MATH 7200: Advanced Elementary Geometry for prospective teachers of secondary school mathematics: Axiom systems and models; the parallel postulate; neutral, Euclidean, and non-Euclidean geometries.
MATH 7210: Further development of the axioms and models for Euclidean and non-Euclidean geometry; transformation geometry.
Prerequisite for MATH 7210: MATH 7200.
Prerequisites for MATH 7200: MATH 3000 (Linear Algebra) and MATH 7200 (Intro to Higher Mathematics). If you do not have these prerequisites, please talk with me. Since differential and inferential calculus are prerequisites for MATH 3000, it is assumed that MATH 7200 students will have calculus background.
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Libeskind, Shlomo (2008). Euclidean and Transformational Geometry: A Deductive Inquiry. Sudbury, MA: Jones and Bartlett Publishers.
Dr. Libeskind is a faculty member at the University of Oregon. The book is first edition, 2008, and is based on materials Dr. Libeskind has used in a two semester study of geometry with prospective teachers. You will find on page ix of the preface that I am acknowledged as a reviewer of the manuscript. I was impressed with the manuscript, in particular that it included many geometry problems and explorations that I have on my EMAT 6600 Problem Solving web site.
Time: Wednesday, 4:40 - 7:40
Place: Rm 111/113 Aderhold Hall. Geometer's Sketchpad will be used extensively
The Course outline will be built around Problem Solving and Exploration with geometry topics and will follow the development of Lebeskind with the following topics
Basic Notions (Appendix)
Congruence, Constructions and the Parallel Postulate
Area and the Pythagorean Theorem
Isometries and Size Transformations
Composition of Transformations
Geometry of Inversion
The following software will be used:
1. Geometer's Sketchpad 4.06
2. Graphing Calculator 3.5
4. Microsoft Word
5. Firefox 2.x
6. Web construction and web editing tools if needed.
7. FTP tools if needed
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