In this course, we shall consider several different geometries as examples of axiomatic systems. In particular, we will look at a couple alternatives to the parallel postulate, and the resulting non-Euclidean geometries. Proof construction and exposition will be discussed and practiced.

We will begin by talking about axiomatic systems in general, and specifically will look at some finite geometries as examples of axiomatic systems. Then we will review some fundamental principles of logic trying to clarify what constitutes a proof. Next we look at several sets of axioms for geometry. In particular, we consider the flaws in Euclid's presentation, and how these flaws are addressed by Hilbert's axioms. A consideration of Neutral Geometry will reveal the theorems which can be proved without any kind of parallel postulate. Following this, we look at attempts to prove the Parallel Postulate, the consequences of assuming the Parallel Postulate, alternatives to the Parallel Postulate and their consequences. Finally, we study some details of Hyperbolic Geometry and mention briefly some other alternative geometries.

The textbook for the course is the second edition of Roads to Geometry written by Edward C. Wallace and Stephen F. West and published by Prentice Hall in 1998. We will cover the first six chapters of the text with supplementary material drawn from various sources. We will focus on problem solving, proof discovery, and proof exposition.

There will be three one hour exams during the semester; an hour exam will be given near the end of each month. Homework will be assigned and graded on a regular basis. The final exam is scheduled for Wednesday, December 11, 2002 at 9:00 a.m., and you will be expected to take the exam at that time. Your grade will be based on the total points accumulated out of a possible 600 points. Each hour exam will be worth 100 points, all homework combined will be worth 100 points, and the final exam will be worth 200 points. This course will be challenging as well as interesting, and will require your best effort applied consistently throughout the semester.

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Created 07/01/2002. Last modified 07/01/2002. Email to ekh@wfu.edu