Mathematics

7:23 AM

@Chris'ssistheartist when i was young, the only thing that pushd me ahead to learning and to not be deceived by peaople who kept reminding me how much i was stupid and stubborn and barin-rigid and not adapted to learn etc... this book amazon.fr/Lintelligence-sapprend-Dietrich-Claude/dp/B0000DO2R7 which my father brough from france, that i was been reading in 10 yo, helped me to go all straightforward and ignore these lame comments , it means in english (intelligence is learnt)

4

all the articles in internet telling that smartness is aquiered from someone's roots are lies, i dont even bother to read em

5

Rigor

9:41 AM

there is no royal road to learning

10:02 AM

@Agawa001 Is there a version in English?

Books have the power to change minds! Just to read the proper books. :-)

Also the same thing with people, to meet in life the right people that help you grow in your way and reach the success.

"Students' beliefs or perceptions about intelligence and ability affect their cognitive functioning and learning."

(Top 20 psychological principles for teachers)

Well, this is true in general, if you're not careful with yourself and consider you unable of doing things, then things happen like that. Maybe you don't even try to do anything.

Even when you feel the hell is going to eat you alive, you don't have the right to give up yourself, you're so special, push yourself, crawl, never give in. Uncover the brilliance, the greatness within yourself.

10:31 AM

@Rigor On the contrary, any road to learning is royal if you're willing to learn.

hi @SamuelYusim

Rigor

and work at it @BalarkaSen

user147690

Looks like I'll get that alg top reading course in 6 months @BalarkaSen and perhaps a representation theory reading course

oh, good.

user147690

@BalarkaSen Is Hatcher a great book, or just the fact it is free is the reason people use it?

@AlexClark I think Hatcher is an extremely good book, although opinions seem to vary person-to-person.

user147690

10:44 AM

@BalarkaSen From what you have said in the past, it seems like it is a good that you have to be extremely tenacious with it. Is there a more verbose text that is good?

Hatcher is pretty verbose, so not sure what you want here.

I usually recommend people to learn basic algebraic topology from Munkres before jumping to Hatcher, as Hatcher is a little bit advanced for beginners on topology.

indeed, Hatcher is actually a graduate text

user147690

Wow Hatcher really is longer than I thought. I tried to read some yesterday and found myself unable to concentrate.

Hatcher talks a lot. That's precisely what the issue is with many people (not with me, though)

I recommend you start learning some algebraic topology from Munkres.

it really won't be motivating enough to start on cell complex and all the point-set details about homotopy extension property. fundamental group is a lot more fun.

user147690

Will do, thanks. I have more free time than at any other point in the semester atm.

user147690

I am finding functional analysis really hard honestly

10:51 AM

really? I thought you had to work a lot on this semester?

user147690

Oh I have been working non-stop, but I have a 4 day lull right now I have been trying to get ahead in, but when I run out of motivation I like to move to different math

user147690

Just handed in a 16 page assignment yesterday

16 page!!

@AlexClark Wow, that is a big assignment.

user147690

I'll screenshot the most painful(and boring of the pages)

user147690

10:53 AM

There was a stupid matrix computation page

That is almost as long as most of my papers (longer than some of them even)

lol

yo @BalarkaSen, how's it going?

(actually there is a 50/50 split between those it is longer than and those longer than 16 pages)

user147690

Prepare for boring::: imgur.com/om1mf4f

user147690

10:55 AM

Behold the killing form of $\mathfrak{gl}(2)$ :P

oh boy

just looking at that makes me $M_{ad}$

user147690

Hahahaha

@AlexClark You do realize that one could just look at a non-zero scalar matrix to show that the Killing form is degenerate, right?

user147690

What?

10:56 AM

@Samuel I'm fine, I think I found a geometric interpretation of Nakayama's lemma. what about you?

doing alright. haven't done much math in the last few days, personally

user147690

@TobiasKildetoft How would you have found the killing form though for it @TobiasKildetoft ?

what's this geometric interpretation?

@AlexClark The Killing form will vanish whenever one argument is in the center of the Lie algebra

user147690

@TobiasKildetoft It asked me to find the killing form explicitly, there is no other way for that though right?

10:57 AM

@AlexClark Ahh, no, that does require the full calculation

user147690

Good xD

@SamuelYusim something something fibers. i'm trying to formulate it right now.

user147690

Anyway I had shown that $\mathfrak{gl}(2)$ was only reductive(from memory) in the previous question

user147690

Since $\mathfrak{gl}(2) \cong \mathfrak{sl}(2)) \boxplus Z(\mathfrak{gl}(2)$(which is simple and abelian respectively and some theorem gave me it from there)

@AlexClark My latest paper was actually about $\mathfrak{sl}_n(\mathbb{C})$

user147690

11:05 AM

@TobiasKildetoft Oh really, what about it?

@AlexClark A classification of projective functors on parabolic subcategories of category $\mathcal{O}$ for that Lie algebra (which is a "nice" category of representations for it)

OK, a corollary of Nakayama's lemma is then if $A$ is a local ring, $f : A \to B$ is a ring homomorphism, then if fiber of the maximal ideal $\mathfrak{m} \subset A$ by $f^* : \text{spec} \, B \to \text{spec} \, A$ has cardinality $1$, then $B$ is a trivial module over $A$. that doesn't seem right.

@AlexClark It is arxiv.org/abs/1506.07008

hmm, I think the intuition of the above statement is better captured if one thinks of $f^*$ as some kind of covering projection.

user147690

@TobiasKildetoft Are the three papers on Arxiv all the papers you have published?

user147690

11:16 AM

@TobiasKildetoft I know some of the words in here :P\

@Chris'ssistheartist i dont believe even if there is still a version of it nowadays, the book is ancient

@AlexClark I have one further paper that I published but never put on arXiv

the one not on arXiv also happens to be the only one of my papers cited by someone other than myself

scientific intelligence goes in parrallel with social intelligence, therefor the brain is always evolving, i know it decelerates badly over the third decade but i know it is still evolving (never decreases)

@Agawa001 I'm sure of it. I was just curious about an English version.

@TobiasKildetoft Hi

11:27 AM

@Moses Hi

@TobiasKildetoft Have you studied Operator Theory?

user147690

@Agawa001 What do you mean by social intelligence?(Because if you are using the word correctly, that is untrue)

@AlexClark Are you free right now?

user147690

@BalarkaSen Yep, for a little bit, gotta sleep soonish

@Moses Not really,no

11:28 AM

ah, was asking out of curiosity. how're your algebra classes going?

@AlexClark the fact you interact with people and earn new knowledge about actual lifestyle and quotidian events

No prob

user147690

@Agawa001 What if someone studies in isolation for a year, you think their social abilities are in parallel?

user147690

@BalarkaSen Algebraic physics is hard, but really really well

@AlexClark i strongly think so

user147690

11:30 AM

Got 100% for the first assignment and 95% for the first quiz

oh, wow, that's brilliant

user147690

@Agawa001 What do you mean by social abilities?

user147690

@BalarkaSen The other algebra is probably worse, but haven't got my grades back, I am hoping for it to be alright

"the other algebra"?

user147690

advanced algebra

user147690

11:32 AM

I am doing two algebra classes, advanced algebra math4301, and alg phys 3103

@AlexClark you have lost me there, i meant scientific and strategic intelligence increases relatively to social intelligence, i dont mean the way round

@AlexClark ah. are they still doing rep theory?

user147690

@BalarkaSen That was alg physics actually xD. Advanced algebra has just finished ring theory stuff and now are finishing field theory stuff

hi @DanielFischer

ok, totally confused. i'm disappointed that you are not doing well on ring/field theory :(

user147690

11:33 AM

Actually, sorry, just finishing part one of the fields chapter. Seems we will be doing it for awhile

@Moses Hi

user147690

Actually I probably did do really well, I just don't have the grades yet, but I was accessed for that assignment on cardano's method, group theory, sylow theory

ah, I see what you mean.

user147690

So I haven't yet got my assessment for rings and fields, but that'll be much nicer I think

you just haven't got the grades back, and hoping it be not so better as your alg phys marks.

i get it.

user147690

11:35 AM

Yeah sorry, typing badly because I'm tired

@Chris'ssistheartist i remember that i made lot of interesting things in my chilldhood, i made a rule of congruence and i was discovering some theorems before i study em in primary and secondary school, teachers kept telling me that you are stupid and mind-obstructed because i have a high difficulty of retaining and minding texts, if i ever listened to em, i would end up a peasan or bus driver

user147690

and it's bloody hot tonight wtf

what's the temp?

user147690

14c outside apparently, but it feels 30 in here...

user147690

Or I am sick again...

11:37 AM

@DanielFischer I proved that if $a$ is idempotent then $\sigma(a) = \{0,1\}$ if $a \neq 0$ and $a \neq 1$. Is there anything special about $f(a)$ where $f$ is analytic on some neighbourhood of $\sigma(a)$. Or can it only be written generally as $f(a) = \frac{1}{2 \pi i} \int_{\Gamma}f(z)(z-a)^{-1}dz$. If it is special don't tell me why, I will figure out.

get some sleep.

2

user147690

@BalarkaSen Alright, talk later :P

@Moses In that case, we have a simpler representation and characterisation of all possible $f(a)$.

@DanielFischer Okay kewl thanks.

@Agawa001 This reminds me a funny happening years ago while I was preparing for driving license test. Well, at some point, the instructor said to my father there is no hope for me to take it because I was not willing to listen to him, I was called stubborn and what not. To my neighbourhoods said a different story, that I didn't have the capacity to learn for taking the driving license.

11:42 AM

I was watching a lecture of Pierre Cartier talking about the "cosmic Galois group" but after a while things seemed to go right over my head.

@Agawa001 In the day of the test he was close to a heart attack, in his team I was the only one that passed the test, the others he trusted failed, and I took the test perfectly with a maximum score.

I think I was the only one with a perfect score from about 200 persons that took the test that day. The problem is that the instructor were good at driving practice (really good), but not at theory, and I couldn't listen to his stupidities.

instructor was*

@Chris'ssistheartist lol dont remind me, i failed two driving tests, i think i must do it this year.

@Agawa001 hehehe :-)))

i drive cars without licence, and the owner s licence is taken by cops due to my stupidities

:p

@Agawa001 :-)))))))))

11:46 AM

but i believe i will succeed this year

@Agawa001 It's like in everything, learn well and succeed. :-)

@Agawa001 And one more thing, since the day of my success the instructor never greated me again.

@Chris'ssistheartist my mother told me so often, that if you are a good mather, y ou are good in everything just because of the beautiful mind you got there. just try to extract this beauty

@Agawa001 As human beings we are endowed with so many qualities, but we need to work hard to uncover them.

2

@Agawa001 Yeah.

Mary Star

12:13 PM

Hello!!
Could you take a look at the proof of Theorem 3 :
http://math.stackexchange.com/questions/1382120/ft-has-undecidable-positive-existential-theory-in-the-language-cdot
and tell me at which point we use the Lemma ? How does this Lemma help us?
I have read the proof several times but I still haven't understood where the Lemma helps us... Do you have an idea?

^ over my head

12:36 PM

@DanielFischer Am I on the right track in simply observing that that for any analytic function $f$ on some neghbourhood of $\sigma(E) = \{0,1\}$ we can write $f(E) := \sum_{n=0}^{\infty}c_{n}E^{n} = \sum_{n=0}^{\infty}c_{n}E = \lambda E$ for some constant $\lambda$?

12:48 PM

@Moses Close, but not quite. Consider $E^0$.

1:07 PM

@DanielFischer Since $E^{0} =1 $ we get $f(E) = c_{0}1+ \sum_{n=1}^{\infty}c_{n}E^{n} = c_{0}1 + \sum_{n=1}^{\infty}E = c_{0}1 + \lambda E$?

@Moses You dropped a couple of $c_n$, but the end result is right, $f(E) = c_0 1 + \lambda E$ for some scalars, $c_0,\lambda$.

Okay thanks.

1:29 PM

Hi @Balarka

hi

@Balarka I have a question . I was solving this paper in which they had said prove that $\Bbb{Z}/n\Bbb{Z} \cong Z_n$. Well I know of the method in which you can use the first isomorphism theorem to this. What I want to do is to find an explicit isomorphism. So lets say if $<a>$ generates $Z_n$ then if I define the map to be $k\pm nm \mapsto a^k$ where $m\in \Bbb{Z}$. Will this map do the job?

First isomorphism theorem gives an explicit map.

And yes, you want to send $k \pmod{n}$ to $a^k$. $k \pm nm$ is bad notation.

Okay sorry. So will this map do?

I just said "yes"

1:36 PM

Okay sorry again. I didn't see it

So what did you do today @Balarka

No need to apologize.

@Rememberme nothing.

No maths?

I mean, nothing very interesting. Some comm. alg. and a bit of cohomology.

Well I was watching this video. All I understood from that was cohomology had something to do with rings. Using rings seems very fascinating. How do we use them in cohomology

cohomology are invariants for topological spaces with a natural graded ring structure, that's all. I think you should learn about fundamental groups before doing cohomology, though.

How much of Munkres have you done so far?

1:41 PM

I am starting countability and separability axioms tomorrow

Though after day after tomorrow I cannot do maths because I have my exams

Assuming you have done sufficiently many exercises on the things you have learnt so far, I think it won't hurt to start reading off ch. 9 part II.

if you want to learn that stuff, that is.

I guess it will be better to start off after the exams because if I start now I might not concentrate enough on it. Though I will still look at it once@Balarka

although I recommend you not to delve an part II. just read ch. 9, do a few exercises. make sure you finish off ch. 4. many important theorems there.

ok, as you wish

we're doing ch. 1 of Hatcher but Hatcher seems pretty hard

@morphic they just skipped ch. 0?

that seems like a silly thing to do.

1:47 PM

Okay @Balarka I guess I will finish chapter 4 and then go to 9

@BalarkaSen we're supposed to self-study cells and stuff and then hand in an assignment

@Remember i mean, you can do both simultaneously.

@morphic oh, i see

so, what have you learnt so far?

Thats better then @Balarka I will do that then :)

Hello@morphic

@BalarkaSen we just finished reviewing point-set

i have to hand in this assignment next week

oh, alright.

let me know when you get to the fun part.

Integral structures on de Rham cohomology

1:53 PM

►

Hi @Rememberme

Is that you lecturing

Nope, morphic

2:16 PM

@Balarka
We define $O_n(F) = \{A\in GL_n(F) , <Au,Aw>=<u,w>\}$ But why would one want to do such a thing to the matrices in $GL_n(F)$

@Remember It's the group of all $n\times n$ matrices which preserves your billinear from on the $F$-vector space you have in mind. What do you mean by "why would one want to do such a thing"?

Also, your notation is a bit weird. It doesn't tell me about the $F$-vector space and billinear form I have on my vector space.

I mean to say that what is the motivation in doing such a thing