MATH 311: Geometry

SYLLABUS

Spring 2008

INSTRUCTOR: Dr. Dixie Metheny CEHS 206 657 - 2087

TIMES: MWF 12:50 – 1:50 CLASS MWF 2:00 - 3:00 OFFICE

COURSE DESCRIPTION: 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.

LEARNING GOALS:

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.

PREREQUISITE: Math 301 or consent of instructor

TEXTBOOK: Modern Geometries, James R. Smart, 5th edition

SCHEDULE

Jan. 16 Orientation

18 Prerequisites

23 Introduction

25 Finite geometries

28 Four-line geometries

30 Four-point geometries

Feb 01 Fano’s geometry

04 Geometer’s Sketchpad 06 The geometry of Pappus

08 Review

11 Test 1

13 Introduction to transformations

15 Euclidian motions of the plane

20 Groups of transformations

22 Sets of equations for motions of the plane

25 Computer Graphics

27 Research

29 Short Paper

Mar 10 Review

12 Test 2

14 Motions of Three-Space

17 Fractals

19 Convex Sets

24 Supporting Lines

26 Convex bodies

28 Convex hulls

30 Width of a set

April 02 Review

04 Test 3

07 Prepare for presentations

09 Fundamental Concepts (Student)

11 Modern Synthetic Geometry 14 Isogonal Conjugates

16 Golden ratio, tessellations and Pick’s Theorem (Student)

18 Basic constructions (Student)

21 Constructible Numbers (Student)

23 Impossibility proofs

28 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.

A: 95-100 B+: 88-91 C: 75-82 F: Below 65 A-: 92-94 B: 83-87 D: 65-74