Mathematics - 2012-11-01 (page 1 of 7)

I used to go to the mexican mathematical olympiad training sessions and they where always like. Using nesbitt this is true or. Using shebyshev this is truem, or using summation by parts bla bla bla. or using arithmetic-harmonic bla bla bla. And I was always like... WTF??

jshin47

once you get into your sophomore or maybe junior year, the professors will try to convert you to their side (algebra or analysis) and typically i think students just go towards the one they are better at, unless they are bad at both, like me :)\

Khromonkey

the hardest ones where always the problems that used muirhead and erdos-mordell

leo

there is no cure for this level os dizzyness

anon

http://www.math.uconn.edu/~kconrad/blurbs/
ftp://joshua.smcvt.edu/pub/hefferon/numbertheory/book.pdf
http://www.topologywithouttears.net/topbook.pdf
http://www.math.uiuc.edu/~hildebr/ant/
http://www-math.mit.edu/~rstan/ec/ec1.pdf

jshin47

3:50 AM

@leo, why the hell is my professor making me study finite fields.

they seem pointless

or @anon

anon

why are you asking people who are not your professor, have no knowledge of your professor or your mathematical relationship with him or her, and do not know what your mathematical aspersions are?

leo

@jshin47 $\mathbb{Z}_p$?

jshin47

@anon, that's a more philosophical ?.

Khromonkey

My math teacher told me that discrete number theory was finished and I had to learn theory of complex function and hypercurves to solve anything new

anon

more commonly $\Bbb F_p$, both to emphasize that they are fields and to distinguish from the $p$-adic integers

jshin47

3:52 AM

@leo, @anon, no, not just fields of order p.

Khromonkey

Is that true?

jshin47

I like those! they are easier to digest

I mean the ugly ones, p^m.

anon

complex analysis and hypercurves (what are those) are hardly the only areas of mathematics

Khromonkey

He meant number theory problems

leo

@anon but they are the same. don't are? I mean are there finite fields that are not isomorphic to some p-adic field?

anon

3:54 AM

surely understanding finite extensions of a field is an interesting problem to field-theoretic investigators

leo

no. Now I see

anon

@leo p-adic fields have characteristic zero and have cardinality equal to the continuum. finite fields are finite and have positive characteristic.

Khromonkey

he told me to read this book amazon.com/Theory-Functions-Complex-Variable-Second/dp/…

anon

have you studied calculus? vector calculus and complex analysis would be a good mix of analysis.

leo

@anon sorry, by $p-$adic I mean $\Bbb Z_p$. Was wrong

Khromonkey

3:56 AM

I have read Stewarts book and Berkey and Blanchards book. Im also planning to read apostols book.

anon

yes, $p$-adic does indeed mean $\Bbb Z_p$, though the latter notation is (in elementary contexts) often used for $C_p$ or $\Bbb Z/p\Bbb Z$ instead of the p-adics.

Khromonkey

I didnt read stewarts book thoroughly, only like 60 hours. But the other one took me like 140

jshin47

@anon and @leo i didnt mean to be vague, to be more specific, why are we interested in taking Traces of elements in fields of prime power order?

*why is this important / what does this do to help me do field arithmetic?

leo

but the $\Bbb Z_p$ is a finite field

math101

anyone a fan of probability?

anon

3:59 AM

the notation Z_p is only the finite field Z_p in elementary contexts; higher up you use it for the p-adic integers (which form a ring not a field btw) instead.

jshin47

@anon, Z_p is appropriate for me, since i only know it to mean cyclic of order p and nothing else at this pt

Khromonkey

thanks guys. Ill read those books starting tomorrow

leo

@anon I see, thanks for clarification

Khromonkey

good night (or day, depending where u live)

anon

@jshin47 the norm and trace allow us to define the discriminant which determines a bit of useful information about number fields. I imagine it's useful in similar ways for finite fields.

jshin47

4:05 AM

@anon i have been taught to use the trace matrix to define another basis besides a, a^2, ... a^(2^m - 1) ... but i guess my question is, what is the use of this new basis

ie if A = [a_ij], then B = A^-1 where column vectors form a basis spanning the same field

anon

then elements of the span of the basis are polynomials in a. I assume this is building up to the fact that finite fields are in fact quotients of polynomial rings over characteristic fields by irreducible polynomials, but who knows what the intended point of it is until you read on to how it's used?

jshin47

Is this kind of like a generalization of the change of basis formula? or does that just naturally apply b/c you can think of a...a^2^m -1 as a vector space?

Yes, much has been made now of the existence/uniqueness of finite fields... up until recently i thought their existence was a trivial fact but when i actually looked into it, its not quite trivial for me...

*basis for a vector space

user19161

4:49 AM

@jshin47 Nope, I don't think so. There are many types of inequalities. Contest math inequalities are quite different from analytic inequalities.

user19161

So how did your presentation go @anon?

anon

only got through 4 sections. will continue on monday.

user19161

@anon Ah, what topics did the others do? The same crazy stuff?

anon

there was only one other guy who talked and he just went over some definitions

user19161

Oh, HAHAHA.

anon

4:53 AM

I am slated to obtain a spare key to the elite conference room, after which my transformation to a bona fide instructor will be complete.

user19161

Where I was, they called some of the rooms colloquium rooms.

skullpatrol

@anon Congratulations! on your "bonafication."

user19161

They sit about 30 people only.

user19161

Me? I only give talks in MSE chat room.

user19161

Let's see what I will talk about next, maybe bananas.

user19161

4:57 AM

@jshin47 Much of mathematics is pointless, like soccer. Why do 22 people kick a ball for 90 minutes?

skullpatrol

To score a $\Huge\text{gooooal!!!!!...}$

Jayesh Badwaik

@JasperLoy If your playing Barcelona, only 11 people kick the ball, others just watch, and provide a touch in between, much like spectators throwing the ball in when it goes out of play.

leo

@JasperLoy It's nice, have you seen Messi?

user19161

@JayeshBadwaik I usually don't play with the ball, I only play with my balls.

Jayesh Badwaik

@leo Did you read my comment?

skullpatrol

5:04 AM

BTW Happy Halloween.... Boo!!!

user19161

@leo No, who is Messi, a soccer player?

user19161

@skullpatrol Boo!

leo

@JayeshBadwaik Yes :-)

@JasperLoy yes :-)

user19161

@jayesh I think it is a score and not a goal, but there's no easy way to take matters further. =)

Jayesh Badwaik

@JasperLoy Football player.

@JasperLoy A goal is a goal is a goal. You score a goal.

user19161

5:09 AM

Hey @wj32 it is so interesting that you are always commenting on my answers.

Jayesh Badwaik

@JasperLoy ohh. that's nice. :-)

wj32

@JasperLoy: what does "always" mean?

user19161

@wj32 a few times

wj32

I agree, very interesting

skullpatrol

He set the world record for most goals scored in a season during the 2011–12 season, with 73 goals.

user19161

5:11 AM

And thanks @wj32 you save me the trouble of explaining further to the op

wj32

you're welcome :)

Jayesh Badwaik

@skullpatrol I wish I could bother about it, frankly, bored of the Barcelona style now. Okay, I agree, its a really good style, but there must be some way to beat it, without playing in the same boring tiki-tiki taka-taka fashion (heavy counter-attack?) I want teams to start kicking Barcelona's ass on counter-attacks. Their (barcelona's) style seems to me the passive-aggresive shit. Cloak and dagger, wolf in sheep's clothing etc etc

user19161

anyway i think i will type like that now and look like a retard

user19161

it saves a few movements of the fingers

user19161

ah today is my friend's birthday

user19161

5:17 AM

@Khromonkey That is three volumes from the Russian edition rolled into one.

skullpatrol

@JayeshBadwaik "The Maradona and Pelé polemics will end."

user19161

@jay Diwali is this month eh? Perhaps Krishna will descend and destroy my inner demons =)

user19161

@skullpatrol m and p stand for madre and padre =)

skullpatrol

@JasperLoy Only you can destroy YOUR inner demons.

user19161

@kahen you seem to be flying in and out of chat frequently these days, and you are still deep in thought from your pic

user19161

5:21 AM

@skullpatrol depends on what kinds, some are too powerful

skullpatrol

@JasperLoy Well, then you must work on making yourself stronger :)

user19161

@skullpatrol indeed, but i just want to point out a line in lord of the rings, frodo says at the end of the last movie, some wounds are too deep to mend, but yes i get your point

user19161

@skullpatrol thanks skullie, it is raining heavily here now, very beautiful

leo

5:41 AM

I have an algorithm to choose the best combination here

do you think is worth post an answer?

the angles and lengths of segments are given arbitrary, so answer o the question "Which ordering of the angles and lengths maximizes the distance between the two endpoints of the chain of segments?" is quite rare

of course the answer is take all combinations, measure all distances, take the max of them, its associated combination works

user19161

6:02 AM

Not a real question. math.stackexchange.com/questions/226575/…

Jayesh Badwaik

@skullpatrol As much as Messi is great, he has not been able to win the games single-handedly. He cannot even take the game by the scruff of its neck, unlike Cristiano Ronaldo, the olden golden Ronaldo, Zidane or even Maradona himself.

@JasperLoy Yup. Diwali is this month, it is actually the celebration of Ram (Another incarnation of vishnu, krishna being one himself). returning to his hometown of Ayodhya after defeating and killing Ravana.

skullpatrol

@JayeshBadwaik In my opinion, his records speak for themselves.

hi @robjohn

56 mins ago, by skullpatrol

He set the world record for most goals scored in a season during the 2011–12 season, with 73 goals.

robjohn

@skullpatrol Hey there... my wireless router keeps flaking out.

skullpatrol

@robjohn Mine too...

user19161

Just answered two low fruits...

skullpatrol

6:10 AM

Where are they hanging?

user19161

Hanging from skullpatrol's banana tree.

skullpatrol

LOL

user19161

Hey it is so exciting to answer, come back after a few hours and see if you have gotten ten points. If so you feel great, if not then sad panda. =)

skullpatrol

@robjohn How did you do this? ¿uʍop-ǝpısdn ǝdʎʇ noʎ uɐɔ ʇnq

user19161

As usual I delete my answers if it does not receive any upvotes after 24 hours.

robjohn

6:14 AM

@skullpatrol ¿uʍop-ǝpısdn ǝdʎʇ noʎ ʇ,uɐↃ ¿ʎɥM

user19161

@skullpatrol You just need to flip your computer over and then type, duh.

user19161

HAHAHAHA.

user19161

Nowdays only I laugh at what I say. =)

robjohn

@skullpatrol ˙˙˙uʍop-ǝpısdn doʇdɐʃ ʎɯ uɹnʇ ʇsnɾ I

skullpatrol

@robjohn I am trying that right now ...

robjohn

6:16 AM

@skullpatrol Visit the bottom of the world

user19161

@robjohn Cheating!

user19161

@anon Is this some kind of a weekly seminar?

robjohn

@JasperLoy Cheating?

user19161

@robjohn I am one of the few who don't bother formatting links.

skullpatrol

@robjohn ◖-: ʞuıʃ ǝɥʇ ɹoɟ sʞuɐɥʇ

user19161

6:20 AM

It is really strange that people post questions here and then delete most of the post, probably to escape detection by the prof.

user19161

It is quite absurd that a teacher trainer here once said that the empty set is equal to the set containing the empty set.

robjohn

@JasperLoy That is !

user19161

Clearly, one is empty and the other is not empty.

skullpatrol

@robjohn )8< ǝɹɐnbs uɐǝɯ uʍop ǝpısdn

user19161

@robjohn I am sick and tired of people claiming that the standards of math education here are high, because it is not.

robjohn

6:22 AM

@JasperLoy No, 0 is empty and 1 contains 0...

user19161

@robjohn What a joke, man!

skullpatrol

)8<

>8(

user19161

You know how students here top international tests? By doing hundreds of problems without understanding a shit about what is going on.

user19161

In fact, I am not sure if the teachers know what is going on either.

skullpatrol

Memorize and regurgitate .

user19161

6:25 AM

@skullpatrol Rinse and repeat!

skullpatrol

In math you don't understand anything you just get used to it.

user19161

Oh, anon has left, sad panda.

user19161

Over and out!

robjohn

@JasperLoy You are aware of the basic definitions of the integers, right?

user19161

@robjohn Yes, I know, hence I understood your joke.

robjohn

6:32 AM

@JasperLoy okay... just wanted to make sure :-)

@JasperLoy Ha! I have been left in charge of the room! >8(

›8( not much better than >8(

@skullpatrol that seems a bit cynical. At least I think I understand some things.

skullpatrol

@robjohn I don't agree with the quotation either :)

robjohn

@skullpatrol Why did you say it, then?

skullpatrol

20 mins ago, by Jasper Loy

You know how students here top international tests? By doing hundreds of problems without understanding a shit about what is going on.

If students can get top marks by memorizing and regurgitating in math, why understand?

26 mins ago, by Jasper Loy

In fact, I am not sure if the teachers know what is going on either.

@robjohn Is your wireless router still flaking out?

skullpatrol

7:09 AM

I think it was Feynman who said "Know how to solve every problem that has been solved."

user19161

@robjohn Actually, there is nothing to take care of!

skullpatrol

@JasperLoy I will take care of you "bro."

user19161

@skullpatrol No need to use "bro", just use bro, there is no difference really.

skullpatrol

@JasperLoy To me there is :)

user19161

@skullpatrol What is the difference? Don't we all use these terms dramatically on the internet?

skullpatrol

7:14 AM

@JasperLoy I do not include myself with the drama of the all.

user19161

@skullpatrol OK but just to point out, when I use bro it is dramatic but not insincere.

user19161

Of course, I speak for myself only.

skullpatrol

@JasperLoy OK

I despise insincerity.

user19161

So do I as you should know by now.

skullpatrol

That is a hard thing to know of on the internet.

robjohn

7:22 AM

@skullpatrol Not right now. I just backed up the settings so that I can move to a new router (I have a new one, I have just never switched them).

@JasperLoy Did I say that I was going to take care of anything?

user19161

@skullpatrol What you say is true. But I am now telling you that I am so.

skullpatrol

@robjohn You said you were going to charge something :-D

@JasperLoy "Telling" or "selling"?

user19161

@skullpatrol Telling.

user19161

And yes, I have met many assholes to know who could possibly be one.

skullpatrol

@JasperLoy Time can only tell that.

user19161

7:27 AM

@skullpatrol Rather, only time can tell that.

user19161

Order matters. Words are not commutative.

robjohn

@skullpatrol I have been left in charge of the room! Though I could charge a rhino with my credit card (the rhino would probably win and not have any more charge).

user19161

@robjohn Anyway what privileges does a room owner have?

robjohn

@JasperLoy Not much.

user19161

@robjohn Which really makes it quite pointless.

user19161

7:29 AM

Perhaps anon should be decommissioned.

robjohn

@JasperLoy There are some small things, like room settings.

@JasperLoy why?

user19161

@robjohn Hehe, which are invariant over time.

user19161

@robjohn Just because the privileges are an epsilon? =)

skullpatrol

He has earned my respect by accepting the commission from the previous owner.

robjohn

@JasperLoy Well, I did set the feed to show new questions, but changed it back.

user19161

7:31 AM

@robjohn Why not show the feed?

robjohn

@JasperLoy It was more spam than anything else.

user19161

@robjohn Are you referring to the question being displayed here? If you see how it is done in ELU room, it is just a dropdown.

user19161

The dropdown does not distract actually, at least for me.

user19161

But if it autoexpands, it is not good.

robjohn

@JasperLoy It is, and I did set it that way. People found it more of an annoyance than a help.

user19161

7:35 AM

Hey @skull the things you say are pretty harmless, no need to remove half of them.

user19161

@robjohn Hmm OK then. Different norms in an infinite-dimensional Banach space!

skullpatrol

@JasperLoy But then I wouldn't be skullpatrol :-D

hi @Pragabhava @wj32

wj32

hi

user19161

You know what @skull? I think I am gonna stop using bro now like you.

skullpatrol

@JasperLoy Good.

N3buchadnezzar

7:39 AM

@JasperLoy Yo bro

user19161

@skullpatrol So as not to be taken to be insincere. =)

user19161

@N3buchadnezzar Hello sis!

skullpatrol

LOL

If he replies by calling you "sis" we may have an issue ;-)

user19161

@skullpatrol What issue? An issue of blood as in the bible? That means menstruation.

N3buchadnezzar

Half sis, half bro, he is Jasper joy!

robjohn

7:42 AM

@JasperLoy or a child

user19161

@N3buchadnezzar Geezis.

skullpatrol

@N3buchadnezzar Good answer.

user19161

@N3buchadnezzar By the way, I am straight, in case you forgot.

robjohn

@JasperLoy I think he is talking more about physical than mental :-D

user19161

@robjohn Oh OK. Yes, I like to look like Justin Bieber!

robjohn

7:45 AM

@JasperLoy Then there is no problem ...

skullpatrol

@robjohn Were you talking about mental?

user19161

@skullpatrol I think that was physical.

robjohn

@skullpatrol no, that was about physical

user19161

Childbirth.

N3buchadnezzar

@JasperLoy You had too many of those? ;)

user19161

7:47 AM

@N3buchadnezzar Yes, my children are all in my underwear, don't you know?

skullpatrol

@JasperLoy Do you have any siblings?

N3buchadnezzar

The pope!

robjohn

@wj32 hey there. Sorry, I didn't mean to ignore :-)

user19161

@skullpatrol No, and I live with my mum only now.

robjohn

@JasperLoy The twins?

user19161

7:49 AM

@robjohn Yes, that is my first thought, though it could also mean something else.

robjohn

@JasperLoy But that might alert Child Services...

user19161

@robjohn Oh no, not that meaning!

N3buchadnezzar

Sigh

Anyonone familiar with the jordan canonical form of a square matrice?

skullpatrol

@robjohn have you read this?
Richard Feynman, the late Nobel Laureate in physics, was once asked by a Caltech faculty member to explain why spin one-half particles obey Fermi Dirac statistics. Rising to the challenge, he said, "I'll prepare a freshman lecture on it." But a few days later he told the faculty member, "You know, I couldn't do it. I couldn't reduce it to the freshman level. That means we really don't understand it."

Can the same be said of mathematics?

robjohn

@skullpatrol I think that there are some things that cannot be brought down to an undergraduate level. Otherwise, there is no reason for graduate level math.

user19161

7:55 AM

@N3buchadnezzar The singular form is matrix, and the plural form is matrices.

user19161

@skullpatrol Some things may just have too many prerequisites.

robjohn

@N3buchadnezzar $\begin{bmatrix}\lambda&1\\0&\lambda\end{bmatrix}$ no, why do you ask?

N3buchadnezzar

I am supposed to find it for a couple of matrices, but I have missed the lectures on it. Everything I read online is greek to me about it..

robjohn

@N3buchadnezzar Do you know how to find the eigenvalues?

Transcript for

$Mathematics$ Mathematics