
designed specifically to prepare prospective mathematics teachers to teach
geometry. The emphasis is on the
axiomatic method and the use of logic.
The course should give the student a rigorous background in geometry and
the history behind the development of non-Euclidean geometry.
C. Prerequisites
Math 122 with
a grade of C- or better.
II. Required
Topics
1. Set Theory
2. Logic: truth tables, negation, quantifiers, proofs.
3. Hilbert's
Axioms: incidence, betweenness,
congruence,
continuity, parallelism.
4. Neutral
geometry: geometry without parallel
axiom, exterior
angle theorems, angle sum of a
triangle.
5. History
of the Parallel Postulate
6. Discovery
of Non-Euclidean Geometry
III. Bibliography
Greenberg Euclidean & Non-Euclidean
Geometries
Hilbert Foundations of Geometry
Moise Geometry
Ryan Euclidean & Non
Euclidean Geometry
Wallace/West Roads to Geometry