MATH 361 - FALL 2009

Instructor: Professor David Singer
Office: Yost 307a
Extension: x2892
E-mail: david.singer@case.edu

Description. MATH 361 is a one-semester, three credit-hour course in geometry. The prerequisite for the course in MATH 122 or its equivalent. This course satisfies the SAGES department seminar requirement.

Places of interest: The Math Forum, Geometry in Action, The Geometry Junkyard, Interactive Geometry, Euclid's Elements , Wolfram Geometry Archive.

Text: Geometry: Plane and Fancy, By David Singer, Springer-Verlag New York, ISBN 0-387-98306-6.

Office Hours. My official hours are posted at the link. I am also available at other times by appointment or you may drop by my office. You are always welcome!

Syllabus:

1. A Little Euclidean Geometry
2. Axioms of geometry
3. Tiling the Euclidean plane
4. Isometries, similarities and other transformations
5. Hyperbolic geometry in the Poincare disc
6. Complex numbers and Mobius transformations
7. Tiling the hyperbolic plane
8. Geometry of the sphere
9. Projective geometry
10. Tiling the sphere and the projective plane
11. Other topics.

Course Information:There will be regular homework assignments, which together with classroom discussion will count for 30% of the grade. Each student will prepare a written report of at least 10 pages on a topic of their choice relating to the subject matter of the course, which will count for 20% of the grade. The topic should be selected by Monday,October 5, 2009. A rough draft and progress report on the project will be due on October 16, 2009. A brief presentation (about 25 minutes) will be made by each student sometime during the term, counting for 20% of the grade. The absolute deadline for written reports December 4, 2009. There will be a midterm exam in class (tentatively) scheduled for Friday, October 9, 2009, which will count for 30%. The final exam period is December 8, 8:30-11:30AM and will be used for presentations; attendance is mandatory.

Phone: (216)368-2892

Fax: (216)368-5163
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