Mathematics - 2012-11-09 (page 2 of 5)

Paul Slevin

2:05 PM

any topologists to whom I can ask two quick questions?

user19161

@experimentX There is no f(0) in the first place.

user19161

@PaulSlevin You should just ask or nobody knows what the question is.

user19161

Wow, I have 2+2+3+3 stars on the wall, amazing!

experimentX

@WillHunting thanks for responding

Paul Slevin

@WillHunting sorry I got distracted

If I take $S^2$ and remove some point and draw a small disc around that point, would an open neighbourhood of $S^2$ strongly deformation retract onto that disc with the point removed?

hmm never mind, i don't even think that disc with the point removed would be closed in $S^2$

user19161

2:17 PM

@aDangerousIdea That has two meanings.

Paul Slevin

I will replace that with a disc with a small open disc removed so it's a closed annulus embedded on the surface of $S^2$

jdoe

2:31 PM

hello

mick

finally ! i did not get in this room :(

jdoe

oh

mick

had to login forever

@robjohn are you here ?

robjohn

@mick I am, but I am going afk for about an hour. Something quick?

mick

@robjohn you said you knew me from another site , which was that ?

robjohn

2:34 PM

@mick sci.math

mick

@robjohn i do not recall seeing you there to be honest

robjohn

@mick I was a frequent poster there until I found MSE

mick

oh well , goodbye @robjohn

yeah sci.math got really bad :)

robjohn

@mick remember: take out the trash before replying

mick

@robjohn what do you mean ?

robjohn

2:37 PM

@mick that was in my sig on sci.math

mick

@robjohn under the same name or another ?

@robjohn were we friends or enemies ? :p

Jayesh Badwaik

@jdoe how are you? I read some of the transcripts yesterday, my observation is that probably any student dormitories will have the same problem you have with so many people having so many different sleeping schedules.

robjohn

@mick similar name; google "take out the trash before replying"

mick

@robjohn thanks and bye :)

sounds more like garbage man from yesterday :p @robjohn

im lolling again

@jdoe hi

@JayeshBadwaik hi

Jayesh Badwaik

@mick hello!!

mick

2:40 PM

@GustavoBandeira hi

@J.M. hi

Gustavo Bandeira

Hello. =)

mick

hi spammer detected ...

Jayesh Badwaik

@mick you are a serial pinger!!

mick

no a hi spammer

robjohn

@mick the aka in my profile is the same as on sci.math.

mick

2:42 PM

@robjohn ah rob johnson. then you probably know tommy1729

robjohn

@mick I was acquainted.

J. M.

@mick hey.

jdoe

@JayeshBadwaik, hiya yes you are right

mick

@robjohn you still here ? :)

robjohn

@mick I am until I can get my shoes on :-)

mick

2:43 PM

@robjohn need help ?

jdoe

but I had a good nice day today

Jayesh Badwaik

@jdoe :D So better get used to it mate.

jdoe

I made a commutative prism

Jayesh Badwaik

@jdoe good. :D

mick

i should probably say " problem " it is more troll like :)

jdoe

2:44 PM

I don't know if I can get used to it

anyway did you have a good day

robjohn

@mick no, just time :-D

Jayesh Badwaik

@jdoe hmm, I am guessing you are in the same time zone as me?

jdoe

maybe I am UTC+0

Jayesh Badwaik

hmm.

@jdoe Yes, my day was good. What is a commutative prism?

mick

@robjohn there are shoes without laces ... or crocks :)

robjohn

2:45 PM

@mick Now I'm outta here fore a while...

mick

@robjohn one hour ?

got something important to do ? @robjohn

oh dear im way to curious again :)

jdoe

@JayeshBadwaik, well do you know a commutative square? it just says f compose g = h compose k

and you can have commutative triangles too, but I put these together to make a prism

Jayesh Badwaik

@jdoe ahh yes I know them.

Hmm. Cool.

mick

@J.M. your pic is from a vid about topology right ?

i seem to recognize the knot

Jayesh Badwaik

@jdoe what subjects are you currently studying?

jdoe

2:53 PM

category theory, number theory and analysis and combinatorics

Jayesh Badwaik

nice.

jdoe

yea I like themall lots!

Jayesh Badwaik

nice!

algebraic number theory? or elementary?

and analysis? what level?

jdoe

it's basically algebra and topology of number fields

Jayesh Badwaik

okay

jdoe

2:57 PM

I'm kind of behind in it from my struggles but it seems very powerful

I have to fill in the details of my big picture view of it

Jayesh Badwaik

hmm, may be. I am still learning basic algebra so I do not know much.

jdoe

do you know ideals of a ring?

Jayesh Badwaik

yup

I did that

jdoe

we're using those instead of prime numbers

Jayesh Badwaik

okay

jdoe

3:01 PM

I'd really like to get some concrete applications of all the theory we're building up though

Jayesh Badwaik

hmm

nice idea

jdoe

2

Q: How would I show that $\sqrt{p}$ is not contained in $Q(\zeta_8)$?

where zeta_8 is the 8th root of unity over Q and p is an odd prime integer.

I book marked this for example

because of his remark about odd primes

but I didn't get time to work it out yet

Jayesh Badwaik

ohh

good example I think

jdoe

that reminds me, I think we got a proof of Fermats Christmas Theorem dropped out of the theory for free

but I need to see if the proofs actually let me compute the result

Jayesh Badwaik

ohh, now its going over my head. :P

jdoe

3:09 PM

oh fermats theorem is which primes you can write as two squares x^2 + y^2

anyway what do you take other than algebra?

Jayesh Badwaik

hmm, I am not enrolled as of now. I have finished my bachelor's in electrical engineering, now appearing for entrance for mathematics grad school. I am learning analysis (baby rudin), algebra(artin), topology(munkres). so basically kiddie stuff.

I know a lot of applied stuff, but it is not grounded in theory.

jdoe

rudin is so hardcore

love this book

Jayesh Badwaik

yeah, I think it is not as clear as it can be though, without losing its hardcore-ness.

jdoe

I didn't learn algebra or topology at this advanced level but I really enjoyed artins galois theory notes

(and thank goodness I did decide to study that since they assumed everyone knows it here...)

Jayesh Badwaik

Hmm, I thought algebra artin is kiddie?

jdoe

3:14 PM

let me put it this way, I could learn a tremendous amount from studying it

Jayesh Badwaik

by galois notes you mean this?

@jdoe ohh. okay.

jdoe

I am not sure if that's the same as what I read amazon.com/Algebra-Galois-Theory-Courant-Lecture/dp/0821841297

Jayesh Badwaik

I read-ahead parts of galois theory in Lang/Artin. Understood them well I think, however, will read them again properly when I get to it.

jdoe

it's a very pretty theory

Jayesh Badwaik

yup. that I agree.

Garbage Collector

3:19 PM

Lets relax a minute...

jdoe

I need to go over all the theory of finite fields again

ok @GarbageCollector

Garbage Collector

jdoe

lol

J. M.

@mick Nope, it's something I made up on my own.

jdoe

@JayeshBadwaik, did you study Gauss 17-gon?

Jayesh Badwaik

3:23 PM

@jdoe yup.

jdoe

I love this :D

even though Gauss proved it before Galois came around, you can phrase it nicely in the galois language

Jayesh Badwaik

@jdoe :D nice. yup, I learnt it the gauss way though.

mick

guys im still here , but im posting a question ...

robjohn

@GarbageCollector Neil didn't have as many bars on the moon...

Garbage Collector

@robjohn What bar is it?

J. M.

3:26 PM

Yeah, pretty sure the nearest tower was hella far... :)

Jayesh Badwaik

@GarbageCollector Space Bar.

robjohn

@J.M. but probably a clear line-of-sight

J. M.

@JayeshBadwaik What do they serve there, Pan Galactic Gargle Blasters?

Garbage Collector

I am eating banana. See you then!

robjohn

@J.M. at the Last Bar, I'm sure

@GarbageCollector K!

potassium

J. M.

3:29 PM

@robjohn Yeah, likely the one at the end of the universe. :)

robjohn

@J.M. That'd be the one :-)

Jayesh Badwaik

@J.M. there is only a restaurant there, no bar. Bars cause too much brownian motion for particles to condense properly into big crunch. (yep, sue me) :P

jdoe

Cantors leaky tent lol

robjohn

@jdoe Oh, no! it rained here yesterday, and there is a 40% chance of more rain today. I'd better make sure that that one point is there in my roof...

jdoe

:p

there's nothing scarier than a guy sitting next to you in lectures who doesn't take notes

mick

3:39 PM

hey guys !

jdoe

hi

mick

i posted a new question ... hope its a clear one.

shameless advertising ? :)

0

Q: What are the Puiseax series for the inverse of $exp(z)(z-a)(z-b)(z-c)$ expanded at the sigularities?

Let $a,b,c$ be real variables. Let $z$ be a complex number and $g(z) = exp(z)(z-a)(z-b)(z-c)$. Let $f(z)$ be the functional inverse of $g(z)$ such that $f(g(z)) = g(f(z)) = z$. Now $f(z)$ must have singularities where $g'(z) = 0$ hence since this equation has at most 3 distinct complex solution...

complex-analysis logarithms power-series inverse puiseax

J. M.

@jdoe Why would that be scary?

jdoe

because he memorize it all

mick

i think jdoe means it gives the impression the student has given up ?

oh i see

robjohn

3:42 PM

mick

can everybody see my link clearly ? :)

jdoe

:D

J. M.

@jdoe Not necessarily, I've found. Personally, I prefer listening to lecturers to writing notes...

mick

@robjohn is that garbage collector ? :)

jdoe

@J.M. me too, but then you have no notes!

robjohn

3:43 PM

@mick the image is titled garbagecollector.jpg

jdoe

does anyone have a proof that p-adics are totally disconnected?

mick

@robjohn i mean the user :)

robjohn

@mick I think it is a more mathematical avatar, perhaps.

mick

btw , guys , i posted a new question. hope it is clear

@robjohn not everybody has a phd ... and even those who do ...

i know someone who used to work for nasa , now he collects garbage :) @robjohn

Bartek

Hi. I think my questions could be badly titled because they get fewer views than others. Can I link to them here so you can tell me if I'm right (and just to plug them)?

mick

3:47 PM

Is my question well titled ?

J. M.

@jdoe That's what the lecture notes and textbook are for...

mick

0

Q: What are the Puiseux series for the inverse of $exp(z)(z-a)(z-b)(z-c)$ expanded at the sigularities?

Let $a,b,c$ be real variables. Let $z$ be a complex number and $g(z) = exp(z)(z-a)(z-b)(z-c)$. Let $f(z)$ be the functional inverse of $g(z)$ such that $f(g(z)) = g(f(z)) = z$. Now $f(z)$ must have singularities where $g'(z) = 0$ hence since this equation has at most 3 distinct complex solution...

complex-analysis logarithms power-series

jdoe

@J.M., "lecture notes"?? You're very lucky

mick

@J.M. i do not feel textbooks are good enough to replace notes ... or better not complete enough ...

J. M.

@mick Then again, I had the rather nasty habit of always being two chapters ahead of the lecturer...

mick

3:49 PM

@J.M. for all classes ? :p

jdoe

that's a good habit!

J. M.

@mick Surprisingly. :D It allowed me to goof off on boring days.

mick

@J.M. problem is with those being 2 behind

robjohn

@J.M. that helps to know what needs note taking and what needs listening to.

mick

0

Q: What are the Puiseux series for the inverse of $exp(z)(z-a)(z-b)(z-c)$ expanded at the singularities?

Let $a,b,c$ be real variables. Let $z$ be a complex number and $g(z) = exp(z)(z-a)(z-b)(z-c)$. Let $f(z)$ be the functional inverse of $g(z)$ such that $f(g(z)) = g(f(z)) = z$. Now $f(z)$ must have singularities where $g'(z) = 0$ hence since this equation has at most 3 distinct complex solution...

complex-analysis logarithms power-series

J. M.

3:52 PM

@robjohn True; back then, I could filter out what I already went through and concentrate on the stuff that wasn't on the books...

mick

spamming :)

J. M.

@mick You've mentioned it at least twice; no need for repetition. :)

It will have its share of attention in due time.

robjohn

@mick only once, at most, please.

mick

@J.M. i want ppl to look at it :) this is free advertising

this saves the world economy !!!!!!!!! xD

J. M.

@mick Posting it a lot actually demotivates most people to look at it.

Same logic with an alarm that goes off too often.

mick

3:53 PM

@J.M. my alarm goes off 5 times and it helps ?

bad example :p

jdoe

p-adic topologyis hard

robjohn

@mick Rule 3

mick

ah rob you spoil my fun :(

there goes the economy ...

J. M.

@mick So, I presume you also have no problem with programs that spit out too many dialog boxes...

mick

windows ?

Bartek

3:56 PM

OK, I'll just ask if my last question is tagged properly because I'm definitely not sure about it. It's here and I'm not sure how to tag it because it's about generalizing something from multilinear algebra to general mathematics. I thought big-picture should be alright, but I'm reading that people dislike this tag very much.

mick

if those dialogue boxes are about math i dont mind :p

robjohn

►

mick

@robjohn yes eggs bacon and spam

i know that very well

i said it before here

eggs bacon

and spam

J. M.

Right, so please keep the promotion to a bare minimum. :)

jdoe

this is abit frustrating, I don't know how to catch up with my number theory notes

J. M.

3:59 PM

Hey @Brian.

jdoe

stuck on things so it's hard to go past them

Brian M. Scott

@J.M. Haven’t seen you in a while.

J. M.

@BrianM.Scott Yeah, been somewhat occupied. Also, the question volume these days is scaring me. :)

Brian M. Scott

@J.M. And I’ve not been in chat very often. The question volume last Sunday was unbelievable; apparently a lot of people were prepping for exams.

jdoe

this is crazy, I'm filling up book after book after book of notes

mick

4:04 PM

►

J. M.

@BrianM.Scott Well, this is the crunch time before winter break, I guess...

I don't remember last year being this hectic, but I guess this site was less popular then.

Brian M. Scott

@J.M. I will say that it was profitable in terms of rep: I actually hit 500 that day!

jdoe

Brian M. Scott

@J.M. I’m definitely seeing more new faces amongst the responders, and I assume that the increase in questioners at least matches that.

J. M.

@BrianM.Scott I saw; you seem to have the knack to get more past the supposed cap... :)

Ed Gorcenski

4:07 PM

Good morning

jdoe

hello

mick

@J.M. thanks for the edit. cant believe my own spelling

i know im bad , but that bad wow :)

@jdoe whats up with the pic ?

jdoe

it's Johann Peter Gustav Lejeune Dirichlet

mick

@jdoe yes Gustav Dirichlet

but why you post it ?

Brian M. Scott

@J.M. It’s partly having the time to answer a lot of questions, and partly writing a fair number of answers that get accepted.

J. M.

4:10 PM

@mick No problem; I've seen it to be a common typo...

mick

@J.M. did you think about it ?

i assume Puiseux to be have been a frenchman ...

i wonder , what you guys think ...
it is better to ask alot of questions on 1 day or to spread them ?

user1097772

Hello, please is this formula correctly wrote?

mick

@user1097772 your number is wrong :)

its 53414 not 1097772 :)

user1097772

I mean if is the multiple implication ok its like:
A => B => C

jdoe

@user1097772, A -> B -> C is the same as A -> (B -> C)

it's right associative

(A -> B) -> C is different to A -> (B -> C)

mick

4:17 PM

i always write brackets personally

jdoe

I prefer not to

mick

@jdoe did you see my question ?

jdoe

no

mick

@OldJohn hi ! i was waiting for you :)

Old John

@mick really?

user1097772

4:20 PM

ok thx :-) right associative - thanks :-)
mick: what number? .. I always write brackets too :-)

mick

@OldJohn yes i have a new question

Old John

OK

mick

should i give link ? i did it already 3 times today here :s

jdoe

don't

mick

lol guess not

but you can see at my profile

@OldJohn k ?

@Charlie hi !

Old John

4:23 PM

@mick OK - looking, but not sure I am going to get time to think about it properly this evening

mick

k

Brian M. Scott

@jdoe That makes life unnecessarily difficult for anyone reading what you write.

jdoe

no

J. M.

@BrianM.Scott It's like that damned arithmetic "quiz" all over again... :)

Brian M. Scott

@J.M. The order of operations thing?

Charlie

4:36 PM

@mick hi

J. M.

@BrianM.Scott Yeah, that one with acute parenthesis deficiency... :D

Brian M. Scott

@J.M. I prescribe lots of vitamin D. Or something.

Old John

@J.M. nasty disease

I would prescribe a course of LISP

Jayesh Badwaik

@OldJohn hahahaahahahahahahahahaha.

jdoe

I'm behind in understand lectures so I made a system where I put a divider where I'm up to in understand things but I can't move it forward because I don't know about this topology

that's so annoying

Jayesh Badwaik

4:41 PM

math learning may not be linear

jdoe

as long as it's non-zero I'm happy

hey this is cool

hmm I can't figure out how to copy a link from google search

math.ethz.ch/education/bachelor/seminars/hs2011/p-adic/…

they make euclidean models of the p-adic topology out of fractals

user1097772

Can I have one additonal simillar question abou associativity?
A ∧ B v C