MA341 HOMEWORK #2
Carl Lee
Due Monday, September 15

As you can see, I am passing out notes during the class, giving you each section twice: the first time the answers are not included (I will call these the non-updated notes), and the second time some of the answers are included (I will call these the updated notes, and the word UPDATED will appear at the top of the pages).

1. Consider the Projective Plane P^2 of Section 2.4.5 of the non-updated notes. POINTS are all ordinary lines in R^3 which pass through the origin. LINES are ordinary planes in R^3 which pass through the origin.
   1. Does Axiom I-1 hold for this model? Why or why not?
   2. Determine whether or not the following property hold for this model, and justify your answer:

      Given a POINT and a LINE not containing that POINT, there is exactly one LINE containing the given POINT that does not intersect the given LINE.

2. Some Maple practice:
   1. Find the program Maple somewhere on campus (e.g., in the King Library computer lab) and type in the commands given on the handout tetra.ms (this handout is between pages 8 and 9 of the non-updated notes). Print out and turn in your results. You only have to type in the commands after the ``>'' sign; you do not have to type in all the comments that I included on the handout.
   2. Try to mimic what was done on the tetra.ms handout to create a picture of an ``Egyptian'' pyramid: one with a square base and four triangular sides that meet at a common apex. Print out and turn in your results.
3. Some numerical computations:
   1. Question #5 of Section 3.1.1 of the non-updated notes.
   2. Questions #1-3 of Section 3.1.2 of the non-updated notes.
   3. Question #2 of Section 3.1.3 of the non-updated notes.

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