First 2 days of Number Theory, and more
Jul. 5th, 2005 07:39 pmThis entry is going to jump around a lot pointlessly.
So yesterday we immediately pegged this year's "says stupid, or at least just utterly wrong, things during lecture" people. One reminded Funto of Sunok, and so she is called Sunok-girl, and the other is called Infinity-boy (well, we actually know his name now, he's Nick Slowey) because he asked if infinity is in N.
As always, Glenn started off the first day with his lecture about what equations we can and can't solve. The only solution to 2*k=8 in Z is k=4, but how do we know this? Can we prove this? Sunok-girl suggested it should be an axiom.
Today, he asked them to list properties of Z. The second one said was that it's countable.
Glenn decided to spare us such things as "the average of all the integers" by just telling the first-years that 0 is the additive identity.
Glenn: Every element of Z has an additive inverse.
Infinity-boy: Except for 0.
Glenn asks what an additive inverse is at one point, someone had said it and it hadn't yet been defined; ∞-boy says "It's the negative number with the same absolute value."
One of the teachers (as in, one of the people in PFT) claimed that 0 was a counterexample to 1 being the multiplicative identity...
This one can't really be blamed on ∞-boy, but is rather a product of the way math is taught in high school... when someone finally named commutativity as one of the properties of Z, ∞-boy asked, "Isn't that true of *all* numbers?"
∞-boy has also been attending Rohrlich's "Values of the Riemann Zeta Function" class as well. Today he asked if the Bernoulli of the Bernoulli numbers was the same Bernoulli of Bernoulli's principle (about the speed and pressure of a fluid). I was afraid Rorhlich was going to go off on a whole tangent about the history of the Bernoulli family, but thankfully he didn't really know about it and Bernie mentioned quickly how there were a whole bunch of Bernoullis.
So today was the first day of Geometry and Symmetry. This year, Rosenberg is doing an actual 2-hour class on the days that we don't have research lab. He used the extra hour today to talk about problems with doing geometry axiomatically.
I went to the first day of Algebra yesterday, I'm not continuing that. Very nice how Margie didn't assume people knew what functions were, but assumed they knew what Cartesian product was, and what cosets are. :P :-/
So yesterday, being July 4th, there was a picnic for much of the day (the number theory problem set was shortened a bit, and the extra problems added to today's). Dina visited and played Mafia (of course).
So this year, unlike the past two, I have ended up with a roommate who goes to sleep earlier than me.
The shades in my room are really bad at keeping out the sun, so I always wake up really early, and then fall back to sleep and wake up again when my alarm goes off at 7:30. Or at least, that's been the case for today and yesterday, which I suppose really isn't very meaningful.
Oh, really funny from Zeta Function today: OK, here, bn denotes nth Bernoulli number, and Bn nth Bernoulli polynomial. So Rohrlich presented today what he called "The 'Huh?' Formula": Bn(x)=(x+b)n. Huh? What's b? Well, it's actually a mnemonic device, the real formula is Bn(x)=sum as k goes from 0 to n of ((n choose k)xkbn-k). So you see, it's what you get if you expand (x+b)n and then change all the superscripts on the 'b's to subscripts. But, Rohrlich complained, there didn't seem to be any name for this (other than The "Huh?" Formula, and that's not a very good name once you know what it means). So Bernie suggested it be called "The Bernomial Theorem".
So I had a really weird dream the night before last. I wrote down a lot of it, but the only part I'm going to bother to repeat here is that in it, I kept singing some really weird song that I learned from Ethan - I mean, even in the dream I knew it made no sense - and all I can remember of it is that one of the lines in the chorus was along the lines of "We're here to get the alligators out of your eyes."
That's all I can really remember right now that I wanted to write.
-Sniffnoy
So yesterday we immediately pegged this year's "says stupid, or at least just utterly wrong, things during lecture" people. One reminded Funto of Sunok, and so she is called Sunok-girl, and the other is called Infinity-boy (well, we actually know his name now, he's Nick Slowey) because he asked if infinity is in N.
As always, Glenn started off the first day with his lecture about what equations we can and can't solve. The only solution to 2*k=8 in Z is k=4, but how do we know this? Can we prove this? Sunok-girl suggested it should be an axiom.
Today, he asked them to list properties of Z. The second one said was that it's countable.
Glenn decided to spare us such things as "the average of all the integers" by just telling the first-years that 0 is the additive identity.
Glenn: Every element of Z has an additive inverse.
Infinity-boy: Except for 0.
Glenn asks what an additive inverse is at one point, someone had said it and it hadn't yet been defined; ∞-boy says "It's the negative number with the same absolute value."
One of the teachers (as in, one of the people in PFT) claimed that 0 was a counterexample to 1 being the multiplicative identity...
This one can't really be blamed on ∞-boy, but is rather a product of the way math is taught in high school... when someone finally named commutativity as one of the properties of Z, ∞-boy asked, "Isn't that true of *all* numbers?"
∞-boy has also been attending Rohrlich's "Values of the Riemann Zeta Function" class as well. Today he asked if the Bernoulli of the Bernoulli numbers was the same Bernoulli of Bernoulli's principle (about the speed and pressure of a fluid). I was afraid Rorhlich was going to go off on a whole tangent about the history of the Bernoulli family, but thankfully he didn't really know about it and Bernie mentioned quickly how there were a whole bunch of Bernoullis.
So today was the first day of Geometry and Symmetry. This year, Rosenberg is doing an actual 2-hour class on the days that we don't have research lab. He used the extra hour today to talk about problems with doing geometry axiomatically.
I went to the first day of Algebra yesterday, I'm not continuing that. Very nice how Margie didn't assume people knew what functions were, but assumed they knew what Cartesian product was, and what cosets are. :P :-/
So yesterday, being July 4th, there was a picnic for much of the day (the number theory problem set was shortened a bit, and the extra problems added to today's). Dina visited and played Mafia (of course).
So this year, unlike the past two, I have ended up with a roommate who goes to sleep earlier than me.
The shades in my room are really bad at keeping out the sun, so I always wake up really early, and then fall back to sleep and wake up again when my alarm goes off at 7:30. Or at least, that's been the case for today and yesterday, which I suppose really isn't very meaningful.
Oh, really funny from Zeta Function today: OK, here, bn denotes nth Bernoulli number, and Bn nth Bernoulli polynomial. So Rohrlich presented today what he called "The 'Huh?' Formula": Bn(x)=(x+b)n. Huh? What's b? Well, it's actually a mnemonic device, the real formula is Bn(x)=sum as k goes from 0 to n of ((n choose k)xkbn-k). So you see, it's what you get if you expand (x+b)n and then change all the superscripts on the 'b's to subscripts. But, Rohrlich complained, there didn't seem to be any name for this (other than The "Huh?" Formula, and that's not a very good name once you know what it means). So Bernie suggested it be called "The Bernomial Theorem".
So I had a really weird dream the night before last. I wrote down a lot of it, but the only part I'm going to bother to repeat here is that in it, I kept singing some really weird song that I learned from Ethan - I mean, even in the dream I knew it made no sense - and all I can remember of it is that one of the lines in the chorus was along the lines of "We're here to get the alligators out of your eyes."
That's all I can really remember right now that I wanted to write.
-Sniffnoy
