MA 331 Course Description

MA331 GEOMETRY (4 Cr.)

COURSE DESCRIPTION

Prerequisite: MA 211 or permission of instructor

Offered: Winter

General Introduction and Goals:
This course is required of all secondary education mathematics majors. It may also be used as an elective for the general mathematics major. Material in the course is essential for mathematics teachers and its major purpose is to prepare students to teach high school geometry.

The course considers classical synthetic and metric geometry as an axiomatic-deductive structure. While many of the Euclidean theorems are familiar to the students from past experience, the course provides an overview of the subject and studies theorems, which heretofore have been accepted without proof. Some attention is given to elementary logic (quantifiers, rules of inference, forms of proof) and to the philosophy of mathematics (axiomatic structures, independence, models, consistency proofs). The student is also introduced to non-Euclidean geometries with the intent to strengthen their knowledge of definitions within Euclidean geometry.

In addition to various geometries, the student is also introduced to current real world applications of Geometry. With the use of The Geometer's Sketchpad, systems such as the Global Positioning System and other applications will be studied. The final project in this course involves students developing an Internet based Geometry unit which incorporates Internet resources and topics covered in class into a typical high school geometry unit.

Course Content

  1. Euclidean Geometry
    1. Similarity theory
    2. Polygonal regions and their areas
    3. circles, arc measure, arc length, and area
    4. Ruler and compass constructions on the Geometer's Sketchpad
    5. The Angle Trisection Problem
    6. Volumes and surface areas of solids
  2. An introduction to various other geometries and systems
    1. Analytic
    2. Parabolic
    3. Taxicab
  3. Mission Mathematics by NCTM
    1. Global Positioning System
    2. Independent study of various geometrical problems
  4. Final Project
    1. HTML quick review
    2. Front Page Review
    3. Design of Internet based