Math 402,   NonEuclidean Geometry,   Spring 2005

Web address:

Course information is available online at http://www.math.uiuc.edu/~stolman/m302/

Textbook:

Experiencing Geometry in Euclidian, Spherical, and Hyperbolic Spaces by David Henderson.

Other materials: You must purchase or aquire, and bring to every class (unless otherwise noted):

- a Mead composition book for your journal entries;

- thin masking tape;
- A Vis-a-Vis wet-erase fine point overhead transparency marker;
- ribbon, string, and three rubber bands;
- a tennis ball (bring only as announced);
- a shoe box or other small box (bring only as announced);
- possible further materials.

Grader:

Lee Janssen(ljanssen@math.uiuc.edu).

Mailboxes:

All department mailboxes are located in 250 Altgeld Hall.

Prerequisites:

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

Homework:

There will be weekly homework assignments, 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.

By doing extra assignments, you may drop up to two homework grades.

Journals:

 Periodically, you will be given a discussion question. Since the journal entries are exploratory, it is not expected that the mathematics will always be completely correct; however, your writing should show some significant thought on the question. Allow about an hour for each journal entry; this includes thinking and writing. The journals are informal writing, but the entries must be legible and the meaning intellible. Focus on communicating your ideas! Read over you entry to see whether what you wrote is understandable. If no, you need to edit to add more. Your journal should be in a Mead composistion book, and be kept separate from your class notes. Each journal should begin on a new page. At the top of the page, put the number of the journal assignment and the date that it is due (not assigned). In general, journal entries should be 1 to 2 pages in length. This work and other in-class activities will count for 15% of your grade.

Exams:

There will be two hour-tests on Fridays in class, on Sept 29 and Nov 3. If you have a forseeable conflict with one of these dates, you are required to tell me now -- not right before the exam. I will hand out a practice exam for each test. 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 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 introduces two-dimensional geometry, in the familiar Euclidean plane, but also in the sphere and the hyperbolic plane, as well as in more general surfaces. Learning to write good mathematical arguments is a goal of this course. We will occasionally meet in a computer lab for interactive demos.

 

 

The first part of the course (covering chapters 1,2, 4, and 5 in Henderson) examines the notion of straightness (allowing us to define lines in our surfaces) and the properties of lines on the Euclidian plane, the sphere, the cylinder, and the hyperbolic plane. The second part of the course (covering chapters 3,5.3, 6, 9.1, and 9.2) examines transformations, congruence, angles, and triangles. The third part of the course (covering chapters 7, 8 and 9.3 and 9.4 and 18) deals with the parallel postulate and related notions. Finally, we shall look at maps of the sphere and hyperbolic plane (chapters 14 and 15.)