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12:11 AM
Hey @Ted!
 
hi Demonark
 
How's it going?
 
@ÍgjøgnumMeg My complete sympathies. You can't fool around with pneumonia. Get well!!
Getting myself organized, Demonark, and you?
 
At the moment, doing an algebra pset
 
So that should keep out of trouble for a while.
 
12:21 AM
This is true, without a pset to keep me occupied I'd probably be committing the worst of crimes at the moment
 
I won't even ask.
 
Zee
Hi
 
Lol, fair. But yeah this pset has been mostly focused on, well you have some polynomial $p\in \mathbb{Q}[x]$, show it's irreducible, let $\theta$ be a root, find various elements in $\mathbb{Q}(\theta)$ (such as $\frac{1}{1+\theta}$, etc)
Our prof did tell us how you could find inverses of elements using matrices which I quite liked though
 
Zee
Mathematics is like botany , you may think it’s a weed but another may think it’s a flower , so keep an open mind
 
I usually teach that in terms of the Euclidean algorithm.
Well, taught.
 
12:32 AM
He did mention the Euclidean algorithm as well, I guess I just preferred the matrix version
 
who's your prof @Daminark
 
The matrix version is more tedious and less conceptually interesting to me.
Hi Eric
 
Emerton
 
hlo
oh cool people like him
 
Yeah he's good. He has a lot of very interesting rants
 
12:33 AM
Demonark, you have any special plans for April Fools/Easter?
(I presume not Easter.)
 
He talks a lot about how we should think about things, and often gets quite... almost philosophical? Like at one point he was talking about how if $p$ is irreducible over $F$ and has a root $\alpha$ in $E\supset F$, then there's a unique homomorphism $F[x]/(p) \to E$ which fixes $F$ and maps $x\mapsto \alpha$
 
I think it's good teaching to give intuition and help students know how to think about things.
Well, that's totally standard, that last sentence. Everyone teaches that.
 
And he spent quite some time talking about why you ought to try defining the map out of $F[x]$ and showing that $(p)$ is in the kernel instead of trying to deal directly with the elements of the quotient as cosets, stuff like how it's better to have a well-defined object and prove a property about it instead of an ambiguously defined object for which you prove well-definedness, etc
 
I don't. I don't want my students to think! They might stop listening to me if they did!
:P
 
In your case, that's probably a valid concern, Xander.
 
12:38 AM
aw :(
 
Demonark: In other words, whenever possible, use the fundamental homomorphism/isomorphism theorems rather than doing everything from scratch.
 
Re April Fools: I actually didn't think about that, though I usually don't have anything terribly fancy planned
 
I figured it would be one of your favorite days. :)
 
Zee
I never could understand eucledian algorithm or high school long division, I learned it 20 times , I still don’t get it
 
Well, the thing is, I've never been good at thinking of pranks that are both interesting and that I'd actually be willing to pull on people. Usually it's just Rick Rolls, maybe if it falls on a day where a pset is assigned I'll inspect edit a chalk post making it seem like it's unreasonable, that kind of thing
 
12:42 AM
I guess I overestimated your skills, Demonark :P
 
A classic mistake. But yeah I could probably think of more elaborate things but I'd either not have the time to pull it off right, or it's the type of thing that might make someone actually upset
 
When I was at MIT, pranks often got people upset. They liked to penny people into their dorm rooms ... even on the 15th floor.
 
Zee
I remember bringing a stack of pancakes to class with p inverse written on it
 
Oof
 
Zee
Whenever I meet a communist , I like to remind them that Stalin and Mao murdered more people than everyone else in history combined
 
12:53 AM
cause everyone knows that being a communist = being a stalinist or a maoist
 
1:04 AM
Good lord combo website still isn't up
 
1:15 AM
Hi guys, I'm looking for numerical methods for computing root locus. Do you suggest specific algorithms for this matter ? Matlab has this command rlocus().
 
@Secret thank you
 
1:43 AM
@XanderHenderson that is right
 
@Zee @EricSilva If they are socialists, however, they will say that the communism in USSR and PRC is not Marxist socialism, because some kind of totalitarian capitalism takes over as worker unions dissolves prematurely due to lack of numbers
 
1:54 AM
what is "marxist socialism" @Secret
 
If I recall correctly, it's the idea of workers forming a state and thus all economics and operations of a nation is controlled completely by the working class. The USSR initially does that, until the growing worker union dissolved some time in 1960s
 
Marx thought the state would wither after capital was abolished so the marxist view wouldnt include nations
 
ah yes, sorry, I only remember the working class takes over all operations (both social and economic), but since I don't recall what do you call for the resulting big thing, my brain just snapped to the word that described the largest landmass that is under some sort of political control, which is why I said nation
 
2:10 AM
the working class taking over is the DotP, the part after capital has been abolished and the state no longer exists is what marx called communism or socialism (he didn't use those two words to mean different things)
 
ah I see
 
an important point is that to marx (and lots of people who would call themselves communists) communism isnt an ideology or a thing to build (see the German Ideology by marx for ex)
 
2:25 AM
So without a state, what is the resulting governing body formed by the working class called, or is there no governing body because there isn't anything to be built according to communism?
 
i mean you dont need a governing body to produce things. organization $\neq$ hierarchy.
 
How do I understand the value, mentioned as 2.6226043701171875e-06? In a programming language
 
but there is no governing body formed by the working class because there wouldnt be "class" @Secret
 
I see, it seems I have not fully grasp the workings of socialism/communism
 
no one does, but people theorize
 
2:58 AM
hi @EricSilva
@EricSilva @Daminark can we just discuss one small geometric issue surrounding sections ?
 
Wouldn’t the answer be + or -
 
@Adeek i would but i am busy, sorry
 
sounds good @EricSilva
 
$\pm\dfrac{1}{\sqrt{2}}(i+j)$
 
3:36 AM
 
@fawad c=ka +lb, where a,b,c are vectors
And dot with a of c is zero
 
 
1 hour later…
5:38 AM
3
Q: defining inequality of natural numbers by case-analysis

beroalIf I add to Peano Arithmetic a relation (predicate?) symbol $\leq$ and an axiom $\forall n\forall m(n\leq m \leftrightarrow n=m \lor S(n)\leq m)$, can I prove $\forall n\forall m(n\leq m \to n\leq S(m))$? Related question: How to compare Peano numbers?

 
6:07 AM
Is there any one who is interested in discussing about material in Kobayashi and Nomizu first two chapters
 
@Daminark and @Perturbative - I thought you might be interested in cello's question, considering that you have previously started differential geometry study group. See also their post here: meta.mathoverflow.net/questions/355/specialized-chat-rooms/…
 
 
1 hour later…
7:25 AM
 
yeah f888 timezones
 

 Mathematics

Associated with Math.SE; for both general discussion & math qu...
that line is^ 06:00
 
hence the quiet time
 

 The h Bar

General chat for Physics SE (physics.stackexchange.com). For M...
 
h bar is slightly better
 
Zee
7:43 AM
Oh man
Just came from bar , snorted a nice line
 
If $g(t_n)\to 0$ as $t_n\to x$, then how to show $\dfrac{g(t_n)}{t_n-x}\to 0$ as $t_n\to x$? Here $g$ is from $\Bbb R$ to $\Bbb C$.
 
@Silent I don't think that is true
 
oh!
@LeakyNun can you give an example?
 
take g(tn) = tn-x
 
7:49 AM
I am trying to write that ^ (in code) using only matrix multiplication and transpose and vector addition / subtraction. ai is each row of a matrix, can anyone give me a hand?
 
@LeakyNun Wow
 
So I think just Ai * w - b would take care of the first part. That would give me a matrix where each row is ai * w - bi, I do not know about that for sure though and I do not know about the rest
Is my question clear?
 
How to show that if $g(x)=0$ and $g'(x)\ne 0$ then $g(t)\ne 0$ in a neighborhood of $x$? @LeakyNun
 
@Silent for every point in the neighbourhood or for some point?
 
@LeakyNun for every point in nbd
 
8:01 AM
that's false
 
oh!
will you please give an example?
 
Take $f\left(x\right)=\begin{cases}x^2\sin\left(\frac{1}{x}\right)+0.5x & x \ne 0 \\ 0 & x = 0 \end{cases}$
then $f'(0) = 0.5$
 
@LeakyNun Thanks for this!
But@LeakyNun, then how does this baby Rudin exercise make sense, when we are not sure that we are not dividing by $0$?
 
@Silent $g'(x) \ne 0$
 
@LeakyNun no, the limit of $f(x)/g(x)$: there we do not know that $g(x)$ nonzero in nbd of $x$.
 
8:10 AM
@Silent let $g'(x) = L$, $\varepsilon = |L|/4$, so there is delta such that $t \in (x-\delta, x+\delta)$ implies $\frac{g(t)-g(x)}{t-x} \in (L-|L|/4, L+|L|/4)$, so $\frac{g(t)-g(x)}{t-x} \ne 0$, so $g(t)-g(x) \ne 0$, so $g(t) \ne 0$
my example was wrong: in my example it is $g'(x)$ that can be zero in every neighbourhood
 
@LeakyNun Thank you so much for this!
a very helpful discussion.
 
indeed
 
Hi guys! I would like to ass: When writing equations using mathjax, what exactly is the difference between inline ($...$) and display ($$...$$) as stated in https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference?
I am visually impaired and am using a screen reader to read texts. It so happens that my version of my screenreader now reads mathjax content, but it reads inline and display mode the same. I am about to create a new question and this is my first time using mathjax to render math equations. What should I use? Display or inline? Thanks.
 
@morbidCode use inline mode for short equations and expressions, and use display mode for longer equations and expressions
 
@LeakyNun thanks!
 
8:36 AM
@LeakyNun For example, is this correct? Let $p1(n)$ be the proposition that $$fib(n)=(fi^{n}-ci^{n})/sqrt{5}$$.
 
@morbidCode I guess we will help you with formatting...
 
8:55 AM
 
9:09 AM
In mathematics, stochastic geometry is the study of random spatial patterns. At the heart of the subject lies the study of random point patterns. This leads to the theory of spatial point processes, hence notions of Palm conditioning, which extend to the more abstract setting of random measures. == Models == There are various models for point processes, typically based on but going beyond the classic homogeneous Poisson point process (the basic model for complete spatial randomness) to find expressive models which allow effective statistical methods. The point pattern theory provides a ma...
 
9:41 AM
Suprematism (Russian: Супремати́зм) is an art movement, focused on basic geometric forms, such as circles, squares, lines, and rectangles, painted in a limited range of colors. It was founded by Kazimir Malevich in Russia, around 1913, and announced in Malevich's 1915 exhibition, The Last Futurist Exhibition of Paintings 0.10, in St. Petersburg, where he, alongside 13 other artists, exhibited 36 works in a similar style. The term suprematism refers to an abstract art based upon "the supremacy of pure artistic feeling" rather than on visual depiction of objects. == Birth of the movement == Kazimir...
This is what suprematism looks like and sounds like
Forever will the soul be one with the supreme unhuman, the purest of all geometries, free from the taint of humanity
All hail the supreme of the n-spheres, for $\circle$'s vision we lead us far and wide into the Supreme
 
Helo
 
??
 
The SSupreme Cube
 
9:56 AM
))
 
(sorry I was bored)
 
np
is there latex notation that i can state that two equations are the same ?
/ latex expression
 
isn't the latex for iff good enough?
 
might be
Yes that should work thanks
 
 
2 hours later…
11:36 AM
Division by zero No-go conjecture:
$\exists 0,1,q \in S \forall x \in S[(1x=x \lor x1=x) \land (0+x=x \lor x+0=x) \land (q0=1 \lor 0q=1)] \implies 0=1=q$
The status of this is still open for distributive algebra $S$ of infinite cardinality
 
12:11 PM
> The axiom of choice is the following statement:

Every surjection in the category Set of sets splits.
@MatheinBoulomenos
 
$f: \text{Set} \to S$ ?
 
No, A -> B where A and B are sets
 
12:40 PM
Hello. A cross-ratio is defined as a linear transformation S which maps $(z2,z3,z4)$ to $(1,0,\ infty)$ respectively. I need to prove that it is unique. Now, if i let T be another linear transformation, then i can see that ST^{-1} leaves $1,0 \infty$ invariant, what to do now?
where $Sz = \frac{z-z3}{z-z4} . \frac{z2-z4}{z2-z3}$
 
Quick sanity check, for sets $A$ and $B$, $A \times B = \emptyset$ implies either $A = \emptyset$ or $B = \emptyset$ right?
 
@Perturbative yes
 
A cross-ratio is defined as a linear transformation $S$ which maps $(z2,z3,z4)$ to $(1,0,\infty)$ respectively. I need to prove that it is unique. Now, if i let $T$ be another linear transformation, then i can see that $ST^{-1}$ leaves $1,0, \infty$ invariant, what to do now?
where $$Sz = \frac{z-z3}{z-z4} . \frac{z2-z4}{z2-z3}$$ if possible, can anyone also tell me what would $T^{-1}$ look like
 
Thanks Leaky :)
 
1:00 PM
@Perturbative to say the same about infinite products you surprisingly need AC!
 
@AlessandroCodenotti I've been noticing that AC has been popping up everywhere in proofs of stuff that are seemingly obvious
Like to prove every infinite set has a countably infinite subset
I don't get how some mathematicians still don't accept AC
 
1:16 PM
@AlessandroCodenotti wow, I used another axiom, what's so special about that
what next, I used the commutativity of addition?
@Perturbative I mean, when people do "real maths", they shouldn't bikeshed on foundational issues
foundations belong to a different area of maths
not what people should care about when doing topology / algebra / analysis / ..
 
How is $|a-b| \le c$ called? Is there a proof for that identity/formula?
 
@Narusan When talking about a triangle ?
That's one of the triangular inequalities
$|a-b|\le c \le |a+b|$
 
thanks.
 
Is $[a, \infty[$ closed?
 
Yes @Lozansky
 
1:30 PM
Thanks
 
Take any converging sequence in this interval, its limit will be in that interval
 
in The Symposium, 9 mins ago, by Secret
So "spacelessness" will sound like something that lack dimensions of any kind, and yet is not a point, hmm... it sounds really structureless. Even sets have a notion of cardinality...
Challenge for the foundation people here: Come up with an axiomatic system such that it is consistent to have sets with undefined cardinality
(That will pretty much mean all notion of bijection to that set has to be screwed up somehow...)
such set, if they are logically consistent, are even structureless than generic unordered sets
 
@Secret ZF?
 
uh, isn't infinite dedekind finite and amorphous sets have some notion of cardinality (except they are not alephs)?
(moreover they don't biject with countable sets, thus they are uncountable)
or maybe I should say: They have incomparable cardinality with the alephs, but e.g. dedekind cardinalities should form a linear order?
 
1:45 PM
IZF?
 
Never heard of that one, what is I?
 
intuitionistic ^^
 
I know that if $\varphi \in \mathcal{S}$ then $\varphi' \in \mathcal{S}$. But is it true that the antiderivative of a test function in $\mathcal{S}$ is also in the Schwartz space?
 
the last time I checked, if A has cardinality 1, and B is a subset of A, we don't know the cardinality of B
(if we knew, it would prove LEM)
 
right, make sense
 
1:52 PM
@Lozansky Which antiderivative ?
 
@Astyx $\varphi' \in \mathcal{S} \Rightarrow \varphi \in \mathcal{S}$?
 
That's my point
A function has only one derivative
But ultiple antiderivative
It's easy to convince you this is not true
 
So what restrictions must we put on $\varphi'$?
 
Because if $\phi \in S$ and $c\in\Bbb R^*$, then $\phi+c \notin S$
 
Does $\int \varphi' = 0$ solve that?
 
1:58 PM
You need (and it's not sufficient) to have $\lim_{\pm\infty} \phi = 0$
Therefor $\int _{-\inf}^{+\inf}\phi' = 0$
This is not given for all $\phi'\in S$
I doubt that's sufficient though
So you take $\phi :x\mapsto \int_{-\infty}^x \phi (t)dt$
And you want to show $\lim_{x\to \pm\infty}\phi(x)x^a = 0$ for all $a\in \Bbb N$
We can assume $\phi \ge 0$ I think
And then $x^a\phi(x) = \int_{-\infty}^x x^a\phi'(t)dt$
 
@Astyx But if $\varphi\in \mathcal{S}$ then $\varphi = \Psi'$ and $\int \varphi = \Psi(\infty) - \Psi(-\infty) = 0$ since $(1+|x|)^n |\varphi^{(k)}(x)| \leq C_{n,k}$ for $n,k \in \mathbb{N}$ which means $\varphi$ (and all its derivatives) tend to $0$ faster than the inverted value of any polynomial?
 
What do you mean ?
Ooops my bad
 
I switched up the variables now, hope that's okay
 
$|\int_{-\infty}^{x}\phi'(t)dt| \le \int_{-\infty}^x M t^{-a} dt = M{x^{-a+1}\over {-a+1}}$
So we have our result
Where $M = ||x^a\phi'||_\infty$
 
Ah nice!
 
2:12 PM
Unless I'm missing something very obvious
 
$a\neq 1$?
 
Yeah, but that doesn't matter
Only large values of $a$ matter
Of course to be rigorous you should state $a\ne 1$
Or even better, take $a+1$ in the integral and $M = |||x^{a+1}\phi'|_{\infty}$
 
Quote: Consider the sequence of subintervals of $[0,1]$, $\{I_n\}_{n=1}^\intfy$, which has initial terms listed as $$[0,1],[0,1/2],[1/2,1],[0,1/3],[1/3,2/3],[2/3,1],0,1/4],[1/4,1/2],[1/2,3/4],[3/‌​4,1],...$$ For each index $n$, define $f_n$ to be the restriction to $[0,1]$ of the characteristic function on $I_n$...
Regarding that last sentence, how does that definition of $f_n$ make sense? The $I_n$ are subsets of $[0,1]$, so how can one restrict from $I_n$ to $[0,1]$?
 
 
2 hours later…
4:01 PM
Hi guys, can someone check my equations? I am visually impaired and using a screenreader. I don't know if my mathjax content is displayed correctly. Some are not formatted for some reason. Can someone help me? Thanks.
https://math.stackexchange.com/questions/2717549/prove-that-fibn-is-the-closest-integer-to-fin-sqrt5
 
 
2 hours later…
5:40 PM
@morbidCode did you delete the question?
 
it says 'it's author' so i suggest yes.
 
5:54 PM
@AlessandroCodenotti Yes I deleted it. I created another question without mathjax. Is it easier to reformat equations without mathjax or wrongly formatted mathjax equations? If it's the latter then I'll just undelete it.
@AlessandroCodenotti ah the question has been undeleted by someone already. I'll just delete my new question without mathjax. Here is the original question with horible mathjax. math.stackexchange.com/questions/2717549/…
 
@morbidCode MJ looks fine except for one tiny thing (only one character, so I can't edit it myself). At one point you have mismatched delimiters--your'e starting an inline equation with $ but then end it with $$. If you search on the word "because" you'll see that one of its instances comes just after that equation.
(Note I didn't actually try to follow the proof--I'm making no judgments on your maths. But the formatting's fine except for that one spot.)
 
@nitsua60 the formatting now is not done by me. It got formatted by someone else. The original formatting is horrible. It's weird in the new formatting, my screen reader reads "factorial" on some equations. Can you explain why?
 
[Random] Infinite dimensional vector space actually teach you one thing:
Permutation is really a rotation of the axes
 
Hi
Is this site always so active? Often I have to compete with other users to answer questions here XD
 
@morbidCode I think in the very last equation the editor moved an exclamation mark (expression of incredulity) into the MJ to make it factorial. Probably not what you intended?
Actually, there's also a spare fi sitting in a displayed equation; sixth one from the end.
 
6:12 PM
@nitsua60 probably not what I intended. But I think fi must be the golden ratio, and ci is the same. The symbols I use are mostly in here (see tree recursion and the corresponding exercise 1.13). mitpress.mit.edu/sicp/full-text/book/…
 
6:34 PM
I asked a pretty complicated mathematics question a while ago and don't understand the answer. math.stackexchange.com/a/2709715/200711 I just need the relevant topic for certain parts so I can learn them. The first one is a general equation for a straight line in 2D space, M:ux+vy+w=0, is that quadratics or is there something more to it?
 
7:03 PM
How do we know that $(ml)(jk)$ does not commute with $\sigma$ here in last line??
 
@KalciferKandari you might be more used to seeing something like $y = mx + c$, that's just the same, it just looks nicer than $y = -(ux + w)/v$ I guess
 
@ÍgjøgnumMeg Where did you get $m$ and $c$ from?
 
@KalciferKandari They're abitrary; they just represent numbers
You might see $y = 2x + 1$ and that's a line with slope $2$ and intercept $1$
 
@ÍgjøgnumMeg Oh I see, just an example, that's interesting.
@ÍgjøgnumMeg Having said that, I'm not really used to any of this. It's just quadratics, right?
 
@KalciferKandari No; a quadratic is something with an $x^2$ term. Like $x^2 + 2x + 1$ for example
These are just equations of straight lines, quadratics describe parabolae
 
7:10 PM
@ÍgjøgnumMeg Okay, so if I'm going to search this topic, what am I looking for?
 
@KalciferKandari Probably "equations of straight lines"
 
Suppose $a,b,c\in G$ where $G$ is a group. If a and b do not commute, is it always true that $ac$ and b do not commute?
 
@ÍgjøgnumMeg Well, that's one part, try this: $\sqrt{\frac{1}{1+\tan^2\phi}}=\frac{a}{\sqrt{a^2+b^2+t^2-2tb}}$. I understand where the left part comes from, but I don't know how to go from that to the right.
Again, that is part of this answer math.stackexchange.com/a/2709715/200711.
 
yep I have it open
@KalciferKandari Do you know what $\sec \phi$ is?
As in, have you heard of this trigonometric function?
 
I have, never used it though.
 
7:16 PM
okay so $\sec \phi = 1/\cos \phi$
so you can find $\cos \phi$ if you know $\sec \phi$
There is an identity which says $\sec^2 \phi = 1 + \tan^2 \phi$
 
That's the part I understand.
 
I see
Okay and then $\tan \phi = \frac{b - t}{a}$
so some rearrangement is in order
 
How do you go from the left side to the right side?
 
you have
the following
$$\sqrt{\frac{1}{1 + \left(\frac{b - t}{a}\right)^2}} $$
the squared term under the square root becomes $\frac{b^2-2bt + t^2}{a^2}$
so you want $1 + \frac{b^2 - 2bt + t^2}{a^2}$ to be over a common denominator, so you can add them. So $1 = \frac{a^2}{a^2}$, and this gives you
$$\sqrt{\frac{1}{\frac{b^2 - 2bt + t^2 + a^2}{a^2}}}$$
now you presumably know that $\frac{1}{1/\text{something}} = \text{something}$?
Because that means that
 
Yes. So he's just expanding the bracket, or is there a reason $a$ should be on the top?
 
7:22 PM
Yes, once you flip this $a^2$ to the top the square root gets rid of the square and you end up with what you want
Sorry I'm not sure of your background so I'm being very explicit
 
Pretty weak mathematic background, so this is good.
 
Please help me with this:
21 mins ago, by Silent
How do we know that $(ml)(jk)$ does not commute with $\sigma$ here in last line??
or, with this:
14 mins ago, by Silent
Suppose $a,b,c\in G$ where $G$ is a group. If a and b do not commute, is it always true that $ac$ and b do not commute?
 
@ÍgjøgnumMeg So I understand the top part of (3), then it get's rearranged with 4 terms of $t$. What topic do I need to look at to understand what is happening there?
 
@KalciferKandari The answerer just rearranges and clears denominators. That's just a pretty robotic task of rearranging equations unfortunately.
 
7:29 PM
Got it. So I think my last question is, what are real roots, and how did he get them?
 
@KalciferKandari Real roots are solutions to equations that are not so called "imaginary" or "complex". That is, the roots don't involve the square roots of any negative numbers, that's all
 
This might be basic, but if we are trying to get those 4 values for $t$, how do we go about that? It doesn't look like there are 2 equations to solve simultaneously.
 
For instance, the equation $x^2 + 7x + 12 = 0$ has the real solutions $x = -3$ and $x = -4$. On the other hand, the equation $x^2 + 1 = 0$ has no real solutions (or real roots, there is some subtle distinction but most people disregard it I believe?) because the solution is $x = \pm\sqrt{-1}$, which is absurd (unless you really want a solution)
erm
it's possible the answerer used something like wolfram alpha or maple to find those solutions
 
Hard to do by hand?
 
quadratics are usually easy enough to solve by hand if the numbers are small enough but anything bigger starts to become quite difficult computationally (and in fact if your exponent is $5$ or higher you're not even guaranteed to find solutions with the usual roots etc.)
@KalciferKandari exactly
there are numerical root finding methods that computers will implement to find the roots of a given polynomial
 
7:34 PM
Oooooh.
So, how hard is it to put that through Wolfram Alpha? He said he used Asymtote, which seems very complicated.
 
To put an equation into wolfram alpha is easy enough, just type something like "Solve >whatever your equation is<"
 
Well that makes things easier.
I have 2 separate questions. Firstly, how would you rotate a straight line about an arbitrary point?
 
Indeed, if the highest power is bigger than $2$ I usually just smash the equation into maple or wolfram ahaha
erm
 
Or at least a topic.
 
I'm not sure, you'd be better off asking that on the main site again for a more thorough answer
and do you mean arbitrary or do you mean "given"?
 
7:39 PM
Yes.
And just in 2D space.
 
I suppose
you might
take everything to the origin, rotate it, and then move it back to your point
so
if your point is $(a, b)$ then you'll have
$$\begin{pmatrix} x_{\text{new}}\\ y_{\text{new}}\end{pmatrix} = \begin{pmatrix} a\\ b\end{pmatrix} + \begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \phantom{-}\cos \theta \end{pmatrix}\begin{pmatrix} x_{\text{old}} - a\\ y_{\text{old}} - b\end{pmatrix}$$
in fact
 
It's the rotation and translation of the equation that is the hard part. Thing is, I need take the line resulting from the answer, make an equation using $\phi$, then move it by rotating and translating it, then shove it back into the answer as $M$.
 
Hmm I'm not sure what you mean but there are much much smarter people than me on this site, you'd probably be better just asking another question on the main site
 
I have one prepared, just need to press ask.
 
Go ahead then! I need to go anyway, I'm procrastinating sitting here.
 
7:48 PM
Well thanks for you help.
I really appreciate it.
 
No problem
 
8:08 PM
There is a train with n seats. There are n passengers to be seated. One is blind. First he sits on a random seat. Then the others sit on their seat if it's available. Otherwise sit on a random one.How probable the last one to sit on his seat?
(blind passenger problem)
A simulation gave me a solution that this always 1/2. How to proove it analytically? Tried to solve using tree diagrams but isn't that easy.
 
@aquire “sit on their seat if available”—so each person (except the blind person) has a preferred spot?
i guess it’s simpler to say that the blind person does have a preferred spot but they have no way to select it
If they happen to pick their preferred spot, though, then everyone else definitely picks their preferred spot too
 
8:27 PM
Is $e^{-|x|^5}$ a Schwartz function?
No it can't be, fifth derivative is discontinuous at $x=0$
 
If the blind person picks the kth spot, then passengers 2 through k-1 pick their own spot, and the kth passenger picks a random seat from k+1 to n
In which case you’ve effectively got a blind passenger problem on these n-k seats
 
@PVAL-inactive ????!!! your avatar is a prank
 
I bought a new comp
actually 2
so it changed
 
Ah I see
Nice
 
8:44 PM
Getting a new computer is the most legendary of pranks
Also @Balarka you actually exist! :O
 
Does he ?
 
Hmm :theenk:
 
I thonk therefore I am - Rene Dankertes
 
@Daminark nah that's being risen from the dead.
 
8:48 PM
This is extremely dangerous to our democracy.
 
Good lawd
 
9:01 PM
yo guys, long time no see
3
 
Hi everyone!
 
Hey @Mathein and @lush!
 
How's it going? @Daminark
 
Everything's going well, how about you?
 
Really good. Had a nice birthday and I my advisor said if I'm done with a certain project and I want to continue to work on that, he'll give my a job for that. So I'd be paid just to do research! No teaching/grading commitments
 
9:11 PM
Oh that's fantastic, congrats!
 
Have you started/are you starting the next semester?
 
I started on preparing a seminar talk, yeah
the actual semester begins in 2 weeks
 
I see, how long will it be going for?
 
until june 28th
what about you? has your next quarter started?
 
9:20 PM
Yeah, just finished first week. And that's a bit shorter than I expected for a semester
Like, usually I thought you had 15 weeks of class in a semester, and 10 in a quarter
 
oh lol, july not june
off by a month
 
Ah
I'm not used to school going on for that long but that makes more sense
 
Which classes are you taking?
 
Officially, I'm doing combinatorics, Galois, complex, and GMT. Also I'm auditing ANT and AT
 
sounds nice
This is the second complex course, right? What are you covering?
 
9:24 PM
So, we don't really have much of a syllabus going. Our prof said we'll spend at least half the class on complex analysis, and then later focus on applications to other subjects. I know the last time she taught the class she did the prime number theorem
 
nice! number theory is always good
 
So far, day 1 was just the basics of holomorphic functions, power series, and integration on curves (she just listed theorems that we should know from undergrad complex)
Then we started talking about local behavior of holomorphic functions, so stuff like holomorphic functions mapping small enough circles to shapes which lie in a tiny annulus, and the fact that aside from a discrete set, you preserve angles. Used that to prove max modulus, then Schwarz lemma
Day 3 we did Hadamard's three circle theorem, two more proofs for max modulus, one of which involved a sort of quantitative version of the open mapping theorem. Then we started on conformal maps
So yeah that's where we're at now
 
sounds good
 
You said you're also doing a second complex class, yeah?
 
yeah, I did that last semester
I'm having an exam in a few weeks
we covered infinite partial fraction decompositions (Mittag-Leffler), infinite products, the gamma function, elliptic functions and modular forms
next semester there's a course just on modular forms as a continuation
 
9:39 PM
Fun
 
yeah, the lecturer is a bit slow, but he's a well-regarded expert on modular forms. One of his students won a 1 million dollar price for some work on a generalization of modular forms and he has some papers in the annals that are cited in quite some books and also wikipedia
there's the "Kohnen space" named after him
 
him = the lecturer or the student?
 
lecturer
 
Ah
 
What's an easy check for if a function can be considered a distribution?
For example, $e^{-2x}H(x)$ where $H$ is Heaviside
 
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