Document changes:

- 4/3/06: Removed term paper as a course requirement.

**Meeting times:**10:00 - 10:50 MTWF Thompson 316**Final Exam:**Friday, May 12, 8:00 AM**required**- I
**nstructor:** - 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***Required: Devlin, Keith:**Wiley, 1998. We will use the first four chapters of this book for a discussion on logic.__Goodbye, Descartes__- 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).

Exam Reviews

- 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).

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

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:

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