Math 386 Fall 2012
Schedules and notes:
Course Number and Title: Math 386: Postulational Geometry
Semester: Fall 2012
Credit Hours: 3
Prerequisites: A grade of 'C' or better in Math 170
Course fee: None
Text: "Euclidean and Non-Euclidean Geometries, 4th Ed.", by Marvin Jay Greenberg. ISBN: 0-7167-9948-0
Instructor: Dr. Craig M. Steenberg
Office: MLH 302
Phone: 792-2343 FAX: 792-2064
OPEN: MTWTh: 10:15AM - 11:45AM
Class Meeting Times: Mon, Wed; 09:00AM - 10:15AM; MLH B30
Purpose: This course presents a rigorous treatment of the foundations of Euclidean geometry, followed by an introduction to some of the non-Euclidean geometries - particularly hyperbolic geometry. Deductive logic is studied in great detail. A significant part of the course will include an in-depth look at the historical and philosophical implications of the non-Euclidean geometries.
Course Objectives: Until the introduction of the non-Euclidean geometries, mathematics was considered more a matter of discovery than invention. While our primary objective is the study of various geometries (there are many!), understanding the significance of the fact that these geometries are the creations of the human mind and the relevance of this fact to the study of all mathematics is a secondary objective that permeates the course. To this end, we will be looking at deductive logic in general, with special concern being given to understanding what it means for a term to be undefined, for a statement to be an axiom, and for a theorem to be proved. Few areas of mathematics are so independent of other areas of mathematics as is Euclidean geometry. Indeed, Euclidean geometry is typically a part of the axiom set of courses such as algebra and calculus. We will study Euclidean geometry from its very creation to its present form, needing only the fundamentals of abstract logic as part of our backgrounds.
Methods of Instruction: I would like to keep formal lectures to an absolute minimum in this course; preferring, instead, to have a sharing of ideas and results between students. The historical and philosophical aspects of the material covered were, and are still, very controversial. Students should keep an open mind when discussing these topics, and respect the possibly diverse opinions that may be expressed by their fellow students. Frequently, students will be asked to demonstrate results in class, using only a few minutes of class time to present work that may well have taken hours to prepare. When you know you are presenting in class, be prepared to be complete, yet brief.
Methods of Evaluation: We will be covering chapters 1 - 8 in the text. Chapter 8 concerns the philosophical implications of the non-Euclidean geometries and will be referred to throughout the course. I will give three hour examinations on the materials covered in chapters 1 - 7. Each will be worth 100 points. These tests will be given at times that seem appropriate and with adequate advance notice. I do not wish to announce specific test dates at the start of the course to allow for flexibility throughout the semester. I will collect homework on a regular basis which will cumulatively be worth 200 points. While homework will be graded on an individual basis, collaboration on it is highly encouraged. Finally, students will be asked to make 2 or 3 in-class presentations each that will cumulatively be worth 100 points. Typically, these will consist of doing a specific homework problem, either to demonstrate a particularly well-done result on the part of a student; but, on occasion to demonstrate classic misconceptions.
The minimum score for each grade is: A: 92; A-: 89; B+: 86; B: 82; B-: 79; C+: 76; C: 72; C- 69; D+: 66; D: 60. Grades below 60 will be scored as F. For those students required to get a 2.0 or better in this course, it should be noted that a grade of C- is insufficient. A grade of at least C must be achieved.
Disability Statement: If course adaptations or accommodations are needed because of a disability, if you need to make me aware of emergency medical information, or if you need special arrangements in case of building evacuation, please contact me immediately. I ask that you put any request in this regard in writing.
FERPA Statement: By FERPA regulations, information regarding a student cannot be given to anyone without the student's written permission. Information cannot be given out over the phone, even to the student, or to any e-mail account other than the student's LC Mail account.
Cell phone use: Cell phones should be shut off at all times during class sessions. The use of cell phones during examinations will be considered to constitute academic dishonesty and appropriate actions will be taken.