07-401/Homework Assignment 10 (and last!)
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.
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 (#).
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:
2. Which of the following three "hexagonal rubik's style" combinatorial games are always solvable?