Modern Geometry
Math 467-500
Fall 2005
Instructor:
Peter F. Stiller
Office: Blocker Bldg. 634B
Office Phone: 862-2905
E-mail: stiller@math.tamu.edu
Office Hours:
Fall Schedule
Course Information
Time: TTh 11:10 to 12:25
Place: CE 136
Text: Euclidean and Non-Euclidean Geometries: Development and History by Marvin J. Greenberg
Prerequisites: Some experience with proofs - for example Math 304.
Grades: We will have two major exams, a mid-term and a final. Both will count for 30% of the grade. The mid-term will include an in class, as well as a take home, portion. We will have three in class quizzes that will count for 15% (5% each) and 5 problem sets
that will count 25% (5% each). The usual scale will apply 100-90 A, 89-80 B, 79-70 C, 69-60 D, 59 and below F.
Overview: This course will introduce students to a rigorous approach to Euclidean Geometry and
to some of the subsequent developments in Non-Euclidean Geometry, particularly hyperbolic geometry.
Syllabus
Detailed Description: We will cover a substantial portion of the book.
Topics
- Euclid's Geometry and Historical Perspective
- Logic and Incidence Geometry
- Axioms of Geometry - Hilbert's Version
- Neutral Geometry
- Parallel Postulate - Some History
- Introduction to Non-Euclidean Geometry
- Independence of the Parallel Postulate
- Geometric Transformations
- Hyperbolic Geometry
Week #1 August 29 - Septmember 2
Read: Introduction and Chapter 1, pages 6-24. Try the following exercises:
- Page 26-27, Review Exercises 1-10.
- Page 27-31, Exercises 1-4, 8, 9, 10, 12
Assignment #1 Due Tuesday September 6th in class.
Do the following exercises: Exercise 6 page 30 and Major Exercise 1 page 31-32.
Week #2 September 5 - September 9
Read: Chapter 2, pages 38-58. Try the following exercises:
- Page 62-69, Review Exercises and Read Exercise 7.
Assignment #2 Due Tuesday September 13 in class.
Do the following exercises: Exercises 2, 5, 6, 9 pages 63 and 64.
Week #3 September 12 - September 16
Read: Chapter 3, pages 70-76.
Quiz #1 Tuesday September 20 in class.
Week #4 September 19 - September 23
Read: Chapter 3, pages 77-82.
Assignment #3 Due Tuesday September 27 in class.
Do the following exercises: Exercises 2d, 3, 4, 5, read 6, 10, 11, 12, 13, 14, 19 pages 105-107.
Week #5 September 26 - September 30
Read: Chapter 3, pages 83-92.
Quiz #2 Tuesday October 4 in class.
Week #6 October 3 - October 7
Read: Chapter 3, pages 93-98.
Assignment #4 Due Tuesday October 11 in class.
Do the following exercises: Exercises 26, 29, 32, 36 pages 109-110.
Week #7 October 10 - October 14
Read: Chapter 3, pages 98-114 and Chapter 4, 115-118.
Quiz #3 Tuesday October 18 in class.
Week #8 October 17 - October 21
Read: Chapter 4, pages 115-121.
Take Home portion of the Mid-Term handed out Tuesday October 18th.
Date of Mid-Term Exam (Tentative) Thursday October 20th.
Take Home portion of Mid-Term Exam handed out October 18th due October 20th.
Week #9 October 24 - October 28
Read: Chapter 4, pages 122-134.
Assignment #5 Due Tuesday November 1 in class.
Do the following exercises: Exercises 4, 12, 13, 15, 21, 25 pg. 136-141.
Week #10 October 31 - November 4
Read: Chapter 5, pages 122-134.
Quiz #4 Due Tuesday November 8 in class.
Week #11 November 7 - November 11
Read: Chapter 5, pages 148-163.
Assignment #6 Due Tuesday November 15 in class.
Do the following exercises: Exercises pg. 164-176.
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