07-401/Homework Assignment 8

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Reading

Read chapters 21 and 23 of Gallian's book three times:

• First time as if you were reading a novel - quickly and without too much attention to detail, just to learn what the main keywords and concepts and goals are.
• Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.
• And then a third time, again at a quicker pace, to remind yourself of the bigger picture all those little details are there to paint.

Also, quickly pre-read chapter 32 of Gallian's book, just once.

Doing

Solve problems 5, 6#, 11#, 12#, 13, 14, 16#, 22, 31 and 34# in Chapter 21 of Gallian's book and problems 1, 2, 3, 4 and 5# in Chapter 23 of the same book, but submit only the solutions the problems marked with a sharp (#).

Due Date

This assignment is due in class on Wednesday March 28, 2007.

Just for Fun

Geometric constructions are related to fields. A related fact is that using "geometrical machines" one can build "analog computers" that are able to "compute" polynomials. For your own entertainment and for that alone, spend some time studying Dori Eldar's java-based interactive site on Linkages as Functions and in particular play with gigantic squaring machine (drag the green dot, read the output in red). While you are at it, spend some time pondering the relationship between Eldar's "machines" and our class material. The subjects are not exactly the same, yet not entirely different either.

http://www.math.toronto.edu/~drorbn/classes/0304/157AnalysisI/HW25/SquaringMachine.gif