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
dmetheny@msubillings.edu
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