Mathematics - 2014-03-01 (page 1 of 2)

@FernandoMartin probly the coolest moment i had during my undergrad was at the very end, they let me TA / co-teach a group theory class my final semester... i ended up giving them this monstrous final exam

Fernando Martin

12:29 AM

didn't prove it that way today though

Alexander Gruber

and afterwards a few students thanked me for making it so easy :)

proudest guy on the planet right then

Fernando Martin

@AlexanderGruber: Niiiice

Ted Shifrin

Sleep well @Pedro ... Glad you made it safely.

What was your best question, @Alex?

Pedro Tamaroff

@TedShifrin Traffic was hell.

I am eating now.

Will sleep after eating.

@TedShifrin There was an accident, actually.

Ted Shifrin

Sounds as much fun as Atlanta traffic ....another reason for me to move when I retire.

Alexander Gruber

12:35 AM

@TedShifrin hmm, maybe showing that groups of order $pq$ with $p<q$ and normal $p$-Sylows were cyclic

i had the nontrivial center $p$-groups thing on there too, proving that groups of order $p^2q$ weren't simple, and a couple other things about automorphisms

Ted Shifrin

Ok, pretty reasonable. No semidirects to classify :)

Alexander Gruber

@TedShifrin yeah- this was a first course in AA

Ted Shifrin

Any cool group actions or index smallest $p$ dividing $|G|$ is normal?

Probably a bit tougher, but cool :)

Alexander Gruber

@TedShifrin i had the latter on the homework, i believe.

Ted Shifrin

Anyhow, I'm antipodal to algebra ... Well, almost ;)

Alexander Gruber

12:39 AM

this was the first extra credit / exam review

Ted Shifrin

Y'all? In Cincinnati? What? :)

Alexander Gruber

@TedShifrin we're right next to kentucky, Cuz. :p

Ted Shifrin

rolls all six eyes

Alexander Gruber

are you a sand spider, @Ted?

Ted Shifrin

On a good day ...

user4140

1:10 AM

How can I prove if a graph is not connected then the complement is?

Pedro Tamaroff

Goodnight y'all.

user4140

good night.

r9m

@user4140 @user4140 what is the meme for ? did you get it ?

user4140

no one ansewerd, but I think I figured it out.

@AlexanderGruber why did you delete my answer?

Alexander Gruber

1:30 AM

@user4140 it was flagged as "not an answer" and i agreed.

N3buchadnezzar

Is it possible to find this integral using complex analysis
$$
\int_{-\infty}^\infty 1 - \exp(-1/x^2)\,\mathrm{d}x = 2 \sqrt{\pi}
$$ ?
The problem for me is that is has an essential singularity at origo

user4140

2:08 AM

I think it was an answer

If the person reading it followed up on it he woul dunderstand how to solve the problem

isn't that good enough to be considered an answer?

and it's not like i'm telling him to read a book.

Alexander Gruber

2:25 AM

@user4140 well, you even said in the comment that you "didn't think we should answer all stars and bars problems" which to me says you don't think it's an answer either

user4140

that was a mistake.

I meant we shouldn't tailor make a solution to each problem in that class.

Alexander Gruber

i would say that identifying the type of problem he's dealing with might be useful information, but it would be more suitable as a comment.

it's fairly likely after all that the unit he's on is called "stars and bars" or something

if you don't want to give a full solution, you could, for example, say what the stars are and what the bars are in his problem, give him a little push towards the computation - the "Hint:" approach

user4140

I still don't see how what I wrote deserved to be deleted, I'm not mad or anything, it's just it's the first time someone deleted my stuff.

Alexander Gruber

@user4140 in retrospect, it may have been better to convert it to a comment. would you like me to do that now?

user4140

no, it's fine. Thanks though.

Joe Stavitsky

4:43 AM

An experienced bricklayer can work twice as fast as an apprentice bricklayer. After the bricklayers work together on a job for 6 h, the experienced bricklayer quits. The apprentice requires 12 more hours to finish the job. How long would it take the experienced bricklayer, working alone, to do the job?

robjohn

5:07 AM

@N3buchadnezzar I don't see any easy contour integral. It seems much easier to evaluate using real methods.

Nathan Osman

6:15 AM

Balarka Sen

7:56 AM

@zombies.

In particular, @robjohn

You there?

robjohn

8:41 AM

@BalarkaSen are zombies really ever there?

Sawarnik

9:03 AM

@robjohn You are one.

robjohn

@Sawarnik that answers nothing

Sawarnik

@robjohn are zombies really ever there? where? if here, then one exists.

Boni Tea

@Sawarnik It's plural. I think you need to find one more.

No idea who they are, since I've just joined. But that would've answered the question, yes.

Sawarnik

@BoniTea You have been a member for 1 year. Anyways, what are your mathematical interests?

Boni Tea

@Sawarnik I've been a member of StackOverflow for a year. Only just found out about this one.

And currently, learning about fractals. I like it, but I'm not sure if I want to take it futher.

Sawarnik

10:49 AM

@robjohn Can you use your moderator powers to delete answers that are worthless and have been down voted many times?

Mike

10:59 AM

@Karl You missed the E4 fight

fight(s) (there were a lot)

Karl Kronenfeld

ah, I can imagine @Mike

robjohn

12:10 PM

@Sawarnik We can, but usually we would rather have the community vote to delete (it only takes 3 people with 10K+ to close, I believe). If there are a number of flags, we will delete also.

N3buchadnezzar

@robjohn Too bad moderators can not vote as members

Eg if a moderator votes the question is automatically deleted / locked

Sawarnik

12:42 PM

@robjohn But if I give a link that is downvoted 3 times, and well is completely worthless?

Jasper Loy

12:57 PM

@Sawarnik Just let the community vote, end of story.

@robjohn You're up early!

Games Brainiac

1:40 PM

Hi there!

Antone home?

skullpatrol

Who is Antone?

Games Brainiac

Sorry, anyone :P

hehe

skullpatrol

wazzup?

Games Brainiac

I just wanted to ask, Concrete Mathematics is a great starting book for CS students, what should someone read after it?

skullpatrol

The Art of Computer Programming is good.

Games Brainiac

1:43 PM

Hmm.

All right then, will read that.

skullpatrol

blog.codinghorror.com/the-enduring-art-of-computer-programming

Kareem Mesbah

Hello, everyone!

skullpatrol

hi

Kareem Mesbah

I want to ask a two part question if you don't mind me asking

skullpatrol

askaway

Kareem Mesbah

1:52 PM

I'm newbie to discrete maths and proofs and I really like it, but, although I know the proof techniques, I still can't prove the simple problems. And by simple, I mean something like:
prove that log base 7 of n is either an integer or an irrational number where n is a positive integer

my first question: is that normal?

my second question: how do I get myself ready to prove such things and the more complex ones?

I mean, is there any sort of training or something?

skullpatrol

first answer: yes
second answer: study a good textbook :)

Boni Tea

1) Yes. 2) Know your definitions and theorems. 3) Yes, practise.

Dominic Michaelis

hi

Kareem Mesbah

@skullpatrol and @BoniTea any textbook suggestions?

skullpatrol

@KareemMesbah go to a library and see what you like.

hi

hu hu :)

Dominic Michaelis

1:57 PM

what again is the name of the inequality which says for the Lebesgue-measure of $\mathbb{R}^n$ that $$ \sqrt[n]{\mu(A+B)} \geq \sqrt[n]{\mu(A)}+\sqrt[n]{\mu(B)}$$

Boni Tea

@KareemMesbah Sorry. I haven't really studied discrete Maths in depth at all.

Kareem Mesbah

No problem. Thanks guys!

Dominic Michaelis

Brunn-Minkowski right

skullpatrol

@KareemMesbah Knuth's Concrete Mathematics is good.

Brunn–Minkowski theorem

In mathematics, the Brunn–Minkowski theorem (or Brunn–Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue measures) of compact subsets of Euclidean space. The original version of the Brunn–Minkowski theorem (Hermann Brunn 1887; Hermann Minkowski 1896) applied to convex sets; the generalization to compact nonconvex sets stated here is due to L. A. Lyusternik (1935). Statement of the theorem Let n ≥ 1 and let μ denote the Lebesgue measure on Rn. Let A and B be two nonempty compact subsets of Rn. Then the following inequality holds: :[ \mu (A + B) ]^{1/n} ...

robjohn

@Sawarnik the downvotes represent community's opinion of the answer, but to delete an answer, the community should vote to delete (needing 3 votes from 20K+) or flag moderators. There are usually cries of power abuse when a moderator performs a unilateral action when the community could have voted instead.

Kareem Mesbah

2:11 PM

@skullpatrol, I just did a search and got the same book as one of the best. Thank you!

skullpatrol

np

robjohn

@Sawarnik since it takes so much reputation to delete an answer, moderators will usually delete answers when there are a number of flags to do so.

skullpatrol

$\Huge \text{POWER ABUSE!!!}$

@robjohn like that?

robjohn

@skullpatrol $\Huge\LaTeX\text{ ABUSE!!!}$

skullpatrol

:D

Sawarnik

3:14 PM

@robjohn Your points are removed, when you delete an answer? Even after there are a number of flags on it. Ridiculous.

robjohn

@Sawarnik what do you mean? You don't get reputation for deleted answers.

Pedro Tamaroff

screen.yahoo.com/…

Sawarnik

@robjohn Umm...I worded that badly... What I meant was that is your points removed, when you remove an answer?

robjohn

@Sawarnik yes, if you remove an answer the points for that answer are also removed

@Sawarnik whose answer are you removing and how?

Sawarnik

@robjohn Oof..I am not removing an answer, I was asking you to do so. You wrote your last comment such that I understood that your points are removed. My bad....leave it.

robjohn

3:21 PM

@Sawarnik If I delete an answer as a moderator, my reputation does not get affected. The person whose answer it is loses (or gains back) the points gained (or lost) from that answer

@Sawarnik if an answer is downvoted a lot, it would be to the author's advantage to delete the answer to get back the reputation lost.

Off to the park in the rain. BBL

skullpatrol

later

Kasper

4:00 PM

almost 3000 :D

Jasper Loy

@Kasper Congrats!

I just watched The wolfman, good movie.

Boni Tea

4:13 PM

@Kasper Yes. Just need to add mine to yours.

Kasper

haha :P

no need :)

Jasper Loy

@Kasper Our names are very similar, lol.

Kasper

Yep :p

Where are you from ?

Jasper Loy

Singapore.

Kasper

ah, it is common name in holland, both kasper and jasper

I've been in singapore once

Jasper Loy

4:24 PM

Ah, Holland seems a nice place, maybe I should be reborn there my next life, lol.

Kasper

It's quite good here, yes. How is singapore ?

Jasper Loy

Not to my liking. I prefer liberal Europe.

Jasper Loy

4:41 PM

@MatsGranvik Have you made any progress towards solving RH?

Chris's sis

Greetings

Chris's sis

4:56 PM

I've not heard of Brian M. Scott since last year. Does anyone know why he isn't active on site anymore?

Mats Granvik

@JasperLoy Not really.

Ram

Hi All, I am having hard time in understanding Orientable surface. How can we say a surface is orientable or not by seeing its Singular complex?

Mike

5:16 PM

@Ram What's your def'n of orientable?

Ram

@Mike, I don't know that even. (Yesterday I saw youtube video about Klein's orientation). Unfortunately my teacher last year spent very less time on this. He said, ordering of vertices should match during identification. By which I assumed that every thing is orientable untill yesterday, I read RP2 is non orientable.

robjohn

Darn. I've got to stop answering questions after I've capped ;-)

Mike

@Ram I don't know of any definition of orientability that isn't incredibly complicated; if it's not something that was covered, that's probably for a reason.

robjohn

@Chris'ssis I heard that his leaving was not health related, but that is all I know.

Chris's sis

@robjohn I see.

Boni Tea

5:26 PM

As I understand it, if you can move a triangle on the surface but somehow landing on the other side, it's not orientable?

(I just read Wiki.)

Ram

@BoniTea, yes, but how to say that directly from Delta complex interms of ordering of edges.

@Mike, well, seems like my teacher himself not familiar with it. Such things usually happens in 3rd grade schools like mine esp in underdeveloped countries.

Mike

5:48 PM

Well, in particular, one thing that may be taken as a definition is that a surface is orientable iff its top homology (the $n$th homology for an $n$-dimensional surface) is finite and cyclic.

And you can calculate that from any simplicial complex structure on your surface.

minopret

Anyone interested to review and comment on my recent question?
https://math.stackexchange.com/questions/692167/how-to-handle-positive-difference-or-zero

Generally what happens to a question after it leaves the front page? This one of mine is possibly lame, but it's mine and it's sincere... I can spend 10% of my measly 500 points to put a bounty on it. Or I can come here and ask whether someone here would review it. Which is what I've done. Maybe I should look/ask in meta about how and whether there is provision for stuff that didn't immediately get attention.

Please note, I'm not expecting volunteers to do anything more than they wish. Just wondering whether the structure of the site is working well for us all. If so, sure, maybe I'm misunderstanding it. And if not, what might help.

Sawarnik

@minopret It is one problem that has also bugged me a lot. One thing I have noted is that choosing the tags are very important in attracting attention.

minopret

OK, I only tagged with "piecewise-linear" which is pretty rarely used. After all, if I knew what I was talking about I'd be closer to answering my question myself :-)

Looking at the last pages of Unanswered / No Answers, I see that people have frequently provided comments that were satisfactory to the asker. I suppose I could go scavenging and paste those comments into the "answer" box. :-)

Another answer for people like me might be, "Pick a good book and read it. Repeat." So OK, I'm reading Learn You a Haskell For Great Good and I have Basic Category Theory for Computer Scientists open beside it. I'll learn something some day :-)

Complex analysis

How is dimension of a manifold defined ?

Mike

how is a manifold defined?

minopret

6:05 PM

Anyway, regarding my question of what to do with expressions in sums and differences of d(m,n) = max(0, m-n), I started thinking, if I'm consider any expression in n variables, I could draw a regular n-gon and consider at each interior point p that the value of d(n_i, n_j) is n_i - n_j if p is nearer to the i-th point than to the j-th point, otherwise zero. I can play with that for a while and see whether I get some insight.

Complex analysis

@Mike I heard that its a collection of Charts , Atlases and Transition map , $(C, A , T)$

minopret

I would have, what, a Voronoi diagram.

Mike

@Complexanalysis What is a chart?

Complex analysis

@Mike Somebody said that its a homeomorphic image of some underlying space and the subset of your "going to be constructed " manifold .

Mike

That's not a definition - what's the underlying space?

Complex analysis

6:10 PM

You can take for example $\mathbb C $ or $\mathbb R^n$ etc.

Whats not the definition @Mike

Mike

OK, let's assume we're talking about a real manifold. (This is not a matter of what you can take - you take complex manifolds or real manifolds or if you run in strange circles, p-adic manifolds; but it is important to specify which one it is.)

Then every chart is homeomorphic to an open subset of $\mathbb R^n$. Agreed?

Complex analysis

i don't, because we haven't finalized what chart you are talking about ? @Mike

Mike

Where are you getting your definitions?

minopret

Maybe not regular. Maybe I break symmetry by looking at, for example, four points on the complex-plane unit circle, e^(i k pi) where k= 0, 2, 7, 10. Well, I'll go off in that direction for a while. That's all I have to say for now, I think.

Whoops, k = 0, 2/17, 7/17, 10/17. Something like that. That is all.

Complex analysis

I am trying to remember what my prof said on friday .

Mike

6:16 PM

It's best to write these down :P A definition is rigorous and not knowing exactly what it is means you can't prove anything about the objects you're defining!

Complex analysis

@Mike Ok, tell me then . I am waiting to know the definition :)

Mike

My definition of manifold is different than yours.

So I'd rather you had the one you're going to be working with.

minopret

p.s. thanks @Sawarnik

Complex analysis

shouldn't be that different i guess . @Mike

Tell me starting from what Chart is , because thats the main thing to be understood while studying manifolds i guess @Mike

Mike

No, find your definition from your professor and review it. If you have a textbook consult that.

Fernando Martin

6:21 PM

Hey @Mike

What was that song with the cool video called?

minopret

6:32 PM

@Sawarnik Well, look at that, I learned something about enumerating permutations (probably I should say automorphisms)

@Sawarnik so, maybe I should go tag my question with "permutations" or "automorphisms" or other stuff that interests more people than "piecewise-linear" does

Is there an IRC channel that would be a good place to go from here? Because I have had good fun in #haskell at freenode but I generally find it difficult to strike up conversation in stackexchange chat rooms.

Balarka Sen

6:50 PM

Genus theory is crazy.

Where is everyone??

Complex analysis

Land of Narnia

Balarka Sen

Hello! I am in Moria right now, do you have some armies to spare, Aslan?

Balarka Sen

7:16 PM

@JasperLoy A.

Studentmath

Hey Pedro

Balarka Sen

@robjohn There?

Mike

@Fernando Can you give me more of a hint than that?

Was it 'State of the Art'?

Studentmath

If anyone can tell me whether I fall into the induction trap here or not, will appreciate. I am trying to prove a lema that a directed graph G with n vertexes has a walk of the length of n iff it is a cycle. One way is easy with induction, and I doubt I fall to any induction trap here - assume G is a cycle with n vertexes, it has a walk of length n. The other side is a bit more 'dangerous'... can I approach it with induction as well? It seems to work, yet.. I am a bit uncertain.

Mike

You certainly don't need to induct for the first direction; assume G is a cycle, explicitly describe the walk.

Studentmath

7:23 PM

Point taken.

Thanks!

What about the other side, though, that worries me

r9m

why does math.stackexchange.com/questions/695343/… have (string-theory) as a tag ??

3

Mike

I see an inductive argument for the reverse direction - but it's done by contradiction. Assume G has a walk of length n+1 and is NOT a cycle...

Balarka Sen

@r9m lol

Studentmath

Why n+1?

Mike

You're going to show that G then has a walk of length n on a sub graph with n vertices - which fails by inductive hypothesis.

Studentmath

7:26 PM

Or do you mean, the last inductive step there?

Ahah, alright! Thanks, Mike!

Mike

Getting that walk on a sub graph is the hard part

Studentmath

Wait,

G could be of n+1 vertices, not be a cycle and have a walk of length n of a sub graph with n vertices - that subgraph being a cycle itself.

But not have a walk of length n+1... Right.

Do you think I could avoid that, by going with simple induction: Digraph with one vertex has a walk of length 1 iff it has a loop, i.e. is a cycle.

Assume for n

Then prove for n+1?

Or am I falling for some inductive trap, there?

Mike

first, we already proved the reverse direction

we only need to do forward now

and that's exactly what I was suggesting, I was just suggesting doing the inductive step by contradiction

Studentmath

Yes, I meant the forward part.. will try it with contradiction then, many thanks!

Should've said digraph with one vertex and a walk of length 1 is a cycle i.e. loop, then assume for n... to be clear

porton

7:49 PM

How to decide, should I make 50 points bounty or 100 points bounty?

Mike

flip a coin

@Fernando was that it?

Studentmath

Managed it mike, many thanks! Contradiction made it easier (though was still hard for me..)

Fernando Martin

8:28 PM

Hi @Mike, I was afk

Yes, that was it. Thanks!

Matthew

9:03 PM

Is deleted a question and resubmitting in an edited form to regenerate interest and get better answer, front upon?

Is deleting a question and resubmitting in an edited form to regenerate interest and get better answer, front upon?

Is deleting a question and resubmitting in an edited form(remove certain parts) to regenerate interest and get better answer, found upon?

Fernando Martin

frowned*

I think it is

Just edit your original question

Matthew

Thank you!

I really do want a proper answer,

Danny

9:23 PM

@robjohn have time to help me on some quantile question

?

JustDanyul

9:33 PM

quick question.. if I do a backwards substitution so solve a definite integral, is there any cases I can NOT solve it by adapting the limits to reflect the new variable i substituted for?

Ted Shifrin

@JustDanyul: Nope, you're fine.

JustDanyul

@TedShifrin oh dear.. i must got a error somewhere then

Ted Shifrin

Sorrrrry. :(

JustDanyul

if i replace the variable i substituted for before calculating the result, i get the correct answer.. if i dont.. I get an incorrect answer lol.

Ted Shifrin

Then you're miscalculating the new limits.

JustDanyul

9:37 PM

thats what I though! but i checked them again and again..

Ted Shifrin

What've you got?

Matthew

Still getting no answers :(

JustDanyul

does it make a difference that i did a integration by parts after i did the backwards substitution

i substituted for u=tan(x)^2 + 1

Ted Shifrin

no, but maybe you messed up evaluating at endpoints when you did integration by parts

What were your original $x$ limits and your $u$ limits?

JustDanyul

i probs shouldn't say its part of an assignment, i suppose it would be cheating if you pointed out the actual answer :D

but basically, I just put in the old limits in the formula and got my new limits, i checked them on the calculator again and again

Ted Shifrin

9:41 PM

I admire your honesty. Truly. I hope you didn't go across an asymptote of $\tan(x)$.

JustDanyul

i think they are fine, so I'll check the endpoints again. or.. just substitute back for tan and do it the long winded way, atleast i get the right result then. its just bugging me now hah

Ted Shifrin

OK ... Well, I've helped all I can, then. :)

JustDanyul

yes, thanks :) i just wanted to know if there was some exception, i was starting to confuse my self

Ted Shifrin

Howdy @Danny @Fernando

Danny

shiffy whats up

Daniel Fischer

9:45 PM

"shiffy"?

Ted Shifrin

Just finished grading homeworks and writing the solutions for the exam for the other class ... Get to go to a concert in a few hours. How're you?

Heya @Daniel

Danny

iam ok struggling with math as usual

Ted Shifrin

Well, @Danny, at least we know all is right with the world (except in Ukraine :( )

Well, and lots of other places, now that I think of it ... Never mind.

Daniel Fischer

Hey, @Ted. I've gone to your site today, download the diffgeo script (time and again I try to learn a bit of that), and saw your photo. You look young.

Fernando Martin

Hi @Ted

Ted Shifrin

9:47 PM

Thanks, @Daniel, although that pic isn't exactly new.

If I ever LaTeX all the notes for my graduate course, I'll be sure to save you a copy :P

Daniel Fischer

@TedShifrin Well. You looked young ;)

Danny

shiffy we will see what happens , i guess, thats the only thing we can do

Ted Shifrin

Yeah, that pic may have been ten years ago. Let me see if there's a more recent one I can post. The ones I took not too long ago are in a t-shirt, which doesn't seem right for the official math department pic.

Daniel Fischer

@TedShifrin Official? Make it Bowler and waistcoat.

Ted Shifrin

Hmm, nothing more recent than 2011. That was pre-cancer surgery.

Um, no, no thanks :P Maybe I'll go outside and take a newer one now.

Studentmath

9:51 PM

Hey Ted!

Ted Shifrin

hi @Studentmath.

Complex analysis

Hey @DanielFischer

How have you been ?

Daniel Fischer

Hey, @Complex.

Studentmath

Also, mike, if it might interest you, I thought of a simpler proof for the forward way, using the indegree-e(G) formula.

Daniel Fischer

Not bad.

Studentmath

9:52 PM

How's it going?

Complex analysis

@TedShifrin Hi .

@DanielFischer cool .

Ted Shifrin

Hi @Complexanalysis.

Well, @Daniel, if I change the photo out, I think you'll modify your remark to say I look old. :D

Daniel Fischer

@TedShifrin Then don't change the picture ;)

Ted Shifrin

Well, @Daniel, there are UTube videos up of all my lectures this semester, so it's not exactly a secret that I'm old :P

Complex analysis

@TedShifrin I was wondering when we could invert the limit equation ? To be more precise if i have $\lim_{n\to \infty}f(x,n)=y$ when could i say $x=\lim_{n\to \infty } f(y,n)$, i hope i am asking you something sensible .

Transcript for

$Mathematics$ Mathematics