Department of Mathematics

Fall 2002 Syllabus
Department of Mathematics
Tennessee Technological University
MATH 3430 College Geometry

Instructor: Dr. Rafal Ablamowicz
Office: Bruner 235D

Office phone:

E-email: rablamowicz@tntech.edu
URL: http://www.math.tntech.edu/rafal/
Office hours: Monday, Wednesday, Friday from 1:00 p.m. to 1:50 p.m. and by appointment (to make an appointment please call ext. 3441)
Class meets: Tuesday and Thursday from 12:00 p.m. – 1:20 p.m. in Bruner 104
Topics: Axiomatic systems and finite geometries; Non-Euclidean geometry; Geometric transformations of the Euclidean plane and space.
Prerequisites: MATH 3400
Credits: 3 credits
Text: "A Course in Modern Geometries" by Judith N. Cederberg, Second Edition, Springer, New York, 2001 (ISBN 0-387-98972-2).
Text web site: http://www.stolaf.edu/people/cederj/geotext/info.htm
Supplementary (optional) Reading: "Journey into Geometries" by Martha Sved, Mathematical Association of America, Spectrum Series, 1997 (ISBN 0-883-85500-3)
Supplementary Mathematical Encyclopedia: http://www-groups.dcs.st-and.ac.uk/~history/index.html
Dynamic Software: "The Geometer's Sketchpad", Student Edition, Version 4, Key Curriculum Press, Key College Publishing
Grading Procedure:

Exam 1, Exam 2, and Exam 3:	300 pts
Homework:	100 pts
Dynamic geometry explorations with Sketchpad	50 pts
Final Comprehensive Exam:	200 pts
Total:	650 pts

Interesting Historical Links: Gino Fano (1871-1952), Finite geometry topics,
A: at least 90%, B: 80% to 89%, C: 70% to 79%, D: 60% to 69%, and F: below 60%
Additional information:

Attendance is required since we will discuss homework problems in class.
Doing homework regularly, reading the book, and class notes are all required and needed to succeed in this course.
We may be using a computer software called "Geometer's Sketchpad".
Scheduled time for the Final Comprehensive Exam is: 10:30 - 12:30 on Tuesday, December 10, 2002.

Students with a disability requiring accommodations should contact the Office of Disability Services (ODS).
An Accommodation Request (AR) should be completed as soon as possible, preferably by the end of the first week of the course.
The ODS is located in the Roaden University Center, Room 112; phone 372-6119.

**Dates and tentative topics of classes**

**MATH 3430, TR 12:00 p.m. - 1:20 p.m., Fall 2002, Dr. Rafal Ablamowicz**

**(This schedule of classes and topics will be revised as we go along.)**
Class	Date	Topic	Assignments / Comments
1	8/20	Sect 1.2: Axiomatic Systems	Read Sect. 1.1 and 1.2 Exercises 1.2: 3,7,8.
2	8/22	Sect. 1.3: Finite projective planes	Read Sect. 1.3 Exercises 1.3: 3,7,10,11,13,15.
3	8/27	Sect. 1.3: Finite projective planes	Read Sect. 1.4
4	8/29	Sect. 1.4: Error correcting codes	Homework 1 on Sect. 1.2 and 1.3 due 8/29
5	9/03	Sect. 1.4: Error correcting codes	Exercises 1.4: 2,3, 7,8,9. Read Appendix A (Definitions, The Postulates, The Common Notions, The First 30 Propositions of Book 1) and Sections 2.1 and 2.2
6	9/05	Sect. 2.1 and 2.2 - Gaining Perspective and Euclid's Geometry	Exercises 2.2: 1, 2, 3a, 3c, 3d Homework 2 on Sect. 1.4 and 2.2 due 9/17
7	9/10	Sect. 2.3 - Non-Euclidean Geometry	Read Sect. 2.3
8	9/12	Sect. 2.4 - Hyperbolic Geometry - Sensed Parallels	Read Sect. 2.4 Exercises 2.4: 1,2,4,5,6,7 Homework 3 on Sect. 2.4 due 9/24
9	9/17	Sect. 2.4 - continued	Proofs
10	9/19	Sect. 2.5 - Hyperbolic Geometry - Asymptotic Triangles	Read Sect. 2.5, proofs
11	9/24	Sect. 2.5 - Hyperbolic Geometry - Asymptotic Triangles	Exercises 1, 3, 4, 6. Homework 4 on Sect. 2.5 due 10/3
12	9/26	Cancelled	Read Sect. 2.6
13	10/1	Test 1 on material covered in classes 1 - 11 including Sect. 2.5
14	10/3	"Geometer's Sketchpad" session in computer lab BR 305	Sketchpad Project #1: Select one of the following sets of problems/assignments from "101 Project Ideas" for The Geometer's Sketchpad" (you can select a second set for additional bonus points): 1. Circles #15-#20. 2. Conic Sections #21-#24. 3. The Golden Ratio #29-31. 4. Lines and Angles #37-39. You are expected to do your work in Sketchpad. Please turn in a printout of your wortksheet and your Sketchpad file (you can email it to me). Due date: December 3. Sketchpad Project #2: In the folder \Sketchpad\Samples\Teaching Mathematics there is a worksheet Tangent Circles.gsp. Prove the result stated in this worksheet. Due date: December 3.
15	10/8	Sect. 2.5 finished and Sect. 2.6 - Hyperbolic Geometry - Saccheri Quadrilaterals	Exercises from Sect. 2.6: 1, 2, 3, 4, 7, 8. Homework 5 on Sect. 2.6 due 10/17.
16	10/10	Sect. 2.6 Finished. Sect. 2.7 - Hyperbolic Geometry - Area of Triangles	Read Sect. 2.7
17	10/17	Sect. 2.7 Finished and Sect. 2.8 - Hyperbolic Geometry - Ultraparallels	Exercises from Sect. 2.7: 1, 2, 3,4, 6. Homework 6 on Sect. 2.7 due 10/24. Read Sect. 2.8
18	10/22	Sect. 2.8 - Finished	Exercises from Sect. 2.8: 2, 3, 4, 5 (6 - Bonus Problem) Homework 7 on Sect. 2.8 due 10/31.
19	10/24	Sect. 2.9 - Elliptic Geometries
20	10/29	Sect. 2.9 - Elliptic Geometry - finished
21	10/31	Sect. 3.1, 3.2, 3.3, and 3.4	Exercises from 3.1-3.4: 3 on page 105, 11 and 12 page 111, 3 on page 119, 6 on page 120. Homework 8 on Sect. 3.1-3.4 due 11/14.
22	11/5	Test 2 on Chapter 2 with an emphasis on sections 2.6 -- 2.9.
23	11/7	Sect. 3.5 - An Analytic Model of the Euclidean Plane	Read Sections 3.5 and 3.6
22	11/12	Sect. 3.6 - Transformations of the Euclidean Plane
23	11/14	Sect. 3.6 - Transformations of the Euclidean Plane	Exercises from 3.5-3.6 pages 127-128: 2, 5, 8, 10, 11, 16, 17; page 135: 1, 3, 4, 5, 7. Homework 9 on Sect. 3.5-3.6 due 11/21.
24	11/19	Sect. 3.6 - Finished
25	11/21	Sect. 3.7 - Isometries	Exercises from 3.7 page 143: 1, 4, 6. Homework 10 on Sect. 3.7 due 12/5 (or earlier)
26	11/26	Sect. 3.7 - Isometries (finished)
27	12/3	Test 3 on Chapter 3
28	12/5	In class presentation of Sketchpad projects	Deadline for Sketchpad projects!
		Final Comprehensive Exam: 10:30 - 12:30 on Tuesday, December 10, 2002.

Revised: November 24, 2002/ra