08-401/Homework Assignment 7

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Contents

Reading

Read chapters 21 (excluding theorem 21.6) and 23 of Gallian's book (6th edition) 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.

Doing

Solve problems 3, 5, S6, 7, S8, 9, 11, S12, S13, 14, S16, S18, 22, 34 in Chapter 21 of Gallian's book (6th edition) and problems 1-5 in Chapter 23 of the same book, but submit only the solutions of the problems marked with the letter "S".

Due Date

This assignment is due in class on Wednesday March 19, 2008.

Here is the solution upload by yangjiay http://katlas.math.toronto.edu/drorbn/images/2/2c/Solution_Assignment_7.pdf

Just for Fun

Geometric constructions are related to fields (see it in another way by reading/solving questions 1-4 on pages 394-5 of our text). 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