TEXT: The text for this course is: Berele, Allan and Jerry Goldman. (2001) Geometry: Theorems and Constructions. Upper Saddle River, NJ: Prentice Hall. ISBN: 0-13-087121-4 We will be using The Geometer's Sketchpad 4.0 throughout the course. Student versions (for $29.95) can be found at: http://www.keypress.com/catalog/products/software/Prod_GSP_Student.html#Anchor-49575 NOTE: It is not essential that you purchase this software as it is available on the computers in the Math lab - S117. DESCRIPTION: Foundations of Geometry presents the different axiomatic approaches to the study of geometry with specific applications to finite, Euclidean, and non-Euclidean geometries with extensive use of constructions to explore ideas, properties, and relationships. Technology will be used throughout the course to encourage these open-ended explorations. The role of different types of proofs will be developed throughout the course. OBJECTIVES: The student will: a) understand the axiomatic development of consistent mathematical systems; b) communicate, both orally and written, about geometric concepts, methods of proof, and different geometries; c) present historical perspectives and implications of the development of new geometries; d) apply geometric modeling to modern mathematical problems; e) use technology to explore and develop geometric relationships; f) understand and use different methods of proof; g) be aware of different learning styles and the implications of that difference in the teaching of geometry. COURSE OUTLINE: Topic Weeks Brief Review of Notation, Terms and Idea of Proofs 1 Euclidean Geometry with Constructions and Proofs 5 Modern Applications of Triangles and Circles 2 Transformational Geometry 1 Finite Geometries 1 The Parallel Postulate and Classification of Parallel Lines 1 Hyperbolic Geometry 1.5 Elliptic Geometry 1.5 REQUIREMENTS AND GRADE: The requirements for the course are: 1) a portfolio of 6 Homework Assignments which will demonstrate knowledge of theory, constructions, applications, and proofs with different geometries. (48%) 2) a project posted to the web either focusing on a specific topic or an implication of a theory. The project must be in the form of a web site which uses the Java Sketchpad applet to explain a specific idea, or a PowerPoint presentation on an idea or theory, or a small web site explaining an idea with interactive applications. These web sites will be linked through a class links page. (20%) The project must cover: 1. the history behind the ideas of your topic 2. the ideas in the topic 3. the geometrical or theoretical implications of the topic Here are some Project Suggestions. 3) 2 Period Tests (16%) 4) Final Exam (16%)

The last possible date to withdraw from this course without penalty is: October 15, 2002.  

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