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Studentmath
Studentmath
12:00 AM
Hm, I think that if I go about the orders, maybe I can derive that if it's of that order it must - balha
 
Alizter
Alizter
@beginner save your breath. Ted smacks a lot.
 
Studentmath
Studentmath
Will go walk the dog, if no idea comes up will head to bed..
 
teadawg1337
teadawg1337
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
 
beginner
beginner
i am going to go do chapter 2&3 of book of proof and ill be back
 
Alizter
Alizter
@Khallil Spivak is a calc text kind of like an analysis text
 
teadawg1337
teadawg1337
12:02 AM
 
Alizter
Alizter
@Khallil There is also Tao's analysis. Tao is loved by many.
 
beginner
beginner
lol behaviours response LOL
 
teadawg1337
teadawg1337
I quite like Apostol, though it's really the only analysis book I've read
 
beginner
beginner
sorry @pedro he got you
 
teadawg1337
teadawg1337
Other than Buck
 
Khallil
Khallil
12:03 AM
Oooh, I haven't heard of Tao's Analysis before!
Thanks, @Alizter!
#Balarka4mod
Runs from @Ted
 
teadawg1337
teadawg1337
@Khallil Please no....
 
Xingdong Zuo
Xingdong Zuo
@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 .....) ?
 
Alizter
Alizter
If we get Balarka or Dr Sonnhard as mod that would be hilarious.
 
Kaj Hansen
Kaj Hansen
LOL
 
Studentmath
Studentmath
Should get both
 
Ted Shifrin
Ted Shifrin
12:05 AM
I should then retire from everything :)
 
Kaj Hansen
Kaj Hansen
I refuse to believe that Dr. Sonnhard could pass a Turing test.
 
Alizter
Alizter
@PedroTamaroff Edit your nomination and write: "Because I am fabulous".
3
 
Studentmath
Studentmath
Maybe we shouldn't get both, then
 
Xingdong Zuo
Xingdong Zuo
@Alizter Seems Tao's analysis put many proofs of theorems be exercise. Good to train.
 
Alizter
Alizter
There is one more analysis book I know
But I have forgotten the author
by god did I love the typesetting though
 
Pedro Tamaroff
Pedro Tamaroff
12:06 AM
@Alizter I was thinking "Because of reasons."
 
beginner
beginner
@KajHansen if you dont like chugging, isnt the song in you face by children of bodom all chugging and you said you liked them
 
Studentmath
Studentmath
Okay, I am off with the dog. Probably g'night!
 
Ted Shifrin
Ted Shifrin
Night @Studentmath
 
beginner
beginner
@Studentmath probably goodnight to you then
 
teadawg1337
teadawg1337
Oh right, I forgot I was gonna read Zorich....
 
Silencer
Silencer
12:09 AM
@XingdongZuo Don't ask me. I know nothing.
 
Khallil
Khallil
If you ever remember it, @Alizter, make sure you let me know!
^_^
 
beginner
beginner
@pedro talks the most on this chat of anyone, he is a shiny golden mod
 
Pedro Tamaroff
Pedro Tamaroff
@beginner Yes. I'm a chit-chatter.
Not that's something good.
Maybe good for people that have questions.
Not for me.
 
Xingdong Zuo
Xingdong Zuo
@Silencer It's ok. Just discuss. :)
 
beginner
beginner
@PedroTamaroff but it means you will be aware of any mod related problems when robjohn isnt around
24/7 mod chat surveillance
 
teadawg1337
teadawg1337
12:13 AM
Brb, ingesting an entire box-worth of Nyquil (not really)
 
beginner
beginner
do you think this is the right direction, or go back??
$$\sum \limits_{n=1}^\infty \frac{9n^2+12n+5}{(3n+2)!} = \sum \limits_{n=1}^\infty \frac{1}{(3n)!}+ \sum \limits_{n=1}^\infty \frac{1}{(3n+2)(3n+1)(3n-1)!}+ \sum \limits_{n=1}^\infty \frac{3}{(3n+2)!}$$
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
 
Alizter
Alizter
I cant find it
 
teadawg1337
teadawg1337
I'm getting off for the day. I feel like complete and utter crap, I should get more sleep tonight.
 
beginner
beginner
bye @teadawg1337
 
Silencer
Silencer
@teadawg1337 Goodnight.
I'm going too. I found funny question in my old notebook and I feel satisfied. Farewell.
 
beginner
beginner
12:27 AM
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
 
Studentmath
Studentmath
1:07 AM
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..
 
Pedro Tamaroff
Pedro Tamaroff
@Studentmath Maybe.
 
Studentmath
Studentmath
It's in Algebra. It's a shiny one
 
Pedro Tamaroff
Pedro Tamaroff
I didn't say no.
 
Studentmath
Studentmath
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.
 
Pedro Tamaroff
Pedro Tamaroff
Let me read.
 
Studentmath
Studentmath
1:11 AM
Beyond tweaking definitions, I have no idea how to go about it - and tweaking definitions lead me nowhere.
Thanks!
 
Pedro Tamaroff
Pedro Tamaroff
@Studentmath OK.
 
Studentmath
Studentmath
It's the number of sylow-P subgroups in $N(P)$
Not necesserily in $G$ I would think, though..
 
Pedro Tamaroff
Pedro Tamaroff
@Studentmath No. Sorry if I confused you. $P$ is the only Sylow of $N(P)$.
 
Studentmath
Studentmath
Wh- Oh.
Silly me
No wait. Why?
 
Pedro Tamaroff
Pedro Tamaroff
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 $A\cap P=1$.
 
Studentmath
Studentmath
1:18 AM
Oh, that's nice indeed
 
Pedro Tamaroff
Pedro Tamaroff
Note that $A$ has order coprime to $p$.
Why?
This finishes your problem.
 
Studentmath
Studentmath
That's what I was thinking, but I am not sure why - I would say, $o(A)|o(N(P))$
 
Pedro Tamaroff
Pedro Tamaroff
It suffices your show $|N(P):P|$ is not divisible by $p$. This should be slightly obvious.
 
Studentmath
Studentmath
Since that's the order of $A$. And that I know how to prove.
 
Pedro Tamaroff
Pedro Tamaroff
(Since the definition of Sylow subgroup is a maximal $p$-group).
Here I am assuming $P$ is a $p$-group, of course.
 
Studentmath
Studentmath
1:22 AM
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?
 
Pedro Tamaroff
Pedro Tamaroff
@Studentmath Why?
 
Studentmath
Studentmath
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
 
Pedro Tamaroff
Pedro Tamaroff
@Studentmath No problem.
 
mod0
mod0
2:04 AM
Hello, Could someone help me with this? Method of Manufactured Solution
 
Committing to a challenge
Committing to a challenge
@mod0 Is that for homework?
 
mod0
mod0
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
 
Committing to a challenge
Committing to a challenge
@mod0 Sorry I wasn't looking at the correct question
 
mod0
mod0
@Committingtoachallenge Ok.
 
Kevin Driscoll
Kevin Driscoll
@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.
 
mod0
mod0
2:12 AM
@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.
 
Committing to a challenge
Committing to a challenge
Maybe @Behaviour can help with that, this is outside of my primary interests sorry
 
mod0
mod0
@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.
 
Committing to a challenge
Committing to a challenge
E.g, I can't solve this problem
 
Kevin Driscoll
Kevin Driscoll
@mod0 Ya I just presumed that knowing the full solution would give some hint as to what kind of functions would be appropriate
 
mod0
mod0
@Committingtoachallenge Thank you for your time. I will wait for @Behaviour to take a look.
 
Kevin Driscoll
Kevin Driscoll
2:14 AM
I have to admit I don't actually understand the question though
 
mod0
mod0
@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
 
Behaviour
Behaviour
@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.
 
mod0
mod0
Thanks @Behaviour
 
Kevin Driscoll
Kevin Driscoll
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
 
mod0
mod0
@KevinDriscoll I will constrain the domain of course. Bessel if an infinitte series stuff.
 
Kevin Driscoll
Kevin Driscoll
2:20 AM
Oh ya I guess if youre doing finite difference it can't really be an infinite domain
 
mod0
mod0
Not the ideal properties I am looking for. I cannot compute f in closed form
 
Kevin Driscoll
Kevin Driscoll
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......
 
mod0
mod0
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.
 
Kevin Driscoll
Kevin Driscoll
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?
 
mod0
mod0
@KevinDriscoll Hmmm... maybe I should give it a thought. Polynomial sounds like a good idea.
 
Committing to a challenge
Committing to a challenge
2:31 AM
hi @kaj
 
Kaj Hansen
Kaj Hansen
Hey hey
 
Committing to a challenge
Committing to a challenge
Hi @freemind
What are you working on @kaj, French?
 
FreeMind
FreeMind
@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
 
Kaj Hansen
Kaj Hansen
Not really right now, but I have a small French assignment due in 2.5 hours.
 
Committing to a challenge
Committing to a challenge
@KajHansen And a spoken exam in a few days? Or is that it? Oh small, not it
 
FreeMind
FreeMind
2:35 AM
@KajHansen How does it feel learning french? Do you recommend it to me? I am stuck between German and French.
 
Kaj Hansen
Kaj Hansen
@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.
 
FreeMind
FreeMind
@KajHansen How do you feel while learning french? the pronunciation sucks dude :D
 
Committing to a challenge
Committing to a challenge
@KajHansen That is good, are you conversationally fluent? Sufficient to live and navigate in France?
 
FreeMind
FreeMind
I mean , it is beautiful, but hard to mimic :D
 
Committing to a challenge
Committing to a challenge
@FreeMind The r, gets me
 
FreeMind
FreeMind
2:37 AM
@Committingtoachallenge Yeah yeah!
 
Committing to a challenge
Committing to a challenge
@FreeMind I was using duolingo awhile ago
Really enjoyed it, since it has the text, the speaking, the listening
 
FreeMind
FreeMind
@Committingtoachallenge I get sore throat pronouncing r.
 
Committing to a challenge
Committing to a challenge
@FreeMind wrong part of the throat I think haha
 
FreeMind
FreeMind
LoL
 
Committing to a challenge
Committing to a challenge
@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
 
robjohn
robjohn
2:39 AM
@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.
 
FreeMind
FreeMind
@Committingtoachallenge Too technical !
@robjohn Thanks, the same here !!
 
Kaj Hansen
Kaj Hansen
@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.
 
FreeMind
FreeMind
@KajHansen Could you please share the resources you use?
 
Committing to a challenge
Committing to a challenge
@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
 
FreeMind
FreeMind
I need something to listen to all the time.
 
Kaj Hansen
Kaj Hansen
2:40 AM
I could probably be reasonably fluent if I was forced to live there for 6 months with a family, say.
 
robjohn
robjohn
@FreeMind If I get an answer, I may undelete your question here and use it.
 
FreeMind
FreeMind
@robjohn Okay, that's good.
 
Kaj Hansen
Kaj Hansen
@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.
 
FreeMind
FreeMind
@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 :)
 
Committing to a challenge
Committing to a challenge
2:58 AM
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
 
Kevin Driscoll
Kevin Driscoll
@Committingtoachallenge Never understood how my old college buddies could do it....
 
Kaj Hansen
Kaj Hansen
@Committingtoachallenge, I've gotten that much sleep in, say, the past 3 nights haha
I've been very busy
 
Committing to a challenge
Committing to a challenge
@KajHansen I can do it, just not while being a good person to be around haha
 
Kaj Hansen
Kaj Hansen
I'm saying combined. So like 2 hrs/night
haha
 
Committing to a challenge
Committing to a challenge
@KajHansen I become really negative
@KajHansen Yeah I wouldn't want to do that :P
 
Kaj Hansen
Kaj Hansen
3:01 AM
I'd say 5 hours / night is my average in a normal, non-stressful part of the semester.
 
Committing to a challenge
Committing to a challenge
@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??
 
Kaj Hansen
Kaj Hansen
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.
 
Committing to a challenge
Committing to a challenge
@KajHansen Yeah all of that adrenaline, but I mean for the recovery
 
Kaj Hansen
Kaj Hansen
Maybe. I usually go to bed shortly after getting back from the gym.
I guess I have no control to compare to.
 
Committing to a challenge
Committing to a challenge
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)
 
nosille
nosille
3:09 AM
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?
 
Committing to a challenge
Committing to a challenge
In what context?
Finance?
@nosille did you leave?
 
Tom Cruise
Tom Cruise
Hello from sunny California
 
Committing to a challenge
Committing to a challenge
@TomCruise Hello from overly hot Brisbane city
 
Tom Cruise
Tom Cruise
When is winter in Australia?
 
Committing to a challenge
Committing to a challenge
Our seasons are the inverse of yours
 
Tom Cruise
Tom Cruise
3:15 AM
oh
 
nosille
nosille
@Committingtoachallenge Im here, it's about computer science
 
Tom Cruise
Tom Cruise
it will get chilly here in San Fran soon
 
Committing to a challenge
Committing to a challenge
@TomCruise (assuming you are in winter right now)
 
nosille
nosille
I get how the tree works, but really looks a bit impractical to me
 
Committing to a challenge
Committing to a challenge
@nosille What would you like? To skip steps in the tree?
 
Tom Cruise
Tom Cruise
3:18 AM
@nosille I think the idea is that you must rule out certain options before coming to the right stage in the tree...
 
nosille
nosille
@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
 
Committing to a challenge
Committing to a challenge
@nosille Do you have an example picture?
 
nosille
nosille
For reasons I don't entirely understand, it starts on the right
hold on
 
Committing to a challenge
Committing to a challenge
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
 
Tom Cruise
Tom Cruise
does anyone here do a math blog ?
i thought about doing one just to keep track of my progress
 
Committing to a challenge
Committing to a challenge
3:22 AM
I do, so does @ashwin @HatMan @mathmonk @be-haviour(wont ping) and many others
 
Tom Cruise
Tom Cruise
this is a really good one I use sometimes dantopology.wordpress.com
 
Committing to a challenge
Committing to a challenge
@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
 
nosille
nosille
@Committingtoachallenge screenshot coming in a sec
 
Committing to a challenge
Committing to a challenge
@nosille Cool :)
 
Tom Cruise
Tom Cruise
yeah thats what mine would be like
 
nosille
nosille
3:24 AM
@Committingtoachallenge I got you excited now
 
Tom Cruise
Tom Cruise
more of a journal for myself
 
Committing to a challenge
Committing to a challenge
@nosille xD
@TomCruise I'd read it. I enjoy reading other's progress, it is motivational
 
Tom Cruise
Tom Cruise
do you have links to some of the ones you mentioned?
 
nosille
nosille
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
 
Committing to a challenge
Committing to a challenge
 
Tom Cruise
Tom Cruise
3:28 AM
Why do they use those small boards and big chalk? Its strange to me.
I like one giant board and standard chalk
 
nosille
nosille
Because they're not from the West Coast
 
Committing to a challenge
Committing to a challenge
So this is like a maximal value spanning tree
 
nosille
nosille
anyway
 
Tom Cruise
Tom Cruise
hehe
 
nosille
nosille
[5,3,2] WEIGHT
 
Committing to a challenge
Committing to a challenge
3:30 AM
Well how could a computer analyse the problem while skipping steps algorithmically?
 
nosille
nosille
[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)
 
Tom Cruise
Tom Cruise
Cohn is good. I have some of those books by Lee and they are beasts. Any reason you chose that particular Topology book?
 
Committing to a challenge
Committing to a challenge
@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?
 
Tom Cruise
Tom Cruise
yes
 
nosille
nosille
@Committingtoachallenge we start from right to left
 
Committing to a challenge
Committing to a challenge
3:33 AM
Right to left? as in the picture above??
 
nosille
nosille
I mean, you read the tuple from left to right
 
Committing to a challenge
Committing to a challenge
@TomCruise It is actually a really nice book if you can have a look at it, and many people recommended it to me
 
Tom Cruise
Tom Cruise
will it be your first in Topology?
 
Committing to a challenge
Committing to a challenge
@TomCruise Yep
 
nosille
nosille
@Committingtoachallenge [5,3,2] 2 is the weight of the zeroth element (computer counts from 0)
 
Committing to a challenge
Committing to a challenge
3:34 AM
@nosille What are the components of the 3-tuple?
 
nosille
nosille
[5,3,2] WEIGHT [9,7,8] VALUE
 
Tom Cruise
Tom Cruise
I guess its just that Munkres is the standard at most schools
 
Committing to a challenge
Committing to a challenge
@nosille Can you tell me in terms of [a,b,c], what are these a,b,c?
 
Tom Cruise
Tom Cruise
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
 
Committing to a challenge
Committing to a challenge
@TomCruise Wait a min, I will compare the contents of munkres to Dugundji
 
nosille
nosille
3:36 AM
@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
 
Tom Cruise
Tom Cruise
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!!!
 
r9m
r9m
@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
 
Committing to a challenge
Committing to a challenge
@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
 
Tom Cruise
Tom Cruise
how do you get up the confidence to tackle an open problem?
 
Committing to a challenge
Committing to a challenge
@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
 
Tom Cruise
Tom Cruise
3:42 AM
when you know some bright folks have tried to solve them already
 
Committing to a challenge
Committing to a challenge
@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
 
Tom Cruise
Tom Cruise
are PhD students expected to solve open problems?
 
Committing to a challenge
Committing to a challenge
@TomCruise Open problems of little interest sure
 
Mathy Person
Mathy Person
Does asking about probability questions classify under this chat room?
 
Committing to a challenge
Committing to a challenge
@MathyPerson Chat about math, chat about your life, chat about whatever(within reason) seems to be the thing here
 
Kaj Hansen
Kaj Hansen
3:44 AM
@MathyPerson, sure. Whether we can help is another question altogether :)
 
Mathy Person
Mathy Person
Ah, ok!
 
Committing to a challenge
Committing to a challenge
 
Tom Cruise
Tom Cruise
so I could just make up a really strange problem that I can solve
 
Mathy Person
Mathy Person
I wanted to ask about power series (generating functions). How would I find the coefficients of a certain power in power series?
 
Committing to a challenge
Committing to a challenge
@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
 
Mathy Person
Mathy Person
3:47 AM
Unfortunately the coefficient of the power I am looking is x^80
 
Committing to a challenge
Committing to a challenge
@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
 
Mathy Person
Mathy Person
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
 
Tom Cruise
Tom Cruise
but isnt all math interesting :)
 
Committing to a challenge
Committing to a challenge
@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
 
r9m
r9m
@Committingtoachallenge open problem wiki
 
Mathy Person
Mathy Person
3:53 AM
@Committingtoachallenge Here was where I asked it math.stackexchange.com/questions/1058032/…
 
Tom Cruise
Tom Cruise
There is one problem I would love to solve. It is not one of the famous problems but nevertheless...
 
Mathy Person
Mathy Person
But the original original statement is here: Determine how many ways I can distribute 80 candies to 3 kids, such that:

The first kid receives an arbitrary number of candies (possibly 0).
The second kid receives an even positive number of candies.
The third kid receives 0, 2, or 5 candies.
Every candy is distributed.
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).
 
Committing to a challenge
Committing to a challenge
@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?
 
Tom Cruise
Tom Cruise
if I told you I'd have to, you know, kill ya
 
Committing to a challenge
Committing to a challenge
@TomCruise Was that a setup lol
 
Mathy Person
Mathy Person
3:58 AM
@Committingtoachallenge I did back in Intro counting and probability, but unfortunately I am hazy on it :(
 
Tom Cruise
Tom Cruise
hehe
its a problem in topology regarding certain weird connected spaces
I would have to define lots of terms
 
Committing to a challenge
Committing to a challenge
@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]$=114$
 
r9m
r9m
@Committingtoachallenge no solution for it should be known .. :-)
 
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