Foundations of Geometry, Math 535, section 7D1. Formal prerequisite: Multivariable Calculus, Math 251.

This course is designed as web based course for 3 hours credit. On line "meeting" time to be arranged.

Excerpt from Graduate catalog:
Math 535: (Designed especially for secondary mathematics teachers; others admitted with departmental approval obtained before registration.) Incidence geometrics with models; order for lines and planes; separation by angles and by triangles; congruence; introduction to Euclidean geometry.

Although the course is at the graduate level, it does not count as such for most of the tracks of mathematics graduate degree at our department. However, it is required for students in the mathematics education track in our department and in the master's certification program in the College of Human Resources and Education. In addition, the course counts (and it is very important) for the mathematical education graduate degree. It is also a very good class for the students that are considering going for a certification in mathematics in the high schools or that are looking for a faculty position in which they may be teaching education majors.

If you have any questions about mathematics education degree or the certification in mathematics in the high schools, please contact Professor Laura Pyzdrowski, our mathematics education specialist and a strong supporter for this course.

The main goal of the course is to teach its participants a good understanding of the axiomatic approach to the Euclidean geometry. To achieve this goal, we will discuss in some generality what the axiomatic theory is and what it means that its axioms are consistent and independent. Our main concern will certainly be the Euclidean axioms. But to understand them well we will be introducing the axioms very slowly, one by one, and will discuss in details the geometrical theories based on these few axioms. To show that the axioms are independent (and consistent) we will discuss many different geometrical models, referred often as the incidence geometrics models.

Although I will assume that the course participants are familiar with the high school level Euclidean geometry, I plan to discuss some geometry at this level. For example, I may discuss some classical straight edge and compass constructions. To facilitate geometrical drawing, I plan to use the program Geometer's Sketchpad. Math Department has a site licence for this program and it is available in the IML 213/215 Armstrong Hall during open lab times. The student version of this program can be also bought for $29.95 at

When I taught this course on Spring 2004 I used the text: The Foundations of Geometry and the Non-Euclidean Plane
by George Edward Martin, Springer Verlag, 4th edition of 1998 (ISBN: 0387906940). However, do not buy it yet. I am not sure if I use this text or any other.

If you are interested in this course and have any questions, please e-mail me at In fact, I would like to receive an e-mail even if you do not have questions. I would like to know who may be interested taking this course, so I could craft it a bit to individual needs.