Prosthaphaeresis

First complex analysis problem set, second real analysis problem set, second algorithms problem set, and third algebra problem set turned in. Proved the five lemma. Found it rather therapeutic after a very long week of steadily losing confidence in my ability to grasp the most basic concepts. Unfortunately, my frustrations with other algebra problems are not helping me to regain that confidence.

Math dreams have continued. They’re kind of scary.

I keep feeling like everything would be fine if I could avoid losing time to non-academic distractions (or, more to the point, somewhat-academic distractions not directly related to the classes I’m taking), but apparently this is impossible.

First real analysis problem set turned in after four days of thinking about nothing else. Second algebra problem set turned in after half a day of flailing through it and probably missing all sorts of important details. First complex analysis and second real analysis problem set completed. Second algorithms problem set essentially done but only half-written; now writing this in order to avoid what promises to be the somewhat irritating task of finishing it. Third algebra problem set to be entirely ignored until I start understanding the material.

Observations after two weeks: necessity really has improved my time management, as I hoped it would (for this week, at least–it maybe also helped that this round of homework was not so difficult, a circumstance which is likely to change). Math all day every day is still incredibly exhausting. I keep having math dreams, which is something that never really happened to me before. There was an orally given real analysis exam which I failed because I couldn’t hear the questions, and something about an algorithm to sort people, or real numbers, or people mapped to real numbers, or something.

Oops, forgot to do this yesterday. Decided to do it now in order to procrastinate more on math homework, because after a very head-meets-brick-wall day of staring at problem sets, I don’t feel capable of stringing mathematical symbols together anymore.

After way too much time spent on the matter, paper issues have finally been fixed. I suspect I never can or will think about such things this quarter again, so I really hope no other major problems come up.

First algebra problem set turned in. First algorithms problem set completed. First real analysis problem set begun (but still far from finished even though it’s due in 38 hours because, well, brick wall). Second algebra problem set and first complex analysis problem set assigned (but not begun because of real analysis). Technically that last one happened this week rather than last week, but including it seemed like the poetic thing to do.

If I’m going to fuzz up the definition of “last week”, I might as well also mention our first Putnam seminar meeting, which was lots of fun, but disappointing because it turns out I didn’t magically improve in problem-solving ability over the summer. (Easy fun problem: the numbers 1 through 81 are written in a 9×9 grid. Prove that there exist two horizontally or vertically adjacent numbers differing by at least 6.)

I knew while planning this schedule that even aside from the difficulty of the classes, it would be a huge challenge to maintain the intellectual stamina to think about math all day, every day. This is the first humanities-free school period of my life. I kind of banked on the assumption that I would get used to it. Right now, though, it is really very very hard.

Not very much. Mostly sat around waiting for school to start. Worked a little more on papers near the end, only to discover a huge amount of handwaving I had forgotten I never got around to fixing. Since this handwaving is all over very obvious things which somehow look much nastier when turned into actual algebra, I don’t look forward to dealing with this, especially with my first problem set of the quarter vying for attention. I have lovely timing.

Other than that I was extraordinarily lazy, so I’ll have to count under Math I Did Last Week long, late-night discussions about math club recruitment. Mostly what I got out of this was feeling sick of being in any way responsible for what other people choose to do with their time. I was math club president for a long time in high school, so I’m used to begging people to take an interest in communal math activities and being at the mercy of the most halfhearted among them, but restructuring the most important social event of my week in order to appeal to others is a new low. So it goes.

I just hope this week goes better than it looks like it will right now.

Papers. It seems that the only way I can make progress on them is to sit around doing nothing for days on end while my conscience plots its escape from the pit that my laziness imprisoned it in. Eventually it succeeds and runs around reading feedback and making edits for about two hours before it gets recaptured.

Ahlfors. Read enough to make myself believe that taking grad complex analysis fall quarter might only be the worst idea I’ve ever had by a factor of 10, not 100.* Unfortunately, I am still quite incapable of convincing myself to do exercises, so I’m still going to show up completely unprepared if I decide to show up at all. Oh well. Baby steps. (Actually, I guess I did do, ah, approximately one exercise. It was to show that an entire function satisfying |f(z)|<|z|^n for some n and all sufficiently large z must be a polynomial. I’m so cool.)

Started Project Euler, which is to say that I made an account and did the first seven problems in order to assuage my guilt over the aforementioned papers.

Serious posts are being withheld for various reasons.

*I have no idea what the second-worst idea I’ve ever had was.

Some more paper progress. Among the edits I’m procrastinating on, the proportion of stylistic ones to mathematical ones is increasing. I guess this is a good thing.

Tried for the second time to read a paper with a result which is very important to me. It made a little more sense this time around, but only a little.

Tried to continue reading Ahlfors. The fact that class is starting in two weeks does help with motivation, but it’s probably too late now anyway. But then there’s no fun in showing up to classes for which one actually has the prerequisites, is there?

Visited problem-solving class at former high school. Heard an easy but mildly fun problem which I have to report just because I’ve done no other contest math in months: an n-by-n grid is filled with arbitrary real numbers. One is allowed to perform the operation of multiplying all the numbers in one row or column by -1. Show that after a sequence of such operations, it is possible to have all row and column sums be nonnegative.

I think a significant part of the reason I keep avoiding writing serious posts is that most of my post ideas are rants and I keep thinking it’s not nice to rant in public. It’ll have to happen eventually, though.

Hmm, it didn’t take me long to start delaying even this. So it goes.

Papers have progressed, but not too much.

The power round mentioned last week has been successfully drafted. The topic is of course a secret, but I have to say that the more I think about it, the more I realize just how perfect our choice is. It bridges easily accessible and rather elegant high-school mathematics with an obscure area of serious research which happens to have immediate–and I mean immediate–applications to our daily lives. These applications may not be quite at the cancer-curing level of importance, but if there even exists a person whose interest in math depends solely on its ability to cure cancer, that person is certainly a hypocrite. This subject is the kind of thing that would have made me want to go into math research if another subject of a similar nature had not already done so. I only hope we can do it justice.

No other math to report. And, evidently, no serious posts in sight. I will continue hoping that this will change without making a real effort to change it.

Attempted to edit three papers, two from work done this summer and one from work done, uh, two years ago. Yeah, so I procrastinate sometimes. The two-year-old paper is finally on submission after a last round of minor edits which took me a total of ten minutes but which I put off for a week after my mentor suggested them anyway, just for the sake of it. I had planned for the other two to be close to ready by now, but naturally, they aren’t.

Started reading Ahlfors’ Complex Analysis. Didn’t do much more than start.

I was hoping to report that I had drafted a power round for a local high school math contest, but nothing of the sort occurred. I was also hoping to report that I had done at least one Putnam problem, but I didn’t.

Actually, now that I think about it, I have no clue what I did do last week. At least I feel a little less antipathy toward the idea of paper editing now than I did a few days ago. I really hope this feeling lasts.