revised 29jan07

Syllabus Math 402 "Post-Euclidian Geometry" Winter 2007
Text: M. Hvidsten, Geometry with Geometry Explorer (GEX)
Instructor: George Francis, MWF9 and MWF10. 
Office Hours: by appointment (MW11-1) 

See also http://new.math.uiuc.edu/math402 
for calendar, updates, notes and frequently asked questions (FAQ). 

Day-Week labels and  text chapter.section in [].
Note: each day is a double lecture in this section.
Note: "seminar" means active learning session. Prepare for it.

Part I (Weeks 1-4)

1 Geometry and the Axiomatic Method [Chapter 1]
W1 [1.1] Greek Origins of Geometry 
W1 [1.6] Euclid's Axiomatic Geometry
F1 [1. 1.7] Computer lab with GEX (see lab/gexF1)  
F2 [] Euclid's Post. 2, Prop. 1, and Prop. 16 (XAT) 
M2 [1.4] Axiom Systems and Systems of Axioms
M2 [] Seminar: Ex. 1.4.3-5, Sec. 1.5, Ex. 1.5.4-7.
W2 [1.5] Properties of axiomatic systems
W2 [1.5] Seminar on section 1.5 (hwkW2 is due) 
F2 Discussion of Chapter I
F2 Quiz 1. 

2 Euclidean Synthetic Geometry [Chapter 2, Section 2.1 only]
[pp51-58 and do 2.1.1-2.1.4 for your portfolio.]
M3 [2.1] Absolute (=neutral) Geometry, Euclid's Fifths Postulate
M3 Seminar: Euclid 5 iff Playfair etc. Exercises 2.1.5, 2.1.6.
M3 Return and discuss Quiz 1.
W3 [2.1] Seminar on Exercises 2.1.7, 2.1.8, 2.1.9 and 2.1.10. 
W3 Lesson on the Pythagorean Theorem. 
[Note: Sections 2.2-2.6 is covered in MA403 ]
F3 Lab on Neutral, Euclidean and Hyperbolic Geometry. 
[Selected readings on Congruence[2.2], Similarity[2.5], Circles[2.6]]
F3 Hand in 2.1.9 and 2.10 for checking.

3 Euclidean Analytic Geometry [Chapter 3]
[Note: Sections 3.1, 3.2, 3.4 on vector plane geometry is a 
 part of the calculus prerequisite for this course.] 
M4 Summary of Cartesian geometry.
M4 Active Learning Session on Splines [3.3]. 
W4 Birkhoff's Axioms for Euclidean Geometry [3.6].
W4 Preview of Models for Non-Euclidean Geometry. 
F4 Discussion of Chapters 2 and 3.
F4 Quiz 2 (Midterm).

4 Non-Euclidean Geometry [Selections from Chapters 7 and 8]