Peter F. Stiller
Office: Blocker Bldg. 634B
Office Phone: 862-2905
Time: MWF 10:20 to 11:10
Place: Blocker Bldg. 164
Text: Euclidean and Non-Euclidean Geometries: Development and History by Marvin J. Greenberg
Supplementary Material: See the bibliography below
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).
Overview: This course will introduce the students to Euclidean Geometry and
to some of the subsequent developments in Non-Euclidean Geometry, particularly hyperbolic geometry.
Detailed Description: We will cover a substantial portion of the book.
- 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 January 14 - 18
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 Monday January 21st in class.
Do the following exercises: Exercise 6 page 30 and Major Exercise 1 page 31-32.
Week #2 January 21-25
Read: Chapter 2, pages 38-58. Try the following exercises:
- Page 62-69, Review Exercises and Read Exercise 7.
Assignment #2 Due Monday January 28 in class.
Do the following exercises: Exercises 2, 5, 6, 9 pages 63 and 64.
Week #3 January 28 - February 1
Read: Chapter 3, pages 70-76.
Quiz #1 Wednesday January 30 in class.
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