@TedShifrin: I think we might need something degree at least three, and we're going to need the symmetries of our set of points to suck. (Symmetries make it easier to find some point which maximizes it, I think.)
hey so @TedShifrin looking back at this problem of center of $D_8$ I think I can generalize it for example the center of that for $D_{2n}$ will be $\{1,r^s\}$ if $\frac{s}{2} = 2k$ for some k then s will be equal to k otherwise the center will be the trivial one but I don't know if my conjecture holds.
Can you take books out of your college library, @Owatch? I'm a bit confused why you had to give the book back since presumably you're taking the next calculus course?
when n is even we will have the symmetries will be kinda of different that is we will have symmetries along the lines that goes through each vertices and through the middle between each vertices while odd we will have symmetries along the vertices only
oke good thank you guys @TedShifrin and @BalarkaSen :D you know what I am doing now guys I am doing 1 week of reading the book and 1 week of just excerises so this way I capture more chapter and don't get bored
hm ok as I read this chapter I came up with this interesting way can you derive that center is subgroup of centralizer using group actions I will think about it when I come back need to go submit my assignment for physics
Half pigeonhole theorem : if you put one pigeon in two half pigeonholes, then at least a rational fraction of a pigeon is in one of the half pigeonholes
Also, if you have two pigeonholes and a single pigeon, whether probability of being in one is greater than being in the other or not depends on the spin of the pigeon.
Why do students not come at office hours, though? I mean, it's meant for them and their questions. I have heard similar complaints from TA's and professors.
oh, the grad students in this uni don't have fun doing office hours with my prof, I guess. he's usually pretty grumpy with someone if he/she can't figure something simple out (although equally friendly with someone when he/she asks/figures out nontrivial stuff)
@TedShifrin Er, fundamental theorem of covering spaces isn't really enough to convince me of anything.
There is even a galois connection for posets :P
What is more interesting is the short exact sequence $1 \to Aut(X, Y) \to Aut(X, Z) \to Aut(Y, Z) \to 1$ of deck transformation group corresponding to the chain of galois covers $X \to Y \to Z$
I'm familiar with the basic rudiments of the FTGT, but someone remarked to me some time ago that Galois theory has a tight correspondence with the theory of fundamental groups. I didn't get it at the time, but I saw a question the other day where it came up, and I became curious again.
Ok, I'll try looking into some of the references you suggested. It's possible it might just be over my head at the moment, but I figured I'd ask. It seems like there must be some very beautiful ideas involved. Thanks!
Anyway, there really is quite a deep connection. I only "know" about it, don't really understand any of it. You can make an almost-convincing connection by considering branched covers of $\Bbb CP^1$ (equivalently, complex Riemann surfaces) and Galois groups over $\Bbb CP^1$. These two categories coincide nicely (keyword : function fields).
Anyhow, @Stan, if by honors analysis you mean the honors sequel to the Spivak course, it's pretty ridiculous. But I'm not sure which courses you're talking about.
Also, if you have two pigeonholes and a single pigeon, whether probability of being in one is greater than being in the other or not depends on the spin of the pigeon.
I just started worldscientific.com/worldscibooks/10.1142/8501 and it has introduced a term "gap functional" which is not in Wikipedia nor MathWorld. I am not trying to learn nonstandard mathematics. Should I be concerned?
That would be great! I have to take the placement test over the summer. I'll ask you for them in a few weeks and I will take it for real with time and everything.
@TedShifrin oh, btw, my mother said if you ever come to Chicago, you are welcome to dinner at our house.
I have to explain in words this formula:
A = -log(X)
My guesses would be either:
A is the minus logarithm of X
A is minus the logarithm of X
Is one of these expressions, or yet another one, correct?
@Ramanewbie Quand je lis "Chaque phrase est une forme linguistique indépendante, qui n'est pas incluse dans une forme linguistique plus large en vertu d'une construction grammaticale quelconque." Là je dis, oui ;).
Je doute qu'il y ait beaucoup plus de réflexion en Français qu'en mathématiques on l'on s'attend à ce que vous appliquiez comme des robots des formules qu'on vous balance sans contexte @Ramanewbie
I have to explain in words this formula:
A = -log(X)
My guesses would be either:
A is the minus logarithm of X
A is minus the logarithm of X
Is one of these expressions, or yet another one, correct?
