Difficult:
I understood most about cycle notation and the product of permutations, etc. But it is a little difficult for me sometimes to see what the product between two permutations will look like. Especially when there are more than two permutations to combine into one. It was also difficult for me to follow the proof of Lemma 7.49. I am sure there is an easy way of explaining it to someone, but the proof was difficult to follow.
Reflective:
I like the idea of cycle notation. I know that it will make it easier for me to write permutations. But I also know that I can potentially get very confused and start mixing up all the numbers. This will call for some serious careful calculations when I am doing my homework. It is sections like these that make me see mathematics as more of a history of ideas; one day someone was thinking about simpler ways to write permutations and then BOOM! he thought of cycle notation.
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