# Modern Geometry

### 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.

### 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.

### 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.

### 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.

### Week #8 October 15 - October 19

Read: Chapter 4, pages 115-121.

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

### 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.

### 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.