I really didn't get the last part of the material: Theorem 9.7, Corollary 9.8, and Theorem 9.9. I should say that the theorems made sense and were acceptable, but the proofs were a little different. For example, in Theorem 9.7, it was proven ultimately by implying that g of f was injective and surjective. I didn't get how that implication could be made. At the end, Example 9.10's solution stated that the ran f was {0,1,4,9}. While I understand that it is necessary to show that ran f is a subset of B', I failed to see how the ran f was defined how it was.
Once again, this material connects with something I've learned in calculus. There were a few ties to derivatives, including the product rule and the chain rule. While I appreciate the tie-ins, I get a little frustrated with it being easier for me to understand the material when it talks about calculus than in other situations. What I mean by this is that I wish it would click in my head easier when reading about non-calculus material in this text. I do think, though, that the text does a good job of bringing in calculus references and other things we've surely learned in previous classes. This forms a nice transition and I generally understand the material better upon first reading.
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