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



Week #1 August 29 - Septmember 2

Read: Introduction and Chapter 1, pages 6-24. Try the following exercises:

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:

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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