Schedule for Math 360Fall 2009 |
Week | Topics | Reading | Homework |
8/31, 9/4 | Administrivia. Introduction, Euclidean geometry. Start incidence geometry. |
Chapter 1, Chapter 2 |
Ch 1: 1. Ch 2: 7, 9 (4th ed), 11, 13 (12 in 3rd ed). (due Fri. 9/11) |
9/7, 9/11 | No class on
Monday, 9/7. Incidence geometry. |
Chapter 2 |
Ch 2: 14, 15,
Major Exercise 4,
Major Exercise 5. Think about Ch2 #18 but do not hand in. (due Friday 9/18) |
9/14, 9/18 | Projective Geometry, Betweenness Axioms | Chapter 3 (Betweenness) | Ch 3: 1, 5, 6, 15 (16 in 3rd ed), 18 (19 in 3rd ed). (due Friday 9/25) |
9/21, 9/25 | Pasch & Crossbar Theorems, Congurence Axioms | Chapter 3 (Congruence) | Ch 3: 17 (18 in 3rd ed), 20, 24, 35,
major exercise 6.
(due Friday 10/2)
Also, try the following constructions:
the midpoint of a segment
and copying an angle.
|
9/29, 10/2 | Continuity, constructible numbers, neutral geometry. | Finish Chapter 3, start chapter 4. | No written homework this week. However, you should do the following constructions: construct a perpendicular, an equilateral triangle in the hyperbolic disk, and an equilateral triangle in elliptic geometry. |
10/5, 10/9 | Alternate Interior Angle Thm, Exterior Angle Thm, Triangle Inequality. | Chapter 4 | Ch 4: 2 (9 in 3rd ed), 4 (11 in 3rd ed), 6 (13 in 3rd ed), 8 (21 in 3rd ed). (due Fri. 10/16) |
10/12, 10/16 | Angle and Segment measure, Equivalence of Hilbert and Euclidean Parallel Postulates, Saccheri quadrilaterals. | Chapter 4, through Saccheri-Lambert Quadrilaterals. | Ch 4: 10 (4 in 3rd ed), 11 (5 in 3rd ed),
14,
major exercise 5.
(due Fri. 10/23) Here are the solutions. |
10/19, 10/21 | More on Saccheri and Lambert quadrilaterals, Angle sum of a triangle, the parallel postulate. | finish ch 4. | none due to midterm. |
10/26, 10/30 | Midterm on Monday, 10/26, discuss midterm, History of Parallel Postulate: Proclus, Clavius, etc. | chapter 5. | Chapter 5: 10(18 in 3rd ed), 13(21 in 3rd ed). (due Fri., Nov. 6) |
11/2, 11/6 | Wallis and similarity, Legendre and defect, more on similarity. | chapter 6. | Chapter 5: 6(10 in 3rd ed), 8(13 in 3rd ed), 14(22 in 3rd ed), 16(24 in 3rd ed). (due Fri., Nov. 13) |
11/9, 11/13 | Non-Euclidean Hilbert planes, defect and similarity, parallels with a common perpendicular. Limiting parallel rays, consistency of hyperbolic geometry. | finish chapter 6, start 7. | Chapter 6: 1(not in 3rd ed), 2(11 in 3rd ed), Major exercise 6 (see these hints). (due Fri. 11/20) |
11/16, 11/20 | Models of Hyperbolic geometry: Beltrami-Klein, Poincaré disk and half-plane. Power of a point, inversion in circles. | Chapter 7. | |
11/23 | SAS in the Poincaré disk model. (No class on 11/27) | chapter 7. | Chapter 7: K-4, K-5, P-6, P-12. (due Fri. 12/4) |
11/30, 12/4 | more on SAS. | chapter 7. | TBA |
12/7, 12/11 | stuff, nonsense | Appendix A. | TBA |
12/16 | Final Exam, Wed 12/16 at 2:15pm in Old Chemistry 144. |
Review problems:
In addition to the assigned homework problems, you might want to look at:
Ch 2: 6, 8, 14a, 15a. 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. Also, here is last spring's final. |