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.