Mathematics - 2012-06-23 (page 4 of 6)

BenjaLim

13:00

@Limitless commutative algebra is a field of maths I believe

but I think we have commutative algebra

and non-commutative algebra

one studies rings that are commutative

the other those that are not

Limitless

Oooh.

BenjaLim

and non-commutative algebra is important too

Limitless

It's a distinction between the objects.

BenjaLim

because matrix rings and such are usually not commutative

yes

and in non-commutative rings

you have to distinguish between left and right modules

in commutative algebra there is no problem like that :D

Limitless

Sorry, I was thinking of something about how there are different algebras...

BenjaLim

13:02

@Limitless There is an algebraic object called an $R$ - algebra.

That's how we define field extensions :D

Limitless

So commutative algebra is a bit more elegant.

BenjaLim

well

Limitless

Or, maybe I should say, easier to work with.

BenjaLim

that's what you use for algebraic geometry and algebraic number theory

I don't know much algebraic number theory

But I believe most of the rings you deal with in there are built out of $\Bbb{Q}$ and $\Bbb{Z}$

Limitless

This is so neat.

BenjaLim

13:04

$\Bbb{Z}[\zeta_n]$ is the integral closure of $\Bbb{Z}$ in $\Bbb{Q}(\zeta_n)$

Limitless

Every day I seem to discover more and more vastness in mathematics.

BenjaLim

@Limitless If I may use some profanities

Limitless

I don't mind.

BenjaLim

the way I like to put it is

THERE IS A FUCK TON OF SHIT OUT THERE

Limitless

LOL.

BenjaLim

13:04

Like for example

At one point when I was doing commutative algebra

I felt shit was so deep I was not able to handle it

actually that point was when I was tackling the direct limit :D

Limitless

I can imagine.

It's... bewildering, really.

BenjaLim

@Limitless Commutative algebra changed my view of maths

Invoking universal properties

Limitless

I basically decided to attempt to learn Abstract Algebra over the summer. It has wowed me in so many ways.

BenjaLim

and if course

establishing tons of isomorphisms

all over the place

Limitless

I love isomorphisms!

BenjaLim

13:07

Millions of diagrams

Limitless

They are so cool.

BenjaLim

not the usual check injective, surjective shit

but the real shit

Limitless

What do you mean?

BenjaLim

using a diagram chase and stuff

Limitless

I haven't seen that before.

BenjaLim

13:08

@Limitless You should learn how to diagram chase in the future :D

Commutative diagram

In mathematics, and especially in category theory, a commutative diagram is a diagram of objects (also known as vertices) and morphisms (also known as arrows or edges) such that all directed paths in the diagram with the same start and endpoints lead to the same result by composition. Commutative diagrams play the role in category theory that equations play in algebra (see Barr-Wells, Section 1.7). Note that a diagram may not be commutative, i.e. the composition of different paths in the diagram may not give the same result. For clarification, phrases like "this commutative diagram" or "th...

Limitless

I really love math now.

I just liked math before--it was a nice hobby. I now love it, because I feel like I am finally doing actual math.

Zhen Lin

@BenjaLim You seem to still be stoned... :p

BenjaLim

@Limitless Get the basics right first son

@ZhenLin Why da ya say that?

Limitless

I definitely am trying.

I've been working in Algebra by B.L. van der Waerden.

It is difficult.

BenjaLim

@Limitless ditch that book

Limitless

13:11

Why?

BenjaLim

do dummit and foote

for one van der waerden's book is a little dated

I used it for my galois theory exam

Limitless

Yeah, I know der waerden's book is dated.

BenjaLim

@Limitless My algebra lecturer who is now an arithmetic geometer said that he was basically trained using that book

@Limitless You want a more "modern" treatment of the subject

Limitless

..."arithmetic geometer"?

BenjaLim

@Limitless yes

Limitless

13:12

I've never heard that term before...

BenjaLim

quomodocumque.wordpress.com/2007/09/25/…

Eugene

@BenjaLim ellenberg huh.

BenjaLim

@Eugene what?

Eugene

@BenjaLim ellenberg's blog

BenjaLim

yes

@Limitless that's another thing I wanted to tell you :D

@Eugene I want to his talk that day

That was when I learned the notation for homology and cohomology groups

Zhen Lin

13:15

You mean $\pi_0 \mathbf{H}(X, \mathbf{B} G)$? :p

Limitless

@BenjaLim, I think I am going to follow up with a modern treatment. I like B.L.'s work because it gives me a sense of what things were like during that time.

Eugene

@BenjaLim yes. he teaches at where i went to do my undergrad. very good at what he does

Limitless

I like some of his ways of proving and showing things, too.

BenjaLim

@ZhenLin No how one is written $H^1$ and another $H_1$

@Eugene I am talking about jim borger

lemiller.net/witt

Limitless

@BenjaLim, do you think that Dummit and Foote treat Abstract Algebra better than Michael Artin does?

BenjaLim

13:18

that book is fucking nonsense

the proof of the cayley hamilton theorem in there is not even rigorous

I can prove that every matrix is diagonalisable using that proof

Limitless

Oh wow, it's that bad?

BenjaLim

@Limitless We used that for Algebra I the semester before. Ditch it.

Limitless

I haven't even looked at it yet. I was curious if I should. I'll definitely avoid it now.

BenjaLim

for example

to make the idea of continuity rigorous and convergence

we need to define a matrix norm

in artin nothing like that is defined

and the rest of the chapters before are shit

Limitless

I'll put Dummit and Foote on my list for reading right after I finish Algebra Vol I.

BenjaLim

13:24

@Limitless Let me tell you something

I realised myself that I have the tendency to go

oh I need to do this first before doing this

and before doing this thing I need to do that thing

there is no infimum

so

You want to get to the heart of the matter

as quickly as possible

and besides

it would be good to first see the modern treatment

not the other way round

Eugene

@Limitless dummit and foote is really the most comprehensive book on abstract algebra i've ever read

i still use it as a reference even today

Limitless

Hmm..

I'll see if I can get my hands on it.

Eugene

@Limitless if i had to pick one it would be between hungerford or dummit and foote

Limitless

It is awful how expensive textbooks are.

Eugene

@Limitless dummit and foote? maybe you can find an international edition of it

Limitless

13:30

Perhaps. Hm.

Eugene

i'm going back to sleep now. bye!

Limitless

Bye, Eugene.

Martin Sleziak

@BenjaLim You should better avoid using swear words. If someone flags your message, you might even get a temporary ban and we would not like that.

Maybe messages containing some words are flagged automatically - I am not sure about that.

aking1012

Guys someone is going flag-happy I think. Avoiding swearing would be a good idea. Lots of blue bubbles flag-vote bubbles doesn't make anyone happy

4

Martin Sleziak

Hm: This user has been automatically suspended for posting inappropriate content and cannot chat for 1 hour 55 minutes.

Zhen Lin

13:35

I guess my "invalid" action wasn't posted fast enough...

Martin Sleziak

@ZhenLin I've marked them invalid too.

leo

Have you seen google.com today?

Martin Sleziak

No big deal, he'll be back in 2 hours.

aking1012

To be clear I didn't validate them, but I suspect eventually someone got tired of seeing them so just started validating

Limitless

@MartinSleziak, what is your opinion of Artin's Algebra?

BenjaLim didn't recommend it.

Martin Sleziak

13:36

@Limitless I haven't read it. So I can't give any opinion on it.

Limitless

Ah.

jokerdino

Back to the bat cave @aking1012.

Limitless

@MartinSleziak, I haven't read it and I'm just now learning Abstract Algebra, so I can't entirely evaluate it for myself.

Tom Wijsman

@aking1012: Someone who got tired of them just validating them at random. If 14 flags deem necessary and some of them refer to drugs and use other offensive words over and over that's a good reason to get half of your sentences removed, on the other hand I don't know whether the two hour suspension was in place. Reading back on what remained, I don't think the suspension should have happened...

aking1012

I would ping a site-mod for that... or weigh in on this SO meta question:

3

A: Add option to declare a chat flag valid without suspension

I personally think this is horribly necessary. Allow me to provide an example: If someone has never had a flag in their life and they are trying to do the right thing with 10k+ rep on multiple sites and they call someone a troll(as was the case in my particular case), then they wind up with a 3...

@TomWijsman --^

Ivo Flipse

13:48

Seriously STOP flagging

aking1012

Is there a site mod in the room that can delete this. Evidently someone is touchier about profanity than someone else and it's not NEW comments that are getting flagged any more

J. M.

@Ivo: unfortunately some people in this room are just gorram touchy. Bleh.

aking1012

To whomever is offended -- please for the love of god -- only flag NEW statements or get up with a site mod about cleaning up the transcript

3

Limitless

I find it weird that anyone would be offended by profanity.

Ivo Flipse

Amen

Limitless

13:50

The word itself makes no sense.

J. M.

@Limitless Well, some people are touchy. However, there is such a thing as gratuitous use, and that's a different matter. Again: make yourself sound like a mathematician, not like a crusty sailor.

The bit that was flagged was nothing particularly egregious so: can it, buddy.

Limitless

"Don't make me send you off the Arrrrrrrrrgand plank!"

Jokes aside...

I wasn't aware the flags were for things other than the use of profanity. In that case, I can understand why someone would be offended.

BenjaLim

I am not suspended anymore?????

What happened?

who removed the suspension???

J. M.

@BenjaLim I undid it out of spite.

2

BenjaLim

@Limitless I wasn't even insulting anyone

@JM Out of spite?

J. M.

13:55

@BenjaLim Exactly. But still, let's be more careful, eh?

BenjaLim

I was trying to add extra juice to what I said

@JM Ok :D

Limitless

@BenjaLim, I'm aware. I wasn't offended by anything you said. But I can kind of understand why people would not want certain things mentioned.

J. M.

@BenjaLim I'm annoyed at the people who flagged and subsequently validated those flags.

Limitless

@JM, I like you.

J. M.

Hence, "out of spite".

BenjaLim

13:56

@Person that Flagged: If you can't even take words like that, grow up for god's sake

J. M.

@BenjaLim Let it go. Not worth it.

Tom Wijsman

Here are Balpha's words on it:

J. M.

Just be careful next time.

Tom Wijsman

BenjaLim

I wasn't even insulting anyone

@TomWijsman

I said those words out of passion

Nothing more

J. M.

13:57

@BenjaLim We get that. Relax. You're free now.

aking1012

@JM @JM - Thanks for being on this.

Martin Sleziak

Maybe Dummit and Foote are in this room.

BenjaLim

In fact that person that flagged should have felt inspired by the passion

@MartinSleziak hahahaha

Tom Wijsman

@BenjaLim: I didn't contribute towards the suspension.

BenjaLim

@TomWijsman I know

J. M.

13:58

@aking1012 Eh, this is one of my frequent haunts. It annoys me when things here erupt into needless kerfuffles.

BenjaLim

@Limitless Artin is terrible

I used it for a one semester course in general algebra

and it was terrible

@JonasTeuwen When we meet you may be stunned by the amount of profanities that I use

I am trying to cut down

Limitless

@BenjaLim, I was seeing if others agreed with you.

That's all.

BenjaLim

@Limitless dummit and foote

is so deep

Transcript for

$Mathematics$ Mathematics