I'm not very skilled at all.
No, honestly, hear me out. When it comes to raw mathematical skills, I have very little in supply. I've suspected this for some time now, but seldomly have I ran into any situation where it was made painfully evident. My entire mathematical success has allways hinged on one overriding fact: my ability to See what was going on. I have almost always been able to (at least to some minor degree) visualize the problem. All the relevant definitions, known facts, and causal relationships surrounding the topic at hand would present themselves, almost like the colours, layers, and brushstrokes of a fine painting. To answer any given question about something I simply had to look carefully at the painting and trace the lines to the result. Any topic I've had trouble with was one where I couldn't see what was going on very well. Sometimes it would be like viewing that painting from outside the gallery, through a dirty window, standing in a thick fog. Other times I could be standing not one foot from it, but all the lights are out and I can't see a damn thing.
It is those moments, when I know that there is a picture around here somewhere if only I could see it, that I realize how it is that other people can get through. Their skill is a flashlight. For some people it may be a little pocket-light from the gas station, for others it's a whopping 6-cell maglight, and sometimes they may fumble in their pockets or bag looking for it but they eventually find it and get to see at least a part of the picture. All the while I'm standing in the dark vainly patting my pockets looking for even something so meager as a matchbook. But to no avail.
I was told once by a teacher of mine, "This may not be very challenging to you now, but eventually we all hit a point where we stop coasting and have to start working at it." No, I wasn't an arrogant little ass and blew her advice off -- I took it to heart and tried to start developing some skill. I actually have managed to pull together some reasonable study habits, an ability to keep my nose in the books for days on end, and a fine appreciation for which side of my head is the best to bang against the wall. And in some cases there have been times where this was enough to give me, if not a grand flashlight or even some matches, at least a piece of flint and a good sturdy knife. And sometimes that has been enough.
I'm now at a point where this might not be sufficient.
So yeah, the take-home test didn't go well. And the in-class version (he gives them in pairs) went even worse. I am somewhat consoled by the fact that this particular part of analysis (infinite sequences and series, for the curious) is only going to be half the final for this semester, and only about 1/6 of the master's comprehensive exams. It is entirely possible for me to finish out the program and get the degree without ever learning to be even partially competant at this specific topic, but I don't want to bank on such an approach. I need to find some way of getting at least the basics of this stuff through my head. The problem is, I don't know how. I've spoken with *many* different professors and they've tried explaining it to me -- no help. I've spoken with a good deal of my classmates and they've tried helping, all in vain. I've read text after text on these things, each describing them in a different way and none of them making any sense to me at all.
I'll keep trying. here's hoping I'll be able to pull something together in the next two weeks (this shit is half the final, and with my grade being so crappy at this point I need a fairly nice showing on the final to not get kicked out of the program).