Mathematics - 2014-04-16 (page 5 of 5)

@GabrielR. The thing about his books is that one needs to read several of them. For example, one needs to read undergrad algebra, algebra for abstract algebra and intro to linear algebra, linear algebra for linear algebra, and they all overlap greatly

Gabriel R.

@PedroTamaroff the algebra book is part of Springer GTM right ?

Will Hunting

@GabrielR. Yes, it is

Gabriel R.

wow 900 pages...

robjohn

10:21 PM

@WillHunting orange and blue are the colors of the chat?

Daniel Fischer

@GabrielR. Mine is Addison-Wesley. Did Springer buy them?

Will Hunting

@robjohn Yes, your own lines show in blue and pings show in orange

@DanielFischer The latest edition is Springer

@DanielFischer Before Lang died, he made sure all his books are Springer

robjohn

@WillHunting ah, those are the only custom colors for each site?

Daniel Fischer

Ah. Well, showing my age here.

Will Hunting

@robjohn Well, different chat rooms have different colours

robjohn

10:23 PM

@WillHunting yes, thus calling them custom :-)

Gabriel R.

@DanielFischer third edition is GTM Springer and it is said "this title was previously published by addison-wesley 1993

Pedro Tamaroff

@GabrielR. Yes.

Will Hunting

@DanielFischer I must say the Addison Wesley version looks nicer in print

Pedro Tamaroff

But it isn't a book to read all at once.

It has a lot of material!

Will Hunting

@PedroTamaroff It is actually what needs to be covered in a one year grad algebra course, though you will need to go terribly fast

Daniel Fischer

10:24 PM

@GabrielR. That's when I bought it.

Gabriel R.

Foreword: "The present book is meant as a basic text for a one-year course in algebra" This can't be true, unless you study only algebra itself

Will Hunting

@DanielFischer I think the 3 volumes by Cohn is superior to Lang's book

@GabrielR. Well, much of it is meant to be revision of undergrad material

Daniel Fischer

@WillHunting That may be. But I've never heard of it.

r9m

@Chris'ssis aha .. use of $\frac{1}{a} = \frac{1}{a+1} + \frac{1}{a(a+1)}$ .. makes sense :) .. but you saw through that immediately .. awesome :) (y)

Will Hunting

@DanielFischer Yes, it is very sad that Cohn's books are dead. They are Classic Algebra, Basic Algebra and Further Algebra, hardbacks terribly expensive, but I got them

Gabriel R.

10:28 PM

@DanielFischer what do you think of Lang's Complex Analysis ?

Will Hunting

@GabrielR. It's strange that many complex analysis books prove little picard but not big picard

Daniel Fischer

@GabrielR. I haven't looked at it.

Gabriel R.

ahh which complex analysis do you recommend anyway @DanielFischer

Daniel Fischer

@GabrielR. One-dimensional, or Several Complex Variables?

Gabriel R.

@DanielFischer One is enough for a beginner I guess :P

Will Hunting

10:31 PM

@GabrielR. Rao's Complex Analysis is cheap, thin and covers lots of material

Daniel Fischer

@GabrielR. For beginning, Fischer/Lieb is good, Remmert too. And lots of books I don't know. Then a bit later, also read Ahlfors and Rudin.

Will Hunting

@DanielFischer Both Ahlfors and Rudin omit big picard lol

Daniel Fischer

@WillHunting But they have a lot of other stuff that isn't (always) covered in other books, and offer a different viewpoint.

Will Hunting

@DanielFischer Yes, so in the end we need to get many books and the publishers make a lot of money lol

@JessicaK is very quiet

JessicaK

I don't want to interrupt

Daniel Fischer

10:35 PM

@WillHunting Actually, they don't make so much money from it. Except the really expensive books.

Will Hunting

@DanielFischer Ahlfors hardback is 200USD, nuts

The great anon has appeared

Hi @seaturtles

Gabriel R.

@DanielFischer Russians are undermining their business lol

Daniel Fischer

@WillHunting Holy wow. My paperback cost about forty Marks way back when.

JessicaK

I liked reading through Gamelin. Silverman has a Doverbook you can buy for about $15 so the price is right at least

Will Hunting

@DanielFischer The paperbacks on abebooks.com are still very very cheap, but I prefer hardbacks now

user127001

10:36 PM

Hi @will

Will Hunting

@user127001 Hey Bart

@JessicaK Yes, Gamelin has lots of material, but his style is a bit informal to me

sea turtles

@WillHunting hi

Will Hunting

@JessicaK I see you have many complex analysis questions on your user profile

JessicaK

@WillHunting

opps

Will Hunting

Relax

JessicaK

10:40 PM

I was actually about to write another one for a reference request, but I am waffling on whether or not I can just find a source myself

Will Hunting

@user127001 Your username is killing me

@JessicaK Ah, what do you need?

sea turtles

@WillHunting it's the universal local ip address: 127.0.0.1

themoreyouknow

JessicaK

@WillHunting I am trying to figure out how the contour integral representations of $\Gamma(z)$ and $1/\Gamma(z)$ are used in fractional differential equations

Will Hunting

@JessicaK Ah, I don't know about that

user127001

@will give me a cool username

sea turtles

10:43 PM

complex analysis gives integral derivatives in terms of contour integrals in such a way that fractional derivatives can be obtained by replacing the parameters appropriately in the integrals

@user127001 chill, ice, frost, snow

user127001

@sea no

sea turtles

they are all very cool

user127001

cooler

r9m

liquid $N_2$

Will Hunting

@user127001 I think you can call yourself Bart Simpson or Peter Parker, since you are Bart Parker

user127001

10:44 PM

@will you know Peter Parker is pretty much dead right

(spoilers)

Will Hunting

@user127001 I don't know, I am gonna watch Spider-man 2 soon

user127001

@will in the main canon of the comics he is pretty dead

Will Hunting

@user127001 I really enjoyed The Amazing Spider-man movie, that kid looks like Ethan lol

user127001

@will who is Ethan

JessicaK

@seaturtles That actually helps me a lot. Thank you.

user127001

10:46 PM

@will are you cheating on me

Will Hunting

@user127001 A user here

@user127001 lol

user127001

@will I don't know many users since I am a newbie

Pedro Tamaroff

@seaturtles Yello.

sea turtles

ello

Pedro Tamaroff

@seaturtles How is it going?

Will Hunting

10:48 PM

@JessicaK You should come to this chat more often. We are all nuts here.

user127001

@will I am a fruit

Will Hunting

@user127001 What fruit? I am a banana

sea turtles

@PedroTamaroff pretty good

user127001

@will I thought you are a nut

@will banana nut?

Will Hunting

@user127001 I can be both

Pedro Tamaroff

10:49 PM

@seaturtles cool

Will Hunting

@PedroTamaroff Are you ahead of all your classmates in terms of math?

user127001

@will I am 3 years behind all my classmates

Pedro Tamaroff

@WillHunting I don't know.

Will Hunting

@user127001 Well, it's OK, you are different. So am I, lol

Enjoys Math

that's IA

Will Hunting

10:54 PM

@EnjoysMath You seem to be a question generating machine, lol

Enjoys Math

Say you have a sequence of sets $X_0 \subset \dots = X$ Then is there a computable way to map $x \in X$ to the smallest $X_i$ containing it?

Mike

there are plenty of those

Enjoys Math

Like?

I'm dumb

Mike

it's the question answering machines that are hard to come by

Will Hunting

@mike can attack all the hhf, I attack the lhf

Enjoys Math

10:55 PM

math.stackexchange.com/questions/756986/… @Mike

it's probably lhf for you

last lemma

it would be if I died right now

Mike

I dunno anything about complexity theory

I didn't mean there are plenty of computable ways of whatever , I meant plenty of question asking machines :P

Enjoys Math

Big O notation

In mathematics, big O notation describes the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann–Landau notation (after Edmund Landau and Paul Bachmann), or asymptotic notation. In computer science, big O notation is used to classify algorithms by how they respond (e.g., in their processing time or working space requirements) to changes in input size. In analytic number theory, it is used to estimate the "error commi...

Mike, that's all you need to know to understand my post

Will Hunting

The big O, lol

Enjoys Math

:O

Mike

but I don't wanna understand it ;P

Will Hunting

10:59 PM

@EnjoysMath Did you just have a big O?

Enjoys Math

how did you no?

Will Hunting

Your spelling is terrible

Enjoys Math

no urs is!

Will Hunting

I have never seen or used the big O in my entire undergrad, lol

Enjoys Math

Um, it's for CS I guess

^_^

whoooo

Will Hunting

11:02 PM

OMG

Enjoys Math

it's nice to take my plant medicine

Will Hunting

@EnjoysMath What are you taking?

Enjoys Math

plant medicine bro, it's the latest thing since the dinosaurs

Will Hunting

Oh dear, you are nuts, like everyone here

Enjoys Math

You're Good Will Hunting, boy. That's great. Are you going to psychoanalyze all us now?

It's Huntin' season will

:D

Will Hunting

11:05 PM

Are you a programmer @EnjoysMath?

Enjoys Math

y?

Will Hunting

Just making small talk

Enjoys Math

lol nice pun

user127001

lol

Enjoys Math

Small Talk (tm) is a prog lang

Will Hunting

11:07 PM

I didn't know that

So I wasn't making a pun

Enjoys Math

you sick punny bastard

Will Hunting

I am quite bad at puns

user127001

Nice pun @will

You made another one

Will Hunting

@user127001 No, not a pun, lol

user127001

lol nice

Another one

Enjoys Math

11:08 PM

Sounds like something the gestapo would ask... are u ein programmerenskraft!!!

Will Hunting

Why is nobody else talking except us?

Enjoys Math

:D

Will Hunting

Are we too talkative?

user127001

I broke up with my non-existent girlfriend

I am too sad to talk

Enjoys Math

ok, work on dis den:

0

Q: All my notes together on $\Bbb{Z}_p$-theoretic comp. complexity theory.

Def 1. A $\Bbb{Z_p}^k$-machine is a theoretical computer with $k$ data memory slots and $p$ is a prime number. All the operations on the machine are done one at a time in the ring $\Bbb{Z}_p$. No self-modifying code is allowed meaning we cannot change the specification of an algorithm on the ma...

Will Hunting

11:09 PM

@user127001 You can find a new one then

user127001

It's difficult @will

Will Hunting

@user127001 okcupid.com

Enjoys Math

shit don't work bro

user127001

@will I've been trying that site

I sent over 300 messages so far and I haven't gotten any responses

Will Hunting

@user127001 Good eh?

@user127001 Did you put up a pic? You need a pic

user127001

11:11 PM

@will Yes, but I am quite unattractive

I put up 3

Will Hunting

@user127001 OK, you need to say good things about yourself in your profile

Enjoys Math

do something funny in the photos

user127001

@will but that would be lying and I don't think it'd work out in the long run

Will Hunting

@user127001 I mean, say the truth in a positive manner, don't lie

Enjoys Math

live hen photo bomb okcupid profile image?

user127001

11:12 PM

@will That's a difficult task I guess

Will Hunting

@user127001 300 is a lot

user127001

@will Is it

Will Hunting

@user127001 Yes, you messaged 300 girls?

user127001

Yes @will I only know that number because I reached the maximum and had to delete some

So I know for a fact it's over that

Will Hunting

@user127001 You should narrow down to fewer people, 30 is enough

user127001

11:14 PM

Yea but nobody is replying

Will Hunting

Awww

Ian Mateus

@Chris'ssis hello, have you found this one by using $\sum_{k\geqslant 1} \frac{|z|^k\sin(k\alpha)}{k}=\Im \operatorname{Log}\left(\frac{1}{1-z}\right)$ for $z=|z| e^{i\alpha}$? If not, I'd like to see your way.

Will Hunting

@user127001 I am going to bed, good night

Chris's sis

@IanMateus No, I only used real tools. OK, I'll show you as soon as I put things in latex.

user127001

Bye @will

sea turtles

11:18 PM

apparently spoilers can't hide colored latex

I am disappoint

Ian Mateus

@Chris'ssis Ok :-)

Chris's sis

@IanMateus You'd love my way. ;)

Ian Mateus

@Chris'ssis A rough sketch is ok, I'd like to work a bit on it

Karl Kronenfeld

@seaturtles Toggle may be an alternative. See here meta.math.stackexchange.com/a/13259/67848

Chris's sis

@IanMateus Then you may use my work in other solution, more exactly the identity I proved and employed here (by the way, that question is a very nice question as well)

@IanMateus I think you may figure out alone what you have to do further. ;) Did you take it?

Ian Mateus

11:27 PM

@Chris'ssis yeah, integrate them all.

Chris's sis

@IanMateus Right. ;)

sea turtles

@KarlKronenfeld sweet

Ian Mateus

@Chris'ssis I used a multiple integration trick sometimes to evaluate some related sums (in terms of $\zeta(2k)$). In retrospect, I believe Cauchy's integration formula could have save me a lot of time. I think Fourier might be involved too, I'll revisit this procedure someday.

Chris's sis

@IanMateus It's helpful to be aware of all these tools and use them all when needed. I like to always come up with more solutions for each question.

Karl Kronenfeld

@seaturtles $\require{action}\toggle{\text{Cool stuff indeed}}{\text{No really}}\endtoggle$

Enjoys Math

11:51 PM

How do you specify a sequence of subsets $X_0 \subset X_1 \subset \dots = X$ that's not necessarily countable?

Is it always countable?

sea turtles

@EnjoysMath let $I$ be a (linearly / partially / ...) ordered set, $(X_I)_{i\in I}$ a collection of sets satisfying $i\le j\implies X_i\subseteq X_j$, and $\bigcup_{i\in I}X_i=X$. if $I$ is directed (every pair of indices have an upper bound) then we can simply call $(X_i){i\in I}$ a "directed system" for expositional expedience

Transcript for

$Mathematics$ Mathematics