MATH 3355 NON-EUCLIDEAN GEOMETRY

Fall 2015

Instructor: Roberto Hasfura

 

 

SCHEDULE:  TR 9:55-11:10 a.m.in room MMH 130

PREREQUISITES: MATH 3326 or equivalent 

TEXT: Euclidean and Non-Euclidean Geometries, M. J. Greenberg, Third or Fourth Edition, (Fourth Edition is about $160; Third Edition can still be found online for far less money)

OFFICE HOURS: MW 4-5 p.m., TR 3:30-4:30 p.m.; and by appointment. In Room MMS 115K

INSTRUCTOR’S COORDINATES---Office: MMS 115K; Phone Extension: X8240; E-mail: jhasfura@trinity.edu

COURSE URL: www.trinity.edu/jhasfura/Courses/Math3355

 

 

COURSE DESCRIPTION:

The discovery of non-euclidean geometries in the early part of the nineteenth century is an event not only of great importance in mathematics and physics, but also one with significant epistemological import.

 

In this course, after a brief discussion of the essentials of axiomatic systems we will examine the merits and deficiencies of the geometry in Euclid's Elements (c. 300 B.C.) and then we will present the system postulated by Hilbert, which redresses those shortcomings. We will also study the role of the parallel postulate in that geometry as well as the history of the controversy surrounding it. Finally, the geometry that arises by postulating the negation of the parallel postulate (a non-euclidean geometry) will be considered along with some of its models.

 

Hopefully, by the end of the semester, the first paragraph in this course description will have been justified.

 

 

HOMEWORK AND GRADING:

The homework will consist of eight to ten take-home problem sets throughout the semester. Your final grade in the course will depend mostly on the grades you get on these assignments so you shouldn't treat them lightly (as you might treat a regular, less weighty homework assignment.) The papers you will turn in must be thoughtful, clear, and as complete as possible. (I will not give credit to illegible or disorganized or otherwise messy work. I suggest that you work out the problems in their entirety and carefully review them before you attempt to produce the final draft. The solutions that you will hand in should be neatly presented with all work shown.)

 

Your final grade in this course will be computed in the following manner:

 

Final Grade = .90(Average Grade on Assignments) + .10(Grade on Attendance).

 

With regard to attendance, each unjustified absence will cost 20 (out of 100) points in your Attendance Grade so that if, for example, you have five unjustified absences your Attendance Grade will be 0 and you will not be able to get an A in the course.

 

 

ACADEMIC INTEGRITY:

“All students are covered by a policy that prohibits dishonesty in academic work. Under Trinity’s Honor Code, a faculty member will (or a student may) report an alleged violation to the Academic Honor Council. Students who are under the Honor Code are required to pledge all written work that is submitted for a grade:  `On my honor, I have neither given nor received any unauthorized assistance on this work’ and their signature.  The pledge may be abbreviated `pledged’ with a signature. As your instructor, I support and adhere to the principles of the honor code. You will be assumed trustworthy in all your dealings with me and with your fellow classmates. However, should a violation of this trust be discovered, it will be reported to the Council which will investigate and adjudicate. The goal is not vengeance against those who violate the honor code, but fairness for those who adhere to it.”

 

NOTES:

1. Please do not use cell phones in the classroom. If you need do it during class, please discreetly leave the classroom and return when you are finished.

 

  

GRADE EQUIVALENCES:

 

94<#<100 A  

90<#<94 A-

87<#<90 B+

83<#<87 B

80<#<83 B-

77<#<80 C+

73<#<77 C

70<#<73 C-

65<#<70 D+

60<#<65 D

#<60 F

 

 

 

HOMEWORK:

 

Hwk 1. Due in my office (please use the accordion envelope labeled Geometry) before 5 p.m. on Friday 9/11. Read Chapter 1. Hand in solutions to all the Review Exercises and Exercises 1, 2, 4, 5, 10, 11, 13 in Chapter 1.

 

Hwk 2. Due in my office (please use the accordion envelope labeled Geometry) before 5 p.m. on Friday 9/18. Read Chapter 2. Hand in solutions to Exercises 1, 2, 3, 4, 6, 7, 9, 11 in Chapter 2.

 

                Hwk 3. Due in my office (please use the accordion envelope labeled Geometry) before 5 p.m. on Friday 9/25. Read Betweenness on Chapter 3. Hand in solutions to Exercises 1, 2, 3, 4, 5, 6, 9, 12 and 15 in Chapter 3. These are Exercises 1, 2, 3, 4, 5, 6, 9, 13 and 16                in the third edition of the book.

 

Hwk 4. Due in my office (please use the accordion envelope labeled Geometry) before 5 p.m. on Friday 10/2. Read Congruence on Chapter 3. Hand in solutions to Exercises 22, 23, 25, 26, 27, 29, 30 in that chapter. They are the same Exercises in the third edition of the text.

 

Hwk 5. Due in my office (please use the accordion envelope labeled Geometry) before 5 p.m. on Friday 10/9. Read Chapter 3. Hand in solutions to Review Exercises 1-17, Exercises 7ab, 35, and Major Ex. 1 in Chapter 3.

(Problem 35 is not in the third edition: I will send an e-mail with a picture of the problem. The other exercises are in your text (with the same numbering.)

 

Hwk 6. Due in my office (please use the accordion envelope labeled Geometry) before 5 p.m. on Monday 10/19. Read Chapter 4. Hand in solutions to Review Exercises 1-14, 16, 18-20 and 22; and Exercises 1ab, 2, 16, 17, 19, 20a, 22, 23 and 24 in Ch. 4.

(In the third edition of the text these are all the Review Exercises; and Exercises 3, 9, 16, 17ab, 18, 19, 23, 27, 28 and 29 in Ch. 4.)

 

Hwk 7. Due in my office (please use the accordion envelope labeled Geometry) before 5 p.m. on Wednesday 10/28. I understand that everyone is working out of the Third Edition of the text. The following exercises are from that edition. Read Chapter5. Hand in solutions to the Review Exercises; and to Exercises 2, 3, 4, 5, 6, 10 and 11 in Ch. 5.)

 

Hwk 8. Due in my office (please use the accordion envelope labeled Geometry) before 5 p.m. on Friday 11/6. The following exercises are from the Third Edition of the text. Read Chapter 6. Hand in solutions to Exercises 6, 8, 10 and 14; and to Major Exercise 10 in that chapter.

 

Hwk 9. Due in my office (please use the accordion envelope labeled Geometry) before 5 p.m. on Tuesday 11/24. The following exercises are from the third edition of the text (in parenthesis I give the corresponding exercise in the fourth edition). Read Chapters 6 and 7 (inversion with respect to circles, and the Klein and Poincare disk models only). Hand in solutions to Exercise 11 (2) and Major Exercise 11 (11) in chapter 6; and exercises K-11 and K-12 (K-11 and K-12) and P-6, P-7 and P-9 (P-6, P-7 and P-9) in chapter 7. .