Mathematics 138 - Classical Geometry; Fall 2000

## Instructor: Danny Calegari 432 Science Center

• Half-course (fall term 2000). MWF at 12 in Room 309 Science Center
• Office hours M 1:30 - 2:30
• Prerequisite: Mathematics 21 a,b
• Assessment: 50% homework, 50% take-home final exam
• Email dannyc

## Course Assistant: Kathy Paur 321b Science Center

• Office hours Tu 4 - 5
• Section Th 6 - 7 in Room 321b Science Center
• Email paur
 Description of course

An introduction to spherical, Euclidean and hyperbolic geometry in two and three dimensions, with an emphasis on the similarities and differences between these flavors of geometry. The most important tool in analyzing these geometries will be a study of their symmetries; we will see how this leads naturally to basic notions in group theory and topology. Topics to be covered might include classical tessellations, the Gauss-Bonnet theorem, scissors congruence, orbifolds, and fibered geometries.

• Course notes for class; available as a .tex file, or as a .ps file. (Under revision. Updated May 4th, 2005)
• Syllabus for class; available as a .tex file, or as a .pdf file.
• Homework 1 - groups; available as a .tex file, or as a .pdf file.
• Homework 2 - the Euclidean plane; available as a .tex file, or as a .pdf file.
• Homework 3 - spherical geometry; available as a .tex file, or as a .pdf file.
• Homework 4 - hyperbolic geometry; available as a .tex file, or as a .pdf file.
• Homework 5 - surfaces and fundamental groups; available as a .tex file, or as a .pdf file.
• Homework 6 - properly discontinuous groups; available as a .tex file, or as a .pdf file.
• Final exam; available as a .tex file, or as a .pdf file.
Answers to homework problems should take the form of complete sentences. It's important not merely to find the solution to a problem, but also to communicate that solution effectively.

The final exam was posted on this webpage at noon on Thursday the 4th of January.

 Recommended texts for course

• Three dimensional geometry and topology W. Thurston Princeton Mathematical Series, 35. Princeton University Press, 1997
• Classical tessellations and three-manifolds J. Montesinos Universitext, Springer-Verlag, 1987 out of print