Math 402,   Non Euclidean Geometry,   Spring 2008

Web address:

Course information is available on-line at http://www.math.uiuc.edu/~stolman/m402/

Textbook:

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

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

• a Mead composition book for your journal entries (not a spiral notebook);
• thin masking tape (one-inch width is optimal);
• A Vis-a-Vis wet-erase fine point transparency marker, not a permanent marker;
• An overhead transparency (I will provide this);
• a piece of ribbon (I will provide this);
• a piece of string (I will provide these);
• three rubber bands in different colors (I will provide these);
• a tennis ball (bring only as announced);
• a shoe box or other sturdy small box for storing your hyperbolic plane (bring only as announced);
• possible further materials.

Grader:

Michael Sommers, msommers@uiuc.edu

Mailboxes:

All department mailboxes are located in 250 Altgeld Hall.

Grades:

• Components of grade:
  • Homework: 25%
  • Journal and class participation: 15%
  • First midterm: 15%
  • Second midterm: 15%
  • Final exam: 30%
• The cutoff for the lowest A-, B-, C-, and D- will be at most 90%, 80%, 70%, and 60%, respectively; it may be somewhat lower.
• Grades will be available on-line; to view scores go to the math department courses homepage and select score reports. (To find the math department courses homepage select "Courses" on the math homepage.

Homework:

  There will be weekly homework assignments. They are due on Wednesdays; they must be either handed in at the beginning of class or else placed in the grader's mailbox before class; not in the instructor's mailbox. They will be assigned in class by the previous Friday, and are available on-line. 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:

  There will be journal questions due in class most Mondays and Fridays. They will be assigned the previous class, and are available on-line.   The journal entries are exploratory; we do not expect 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 intelligible. Focus on communicating your ideas! However, don't worry; if you do all the journals and make an honest effort to do them well, you will do well in this component of the class.   Your journal should be in a Mead composition 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.

Exams:

There will be two one hour tests in class, on Friday, Feb. 15 and Friday, March 28. If you have a conflict with either of these dates, you are required to tell me now -- not right before the exam. Practice exams will be available.

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.

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 may 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. We shall end with some additional material to be chosen later.