3.3

1. What was the most difficult part of the material for you?
Something that worried me during the reading was something that was addressed during the reading. I am pretty sure that I understood the concepts as they were explained in the reading, but it made me nervous to think about HOW to figure out what f was. It reminded me of those word puzzles in the newspaper that I suck at so badly -- you know, the one with the letters all mixed up and one letter stood for another letter and you have to figure out the code to get the message? It seems to me that that is exactly what is going on here, and I am so bad at those puzzles. But, the good thing is that it seems like it won't always be necessary to define f, but rather to understand if your two fields/rings are isomorphic/homomorphic or not.

2. Remembering injections and surjections
One issue I've had that go back years and years is remembering what it is to be injective and surjective. Like, I understand the two different definitions, and I know the two different words, but I struggle to remember which is which. So, tonight I am trying to think of a way to remember which is which. As far as I can remember, an injection is the 'one to one' thing where each element of R is going to be 'transformed' to an element of S (f(R)=S). The way I plan to remember that is by imagining "1-1" which looks like an "I" sideways, so "I"njection means "one to one". Then, a surjection (or 'onto,' which still sounds so stupid to me) means that each element of S comes from exactly one element of R. In other words, if it is surjective it would not be true that f(3)=5=f(2). The lame way I plan on remembering that is by remembering that a surjection doesn't look like this: f(S)=U=f(R). You know? If I knew how on this blog, I'd just write a "does not equal" sign and remember that as being a surjection, but we have to use what we've got.