Math 302,   NonEuclidean Geometry,   Fall 2002

Prerequisites:

The prerequisite is the maturity associated with sophomore-level calculus. Mathematical curiosity, fascination with geometry, appreciation for visual mathematics, and industry are equally important.

Homework:

There will be weekly homework, due on Wednesdays. The homework counts for 25% of the course grade. Homework will be graded on clarity and conciseness as well as content. No late homework will be graded. However, late homework is worth doing and handing in, and will be considered in borderline cases. You have an opportunity to drop an agreed upon number of your lowest homework scores and make up the work in another manner.

Journals:

Periodically, you will be given a discussion question. You should think about this at home and record your conclusions in a bound journal, which will be graded every two weeks. Your thoughts will form the basis of our discussions in class. Your class participation and journal will count for 15% of your grade.

Exams:

There will be two hour-tests in class, on Oct 4 and Nov 8. The exact material covered on each will be announced by the preceding Monday. Each test counts for 15% of your grade. The final exam covers the entire course, and counts for 30% of the course grade.

Different Sections:

The two sections of Math 302 (11am and 12pm) are taught by the same instructor. If you must miss your regular lecture you may visit the other lecture that day. You must take exams with your assigned section.

Outline:

This course examines the way non-Euclidean two-dimensional geometry can help us understand the 3-D space we live in. In addition to the familiar Euclidean plane, we study the geometries of the sphere, the hyperbolic plane, as well as in more general surfaces such as cylinders, cones and tori. Learning to discover geometrical insights, to discuss them effectively with your classmates and to write sound mathematical arguments in clear and consise, mathematical English, is a goal of this course. Henderson's pleasantly written and easy to read textbook supplements the class lectures and discussions. Students are expected to read the text and do problems in the textbook as homework. The material presented in class is the principal reference on exams. We will also meet in a computer lab for interactive demos.

We start (with chapters 1, 2, 4, and 5) by examining the notion of straightness (to define lines in our surfaces) and the properties of geodesics on the various surfaces. The second part of the course (chapters 3, 6, and 9.1-2) examines transformations, congruence, angles and triangles. Next, we investigate maps of the sphere and hyperbolic plane (chapters 15 and 16). The final part of the course (chapters 7, 8, 9.3-4, and 10) deals with the parallel postulate and related notions.