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SYLLABUS Title: Number: Catalog description: Geometry Math 311 Geometry Math 311 Prerequisite: Math 301 or consent of instructor Deals with the fundamentals of synthetic and modern geometry. Covers topics in non-Euclidian geometry as well as topics in Euclidian geometry, such as finite geometry, space geometry, constructions and solid geometry. Instructor: Dr. Dixie Metheny Office: COE 206 657-2087 [email protected] Hours: 10:30 – 11:30 MWF and 1-2TTH Course goals and Purpose: 1. An understanding of mathematics as a deductive system as evidenced by an ability to formulate logical arguments. 2. The ability to communicate, both in writing and verbally, mathematics and mathematical ideas. 3. Demonstration of pedagogical knowledge specific to mathematics teaching and learning. Textbook: Modern Geometries, James R. Smart, 5th edition Course Outline: Jan. 17 Orientation 19 Prerequisites 22 Introduction 24 Finite geometries 26 Four-line geometries 29 Four-point geometries 31 Fano’s geometry Feb Mar April 02 Geometer’s Sketchpad 05 The geometry of Pappus 07 Review 09 Test 1 12 Introduction to transformations 14 Euclidian motions of the plane 16 Groups of transformations 21 Sets of equations for motions of the plane 23 Computer Graphics 26 Research 28 Short Paper 02 RCML 12 Review 14 Test 2 16 Motions of Three-Space 19 Fractals 21 Convex Sets 23 Supporting Lines 26 Convex bodies 28 Convex hulls 30 Width of a set 02 Review 04 Test 3 09 Prepare for presentations 11 Fundamental Concepts (Student) 13 Modern Synthetic Geometry 16 Isogonal Conjugates 18 Golden ratio, tessellations and Pick’s Theorem (Student) 20 Basic constructions (Student) 23 Constructible Numbers (Student) 25 Impossibility proofs 30 Final Exam (2 p.m.) Course Requirements: Group Activities (__ % of grade) 1. Daily homework -- one set to be turned in by each group or presented by a group member to whole class 2. Presentation of a section of the textbook to the class. Each major grade will be weighted by the average of peer evaluations given for a student by his group members. These evaluations should consider both attendance and group participation. Individual Activities (__ % of grade) Three Tests and a Final Exam Assessment: Learning goals 1 and 2 will be assessed by student performance on homework and tests. Learning goals 2 and 3 will be measured through student presentations of homework and his/her group’s major teaching lesson. Grades will be based on the following percents: A: A-: 95-100 92-94 B+: B: 88-91 83-87 C: D: 75-82 65-74 F: Below 65