Up: Math 124 Course Policies (Winter 1997)

Math 124 Course Goals:

This course should serve as an introduction to several important topics in geometry. The first part of the course will cover some ideas in plane geometry using the language of mappings and algebra. We will use the ideas of symmetry and isometry to investigate patterns in the plane (called "frieze" and "wall paper" patterns) and will classify all possible patterns of these types.

From there, we will look at a related topic, that of tilings, and will use these ideas to introduce the Platonic and Achimedean solids, their inter-relationships, and their symmetries. This will lead us to various properties of the sphere and possibly to investigations of the fourth dimension.

We will turn then to an historical look at Euclid and what it means for a geometry to be non-Euclidean. This will lead to the elliptic and hyperbolic geometries and some of their properties, particularly the properties of triangles, areas and angle measures. The capstone for the course will be a proof of (a limited version of) the Gauss-Bonnet theorem.

The final week will consist of student presentations of group projects.

See also the course outline for the timing of these topics.

Up: Math 124 Course Policies (Winter 1997)

Comments to: dpvc@union.edu
Created: Jan 06 1997 --- Last modified: Thu Jan 9 09:07:08 1997