MATH
3355 NONEUCLIDEAN GEOMETRY 
Fall 2015 
Instructor:
Roberto Hasfura 
SCHEDULE: TR 9:5511:10 a.m.in
room MMH 130
PREREQUISITES:
MATH 3326 or equivalent
TEXT: Euclidean and NonEuclidean
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 45 p.m.,
TR 3:304:30 p.m.; and by appointment. In Room MMS 115K
INSTRUCTOR’S COORDINATESOffice: MMS 115K;
Phone Extension: X8240; Email: jhasfura@trinity.edu
COURSE URL: www.trinity.edu/jhasfura/Courses/Math3355
COURSE
DESCRIPTION:
The discovery of noneuclidean 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 noneuclidean 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 takehome 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 1/27 Read Chapter 1. Hand in solutions to all the
Review Exercises and Exercises 1, 2, 4, 5, 10, 11, 13 in Chapter 1. Due in my office (please use the accordion envelope labeled
Geometry) before 5 p.m. on Friday 9/11.