it takes you all the way to homological algebra and category theory

....oh wow

That is deep...

@Limitless That puts you in good company, I'm told... :)

@Limitless Though one thing that Artin does well I think

is that

he covers a lot of material

and gives you a general understanding of the matter pretty quick

like in dummit and foote for example

you just want to get to the heart of the matter quickly

there are sometimes too many details

Have a happy day everyone. :/

@RagibZaman You should skip the continuity section

it's not rigorous

@BenjaLim Given how terrible you think Artin's Algebra is, I must admit I am somewhat saddened you didn't offer that opinion to me before you sold me that book 2 days ago.

@RagibZaman Honestly I forgot to tell you that.

I did not mean to "make a quick buck" or anything like that

Artin does have its strengths

@RagibZaman I am willing to offer a full refund if you don't think the book is good.

@RagibZaman Wait, he sold you a book that he thinks is crap? Is this right?

@BenjaLim, I am glad you're offering a full refund.

@Limitless A consolation, that.

@J.M. I'm not really sure what to say.

@RagibZaman They however do cover linear groups and things like that

@JM, I find it's... well, a confusing situation.

that dummit and foote does not cover.

@RagibZaman I am sorry that I forgot to tell you that.

@RagibZaman Perhaps I was too quick to sell it.

@BenjaLim Can you enumerate them now for Ragib's sake?

@RagibZaman Like I said

@JM One:

and what I found was good about artin was

that there was an exercise in there

Artin covers isometries, linear groups

assuming that finite subgroups of $SO_3$ exist

I haven't been through it yet but flicking through, I have enjoyed its style, layout and concrete presentation. If all of its proofs aren't rigorous then I can deal with that, I don't intend it to be my final course on the subject. So all in all, I think I'll still be happy with the book even if Ben wasn't, so it's not a big deal, we can just forget about it.

@RagibZaman That one can show that there are all in all 5 platonic solids

@RagibZaman Now that Dummit and Foote does not cover.

@RagibZaman Oh, okay then. "One man's meat..." and such, I suppose.

@RagibZaman And that I was told was by jim himself why he wanted the book.

his email is

I believe we can all collectively enjoy a glass of tea now.

[email protected]

You can ask him why he chose it

@RagibZaman You can use orbit stabiliser to classify all platonic solids

that's crazy

A little thing: Ben, Ragib, which one of you is more senior?

@JM why?

@Limitless Perhaps I went a little overboard by that one proof of cayley hamilton

@BenjaLim Just curious. If you can't or won't answer, it's fine.

@Limitless Actually to tell you the truth, I used chapter 10 of Artin for representation theory

I found that a lot easier to understand than Serre's book. @RagibZaman

@BenjaLim I can't see any reason not to answer J.M's question. Do you have any problems with it?

@JM Ragib is one year older than I am. Almost exactly.

@RagibZaman Chapter 10 does a good job at explaining the permutation representation

You will get quickly one it means to have a representation of $S_3$ say

@RagibZaman And it may be a good idea to look at it like that before full - fledged $G$ - modules and stuff

@RagibZaman Do you accept my apology; if you are not happy with Artin (I do think it was dishonest of me not to tell you) I am willing to give a full refund

Ahoy

I don't think I'll have a chance to see it in the elementary way before I learn it, next semester I'm taking Modules/Group Representations, so we will cover modules before the group reps anyway.

@BenjaLim It's okay, no apology is required. I was a little disappointed, but I doubt anything like "I'll sell him this book even though it sucks!" crossed your mind, and I'll still enjoy the book so no harm done.

I honestly feel so bad right now...

No, seriously it's fine.

@RagibZaman I'll type up a full solutions manual to the questions I gave you

@RagibZaman You should know that right now I'm a little stoned too...... :D :D

You've been on holidays for just 2 days, instead of doing that do something else lol.

@BenjaLim You're damn lucky that Ragib's forgiving... ;)

@JM We know each other too well to know that it's always maths first....

Ah, I guess it must be Christmas holidays Down Under about now... :p

@ZhenLin what???

lol

@JM I am so glad that we have like two people from math.se that frequently meet up in sydney and stuff to discuss maths. Sometimes I need help with analysis I go to ragib. Sometimes he asks me about algebra.

Gerry Myerson also lives in Sydney.

I might visit Sydney next year or the year after. The next Category Theory conference is supposed to be there...

It is nice that the community here is so rational about resolving issues.

@RagibZaman Would you like to meet up sometime to prepare for your galois theory exam

@RagibZaman How far is Macquarrie from ANU?

@JM 300km

200 or 300 Km?

@JM Canberra to sydney is about 280

Macq Uni is in Sydney, ANU in Canberra

Ben doesn't normally live in Sydney, he comes back for the hoildays.

@RagibZaman Let's go and visit gerry one day :D :D :D

@BenjaLim I must admit, I have contemplated that before, but I think it might just be a bit weird.

why not

@RagibZaman when is your galois theory exam

E-buddies: Real Life Style

Let's pawn this ****

@Limitless hahahahahahahahahhahahaha

I can't say a single thing against the idea.

The exam is on tuesday but I've seriously got this shizz, don

I've traveled to Illinois before, which is like two states away.

*don't need your help for this exam lol.

just offering

@RagibZaman Do all those questions and you're set

@Limitless That exercise on showing that there are only 5 platonic solids is rad

in artin

that was pretty pro

using orbit stabiliser

its pretty easy with some basic number theory too though

@BenjaLim, I still have yet to fully appreciate platonic solids.

I hear so much goodness about them.

And I'm like... "Meh."

@RagibZaman You will see the full power of orbit stabiliser

@Limitless same lol

what's "meh"?

Meh is like, "okay..."

Just a short saying that indicates "I dont care"

It's not fully an "I don't care", in my opinion @RagibZaman.

ah

It's more of a, "Well... I don't really know if I care."

@RagibZaman It's really cool that you can prove that there are only 5 without invoking euler's formula

@RagibZaman The one problem with Dummit and Foote is

Well it does invoke eulers formula

there is too much material

but its not too hard to derive eulers formula without orbit stabilizer

so the proof of euler's formula uses orbit stabiliser?

I think some proofs might? I don't know

lol

Wait, which Euler formula are we talking about? the one with the exponential function?

V+E-F=2

or something of that variant, i always work it out again with a cube

@RagibZaman, that one makes more sense..

@RagibZaman I always thought it was done some other way

I was kinda like, "wut, where did $e^{ix}$ come in..?"

That's the problem with things like "Euler's formula", or "Cauchy's theorem"...

@JM, I know, right?

V+F-E = 6+8-12 = 2 with a cube

...they were so prolific, you need a few more words to distinguish their results.

so its V+F-E=2, my bad

Euler has over... 105 different topics named after him.

Cauchy published every single thought he had, basically.

Re: polyhedral formula, I tend to treat it more as a graph theory theorem than anything....

It's kind of like combinatorics to me

I recall reading that Cauchy had his own sort of journal/publishing company where he wrote just about every result he could work out.. Do you recall anything like that, @JM?

@RagibZaman Next sem 240 pages on several real variables

Analysis on Manifolds?

I'm doing Differential Geometry next sem.

@RagibZaman no duistermaat and kolk

@RagibZaman I would suggest doing several variables properly first

@BenjaLim, I gave up on properly pronouncing that as soon as I got to the double a in duistermaat...

@BenjaLim In a perfect world where I have plenty of time and motivation, yes.

@RagibZaman it's really important :D

@RagibZaman inverse and implicit function theorems are the start of DG

But the holidays are only 30 days long, and I'm going through the first 9 chapters of Artin's Algebra in that time so I'll hardly have any time for a several variables course too.

@RagibZaman

YOu don't need all 9 chapters

@Limitless I forget. I believe Crelle was way after his time, so it's not that journal...

I know, I'm skipping a few

chapter 2 is grouops

3,4 on vector spaces

5 on orthogonal groups I believe

skip the cayley hamilton thingy

look at AM or something

replace "module" with vector space

and finite generated with finite dimension

lol I've done courses in linear algebra and group theory before, I've seen proofs of the Cayley Hamilton theorem already.

And I'll be seeing another one soon enough in my Modules/Group reps class.

hahahahahahahahahahahaha

that will be for an endomorphism of finitely generated modules

Forgive me if I can take the theorem on good faith until then =P.

:

The proof in AM is just matrix algebra

@RagibZaman most importantly

@RagibZaman Can't blame the theorem for having so many conceptually different proofs, y'know... ;)

read chapter 10

In due time Ben!

I'm not as quick a learner of Algebra as you.

hahahahahaha

ragib

I'm not officially enticing you over the bridge

algebra is beautiful

quit the dominated convergence theorem

The main reason I'm going through Artin's Algebra and doing Groups and Vector spaces and things like that again, is because I want some time to revise it and really "own" it, I don't feel like I've got that it.

No, you come over to MY SIDE, DCT is awesome.

@RagibZaman I am going to see Arzelà's domiinated converngece theorem

I'm gonna get off here for a bit and read some more on rings.

@RagibZaman crap I am still high from last night

@Limitless what kind of stuff?

@RagibZaman In avalon last night the cops pulled up9

was in real trouble

Hi guys!

@Limitless Like, a first course, or commutative algebra type things?

@RagibZaman, just a chapter over them. Still haven't learned ideals. First course.

Just now starting to learn abstract algebra.

@Limitless cool, enjoy it before it becomes abstract abstract algebra O.O.

lololol

Isn't that category theory?

Category theory is a level above that! lol

Oh my.

and then there is "Higher Category Theory"

What have we done...

....the intimidation! :P

It was nice chatting. I'll possibly be back later. Thanks everyone.

Cya

And then you can put it all together as "internal enriched higher category theory" :p

@RagibZaman Bye man!!!

I wonder how many people in the world know the in's and out's of "internal enriched higher category theory"

100?

@BenjaLim are you off now?

dude I need to go to bed still a little high

lol ok. do mathematics, something interesting could ensue.

Paul Erdos was constantly on methamphetamines and he managed to do a little bit of math =].

@ZhenLin Is this another one of those "turtles all the way down" sections of math?

@J.M. Do you really care/keep track of the many different proofs? I just remember the vague summary of the one I've seen: It's easy to prove for diagonalizable matricies, then one you prove we can write every matrix in Jordan normal form, it's relatively easy to show it for those forms as well.

And the only reason I managed to remember that one was because it reminds me of using density theorems in analysis.

@RagibZaman I've seen a good lot, but that proof you speak of (and the slightly fancy one involving complex analysis) are the only ones I really care about.

Factor the denominator, then partial fractions go go go!

Complex analysis?

@RagibZaman I tried with partial fraction.. seems to not work.. see this:

To prove that every matrix can be written in jordan normal form...?

whoops

of Cayley Hamilton*?

@RagibZaman No, Cayley-Hamilton. Let me see if I still have the ref somewhere...

Wow

I just googled "Cayley Hamilton with Complex analysis"

and the second link is a paper written by my assigned mentor and a student in the year above me.

@unNaturhal I think you should have $\frac{Bx+C}{x^2+1}$.

@RagibZaman Why am I not surprised it's on math.SE already...

It's a long time since I did something like that.

@J.M. Wow and that too!

Yes, Martin's right; if your denominator in the partial fraction splitting is an irreducible quadratic, your numerator ought to be linear.

@MartinSleziak Never seen before... You mean something like a double partial fraction?

@unNaturhal No, it's just part of the rules of the game for splitting into partial fractions. If your denominator is linear, your numerator ought to be constant. If your denominator's quadratic, you need a linear numerator. And if you have repeated factors, then things are somewhat more colorful...

I always though this fancy Holomorphic Function Calculus was just "Functional Analysis".

@RagibZaman It's surprisingly practical... :)

"Practical"?

I audited a Functional Analysis class this semester, it was really interesting, I've seen a lot of stuff on that Wikipedia page without realizing it was "Holomorphic Function Calculus" lol

@JM So, I have to found something linear to put in place of B?

@unNaturhal Yes, you have a $Bx+C$ over your quadratic factor. Then you figure out what $B$ and $C$ are...

@RagibZaman It turns up in applications with surprising frequency, I mean.

What kind of applications?

If I did not mess up something there. It's easier to write stuff like that on paper than in TeX.

@RagibZaman Well, functions of matrices are starting to become a bit more widespread in applications. In the absence of other more efficient methods, some of the machinery of HFC comes into play before you can apply the numerics.

People are also having fun with Banach spaces, but I haven't gotten around to looking at those particular applications, so I can't say more about them.

@J.M. I see. What "field" is this happening in?

@RagibZaman At least for the matrix functions, here is a sampler. For the purposes of my hobby, though, I'm more interested in the algorithms than in the applications...

Excellent link, thanks J.M!

Wow, applications to theoretical particle physics..

I do believe they're almost always one of the first fields that make good use of what was once thought to be too "abstract"...

They're peculiar that way. :)

I am constantly amazed at how much mathematics physicists learn to apply to their field, the amount is so deep, it's like learning heaps of Geometry when you are really interested Topology, but, 10 times more difficult.

c

@RagibZaman (BTW, you can fix typos within a short time period by pressing the up arrow key and editing. :) )

NICE!

lol

Is there also a shortcut to get the @ Tags to appear quickly? Typing them out every time is kind of a pain.

@RagibZaman Well, typing out the first few letters of the guy you want to address should bring out a popup.

Yea it does, I've noticed that which is why I ask, I can't seem to take advantage of it other than my moving my mouse over it and clicking the pop up, which takes more time than just typing the rest out

(OTOH, due to the peculiar nature of the software, I am mostly immune to pinging.)

Any particular reason? Is it just you?

@RagibZaman Also t.b.; it's that our names are too short. The only way you can ping us is if you link to one of our previous messages... (using that arrow link at the rightmost part of whatever we typed.)

(Of course, it works for everybody else, too.)

@JM I see.

@RagibZaman Yes, that pinged me. :) Just typing "@JM" won't. (Dots don't count.)

@unNaturhal I was just trying whether I can see there some things that are easy to integrate. E.g. $\displaystyle\frac{3x^2+1}{x^3+x}$ is obvious.

The software automatically generates the @JM part, I wonder why it doesn't include the dots?

I don't claim that it's the best way to do it.

@MartinSleziak It's "displaystyle"

Thanks!

@RagibZaman Well, it seems that to make things easy, anything that isn't alphanumeric is automatically stripped.

Which makes for peculiar behavior, like me and t.b. being un-pingable.

@MartinSleziak Yeah, it is obvious, but it's all the rest that is not so easy :p

I agree.

I was trying if I am able to find more things like that there.

@unNaturhal Sometimes, you just have to remember the tricks. It's not the best way, but there you are...

E.g. $\displaystyle\frac{x}{x^3+x}=\frac1{x^2+1}$ is easy too, so I can get rid of $x$.

@MartinSleziak Ehm.. sorry but, what do you mean with "rid"?

If I have $\displaystyle \frac{x^2+x+1}{x^3+x}$, I can divide it into two easy integrals $\displaystyle \frac{x^2+1}{x^3+x}+ \frac{x}{x^3+x}$.

@JM Yeah, I'm trying to solve integrals using tricks.. Like the one of yesterday ($\sqrt{1+\sin(x)}$ do you remember? I solved with a trick using substitution instead of using duplication formulas :) )

@MartinSleziak Ok, this is clear

@unNaturhal How did you do it? And whats wrong with duplication formulas lol?

Wiktionary: get rid of; just in case it was language problem

$\sqrt{1+\sin x} = \cos(x/2) + \sin(x/2)$ seems pretty quick to me.

I'd prefer $\sqrt{1+\cos(\pi/2-x)}=\sqrt2|\cos(\pi/4-x/2)|$. It seems to be easier to integrate without further manipulation.

But it's essentially the same.

This was really stupid remark.

@RagibZaman The wrong in duplication formulas is that it's impossibile to me to learn by memory.. I will never remember formulas (a part the resolution formula of quadratic equation).. I have a problem in learning things by memory, I need to undestood to can use...

@MartinSleziak ?? What was stupid?

My remark was stupid.

Why?

I said that my result is easier to integrate and that's obviously not true.

@unNaturhal That's the funny thing with trigonometric integrals; there's a plodding way, and there's a clever way, if you can only manage to figure out which identity out of many to use...

@MartinSleziak Thanks :p

It seems just as easy as the other one

Which reminds me, I forgot to put the absolute value signs!

@JM I think that to be able to figure which is the best way I need mooooore practice.. And I'm trying to do it :p

Not to mention I'm improving my typing skills.

@unNaturhal: note that Ragib's error with the absolute value is something to be careful about. :) Just a heads-up.

@unNaturhal Practice is key, yes.

@JM Like the common error with absolute value in a $\int{\frac{1}{x}}\,dx = \log|x| + c$ and not just $\log(x)$

@unNaturhal Yes, that too.

@MartinSleziak betwixt is a nice word too

Why did you change $\displaystyle -3\int x\,d x$ to $\displaystyle \int x\,d x$?

@JM voting to close doesn't have the same god-like power on MSE comparted to MO

At the beginning of the second line.

@MartinSleziak I misunderstood.. Just missed, if you see in the solution there is the missing 3

And what about the sign? +/-

@MartinSleziak Details :p

(I can't edit that message 'cause the time is up)

I apologize for the promoting my own post, but this might be of interest for some people here.

(It would be more interesting if there were also an answer.)

What happened to Google Scholar search by subject area?

@Eugene Weeell... :)

@MartinSleziak Google is starting to be a bit more inconvenient as time passes... :(

@JM Are there other recent problems?

@MartinSleziak I'm still annoyed at not being able to right-click on links to copy them...

Oh yes, the links are ugly.

GMail is starting to look a bit too complicated for my taste.

Those are my top Google annoyances. There are others I can't remember at the moment...

Maybe you could Google them.

@JM their "don't be evil" motto is starting to look like a relic of the past

I guess you all have seen this picture.

@MartinSleziak i haven't thank you for sharing that!

that picture was very soothing!

@MartinSleziak it doesn't seem to work any longer though

@Eugene You tried it?

funny

@MartinSleziak :D

What is a "long division"?

@MartinSleziak Wow, that was a long time ago...

@unNaturhal What methods do you use to divide your polynomials?

@unNaturhal : Long division

Or integers, for that matter?

@JM i looks like it. did you see googlemaps in 8-bit though?

Do google before asking

Perhaps better: Polynomial long divison.

@JM Partial fraction?

@Eugene I don't think so.

@unNaturhal Nono, partial fractions is a different matter. Did you have to divide polynomials in your previous algebra courses?

@JM Aaaah Yeah, I got it with the integral, just dividing the numerator for the denominator, a normal division.

@JM it was one of their april fools pranks

@Eugene Ah. I don't always visit their site on April 1st. The last gag I remember was the one with pigeons...

@JM ah pigeonrank™

Hmm, can someone explain me this: If I want to define sets I need a language right and some logical scheme of deduction.

But I also need variables otherwise I cannot say anything can I?

But... so you assume a set of variables. But you did not define a set yet.

Ahiy thar @JonasTeuwen boy =)

I wonder whether someone already has asked this on main site.

@Jonas : Hi

I guess no need for variables to define a set. I may be wrong.

I found this

When I read it, I have feeling that I do not understand metamathematics at all.

If I tried to answer your question @Jonas, I would say that there are two levels: 1) Logic in the sense how do we think 2) our attempt to formalize the logic using theories, first order languages and stuff

@MartinSleziak It is always like that. Looking at mathematics you should encounter in two-three years always looks greek.

So your set of variables is like in a metalanguage?

So we start with natural logic.

Aha.

Yea, I see.

You describe the elements in a metalanguage.

And then you do logic with that.

And if you want to describe the metalanguage you need another one...

Holy cow! Infinite! Blows up!

:-)

@JonasTeuwen Turtles again... :)

This seems related: p.45 in Just-Weese, the paragraph which starts: Isn't Definition 3 circular? That is, aren't we defining natural numbers in terms of natural numbers?

Although it is about definition of natural numbers, but kind of about similar circularity.

@Jonas : How did you happen to run into this?

Just thinking about things.

In particular, Stefan Geschke's answer seems nice.

@MartinSleziak Thanks this is great stuff. I will go to a friend to have dinner now. Check it out later.

ok, have a nice evening!

@JonasTeuwen its a date!

:5084222 Hey there! nice new gravatar!