07-401/Homework Assignment 10 (and last!)

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Contents

Reading

Read chapter 32 of Gallian's book and the statement and proof of the Primitive Element Theorem (Theorem 21.6 on page 375 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.

Doing

Solve problems 1, 4, 6#, 8#, 14#, 15#, 16 and 18 in Chapter 32 of Gallian's book but submit only the solutions of the problems marked with a sharp (#).

Due Date

This assignment is due in class on Wednesday April 11, 2007.

Just for Fun

1. Prove that the following two "pentagonal rubik's style" combinatorial games are always solvable:

07-401-Pentagon Games.png

2. Which of the following three "hexagonal rubik's style" combinatorial games are always solvable?

07-401-Hexagon Games.png