Math 31 Homework #7 Work is the greatest thing in the world, so we should always save some of it for tomorrow. Don Herald

	Reading Read what we will cover in class on 1/21: Chapter 5 Read what we will cover in class on 1/22: Chapter 6 When reading Chapter 5 pay special attention to the following concepts: permutation, permutation group, symmetric groups (Sn), cycle notation properties of permutaions: Theorem 5.1, products of disjoint cycles; Theorem 5.2, disjoint cycles commute; Theorem 5.3, order of a permutation. 2-cycles, even and odd permutations, the alternating group of degree n and its order When reading Chapter 6 pay special attention to the following concepts: isomorphism, operation preservation, the four steps, the basic examples Cayley's Theorem Properties of isomorphisms and the proof. we might also start talking about automorphisms

	Problems The following problems are due by the beginning of class on Friday 1/22. Ch 5 : 2, 3, 4, 5, 17, 18, 28, 29, 30, 34, 38. Ch 5 : 12, 13, 15, 20, 21, 40, 42.