MTG 4212-01
TR 9:30 - 10:45
201 LOV
College Geometry
Spring 1998

instructor
Philip L. Bowers
113 Love Building
bowers@math.fsu.edu
http://www.math.fsu.edu/~bowers/
644-2889 (office)
644-2202 (front desk)

office hours

M 9:00 - 10:00
W 9:00 - 10:00
R 11:00 - 11:45
F 1:00 - 3:00
and by appointment

eligibility
You must have completed MAC 3312 and MAS 3105 with grades of "C-" or better.
text
There is no text. Instructor notes will be provided as the course progresses.
content
The course is organized into three units.
Unit 1. Finite Geometries and Parallel Postulates. Finite geometries, parallel postulates, finite affine planes, finite projective planes, projective completion, incidence matrices.
Unit 2. Projective Planes over Fields. Fields, projective planes over fields, isomorphism, automorphism, symmetry, equivalence relations, projective completions revisited.
Unit 3. Desargues, Pappas, and Projective 3-Space. Axioms for projective 3-space, elementary propositions, Desargue's Theorem, Pappas's Theorem.
homework
Assignments are listed here.
objectives
The main objective of this course is to introduce the student to the axiomatic method in mathematics through the vehicle of Axiomatic Geometry. The emphasis is on precise thinking and careful argument rather than on calculations. Starting with undefined terms and a set of axioms governing the use of those terms, we will explore the implications of those axioms by building models and discovering and proving theorems that logically follow from the axioms. We will concentrate much of our effort on constructing concrete models of geometries from simple or familiar objects that appeal directly to the intuition. Our approach will be to proceed from the concrete to the abstract, from the simple to the sophisticated as we gain experience with our models.
attendance
I strongly advise you to attend class regularly. A student absent from class bears the full responsibility for all subject matter and procedural information discussed in class.
courtesy
Generally, I expect you to get to class on time and not to leave class until I have dismissed it. If you must leave class early, please let me know before class begins.
grading
Unit 1 Test............................................20%
Unit 2 Test............................................20%
Final Examination................................40%
Homework............................................20%
makeups
No makeups are given. If you miss a test, a 0 will be entered for your grade on that test.
final exam
The final examination will be comprehensive and given on Friday, 1 May, from 12:30 until 2:30.
Although mathematics can and is put to many practical uses, it is basically a very abstract discipline, the study of abstact objects using a limited system of axioms. Consider Euclidean geometry as an example. It studies objects such as lines, points, circles, etc. which are conceptual abstractions of physical objects that occur in the world around us. These concpts are defined by a set of axioms which they are required to satisfy. The pure mathematicians who developed this field, going back at least to Euclid, studied these abstract concepts, and proved theorems about them using only this well-defined set of axioms. These theorems were proved without specific reference to any particular application such as land surveying or engineering, or any other of the many applications of Euclidean geometry. However, the profound importance and usefulness of the field comes from the fact that any theorem, proved strictly from a limited set of axioms, is valid for all of the many diverse areas of application.

Check out the geometry links from my mathematics topics list.