Course: Math 302, MWF, 3-4pm, Danforth University Center, Room 236
Instructor: Quo-Shin Chi
Office: Room 210, Cupples I
Office hours: MW 4-5pm
Textbook: Euclidean and Non-Euclidean Geometries, 4th ed., by Marvin
Jay Greenberg
We shall study Euclidean and Non-Euclidean
geometries from the axiomatic view brought forth by David Hilbert
around the turn of the 20th century. The axiomatic view starts with
setting up certain axioms as the genesis of a geometry and derives all
the geometric properties of that geometry through rigorous logical
reasoning. We shall see that Euclidean and Non-Euclidean geometries
differ from each other only by one single axiom, namely, the parallel
postulate of Euclid's that had baffled some best brains in the history
of
mathematics. Moreover, we shall use complex numbers to construct
a
model space (the Poincare' disc or upper half space) for
Non-Euclidean geometry.
There will be several homework assignments (30%),
one take-home midterm (30%), and one take-home final (40%).
Last but not least, to master mathematics is to
constantly think and do mathematics yourself, not just to watch your
teachers perform the tasks and try to grab a solution manual (most
often they are nonexistent) whenever you are asked to tackle a
problem.