Department of Mathematics Syllabus
This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.
Search by ISBN on Amazon: 0716724464
Suggested Schedule:
Lecture(s) 
Sections 
Comments/Topics 
1 
Chapter 1 
Geometry, the five axioms of Euclid (have students read Chapter 1) 
5 
Chapter 2 
Logic, incidence geometry, models, affine and projective planes. 
3 
Chapter 3 
Hilbert’s axioms (add axiom 0: a line is a set of points.Proposition’s 3.2 proof is incorrect). 
3 
Chapter 4 
Neutral geometry. 
0 
Chapter 5 
(Have students read) 
1 
Chapter 6 
(Have students read selected sections) 
5 
Chapters 7 and 10 
Models and properties of hyperbolic geometry. 
2 
Spherical geometry. 

5 
Chapter 9 
Geometric symmetries and group theory. 
Additional Notes:
 Spherical geometry and trigonometry.Area of spherical triangle.Spherical barycenter, orthocenter, and incenter.Spherical Ceva’s theorem.(George A. Jennings, modern Geometry with Applications, Section 2, and online sources.)
 Advanced Euclidean geometry: Ceva’s theorem and its applications.The Euler line and the 9point circle.The Fermat point.Napoleon triangles. Morley’s theorem.(Sources: H.S.M. Coxeter, Geometry revisited, and multiple online sources [for instance, http://www.cuttheknot.org/goemetry.shtml])
 Have students explore hyperbolic geometry with NonEuclid, a hyperbolic geometry freeware developed by Joel Castellanos (currently at http://cs.unm.edu/~joel/NonEuclid/).Requirements: Javaenabled internet browser.A possible project is to experimentally verify that heights/medians/bisectors or a hyperbolic triangle are concurrent.
 Have students explore Euclidean geometry with Geometers Sketchpad or similar available online free software.