# Modern Geometry

### Math 467-500

### Fall 2007

**Instructor:**
Peter F. Stiller

**Office:** Blocker Bldg. 623F

**Office Phone:** 862-2905

**E-mail:** stiller@math.tamu.edu

**Office Hours:**
Fall 2007 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 portion, as well as a take-home portion. We will have in class quizzes and problem sets that will count 40% (best 8 at 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 Neutral and Euclidean Geometry and
to some of the subsequent developments in Non-Euclidean Geometry, particularly hyperbolic geometry. The approach be a rigourous one that uses Hilbert's Axioms as a foundation.

## 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
- Hyperbolic Geometry
- Geometric Transformations

**Week #1 August 27 - August 31 **

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 4 in class.**

Do the following exercises: Exercise 6 page 30 and Major Exercise 1 page 31-32.

**Week #2 September 3 - September 7 **

Read: Chapter 2, pages 38-58. Try the following exercises:

- Page 62-69, Review Exercises and Read Exercise 7.

**Assignment #2 Due Tuesday September 11 in class.**

Do the following exercises: Exercises 2, 5, 6, 9 pages 63 and 64.

**Week #3 September 10 - September 14 **

Read: Chapter 3, pages 70-76.

**Quiz #1 Tuesday September 18 in class.**

**Week #4 September 17 - September 21 **

Read: Chapter 3, pages 77-82.

**Assignment #3 Due Tuesday September 25 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 24 - September 28 **

Read: Chapter 3, pages 83-92.

**Quiz #2 Tuesday October 2 in class.**

**Week #6 October 1 - October 5 **

Read: Chapter 3, pages 93-98.

**Assignment #4 Due Tuesday October 9 in class.**

Do the following exercises: Exercises 26, 29, 32, 36 pages 109-110.

**Week #7 October 8 - October 12 **

Read: Chapter 3, pages 98-114 and Chapter 4, 115-118.

**Quiz #3 Tuesday October 16 in class.**

**Week #8 October 15 - October 19 **

Read: Chapter 4, pages 115-121.

Take Home portion of the Mid-Term handed out Thursday October 18.

**Date of Mid-Term Exam (Tentative) Thursday October 25.**

**Take Home portion of Mid-Term Exam due Thursday October 25th.**

**Week #9 October 22 - October 26 **

Review and MID-TERM EXAM

**Week #10 October 29 - November 2 **

Read: Chapter 4, pages 122-134.

**Assignment #5 Due Tuesday November 6 in class.**

Do the following exercises: Exercises 4, 12, 13, 15, 21, 25 pg. 136-141.

**Week #11 November 5 - November 9 **

Read: Chapter 5, pages 148-163.

**Quiz #4 Tuesday November 13 in class.**

**Assignment #6 Due Tuesday November 13 in class.**

Do the following exercises: Exercises TBA pg. 164-176.

**Week #12 November 12 - November 16 **

Read: Chapter 6, pages 177-191.

**Assignment #7 Due Tuesday November 20 in class.**

Do the following exercises: Exercises TBA pg. 201-222.

**Week #13 November 19 - November 23 **

Read: Chapter 6, pages 191-201 and Chapter 7, pages 223-232.

THANKSGIVING - no class Thursday November 22.

**Week #14 November 26 - November 30 **

Read: Chapter 7, pages 232-248.

**Assignment #8 Due Tuesday December 4 in class.**

Do the following exercises: Exercises TBA pg. 270-289.

**Week #15 December 3 - December 7**

Read: Chapter 7, pages 248-256.

FINAL EXAM on Friday December 7.

**Date and Time of Final Exam Friday December 7, 3PM-5PM.**

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