Syllabus Math 402


Math 402. Non Euclidean Geometry
Instructor Syllabus

Text: M. Hvidsten, Geometry with Geometry Explorer (GEX)

Day-Week labels and text sections in [ ] precede topics.

1 Geometry and the Axiomatic Method [Chapter 1]
W1 [1.1] Greek Origins of Geometry
F1 [1.2] Thales and Pythagoras
M2 [1.4] Axiom Systems and Systems of Axioms
W2 [1.5] Consistency of axiomatic systems
F2 [1.5] Independence and Completeness
M3 Labor Day, No Class
W3 Quiz 1 and Introduction to Lab 1
F3 [1.7] A Computational Axiomatic System using GEX

2 Euclidean Geometry
M4 [Appendix A] Euclid's Elements, Book I
W4 [2.1] Absolute (neutral) Geometry, Exterior Angle Theory
F5 [2.2] Congruence, SAS, ASA, SSS, Pons Asinorum, Pasch
M4 [2.1] Parallels, 5th Postulate, Playfair, Propositions 28/29
W4 [2.5] Similarity, AAA, Altgeld Tower Project
F4 Quiz 2 and Birkhoff's Axioms begun [3.6]

3 Analytic Geometry
M6 [3.1, 3.2] Review of Cartesian Coordinates and Plane Vectors
W6 Lab 2 [3.3] Bezier Splines with Xfig
F6 [3.4] Pappus' proof of Pythagoras' Theorem and the Law of Cosines
M7 [3.4] Peripheral Angle Theorem, Law of Sines, Cross Ratios [cf 2.6]
W7 [3.6] The Cartesian Model of Euclid's Geometry (Birkhoff concluded)
F7 [7.1] The Poincare Disk Model of Non-Euclidean Geometry
M8 [7.2] The Klein Model of Non-Euclidean Geometry
W8 [7.8] Sphere Projections and Isomorphism of Models
F8 Midterm Hourly

8 Transformation Subgroups of the Moebius Group.
M9 [3.5] the complex plane, polar and cartesian representation
W9 [3.5] complext functions and conformal mappings
F9 discuss midterm and preview of the second half semester

The syllabus for weeks 10-15 consists of selections from chapters 8 and 9 of Hvidsten, student reports, field trips and review, as posted on the class calendar.


approved by R. Muncaster, August 24, 2005.