Miscellaneous stuff from today
Jul. 19th, 2005 06:37 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
sniffnoyCorrection: The guy who gave yesterday's awful lecture was named Curt Monash, not Carl.
Random stuff from a while ago I forgot about:
It happened a while ago that we happened to see a truck on Comm Ave for a company called "Assured Collision". Matt took a picture of it on his phone.
So a few classes ago in Zeta Function, Anton (I think it was Anton) drew on the board before class "The zeta pirate". It was the letter ζ, but made to look like a pirate, with a pirate hat and going "Yar!". It was equal to the product over all p∈pirates of (1-1/p)-1. There was a thing below it, noting s=1⇒ - and what it implied was a picture of the zeta pirate exploding, with the sound effect "Splurt!" below it. I think someone thought to take a picture of that one too.
So today Rohrlich introduced the p-adic integers! He didn't introduce the fun notation for p-adic expansions, though...
Also, today Steve is here!
I think we finally have an idea of what we're going to do for the talent show. Very few people have signed up so far... we may have to stick a lot of them in the Default Act, which is supposed to be really horrid this year...
Fergie insisted on talking about various disgusting things appearing in Elfen Lied today at lunch, and Rebecca finally declared that his right to speak was revoked.
Josh: You're allowed to talk about math, but that's it.
Fergie: So let's discuss combinatorics in terms of little boys and little girls.
Apparently Lucas had some dream last night about ITRPers hunting him with Dirichlet functions.
Glenn: Different people's eyeballs will work differently.
[Meaning that different people will find different things obvious, IIRC.]
More uselessness from ∞-boy:
Glenn asks how we proved something. Infinity-boy raises his hand and answers, "We did a problem like that."
Today in lecture Glenn asked who could find a primitive root of U191, and Phil suggested 173. Someone else (I'm not sure who) responded, "A normal person would just say -18."
So remember how I was saying before about how I ended up in the easy lab? Yeah, I don't think I mentioned this before, but immediately, Seo Hyung left, so the two groups were joined into one. So I'm in the easy lab, but the other people in it are Chang, Brian Lee, Man-Yu, and... I can never remember his name.
Well, as you may recall, one of the reasons I said this was an easy lab is because the big problem is, well, already solved for us in the packet, near enough. Namely, as we're doing integral-valued polynomials, the classification of such. I'll go ahead and tell you, they're the integral combinations of x choose k polynomials. And yet, it seems nobody else in my group has really realized the importance of writing polynomials in x choose k form rather than xk form, even though the packet makes this pretty clear. As well as being obviously the "right" way to write integral-valued polynomials, it makes the difference operator (as in f(x+1)-f(x)) a lot cleaner, and gee, what are [guy whose name I can't remember] and Chang doing? Looking at successive differences of the things! Although that's not really an integral-valued polynomial thing, that's really just a "write a polynomial in x choose k form" thing, but they're doing it anyway.
So I take a break from trying to prove my periodicity conjecture to try what Man-Yu is working on, problems 15 and 16. Or rather, he was just doing 16. Problem 15 goes like this: Say we have a polynomial in Z[x]. If m divides all the coefficients, obviously it divides all of the polynomial's values. However, the converse is false (consider x²-x). However, if we write the polynomial in x choose k form, then the converse is true (along with the forward direction, obviously). Problem 16 just lists some polynomials, in x^k form, and asks you to find the GCD of all their values. Any conjectures? Generalizations? Now, obviously, once you've solved Problem 15, you can just say that the GCD of all of a polynomial's values is just the GCD of its x choose k coefficients. Man-Yu hadn't even looked at problem 15. I find the other day he's just working on 16, doing calculations, I tell him, "You know 15 is a generalization of 16, right?" I don't think he even understood how. Today again he seemed to be doing just 16, if anything. "15 is a generalization of 16, that's what he told me." Ugh. Anyway, so I take a break from the periodicity stuff to work on problem 15, and I solve it immediately. The proof's pretty simple, I'll leave it for you guys. I then have to spend a good number of minutes explaining it to Man-Yu. Blech.
Brian Lee, meanwhile, is asking me if there's any good way to convert polynomials from x^k to x choose k form. I tell him again, as I've told him before, the obvious way is fine. He wants to know if there's an efficient way to do it. I tell him it is efficient. I say, if you want to do it by hand, make a big table of the x choose k polynomials so you don't have to recalculate them; if you want to do it by computer, it'll be incredibly fast anyway, there's no need for a more efficient way to do it, if such a thing exists (I doubt it). He asks if I can write a program to do the conversion. "Of course I can!" So I stay in the computer lab for an hour afterward, writing this thing up (and making lots of syntax errors, not having done any programming in some time :P ). So finally about 17:00, I've fixed all that and I get it to compile. As expected, this being the first run, it doesn't work. I'm getting a 0/0 at some point, apparently. However, it's now 17:00 so I decide to go get dinner and finish it tomorrow.
Brian Lee himself, of course, spent much of the lab looking up IMO results.
-Sniffnoy
Random stuff from a while ago I forgot about:
It happened a while ago that we happened to see a truck on Comm Ave for a company called "Assured Collision". Matt took a picture of it on his phone.
So a few classes ago in Zeta Function, Anton (I think it was Anton) drew on the board before class "The zeta pirate". It was the letter ζ, but made to look like a pirate, with a pirate hat and going "Yar!". It was equal to the product over all p∈pirates of (1-1/p)-1. There was a thing below it, noting s=1⇒ - and what it implied was a picture of the zeta pirate exploding, with the sound effect "Splurt!" below it. I think someone thought to take a picture of that one too.
So today Rohrlich introduced the p-adic integers! He didn't introduce the fun notation for p-adic expansions, though...
Also, today Steve is here!
I think we finally have an idea of what we're going to do for the talent show. Very few people have signed up so far... we may have to stick a lot of them in the Default Act, which is supposed to be really horrid this year...
Fergie insisted on talking about various disgusting things appearing in Elfen Lied today at lunch, and Rebecca finally declared that his right to speak was revoked.
Josh: You're allowed to talk about math, but that's it.
Fergie: So let's discuss combinatorics in terms of little boys and little girls.
Apparently Lucas had some dream last night about ITRPers hunting him with Dirichlet functions.
Glenn: Different people's eyeballs will work differently.
[Meaning that different people will find different things obvious, IIRC.]
More uselessness from ∞-boy:
Glenn asks how we proved something. Infinity-boy raises his hand and answers, "We did a problem like that."
Today in lecture Glenn asked who could find a primitive root of U191, and Phil suggested 173. Someone else (I'm not sure who) responded, "A normal person would just say -18."
So remember how I was saying before about how I ended up in the easy lab? Yeah, I don't think I mentioned this before, but immediately, Seo Hyung left, so the two groups were joined into one. So I'm in the easy lab, but the other people in it are Chang, Brian Lee, Man-Yu, and... I can never remember his name.
Well, as you may recall, one of the reasons I said this was an easy lab is because the big problem is, well, already solved for us in the packet, near enough. Namely, as we're doing integral-valued polynomials, the classification of such. I'll go ahead and tell you, they're the integral combinations of x choose k polynomials. And yet, it seems nobody else in my group has really realized the importance of writing polynomials in x choose k form rather than xk form, even though the packet makes this pretty clear. As well as being obviously the "right" way to write integral-valued polynomials, it makes the difference operator (as in f(x+1)-f(x)) a lot cleaner, and gee, what are [guy whose name I can't remember] and Chang doing? Looking at successive differences of the things! Although that's not really an integral-valued polynomial thing, that's really just a "write a polynomial in x choose k form" thing, but they're doing it anyway.
So I take a break from trying to prove my periodicity conjecture to try what Man-Yu is working on, problems 15 and 16. Or rather, he was just doing 16. Problem 15 goes like this: Say we have a polynomial in Z[x]. If m divides all the coefficients, obviously it divides all of the polynomial's values. However, the converse is false (consider x²-x). However, if we write the polynomial in x choose k form, then the converse is true (along with the forward direction, obviously). Problem 16 just lists some polynomials, in x^k form, and asks you to find the GCD of all their values. Any conjectures? Generalizations? Now, obviously, once you've solved Problem 15, you can just say that the GCD of all of a polynomial's values is just the GCD of its x choose k coefficients. Man-Yu hadn't even looked at problem 15. I find the other day he's just working on 16, doing calculations, I tell him, "You know 15 is a generalization of 16, right?" I don't think he even understood how. Today again he seemed to be doing just 16, if anything. "15 is a generalization of 16, that's what he told me." Ugh. Anyway, so I take a break from the periodicity stuff to work on problem 15, and I solve it immediately. The proof's pretty simple, I'll leave it for you guys. I then have to spend a good number of minutes explaining it to Man-Yu. Blech.
Brian Lee, meanwhile, is asking me if there's any good way to convert polynomials from x^k to x choose k form. I tell him again, as I've told him before, the obvious way is fine. He wants to know if there's an efficient way to do it. I tell him it is efficient. I say, if you want to do it by hand, make a big table of the x choose k polynomials so you don't have to recalculate them; if you want to do it by computer, it'll be incredibly fast anyway, there's no need for a more efficient way to do it, if such a thing exists (I doubt it). He asks if I can write a program to do the conversion. "Of course I can!" So I stay in the computer lab for an hour afterward, writing this thing up (and making lots of syntax errors, not having done any programming in some time :P ). So finally about 17:00, I've fixed all that and I get it to compile. As expected, this being the first run, it doesn't work. I'm getting a 0/0 at some point, apparently. However, it's now 17:00 so I decide to go get dinner and finish it tomorrow.
Brian Lee himself, of course, spent much of the lab looking up IMO results.
-Sniffnoy
