- NASA’s photo of the day has an awesome caption.
- the Google empire has gone crazy... gmail offers a "send emails from the past" option, google calendar is offering a "wake up kit" and an "i’m feeling lucky" option to set up appointments with celebrities, youtube is rickrolling all the featured videos... and apparently they’re starting a colony on mars. hmmm... and google australia is letting you search the future with gDay. the testimonials are funny.
- my advisor, already famous for his online opinions, continues his almost-annual april fool’s opinion tradition.
- and finally..., speaking of my advisor, yesterday he sent out the following email:
Dear Math 640 students,
I just finished posting two homework sets. The first one is due tomorrow (please slide them under my door), and the second one is due Thurs. I am rather disappointed at some of you who have been late handing-in the homework (and I commend those who always hand them in on time).
Anyway, the homework problem set that is due tomorrow should be completed by tomorrow, 11:59pm, or else you would get zero, and be in danger of failing this class (i.e. getting a B).
this is already suspicious, since we know he loves april fools pranks, but it was worth figuring out anyhow... the problem set he posted for today is:
~~~~~~~~~~~~First Homework Set for March 31, 2008 class, Due April 1, 2008
[No extensions!]- Recall that for any set of non-negative integers A, mex(A) is
the smallest non-negative integer not in A. For example,
mex({2,4,5})=0, mex({0,1,2,5,8})=3, etc.
Define a sequence ai recursively by a1=2, and for i >= 1 by:
ai=mex({0,1} U { j ar, j >= 1 , 1 <= r < i}),
Prove the following properties of ai- There are infinitely many i such that ai+1-ai=2
- Every even intger n >= 6 can be written as
ai+aj, for some pos. integers i and j. - Define a sequence F(n) by,
F(ai1 ai1 ai2 ...air)=(-1)r if n can be expressed as a product of distinct ai’s , and 0 otherwise.
Let G(n)=add(F(i), i=0..n)
Prove that |G(n)| <= Cn.999, for some fixed constant C.
- There are infinitely many i such that ai+1-ai=2
- Remember that Euler’s pentagonal product
eta(q)=(1-q)(1-q2)(1-q3) ... ,
when expanded, has lots of 0-coefficients and the rest are 1 or -1.
Condider the 24-th power of that
eta(q)24=[(1-q)(1-q2)(1-q3) ...]24,
and let’s call the coeff. of qn, tau(n). Prove that tau(n) is never zero.
~~~~~~~~~~~~~~~
thus, almost instantly, emails started flying between his ph.d. students as follows:
~~~~~~~~~~~
is it an april fools joke? the homework that he posted looks hard. i don’t want to do it.
-em
~~~~~~~~~~~
i assume it is. i was just wondering if it was equivalent to one of the clay problems or something equally ridiculous ;) why else would it be due on april 1?
lara
~~~~~~~~~~~
and finally...
Don’t read below if you haven’t looked at the homework. To make a buffer, here’s the Millenium Falcon:
c==o
_/____.._
_.,--’" ||^ || "..z._
/_/^ ___..|| || _/o.. "..-._
_/ ]. L_| || .|| .._/_ . _..--._
/_~7 _ . " ||. || /] .. ]. (_) . "..--.
|__7~.(_)_ []|+--+|/____T_____________L|
|__| _^(_) /^ __..____ _ _|
|__| (_){_) J ]K{__ L___ _ _]
|__| . _(_) ..v /__________|________
l__l_ (_). []|+-+-<..^ L . _ - ---L|
..__.. __. ||^l ..Y] /_] (_) . _,--’
..~_] L_| || ... ...../~. _,--’"
.._.. . __/|| |.. ....-+-<’"
"..---._|J__L|X o~~|[....
..____/ ..___|[//
..--’ ..--+-’
"Millenium Falcon" Modified Corellian YT-1300 Transport
(No, I did not draw that - I don’t have the patience for ASCII art).
It’s certainly April Fool’s Joke. I didn’t recognize that a(n) is the nth prime at first, but now I see that his problems are:
1. The Twin Prime Conjecture
2. Goldbach’s conjecture
3. His G is the Merten’s function (I had to look this up). This result
would be equivalent to the Riemann Hypothesis, apparently.
The partition-related function is Ramanujan’s tau function. That tau(n) is never zero is another unsolved conjecture. It’s a shame - I was kind of hoping this one would be a ridiculously easy problem, but that everyone would be scared off by the first three.
-Baxter - Recall that for any set of non-negative integers A, mex(A) is
hooray for clever fun. ;)
No comments:
Post a Comment