Algebraic Geometry Realization III: Digging Deeply

Observation III. When trying to learn new things, digging deeply isn’t always the necessary first course of action; sometimes, the information you’re searching out is surprisingly close to home.

This comes on the heels of me realizing something that makes me both irritated and very happy at the same time.

When I was reading through Elliott’s manuscript, I came across a notation with which I was unfamliar. I tried searching through a couple of the sources he cited and found the same notation used several times without ever being fully explained. That made me uncomfortable, because the things being discussed are abstract to the point that much of the intuition stems from being able to decipher what the objects of our structures are, and what the operations acting on these structures actually do.

So I got to digging.

I felt as if the notation (in this case, juxtaposition of structures for which juxtaposition doesn’t immediately make sense to me) was pretty similar to something discussed in elementary ring theory, so I pulled up my digital copy of Dummit and Foote and decided to do some digging.

While digging, I realized something that I’d never realized before: The last part(s) of Dummit and Foote discuss lots of topics I’d never read about, one of which is algebraic geometry! You see, despite my having used Dummit and Foote for a total of four semesters, I’ve never done so in a class that made it to parts 5 and 6 of the text. As such, for all intents and purposes, those sections didn’t even exist in my mind.

This is irritating because it means I missed out on a pretty easily-accessible source of information that I had close by for the past three years, but makes me very happy because I have a source close by that’s pretty easily-accessible! This is definitely a winning scenario for me.

So the lesson for today, kids, is that you should never ever forget what you have close by.

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