I have a question for people here and it is not particularly mathematical in nature.I will really appreciate it if someone could help me here. In general, is it very normal for undergraduate students to be made a party to department politics?
@MikeMiller, to take a concrete example, Prof. X does not like Prof.Y and X perceives me to be close to Y,so in a private conversation X erupts at me and accuses me of being always shielded by Y?
@MikeMiller Note that X does not even mention what I am being shielded against(and I am not sure what I am being shielded against myself!)
Hi guys, I was wondering if someone could point me to a book for learning and understanding (weak and strong) induction thoroughly; including the write-up. :D
@MikeMiller, Also take this example: I cannot (and do not want to) speak to X. But when I need to, I drop by X's office(I don't email X for reasons I will mention) and ask if he is free to talk to me, he replies with a no and a rude monologue saying why he is not free . The conversation seems to take us to asking me to go to asking me who among the faculty are researchers and have a publication in the last two years.(Ours is not a very researchy university)
And the same conversation seems to happen again and again.
You have never encountered professors like that?
(sorry, if i am ranting endlessly)
@Semiclassical, I am so happy to see X being bashed!(wonderful way to relieve frustration). :D
No. He very well could be busy; a rant in response is unnecessary. In any case, I am not equipped to give you advice on how to deal with this, since I am neither party to this situation, nor at your university. Speak to someone there.
it's worth pointing out that there is an Academia Stack Exchange. they might have more concrete suggestions for how to handle the situation, either on chat or their main site
@user96343 We have some drama here as well, like I know one professor's research student is not allowed to attend conferences where another professor they don't like is attending at the same time lol
It kind of sucks for the student because the other professor has a lot more funding and goes to a lot of good conferences that the student can benefit from
Sigh, bad things happen. All the student can do is come online and anonymously(?) rant about it and feel good when others seem to be even mildly supporting her. :D
In any case, I never was able to prove that any map would have to kill something in first homology. I had a geometric argument but it relied on a (false) fact. Which was a shame.
That's just because everything cool that you don't know yet requires harder math. The same will be true when you know cohomology and the basic duality theorems.
really? the only relevant bridge between homology and homotopy i know of is Hurewicz, and that's seemingly not at all enough to compute homotopy in general.
a term which i kind've wish i knew the meaning of (only kind've, since it's not clear if it's at all relevant to the stuff i like to do) is "group cohomology"
i've seen that occasionally in connection to certain physics things, but never in a terribly clear way
speaking of homotopy, i remembered that $[A, \Omega B] = [\Sigma A, B]$ thingy. i have one or two ideas in mind, but haven't had the time to think about it.
@BalarkaSen The usual proof for the disk generalizes to manifolds with boundary if you know a little bit about differential forms and Stokes's Theorem. (It's an exercise in my book, btw.)
@Remember: Gaussian elimination works over any field.
@Remember take the first row, subtract this row times appropriate constant from all the other rows and finally multiply the first row by reciprocal of the a_11 term so that you get the first term of the first row as 1 and all the others 0 below.
now take the second row, do the same as above.
can you prove that you end up with a row reduced echelon matrix after doing all this?
(some nonzeroness assumptions are needed to do what i have suggested, but i have skipped them here. you should explicitly prove what happens for those cases)
@Mike the map $[\Sigma X, Y] \to [X, \Omega Y]$ seems to be the one obtained from restricting a map $\Sigma X \to Y$ to the lines $x \times [0, 1]/0 \sim 1$, but i haven't verified if it's a surjection. i'll check later.
let $G \approx <a,b | b^{-1}a^3b = a^5 >$. let $H$ be a finite group and $\varphi: G \to H$ a homomorphism. then $g=a^{-1}b^{-1}a^{-1}bab^{-1}ab \in \ker \varphi$
how do i use the fact that $H$ is finite?
does this imply that $\varphi(a)^n = 1$ for some $n$?
you have to prove that that horrendous element is inside the kernel for any finite group $H$? that's just false, so i guess the question must be something else
ah, @Pureferret. If there's something you can expand on from your particular question - maybe narrow it down to a single, specific question, that you felt went particularly unanswered, you should post a new one. I don't think you'll get anything further out of editing the old one, or anything.
(In particular, 'what's the longest known Collatz sequence' is probably just going to get a number someone computed, and it seems you find that unsatisfying; just be careful not to ask something that's probably open!)
you have to understand that i've never went through any serious mathematical course-y stuff, @Alex. i am doing the best i can by studying most of the things by myself.
@Balarka: sure. That remark wasn't meant to be pejorative at all, so I hope that it didn't come off that way. In case it's not clear, I find your accomplishments very impressive. :)
no, no, i knew you didn't mean anything. i guess i am just used to taking everything as a sneer, never receiving much of an encouragement before; neither from people in here nor from the people around me.
I asked Longest known sequence of identical consecutive Collatz sequence lengths? some time ago, but I don't feel like it really got to the bottom of things.
See, in the answers lopsy find a sequence in the range of $596310 ... 596349$ and makes a heuristic argument:
There's nothing special ...
I'm not sure how to go around this one. Factorizing doesn't seem to work and there isn't a clear pattern to work by that I see.
EDIT:
So apparently I need to add context and stuff. I removed the checkmark from the answer because the answer for this question is one of these options (according to ...
@John: users have to vote to reopen the question. I've just cast the first nomination. You'll need four others to vote as I have for it to be reopened. (I don't recommend soliciting those votes here, though, unless it's really been too long.)
@Balarka: depends on your definition of fun. :) But I certainly think so.
Been learning topology with a manifold-oriented (hehe) approach from Lee's "Introduction to Topological Manifolds". Still working on commutative algebra from AM. A bit of representation theory from Serre's "Linear Representations of Finite Groups". That mostly covers it as of late.
AM is great, a lot of fun. They've all been a bit slow going, partially because I'm still at my job, partially out of sluggishness, and I'm also trying to be pretty thorough.
Hmm, about four chapters on some elementary point-set stuff. Another two on some prepatory-looking stuff for algebraic topology. And then the remaining five on basic algebraic topology (below the level of Hatcher, I'd say).
@Balarka: I know what you mean, just having a little fun. Truth be told, I wasn't really sure what to draw. My drawing didn't look anything really like Mumford's treasure map, that's for sure. But I just spent a little time computing the prime ideals, and then drew a standard cartesian system. Put points at all prime numbers along the "x"-axis, and put points above primes $p$ at various irreducible polynomials (mod $p$) along the "y"-axis, if that makes sense.
@robjohn Well, it was, but the answer had a mistake and using his method I couldn't get one of the right answers in my textbook. Probably my mistake but I've been on it for hours so I've reopened the question
@AlexWertheim it represents how much information every ideal contains about the space. more precisely, it represents how large the localization of Z[x] at those ideals are.
@Alex But, there is more to the curve than you think there is. It's actually an arithmetic version of branched covering maps.
I don't really know about that stuff, but you see, when you pull up a prime ideal of Z to a prime ideal of Z[i], it splits. so these are kinda stuff like covering maps.
the real precise-version of this is complicated, i guess. goes back to grothendieck.
Hmmm. I know some of what you're talking about, but I don't know what a covering map is, let alone a branched covering map, or an arithmetic version of a branched covering map. I'll have to keep reading.
@AlexWertheim: If someone aggravates, annoys, or otherwise upsets me, I do, so as to avoid being further aggravated, annoyed, or upset. It's worked fine for me thusfar.
In particular, you don't get pinged anymore, if the person in question pings people problems whenever they enter.
@MikeMiller: that makes sense. Sometimes I get a bit rattled by some of the stuff posted here, and make the mistake of responding instead of ignoring things. I should know better.
@LeGrandDODO: C'est ridicule, alors. If we gave any sort of entrance exam in the US, almost no one would/could major in math. Hmm, what a nice thought :P
I asked Longest known sequence of identical consecutive Collatz sequence lengths? some time ago, but I don't feel like it really got to the bottom of things.
See, in the answers lopsy find a sequence in the range of $596310 ... 596349$ and makes a heuristic argument:
There's nothing special ...
