Euclidean and Non-Euclidean Geometry
Bob Matthews
Department of Mathematics and Computer
Science
January, 2006
Document changes:
- 4/3/06: Removed term paper as a course requirement.
Administrivia:
- Meeting times: 10:00 - 10:50 MTWF Thompson 316
- Final Exam: Friday, May 12, 8:00 AM required
- Instructor:
- Bob Matthews (email matthews@ups.edu)
- Thompson 321B
- Extension 3561
- Office hours (tentative):
- 2:00 - 2:50 MTWF
- Or by appointment.
- If you catch me free at any time, please feel free to drop
in. Messages sent via email are welcome, and can be used to ask
a question or to set up an appointment.
- Textbook
- Required: Greenberg, Marvin J.: Euclidean and
Non-Euclidean Geometries W.H. Freeman and Company, 1993. We
will work our way through the first eight chapters of the
textbook.
- Required: Devlin, Keith: Goodbye,
Descartes Wiley, 1998. We will use the first four
chapters of this book for a
discussion on logic.
- Other readings as assigned. In addition to readings from
the textbook (which will be our primary reference), we will,
from time to time, leave the textbook to explore ideas and
questions generated by the text using other sources.
- A particularly
useful resource is
The
MacTutor History of Mathematics web page at the University of St.
Andrews (Scotland).
Weekly reading and lecture schedule
Exam Reviews
Assignments
Evaluation
- Four hour exams + a comprehensive final: (The final exam will
have the weight of two hour exams). I will drop the lowest hour exam score.
- Written exercises will be given the weight of one hour exam. I
will make assignments from the textbook on a routine basis, and
will select problems from each assignment to grade. You will also
be asked to present your work on the board (though this will not
generally be graded, except for participation).
Some comments on the course:
A course in Euclidean and non-Euclidean geometries serves several
purposes in the undergraduate mathematics curriculum. For prospective
teachers, it is a course required by most states for teacher
certification. For many, it is the first course that involves
rigorous proof. For students interested in the philosophy and history
of mathematics, it provides an important example of how mathematics
works, how one does mathematics, how mathematics has developed over
time (together with false starts and wonderful surprises), and gives
insight into what are commonly called 'foundational issues' (What are the role
of axioms? What is
the nature of proof? What is the nature of mathematical truth? What,
if anything, does this all mean? What is the geometry of the space
around us?).
We will approach all of these issues in the course of this term.
We will study geometry by doing it. From the practical point of view,
this means that we will spend time learning how to prove things and
how to present results both orally and in writing. Along the way we
will talk about and work with the process of discovery, the
uncovering of assumptions, the rigorous presentation of results, and
the logical and philosophical foundations of mathematics (and some of
the issues surrounding those foundations).
So... expect
- Logic
- Foundational issues
- Proofs and methods of proofs
- Writing
- History
- Lots of geometry, and
- Philosophical issues
It will be a lot of work, but it should also be a great deal of
fun.
The last time I taught this class
Some Important Dates:
Please check the Master
Calendar for important dates in the term (last day to add/drop,
etc.).
Hour Exams will be held on the following dates:
- Exam 1: Friday, February 10
- Exam 2: Monday, March 6 (rescheduled from Friday, March 3)
- Exam 3: Friday, March 31
- Exam 4: Wednesday, April 26. Please note that this is during the
last full week of classes.
The lecture schedule for this course can be found
here
The final exam for this class will be at 8:00 AM Friday, May 12. It
will be a comprehensive, two hour in-class examination.
Since this course includes students from both Math 300 and Honors 213, I have
included links to both syllabi:
Return to my
home page