Hm, I think that if I go about the orders, maybe I can derive that if it's of that order it must - balha

@beginner save your breath. Ted smacks a lot.

Will go walk the dog, if no idea comes up will head to bed..

Here's my excuse for my delay in mathematical rigor: the two terms "prodigy" and "IEP" don't look very good in the same sentence

i am going to go do chapter 2&3 of book of proof and ill be back

@Khallil Spivak is a calc text kind of like an analysis text

It's official

@Khallil There is also Tao's analysis. Tao is loved by many.

lol behaviours response LOL

I quite like Apostol, though it's really the only analysis book I've read

sorry @pedro he got you

Other than Buck

Oooh, I haven't heard of Tao's Analysis before!

Thanks, @Alizter!

#Balarka4mod

Runs from @Ted

@Khallil Please no....

@TedShifrin @Silencer Thanks. By the way, after finish reading Courant, is it recommended still to read something like Apostol's Calculus I, II. Or it's just enough to move on to analysis (Rudin/Zorich .....) ?

If we get Balarka or Dr Sonnhard as mod that would be hilarious.

LOL

Should get both

I should then retire from everything :)

I refuse to believe that Dr. Sonnhard could pass a Turing test.

@PedroTamaroff Edit your nomination and write: "Because I am fabulous".

Maybe we shouldn't get both, then

@Alizter Seems Tao's analysis put many proofs of theorems be exercise. Good to train.

There is one more analysis book I know

But I have forgotten the author

by god did I love the typesetting though

@Alizter I was thinking "Because of reasons."

@KajHansen if you dont like chugging, isnt the song in you face by children of bodom all chugging and you said you liked them

Okay, I am off with the dog. Probably g'night!

Night @Studentmath

@Studentmath probably goodnight to you then

Oh right, I forgot I was gonna read Zorich....

@XingdongZuo Don't ask me. I know nothing.

If you ever remember it, @Alizter, make sure you let me know!

^_^

@pedro talks the most on this chat of anyone, he is a shiny golden mod

@beginner Yes. I'm a chit-chatter.

Not that's something good.

Maybe good for people that have questions.

Not for me.

@Silencer It's ok. Just discuss. :)

@PedroTamaroff but it means you will be aware of any mod related problems when robjohn isnt around

24/7 mod chat surveillance

Brb, ingesting an entire box-worth of Nyquil (not really)

i dont know how to use partial fraction on a factorial

none of the running mods have any real flag count, nor meta points. user @behaviour should run

I cant find it

I'm getting off for the day. I feel like complete and utter crap, I should get more sleep tonight.

bye @teadawg1337

@teadawg1337 Goodnight.

I'm going too. I found funny question in my old notebook and I feel satisfied. Farewell.

cya @silencer

26:30 in this is hilarious!!! youtube.com/watch?v=SXHHvoaSctc (its topology by Dr Tadashi Tokieda)

25:44 is probably where to start

Speaking of good for people that have questions, @Pedro mind guiding me slightly with this exercise? I can't sleep with it stuck in my head..

@Studentmath Maybe.

It's in Algebra. It's a shiny one

I didn't say no.

I will just ask. So, I have $P$ a p-sylow subgroup of some finite group $G$. $N(P)$ is its normalizer in $G$.

I want to show that if $A$ is a subgroup of $N(P)$, and $o(A)=o(N(P)/P)$, then $PA=N(P)$

Thinking a bit about it, I think what I want to show is that, in that case, $A$ has the $g\in G$ so that $gP=Pg$, yet also for every $a,b \in A$ $aP\neq bP$. Or something like that.

Let me read.

Beyond tweaking definitions, I have no idea how to go about it - and tweaking definitions lead me nowhere.

Thanks!

@Studentmath OK.

It's the number of sylow-P subgroups in $N(P)$

Not necesserily in $G$ I would think, though..

@Studentmath No. Sorry if I confused you. $P$ is the only Sylow of $N(P)$.

Wh- Oh.

Silly me

No wait. Why?

Have you tried to show that $P\cap A=1$?

Note that $$|PA|=\frac{|P||A|}{|P\cap A|}=\frac{|N(P)|}{|A\cap P|}$$ by hypothesis.

Since everything is finite, it suffices you show that $A\cap P=1$.

Oh, that's nice indeed

Note that $A$ has order coprime to $p$.

Why?

This finishes your problem.

That's what I was thinking, but I am not sure why - I would say, $o(A)|o(N(P))$

It suffices your show $|N(P):P|$ is not divisible by $p$. This should be slightly obvious.

Since that's the order of $A$. And that I know how to prove.

(Since the definition of Sylow subgroup is a maximal $p$-group).

Here I am assuming $P$ is a $p$-group, of course.

Indeed - and from their everything falls back to what I want to prove

Thanks a lot Pedro

Which it is, since it's a sylow-p group, and any sylow-p subgroup is, as you said, the maximal p-subgroup

Also, if $N(P)/P$ is cyclic, I can show that there is such an $A$, right?

@Studentmath Why?

Well, $N(P)/P=\{nP|n\in N(P)\}$,

And if it is cyclic, then $N(P)$ is cyclic.. no, that's silly.

But I do know there is an $n$ whose order is $o(N(P)/P)$, and therefore it creates a cylcic subgroup of that order, which is $K$.

I think.

Anyhow, that's been a lot of help @Pedro! Thanks

@Studentmath No problem.

Hello, Could someone help me with this? Method of Manufactured Solution

@mod0 Is that for homework?

Well, not the whole homework. I just need it to get started. From there on, I need to propose a finite difference method, study its stability, add additional terms propose a new method. Etc. Since I do not know the physics, I don't know what is a reasonable function. I could choose Cos(r^3) but f turns out to be terrible.

:18967246 I don't think it involves Z-transforms

@mod0 Sorry I wasn't looking at the correct question

@Committingtoachallenge Ok.

@Committingtoachallenge Don't heat equations usually have Bessel Functions as solutions?

At least I'm pprety sure thats the case in even dimensions. DOn't remember about odd dimensions.

@KevinDriscoll Possibly. But I am not trying to solve the heat equation exactly. I am trying to come up with a finite difference scheme that approximates that PDE well.

Maybe @Behaviour can help with that, this is outside of my primary interests sorry

@KevinDriscoll So, if a solution satisfies the PDE and finite difference scheme approximates that solution well given appropriate IC/BC, then it will be able to solve it.

E.g, I can't solve this problem

@mod0 Ya I just presumed that knowing the full solution would give some hint as to what kind of functions would be appropriate

@Committingtoachallenge Thank you for your time. I will wait for @Behaviour to take a look.

I have to admit I don't actually understand the question though

@KevinDriscoll Basically, I am trying to find a u, with the desired symmetry properties that I mentioned in the question so that when I subsitute it in the equation, I get a not so bad f. Basically the solution is being manufactured.

Which means, since you know the u with which you start, you can find the IC/BC

and now run your FD method against those conditions and with the computed f as RHS

@mod0 Looks like you can take u to be any function you want, e.g., a polynomial, and compute f from that. I don't know what's good for testing FD. That's more of a Computational Science territory.

Thanks @Behaviour

I'd at least try some kind of Bessel function, it has properties sort of like the cosine function

Cosine seems like a poor choice because it won't decrease as you get farther from the origin

but I guess thats not so important

you're just looking for a simple example for some reasonable f

@KevinDriscoll I will constrain the domain of course. Bessel if an infinitte series stuff.

Oh ya I guess if youre doing finite difference it can't really be an infinite domain

Not the ideal properties I am looking for. I cannot compute f in closed form

And what about infinite series?

I'm sure you can. Bessel funciton and their deirvatives are well-known

Unless the program you're working with doesn't natively support Bessel functions??? Sorry I use Mathematica so......

Ok. Sorry, pardon my ignorance. I am using MATLAB, but somehow I feel uncomfortable using Bessel even though it is a solution to the heat equation.

Ya, MATLAB is something of a mystery to me. Why not just try the simplest thing you can think of like some kind of polynomial?

@KevinDriscoll Hmmm... maybe I should give it a thought. Polynomial sounds like a good idea.

hi @kaj

Hey hey

Hi @freemind

What are you working on @kaj, French?

@Committingtoachallenge Hey yo!

@robjohn I'm just beating around the bush, how the hell am I supposed to calculate the inside function?! I dunnO! :D

Not really right now, but I have a small French assignment due in 2.5 hours.

@KajHansen And a spoken exam in a few days? Or is that it? Oh small, not it

@KajHansen How does it feel learning french? Do you recommend it to me? I am stuck between German and French.

@Committingtoachallenge, we already had such an exam. Our final is written thank god.

@FreeMind, I like it a lot, but I've never experienced German.

Maybe ask Ted since he knows both.

@KajHansen How do you feel while learning french? the pronunciation sucks dude :D

@KajHansen That is good, are you conversationally fluent? Sufficient to live and navigate in France?

I mean , it is beautiful, but hard to mimic :D

@FreeMind The r, gets me

@Committingtoachallenge Yeah yeah!

@FreeMind I was using duolingo awhile ago

Really enjoyed it, since it has the text, the speaking, the listening

@Committingtoachallenge I get sore throat pronouncing r.

@FreeMind wrong part of the throat I think haha

LoL

@FreeMind As a kid I made this weird pigeon sound a heap, and it was actually pretty similar

@FreeMind If it made your throat sore you were probably using your adams apple area or something haha, but I am not expert

@FreeMind I will look again at it this evening. we are about to start dinner, and we have guests, so it won't be for several hours, but I will look at it.

@Committingtoachallenge Too technical !

@robjohn Thanks, the same here !!

@Committingtoachallenge, not really. I can read and write a lot better than I can speak/listen.

@FreeMind, my pronunciation is slowly coming along with lots and lots of practice.

@KajHansen Could you please share the resources you use?

@KajHansen Fair enough, I think it would be nice to be able to write in a language the people around me didn't understand, e.g. something like a journal that would actually be private haha

I need something to listen to all the time.

I could probably be reasonably fluent if I was forced to live there for 6 months with a family, say.

@FreeMind If I get an answer, I may undelete your question here and use it.

@robjohn Okay, that's good.

@FreeMind, for one, I do lots of worksheets, similar to the ones you got in grade school for English for the reading/writing practice. We're also made to do some speaking exercises and then compare our attempt to a native speaker.

@KajHansen Good, I wish I had the available environment, but the problem is, my environment sucks in a way that I'm forgetting my mother tongue :)

I wish I could stay sane sleeping 4-6 hours a night like Robjohn.

I can deal with it, but definitely not well, especially conversationally

@Committingtoachallenge Never understood how my old college buddies could do it....

@Committingtoachallenge, I've gotten that much sleep in, say, the past 3 nights haha

I've been very busy

@KajHansen I can do it, just not while being a good person to be around haha

I'm saying combined. So like 2 hrs/night

haha

@KajHansen I become really negative

@KajHansen Yeah I wouldn't want to do that :P

I'd say 5 hours / night is my average in a normal, non-stressful part of the semester.

@KajHansen 2 hrs/night for three nights, I would be micro-sleeping randomly

@KajHansen Wow that is awesome, but doesn't that hurt the fitness routines??

Not really, for some reason. Often I go to the gym very tired, but "wake up" very fast during my first set. It's actually kind of cool.

@KajHansen Yeah all of that adrenaline, but I mean for the recovery

Maybe. I usually go to bed shortly after getting back from the gym.

I guess I have no control to compare to.

It would be really difficult to have a proper control

My test was to start eating a series caloric surplus and sleeping properly for two weeks. I was definitely happy(e.g. undereating and sleep deprivation were making me depressed)

I can't get my head around about why we ahave to go though every option (left to right) in a decision tree, instead of just skipping an item to get a next one that satisfies the rules

Is anyone here used to decision trees?

In what context?

Finance?

@nosille did you leave?

Hello from sunny California

@TomCruise Hello from overly hot Brisbane city

When is winter in Australia?

oh

@Committingtoachallenge Im here, it's about computer science

it will get chilly here in San Fran soon

@TomCruise (assuming you are in winter right now)

I get how the tree works, but really looks a bit impractical to me

@nosille What would you like? To skip steps in the tree?

@nosille I think the idea is that you must rule out certain options before coming to the right stage in the tree...

@Committingtoachallenge Id't like to know why the algo starts at the back end and then works it's way from left to right thorugh the elements not satisfying it's requirements and leading to dead end branches

@nosille Do you have an example picture?

For reasons I don't entirely understand, it starts on the right

hold on

My guess(I still want the picture) is that it is because you want a tree that fits the general case, not just your current case

does anyone here do a math blog ?

i thought about doing one just to keep track of my progress

I do, so does @ashwin @HatMan @mathmonk @be-haviour(wont ping) and many others

this is a really good one I use sometimes dantopology.wordpress.com

@TomCruise I'll check it out, thanks. My blog is more about my challenge for now, and eventually, when I know some real math, it will have math posts that are interesting :P

@Committingtoachallenge screenshot coming in a sec

@nosille Cool :)

yeah thats what mine would be like

@Committingtoachallenge I got you excited now

more of a journal for myself

@nosille xD

@TomCruise I'd read it. I enjoy reading other's progress, it is motivational

do you have links to some of the ones you mentioned?

It's an MIT lecture, it deals with the knappsack problem

So

there are 3 items that the thief can get, each with different weight and value

goal is to extract most value

@TomCruise mine, Ashwin, mathwonk, behaviour

Why do they use those small boards and big chalk? Its strange to me.

I like one giant board and standard chalk

Because they're not from the West Coast

So this is like a maximal value spanning tree

anyway

hehe

[5,3,2] WEIGHT

Well how could a computer analyse the problem while skipping steps algorithmically?

[9,7,8]

is the value

left branch is the no-take

so, one cannot progress on the right if the space (or weight) of the next item exceeds tha available (which is 5 at the start)

Cohn is good. I have some of those books by Lee and they are beasts. Any reason you chose that particular Topology book?

@nosille So you are saying that the first option breaks the tree? Well than there is no point in computing the rest of the tree.

@TomCruise Which book? Dugundji?

yes

@Committingtoachallenge we start from right to left

Right to left? as in the picture above??

I mean, you read the tuple from left to right

@TomCruise It is actually a really nice book if you can have a look at it, and many people recommended it to me

will it be your first in Topology?

@TomCruise Yep

@Committingtoachallenge [5,3,2] 2 is the weight of the zeroth element (computer counts from 0)

@nosille What are the components of the 3-tuple?

[5,3,2] WEIGHT [9,7,8] VALUE

I guess its just that Munkres is the standard at most schools

@nosille Can you tell me in terms of [a,b,c], what are these a,b,c?

But my favorite is Kuratowski... it is in 2 volumes and a little difficult to find now

it all depends on which area of topology you want to focus on

@TomCruise Wait a min, I will compare the contents of munkres to Dugundji

@Committingtoachallenge So, this way element 0 (the one on the right) has a weight of 2 pounds and value of 8. Maximum weight the thief can carry is 5, so this satisfies the rules

My guess would be that Munkres spends a little more time on homotopy theory and algebraic topology

whereas Dugundji will be more of the "point-set" topology

being an older book

Calculus VII, lol, no thanks!!!

@Venus 8 atm .. ;) (-5) + (-3) shows 3 additional downvotes were cast even after the post was at (-5) ... I'd say it was vigorously downvoted ! =P

@TomCruise It looks like you may be right, but also Dugundji has a good portion of Munkres chapters, with intermediate knowledge between them. E.g. Instead of doing ABC in monkres I have $A_1A_2B_1B_2C_1C_2$

@nosille Okay I see, one second

how do you get up the confidence to tackle an open problem?

@nosille So your problem lies in the fact that when computing this by hand, there are redundant steps? But the algorithm is made for computers in the first place

when you know some bright folks have tried to solve them already

@TomCruise Most don't

@TomCruise I don't think there is much point unless you have done major research in a field you are interested in, and that gives you incite serendipitously into the open problem

are PhD students expected to solve open problems?

@TomCruise Open problems of little interest sure

Does asking about probability questions classify under this chat room?

@MathyPerson Chat about math, chat about your life, chat about whatever(within reason) seems to be the thing here

@MathyPerson, sure. Whether we can help is another question altogether :)

Ah, ok!

@MathyPerson Get the bookmarklet to render mathjax here

so I could just make up a really strange problem that I can solve

I wanted to ask about power series (generating functions). How would I find the coefficients of a certain power in power series?

@TomCruise If it will interest someone yes :P

@MathyPerson By brute force unfortunately

@MathyPerson You will need to do it computationally, and use stars and bars for on the hand cases

Unfortunately the coefficient of the power I am looking is x^80

@MathyPerson I imagine this is for partitions or for integer solution counting?

Yep, you will need to use Mathematica, Maple etc

@TomCruise If it is interesting or significant it would be published, otherwise noone will take you seriously and won't care

I found that the "power series representation" for the product was (x^5+x^2+1) / (1-x)(1-x^2). I used Wolframalpha and it said 119 for the coefficient but I entered it in and it was incorrect :O

but isnt all math interesting :)

@MathyPerson That doesn't sound right? What is the problem, maybe I can help

@TomCruise Not being the first person to compute 12491295215*127512569014261209412412 and prove what it is modulo 12431245, even though you would probably be the first person to do it, thus solving the 'open' problem :P

@Committingtoachallenge open problem wiki

@Committingtoachallenge Here was where I asked it math.stackexchange.com/questions/1058032/…

There is one problem I would love to solve. It is not one of the famous problems but nevertheless...

From there, I got the three power series. For the first kid, it is (1+x+x^2+...). For the second kid, it is (x^2+x^4+x^6+....). For the third kid, it is (1+x^2+x^5)

From there I deduced that the power series representation was (x^5+x^2+1) / (1-x)(1-x^2).

@MathyPerson I imagine this is an assignment, and you have also learnt stars and bars?

@TomCruise What is it?

@r9m Are you saying my example doesn't fit the description?

if I told you I'd have to, you know, kill ya

@TomCruise Was that a setup lol

@Committingtoachallenge I did back in Intro counting and probability, but unfortunately I am hazy on it :(

hehe

its a problem in topology regarding certain weird connected spaces

I would have to define lots of terms

@MathyPerson It can't be used here, but in my course the lecturer said specifically: "You will not be expected to generating functions on the exam, this, being impossible. But you will be given easier forms that can be solved using stars and bars. Generating functions are for assignments only"

@MathyPerson Furthermore, Coefficient[ Sum[t^i, {i, 5}] Sum[t^i, {i, 2, 6}] Sum[t^i, {i, 3, 9}], t, 15]$=114$

@Committingtoachallenge no solution for it should be known .. :-)