No, flagrant disregard of academic honesty is much more serious than that.
I get it that the OP is frustrated by his teacher, but he shouldn't be posting in the first place. Given that he put red flags all over it and said what he said, I'm pissed off that someone with 100+K has to be such a stubborn child.
And there are enough people with 100+K who agree with him that it's pointless for me to raise a stink on meta.
@TedShifrin: sorry for the confusion. I am as well. I was merely agreeing that I don't think this was an appropriate situation to have posted a question.
I've even posted in my syllabus for Probability in the fall that I'm aware that there are solutions to the textbook available on-line. I'm not going to even try to police it.
@Sawarnik: I presume the downvotes are because of my ranting here ... and nothing else.
@AWertheim: Give my regards to Robert Bryant :) (I won't list all the people I know at Duke.... :) )
I also don't think it should have anything to do with my being a professor ... Most of the students I've gotten to know in this chat are very serious and honest folks.
@TedShifrin: I'd love to, but I'm afraid I just recently graduated and never got the pleasure of knowing Dr. Bryant. I very much wanted to take his differential geometry course but had a schedule conflict :(
@TedShifrin: haha, well, it is hard to say, since I have so much yet to learn. I am most interested (at the moment, at least) in algebraic number theory and algebraic geometry.
I wrote my senior thesis on complex multiplication, which I found very beautiful, so that has been a source of interest. But of course, I've been warned by wise folks not to marry myself to one research area before grad school.
People have a conscience which does not disappear when going "online". Being anonymous is not and never will be the same as "acting as a douche" and does not justify it in any way.
@Sawarnik It's not true what you suggested yesterday. I can live with anyone in chat, and I don't expect someone to leave the chat. When things get worse, it's up to me to leave the chat (and return later).
But Bryant is a superstar and fabulous teacher and it's a pity you missed out on the opportunity to take a course from him. (I've known him for close to 40 years. Yikes.) @AWertheim
Does anyone know if there is a result which states that if an uncountable family of sets has the finite intersection property then the intersection of all members of the family is non-empty?
@TedShifrin: I've heard! One of my good friends at Duke is a graduate student who is studying differential geometry. He took Dr. Bryant's course and had nothing but great things to say! (I was given a similar recommendation by another one of my professors, who said I should take his course if at all possible).
@TedShifrin Recall the MathStackExchange.SE T-shirt that people commented on as being the place where students go to cheat? I posted that answer on Meta and got very little support, no?
@Ted what do you mean? I have only learnt about the f.i.p property in the last 15 minutes, so I am working with the definition that a family of sets has the f.i.p property if the intersection over any finite subcollection of the family is nonempty. What I want to know is if the family has uncountably infinite cardinality then can we conclude that the intersection of all uncountable members is non-empty?
@Alex: So there's a theorem that says that a topological space $X$ is compact if and only if any collection $\mathscr C$ of closed sets has the finite intersection property (i.e., any finite subset has nonempty intersection), then the intersection $\bigcap_{C\in\mathscr C} C$ is nonempty.
This theorem holds for any collection ... no countability hypothesis.
I was about to say I had seen a lot of @PedroTamaroff 's posts starred at once before but seeing as he just joined and that blew my mind I am going to not say that.
@Hippalectryon @TedShifrin What I do is an art, and being so, it's also about beauty, and sometimes letting terms that way, aesthetically speaking, everything looks much nicer. ;)
I was wondering that for a while and the only example of nonisomorphic groups with same class eqns I can find is $D_8$ and $Q_8$, @PedroTamaroff, but funny enough both of the inner aut groups are isomorphic to $V_4$.
Instead of adjoining special torsion points of an elliptic curve, one adjoins special torsion points of a more general abelian variety to get the desired extension.
Forgive me if this information you already know, but if you are more interested, the paper "Class Fields Over Real Quadratic Fields and Hecke Operators" by Goro Shimura is wonderful.
No, not really. I have learned modular functions from a different perspective.
The geometry behind the algebraic geometry scares me.
@AWertheim well you seem quite a lot of partial to the geometric side instead of the algebraic one. you're adjoining torsion points of abelian varieties instead of algebraic values of hyperelliptic functions!
@BalarkaSen: I'm afraid I know very little about the geometric side of things, as I've only got a very basic understanding of algebro-geometric ideas. I have had only a superficial exposure to modular forms as well. But there are certainly more algebraic ways to think about adjoining torsion points :)
I am more interested in the algebraic side, @AWertheim. Modular forms (well, modular functions (well, automorphic forms)) can be described in terms of purely algebraic language. The most general idea is to use the fact that modular equations have algebraic points on them that satisfy a polynomial relation over some field.
Can I have a sanity check? $|G|=p_1^{a_1}\cdots<\infty$, then by Cauchy's theorem $\exists H\subseteq H : |H|=p_1$. $H$ is cyclic so abelian, thus $G/H$ is a group of order $p_1^{a_1-1}\cdots$.
Thus if $d|n=|G|: \exists H\subseteq G: |H|=d$.
Indeed. I'll never have school chemistry again though, which is pleasing.
