Math 302,   NonEuclidean Geometry,   Fall 2001

Professor:
John M. Sullivan, jms@math.uiuc.edu, 244-5930
Sections:
D1, MWF 11am, 143 Henry; final exam 8-11am Fri 14 Dec
X1, MWF noon, 149 Henry; final exam 7-10pm Wed 12 Dec
Web address:
Course information is available online at http://www.math.uiuc.edu/~jms/m302/
Textbook:
Experiencing Geometry: In Euclidean, Spherical and Hyperbolic Spaces by David Henderson.
Other materials (please bring these to every class):
- a bound (Mead) composition book for your journal entries;
- scissors and construction paper;
- transparent tape and thin masking tape;
- a tennis ball or similar size model sphere;
- further materials as announced in class.
Hyperbolic Regular Tesselation
Prerequisites:
The official prerequisite is sophomore-level calculus, but this course does not build on that material. What is necessary is a certain amount of mathematical maturity.
Homework:
There will be weekly homework assignments, due on Wednesdays (and assigned by the previous Friday). 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 can earn the right to drop up to two of your lowest homework scores.
Journals:
Before every Monday and Friday class, 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 checked each day and turned in near the end of the semester. Your thoughts will form the basis of our in-class discussions. This work and other in-class activities will count for 15% of your grade.
Exams:
There will be hour-tests in class on Wed. Sep. 26 and on Wed. Oct 31. The exact material covered on each will be announced by the preceding Friday. 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 have the same instructor, and will cover the same material at the same pace. The exams will be comparable but slightly different. Discussing the contents of an exam with students in the other section between the two administrations of the exam is considered cheating.
Outline:
This course examines two-dimensional geometry, in the familiar Euclidean plane, and also in the sphere and the hyperbolic plane, as well as in more general surfaces such as the cylinder. Learning to write good mathematical arguments is a goal of this course. We will occasionally 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 lines 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.