Read: Finish Section 4.3, skim 4.4, and read 4.5
Turn in: 4.95(a), 4.96, 4.97, 4.113, 4.115
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Please read Theorem 4.99 and Corollary 4.100—they’re important.
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On 4.112–4.115, you should be able to make use of what you found in 4.97.
Remark about even/odd permutations: the point of Theorem 4.110 and Definition 4.111 (which are very important) is that if $\alpha$ is a permutation and you can find some way to write $\alpha$ as a product of an even (respectively, odd) number of transpositions, then every possible way to write $\alpha$ as a product of transpostions will involve an even (respectively, odd) number. For example, since $(1,2,3)(5,6) = (1,3)(1,2)(5,6)$, we say $(1,2,3)(5,6)$ is an odd permutation because we wrote $(1,2,3)(5,6)$ as a product of three transpositions; notice that $(1,2,3)(5,6)$ can also be written as $(1,2,3)(5,6) = (5,6)(1,2)(5,6)(2,3)(5,6)$ (and lots of other ways, but always using an odd number of transpositions).
Extra practice: 4.98, 4.99, 4.106, 4.107, 4.112