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sniffnoy(TWO HOURS LATER: Various stuff I left out added in - what happened with the third email to Novak, and elaboration on my weird polynomial mistake..)
So that Civ paper I haven't mentioned here but has been a giant pain in my side the past few days, and that was due at 4:00 PM today? (Actually, the real problem was not the paper itself, but the fact that I had to stay awake for the final the same day, meaning I couldn't just stay up all night and do it. Instead I slept from about 4 to 7.) I finished it at 1:30, the time the combinatorics final started. Or, was supposed to start. I had figured at 3:30 I would rush home, print the thing, and rush back south and turn it in, but in fact due to the delay the combinatorics final didn't *end* until 4:00. (I suppose I could have simply turned in my test early rather than go for as many problems as possible... but that seems like just such a dishonor.)
So I rush back. Stop in the Reynolds club, email Novak, tell him I got out of the final late and am going to rush back, print it, and then rush back down to hand it in.
I rush home, remembering then that his email isn't "novak" but rather "novak9". I email him again. I make a few small changes I thought of right before the test. I print it. The printer freezes.
I get a bounce message on my second email too. This time I just look up his address (it's "nov9"), quickly get a reply saying he's out - guess it didn't make much difference, did it? - but he probably has a guy collecting them for him - print it on the downstairs printer, run downstairs. Print it all out, hold it up, take a look at it...
Staring me in the face are the words "[I NEED A TITLE]". Well, shit.
Run back upstairs. Can I come up with a title? No, screw it. I don't need a title. I erase my title line, print again downstairs, run down, get it, and then walk all the way south again to his office (not going to run at this point). I found some other people turning in papers late, one of whom had a pen, so I marked the time I turned it in (4:43), and headed home.
Well, I almost made it. Sort of. On the other hand, the paper was, I think, merely bad, and not, in fact, extremely shitty, as it almost was.
As for the combinatorics final, something interesting.
We define the Kneser graph K(s,t) to have the t-subsets of [s] as the vertices, and two are adjacent if they're disjoint. We'll only consider s≥2t+1 as it's trivial (in one way or another) otherwise.
One of the bonus problems on the test was to show that the odd girth[0] of K(s,t) is at least (the test said "greater than", but that's not correct) s/l, where l=s-2t. (Worth all of 2 points - bonus problems are worth less than their actual difficulty to get people to do the ordinary problems first.)
Now this problem had been assigned much earlier in the year, in a different form (namely, find the odd girth of K(s,t) in terms of s and l; so I suspect it's just ⌈s/l⌉ but I'm not quite certain). Anyway, I had been able to solve it for l=1, but I didn't get anywhere with larger l.
Well, it's the test, time's almost up, this problem I at least partly know how to do, so I figure, why not. I write down "I only know how to prove this for s-2t=1, so I'll prove that." I nearly do, but time runs out before I can finish the proof.
Afterwards, I'm thinking, you know, it's too bad that proof doesn't generalize... or wait... holy crap, it *does* generalize. Very easily and directly. And somehow I missed this the first time around. And I think it's due to how the problem was presented and how I thought about it. The first time, the way I was thinking about it caused me to miss the generalization, as for higher l I was first trying to formulate a conjecture, then get an upper bound. But this time, I just reconstructed the proof from what I remembered. And with just the proof, alone, without all that distraction, I noticed it. But only after the test.
Although, I realized *much* later, I said also on that test that the solution to ax+b=0 is x=-b. Because apparently all polynomials are monic, or something. Which is a strange mistake to make when I made a big point of noting that the polynomial that I factored into these linear factors was not monic. Though it didn't make much difference as the problem was just to prove that the roots were real, though it probably would have been a good thing if I had noticed that a can be 0, though it ultimately just means you get a constant factor instead of a linear factor and the polynomial is of lower degree than you thought...
In an unrelated story of absent-mindedness, the other day at Bart Mart I just took some things and walked out of the store, entirely forgetting to pay. No-one noticed, but I realized something was wrong a few seconds after leaving and I circled back and actually payed for it.
Also, my computer is occasionally failing to boot up. I'm getting an "Unmountable boot volume" error. I have to presume this is a hardware error, given that, well, it's inconsistent - the thing can in fact boot - and, well, I haven't been playing with the boot sector, or with bootloaders at all. (I mean, this machine only has XP installed on it.) Maybe Mickey's right and I really should just get a new computer. It doesn't seem worth my time to try to repair a laptop.
It is also excessively hot and slow right now for reasons unclear, so I think I'm going to turn this thing off...
-Harry
[0]Girth where you only consider odd cycles.
So that Civ paper I haven't mentioned here but has been a giant pain in my side the past few days, and that was due at 4:00 PM today? (Actually, the real problem was not the paper itself, but the fact that I had to stay awake for the final the same day, meaning I couldn't just stay up all night and do it. Instead I slept from about 4 to 7.) I finished it at 1:30, the time the combinatorics final started. Or, was supposed to start. I had figured at 3:30 I would rush home, print the thing, and rush back south and turn it in, but in fact due to the delay the combinatorics final didn't *end* until 4:00. (I suppose I could have simply turned in my test early rather than go for as many problems as possible... but that seems like just such a dishonor.)
So I rush back. Stop in the Reynolds club, email Novak, tell him I got out of the final late and am going to rush back, print it, and then rush back down to hand it in.
I rush home, remembering then that his email isn't "novak" but rather "novak9". I email him again. I make a few small changes I thought of right before the test. I print it. The printer freezes.
I get a bounce message on my second email too. This time I just look up his address (it's "nov9"), quickly get a reply saying he's out - guess it didn't make much difference, did it? - but he probably has a guy collecting them for him - print it on the downstairs printer, run downstairs. Print it all out, hold it up, take a look at it...
Staring me in the face are the words "[I NEED A TITLE]". Well, shit.
Run back upstairs. Can I come up with a title? No, screw it. I don't need a title. I erase my title line, print again downstairs, run down, get it, and then walk all the way south again to his office (not going to run at this point). I found some other people turning in papers late, one of whom had a pen, so I marked the time I turned it in (4:43), and headed home.
Well, I almost made it. Sort of. On the other hand, the paper was, I think, merely bad, and not, in fact, extremely shitty, as it almost was.
As for the combinatorics final, something interesting.
We define the Kneser graph K(s,t) to have the t-subsets of [s] as the vertices, and two are adjacent if they're disjoint. We'll only consider s≥2t+1 as it's trivial (in one way or another) otherwise.
One of the bonus problems on the test was to show that the odd girth[0] of K(s,t) is at least (the test said "greater than", but that's not correct) s/l, where l=s-2t. (Worth all of 2 points - bonus problems are worth less than their actual difficulty to get people to do the ordinary problems first.)
Now this problem had been assigned much earlier in the year, in a different form (namely, find the odd girth of K(s,t) in terms of s and l; so I suspect it's just ⌈s/l⌉ but I'm not quite certain). Anyway, I had been able to solve it for l=1, but I didn't get anywhere with larger l.
Well, it's the test, time's almost up, this problem I at least partly know how to do, so I figure, why not. I write down "I only know how to prove this for s-2t=1, so I'll prove that." I nearly do, but time runs out before I can finish the proof.
Afterwards, I'm thinking, you know, it's too bad that proof doesn't generalize... or wait... holy crap, it *does* generalize. Very easily and directly. And somehow I missed this the first time around. And I think it's due to how the problem was presented and how I thought about it. The first time, the way I was thinking about it caused me to miss the generalization, as for higher l I was first trying to formulate a conjecture, then get an upper bound. But this time, I just reconstructed the proof from what I remembered. And with just the proof, alone, without all that distraction, I noticed it. But only after the test.
Although, I realized *much* later, I said also on that test that the solution to ax+b=0 is x=-b. Because apparently all polynomials are monic, or something. Which is a strange mistake to make when I made a big point of noting that the polynomial that I factored into these linear factors was not monic. Though it didn't make much difference as the problem was just to prove that the roots were real, though it probably would have been a good thing if I had noticed that a can be 0, though it ultimately just means you get a constant factor instead of a linear factor and the polynomial is of lower degree than you thought...
In an unrelated story of absent-mindedness, the other day at Bart Mart I just took some things and walked out of the store, entirely forgetting to pay. No-one noticed, but I realized something was wrong a few seconds after leaving and I circled back and actually payed for it.
Also, my computer is occasionally failing to boot up. I'm getting an "Unmountable boot volume" error. I have to presume this is a hardware error, given that, well, it's inconsistent - the thing can in fact boot - and, well, I haven't been playing with the boot sector, or with bootloaders at all. (I mean, this machine only has XP installed on it.) Maybe Mickey's right and I really should just get a new computer. It doesn't seem worth my time to try to repair a laptop.
It is also excessively hot and slow right now for reasons unclear, so I think I'm going to turn this thing off...
-Harry
[0]Girth where you only consider odd cycles.
