Approximate Schedule for Math 360

Spring 2009

Week Topics Reading Homework
1/27, 1/29 Administrivia.
Introduction, Euclidean geometry.
Chapter 1 Ch 1: 1,2,3,4. Major exercise 1.
Exercises 8,9,10,11 (do not hand in). (due Thurs. 2/5)
2/3, 2/5 Incidence geometry. Chapter 2 Ch 2: 7, 9 (4th ed), 11, 13 (12 in 3rd ed). Major Exercise 5 (4th ed). (due Thurs. 2/12)
2/10, 2/12 Projective Geometry, Betweenness Axioms Chapter 3 (Betweenness) Ch 3: 1, 5, 6, 16 (17 in 3rd ed), 18 (19 in 3rd ed). (due Thurs. 2/19)
2/17, 2/19 Pasch & Crossbar Theorems, Congurence Axioms Chapter 3 (Congruence) No homework this week.
2/24, 2/26 No class on 2/24, Congruence continued. Finish chapter 3. Ch 3: 20, 24, 30, 35, major exercise 6. (due Thurs. 3/5)
3/3, 3/5 Continuity, Exterior angle theorem, SAS. First half of chapter 4. Ch 3: 26.
Ch 4: 2 (9 in 3rd ed), 4 (11 in 3rd ed), 6 (13 in 3rd ed). (due Thurs. 3/12)
3/10, 3/12 Angle and Segment measure, Equivalence of Hilbert and Euclidean Parallel Postulates, Saccheri quadrilaterals. Chapter 4, through Saccheri-Lambert Quadrilaterals. Ch 4: 8 (21 in 3rd ed), 10 (4 in 3rd ed), 11 (5 in 3rd ed), 14, (due Thurs. 3/19) major exercise 5. (due Tues. 3/24)
3/17, 3/19 More on Saccheri and Lambert quadrilaterals, Angle sum of a triangle, the parallel postulate. finish ch 4. no homework.
3/24, 3/26 History of the parallel postulate. Midterm on Thursday, 3/26 chapter 5. midterms screw everything up.
3/31, 4/2 discuss midterm, Non-Euclidean Hilbert planes, defect and similarity, parallels with a common perpendicular. chapter 6.  
4/7,4/9 Spring Break
4/14, 4/16 Limiting parallel rays, consistency of hyperbolic geometry. finish chapter 6, start 7. Chapter 5: 10, 13, 16. (due Thurs. 4/23)
Chapter 6: 1 (don't hand in yet)
4/21, 4/23 Models of Hyperbolic geometry: Beltrami-Klein, Poincaré disk and half-plane. Power of a point, inversion in circles. Chapter 7. Chapter 6: 1, 2, 8, 12. Major exercise 6 (see these hints). (due Thurs. 4/30)
4/28, 4/30 SAS in the Poincaré disk model. chapter 7. Chapter 7: K-4, K-5, P-6, P-12. (due Thurs. 5/7)
5/5, 5/7 Elliptic geometry (briefly), review. Appendix A. Six Constructions for Extra-Credit (best tried in order):
Euclidean: the midpoint of a segment, the tangent to a circle, and an octagon.
Hyperbolic (Poincaré disk): an equilateral triangle, an inscribed quadrilateral, and a circumscribed quadrilateral.
(due Wed. May 20)
5/19 Final Exam, Tuesday 5/19
at 11am in ESS 131
Review problems: In addition to the assigned homework problems, you should look at:
Ch 2: 6, 8, 14a, 15a, and this problem.
Ch 3: 8, 9, 10.
Ch 4: 1, 3, 15, 17, 18, 19, 27.
Ch 5: 9, 14, 15.
Ch 6: 3, 4, 11.
Ch 7: K2, K3, P4.

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Page last modified on Thursday, 14 May 2009 at 05:32 PM EDT.