Math 31 Homework #22 Mathematicians are like lovers... grant a mathematician the least principle, and he will draw from it a consequence, which you must also grant him, and from this consequence another... Fontenelle

	Reading Read what we will cover in class on 2/24: Chapter 12 When reading Chapter 12 pay special attention to the following concepts: ring, examples and nonexamples, properties of multiplications, uniqueness of the unity and inverses, subring and the subring test.

	Problems The following problems are due by the beginning of class on Wednesday 2/24. Ch 29 : 3, 4, 5, 11, 12. Prove that if G is a group of permutations on a set S and s,t from S are in the same orbit under G, then orbG(s) = orbG(t). For 3,4,5 are asking you to consider "necklaces" as opposed to "tiles." The answer for 4 is 92. For 11, 12, you just need to show that the given map g -> \phig is a homomorphism; this is the definition of a group action.