Math 302,   NonEuclidean Geometry,   Spring 2001

Sec. Meetings Professor/Email Office Phone Office Hours Final Exam 
C1 343 Altgeld,
MWF 10am
John M. Sullivan
jms@math.uiuc.edu
326 Illini Hall 244-5930 M 1pm, F 11am 8-11am Fri 4 May
D1 147 Altgeld,
MWF 11am
Karen Mortensen
kmortens@math.uiuc.edu
247 Illini Hall 244-4128 1-2pm MWF 8-11am Thu 10 May

Hyperbolic Regular Tesselation

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 (will be provided);
- further materials as announced in class.
Graders:
Weiting Cao, Department of Mathematics
Mailboxes:
All Math Department mailboxes are located in 250 Altgeld Hall.
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. Feb. 21 and on Wed. April 4. 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 different instructors, but will cover the same material at roughly 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. The third part of the course (chapters 7, 8, 9.3-4, and 18) deals with the parallel postulate and related notions. Finally, we investigate maps of the sphere and hyperbolic plane (chapters 14 and 15).