Mathematics - 2015-01-17 (page 1 of 2)

saadtaame

12:21 AM

hello

Ramanewbie

12:43 AM

hi there

is there anyone ?

hellooooooooooo

quid

Hell @Ramanewbie

Ramanewbie

hi quid

i've a question

quid

Go ahead.

Ramanewbie

I'm sure you can help me,

it's just an inequation :

$\left(\dfrac{x+\frac{b}{2a}}{2a}\right)^2\geq0$

wut ??

yes it's dine

fine *

evinda

@DanielFischer I am looking at the description of Select(A,p,r,i).
At the first step, we divide the n elements of the array into $\lfloor \frac{n}{5} \rfloor$ groups of 5 elements each of them and at most one more group that contains n mod 5 elements.
Then we find the median of each of the $\lceil \frac{n}{5} \rceil$ groups, by sorting the elements of each group and then by choosing the median of the sorted catalogue of the elements of the group.
Then at the third step, using the procedure SELECTION recursively, we find the median x of the $\lceil \frac{n}{5} \rceil$ medians that were dete…

quid

12:50 AM

@Ramanewbie I cannot quite make sense of this. You have a square so it should always be nonnegative.

Ramanewbie

hem of course...

and what about it's equal to 0 ?

quid

It is equal to 0 when x + b/2a is 0 so when x = - b/2a

Ramanewbie

tks

saadtaame

how many pieces of information do we need to store a permutation on n elements?

better than O(n).

quid

@saadtaame what do you mean by better more or less?

@evinda I have no idea about the specifics but generally I would assume that the median of the median is the median of the data given by the earlier computed medians. So if you first computed medians m1, m2, m3, m4 then the median of the media should be just the median of those four numbers.

evinda

1:03 AM

@quid A ok... And how could this be implemented at an algorithm although there are other elements between them?

quid

Sorry I do not know an answer to this @evinda

evinda

Ok, no problem... Thanks for your answer :) @quid

robjohn

@Ramanewbie Are you aware that you can edit old comments for up to two minutes?

Ramanewbie

I know that . Why ?

robjohn

@Ramanewbie I just noticed that you typed "fine*" on the line after "yes it's dine" instead of simply correcting it.

Ramanewbie

1:15 AM

oh yes that's right

it's just because I'm habitued to that

I don't know many chats where this feature is available ;)

robjohn

@Ramanewbie Ah... I am used to correcting and to linking my chat comments.

Ramanewbie

because you're used to this forum maybe ?

robjohn

@Ramanewbie yes

Ramanewbie

Do you kow hippa ?

robjohn

@Ramanewbie from this chat, yes. Not in person.

Ramanewbie

1:18 AM

Hippalectryon right ?

robjohn

@Ramanewbie yep

Ramanewbie

ok

where're you living ?

robjohn

@Ramanewbie In the sidebar is pinned a URL to a chat map.

Ramanewbie

so what time is it where you live ?

saadtaame

1:47 AM

@quid 2 or 3 integers for example so that i can recover the permutation by using these 3 integers (they somehow define the permutation uniquely).

i can map permutations to unique numbers but those will be too large to store in computer

quid

I see. Note that you have n! permutations. This is more than 2^n. So you cannot get by with less than n bits.

saadtaame

can we count the number of permutations that have order m?

or somehow make use of decomposition into disjoint cycles

quid

Likely yes, for both. The first could be a reasonable question for main.

saadtaame

0

Q: Number of permutations of order m

Is there a closed form for the number of permutations (on n letters) that have order m? If not, is there a tight upper bound?

Kevin Driscoll

4:12 AM

How would you go about formally showing someone that $$\sum_{n=1}^{\infty} 2n + \sum_{n=0}^{\infty} (2n+1) = \sum_{n=0}^{\infty} n$$

Kaj Hansen

4:45 AM

@KevinDriscoll, both sides diverge to infinity?

Kevin Driscoll

@KajHansen Yea whatever, substitute any convergent sum you wish with the same property, all the even terms are in one sum and the odd ones in the other sum

I mean without appealing to what the value of the sum may/may not be

Kaj Hansen

Oh, so really you wish to write $\displaystyle \sum a_{2n} + \sum a_{2n+1}$ etc

Kevin Driscoll

@KajHansen Sure

robjohn

7:49 AM

@KevinDriscoll You're missing $0$ from the left side.

Martin Sleziak

8:47 AM

@KevinDriscoll You probably want to have some conditions on the terms of your sequence. For example for $a_n=(-1)^n$ the equality $\sum a_{2n} + \sum a_{2n+1} = \sum a_n$ is not true.

If all $a_n$'s are positive, then both sides are equal to $\sup \{\sum\limits_{n\in F} a_n; F\text{ is finite}\}$.

Shi...

10:05 AM

I[r]=∫(arExp[-r]-brSin[k(r-d)]Exp[-r])Besse1J[0,kr]dr can I get the integration of this function?

evinda

11:00 AM

Hello @ThomasAndrews !!!
Could you maybe tell me when it holds that $\log_a n<\log_b n$ knowing that $a>b$ ?

Alessandro

Still dealing with those logs @evinda?

evinda

Yes :/ @Alessandro

On Tuesday I have an exam in Design and Analysis of Algorithms @Alessandro

robjohn

@evinda $\log_a(n)=\frac{\log(n)}{\log(a)}$

@evinda so I'd say when $\log(n)\gt0$, assuming $a,b\gt1$

evinda

@robjohn It holds this:
$$\log_a n=\frac{\log_b n}{\log_a b}$$
right? How can we use the fact that $a>b$ ?

robjohn

@evinda That is quite mixed up... $$\log_a(n)=\frac{\log_x(n)}{\log_x(a)}$$ for any $x\ne1$

evinda

11:12 AM

@robjohn Yes, that's what I meant :)

robjohn

Since $\log$ is monotonic increasing, and $\log(n)\gt0$, then $\log_a(n)\lt\log_b(n)$

evinda

@robjohn So you use the fact that $\log_a n \geq 1$ ?

robjohn

11:38 AM

@evinda No, the fact that $\log(n)\gt0$

Chris's sis

12:33 PM

Greetings

ADG

me? thanks

@Chris'ssis ??

Chris's sis

@ADG What do you mean?

ADG

nothing btw? what r u doin now?

Chris's sis

@ADG Working on my book. You?

ADG

oh great. I'm messing with my phone technnically

Makoto K.

12:41 PM

Any downvoters here? meta.math.stackexchange.com/questions/19255/…

@Chris'ssis Could you do me a favor and view that thread and tell me the upvote and downvote counts? I only ask because I believe you have sufficient reputation

+3/-4

@ADG Thank you ADG

@MakotoK. +3/-4

Thanks to you aswell @Chris'ssis

Chris's sis

Welcome

Balarka Sen

12:47 PM

@DanielFischer Lend me a hand at an altop question.

ADG

@BalarkaSen why are you calling him?

anyways @Chris'ssis, you've been long around, can I ask you smthg?

Balarka Sen

@DanielF I want to prove that the usual immersion of the Klein bottle in $\Bbb R^3$ is homotopy equivalent to $S^2 \vee S^1 \vee S^2$

Chris's sis

@ADG Ask me.

Balarka Sen

I don't see how one can do it. Apparently they're contracting the whole handle to a single stick, but that's not a homotopy equiv.

ADG

Does answering in short a bad thing like giving hints to homework type question @Chris'ssis

Balarka Sen

12:50 PM

Depends on the question @ADG

ADG

And also not citing sources ?

Chris's sis

@ADG Agree with @BalarkaSen

ADG

Don't know why but the moderator at Chem.SE is after me for both the things. Even if I write an answer on my own he usually deletes them and says cite resources?

Chris's sis

@ADG Which moderator?

ADG

Should I name him?

Chris's sis

12:52 PM

@ADG Sure (if you want to)

ADG

jonsca

like the one here

@Chris'ssis r u there?

Chris's sis

@ADG I was looking at that.

ADG

Oh so great of you @Chris'ssis ;( sob

@Chris'ssis like someone asked "Is there any reactivity series of ligand? Can it be possible to make a list of the reactivity series of ligand? Please help me." and I answered "Do you know about the Spectrochemical series?This is what you're looking for. There's many around."

Chris's sis

I see.

ADG

@Chris'ssis what do you think, am I overreacting, is he right?

Chris's sis

1:02 PM

@ADG Well, maybe I'm not the proper person to say that since I also overreacted sometimes (as some said) ... :-)

ADG

@Chris'ssis anyways thanks for your time, I know you tried to help

Chris's sis

@ADG I also become "evil" once in a while when I'm provoked systematically and then say things, but otherwise I'm a very peaceful person. :-)

Daniel Fischer

@BalarkaSen Hmmmm, what is the usual immersion of the Klein bottle in $\mathbb{R}^3$?

Lord_Farin

@Chris'ssis This happens to all of us, right?

Chris's sis

@Lord_Farin Yeah, more or less :-)

evinda

1:13 PM

@robjohn How did you use this? :/

Pedro Tamaroff

►

evinda

@DanielFischer Hey!!!
Could you take a look at this?
http://stackoverflow.com/questions/27999839/execution-time-of-breadth-first-search

Pedro Tamaroff

@DanielFischer Hello Daniel san.

iwriteonbananas

@BalarkaSen what's an immersion btw.?

Daniel Fischer

@PedroTamaroff Hola hermano.

Pedro Tamaroff

1:18 PM

@DanielFischer Feeling religious, eh?

=D

Daniel Fischer

@PedroTamaroff Religious?

Pedro Tamaroff

@DanielFischer Yes. Sometimes "hermano" is used as in "we're all sons of the one Father."

Since we're not kindred.

Daniel Fischer

@PedroTamaroff Well, I thought of "hermano moderator".

Pedro Tamaroff

@DanielFischer Brother in arms!

iwriteonbananas

@DanielFischer daniel, the set $\{(x, \sin(1/x)) : 0<|x|<1\}$ has exactly one component, right?

Daniel Fischer

1:21 PM

@PedroTamaroff And who's Henry V.?

Pedro Tamaroff

@DanielFischer I have no idea! Or do you mean the King?

Daniel Fischer

@iwriteonbananas By component you mean connected component? Then two.

iwriteonbananas

@DanielFischer yeah i mean connected component. why two?

Pedro Tamaroff

@DanielFischer That thing is path-connected, isn't it? He didn't adjoin $0<y<1$. Ah, he wrote $0<|x|<1$.

iwriteonbananas

oh yeah nvm im stoopid

Daniel Fischer

1:22 PM

St Crispin's Day Speech

The St. Crispin's Day speech is a famous speech from William Shakespeare's play Henry V in Act IV Scene iii 18–67. On the morning of 25 October 1415, shortly before the Battle of Agincourt, Henry V made a brief speech to the English army under his command, emphasizing the justness of his claim to the French throne and hearkening back to the memory of previous defeats the English kings had inflicted on the French. According to Burgundian sources, he concluded the speech by telling the English longbowmen that the French had boasted that they would cut off two fingers from the right hand of every...

Pedro Tamaroff

@DanielFischer Well, now you see I'm an ignorant brute.

iwriteonbananas

@DanielFischer does it have 3 path components?

Daniel Fischer

We few, we happy few, we band of brothers;
For he to-day that sheds his blood with me
Shall be my brother;

Pedro Tamaroff

Let me re-read.

iwriteonbananas

@PedroTamaroff okay

Daniel Fischer

1:25 PM

@iwriteonbananas If you take the union with something like $\{0\}\times I$, then you have three path components, but the thing is connected.

Pedro Tamaroff

@iwriteonbananas It has two path components.

Daniel Fischer

(Where $I$ is an interval intersecting $[-1,1]$.)

@PedroTamaroff We have no point with $x = 0$ in the set.

Pedro Tamaroff

:19584276 Yes, sorry.

iwriteonbananas

i guess the connected components are also path components?

Pedro Tamaroff

@iwriteonbananas Yes.

Unless again I'm missing something.

iwriteonbananas

1:28 PM

@PedroTamaroff ok

i guess it's not homeomorphic to $\mathbb{R}$ then, right? since $\mathbb{R}$ just has one (path) connected component but this space has two

Daniel Fischer

@iwriteonbananas A connected component is always a union of path components. So if a space has the same finite number of connected components and path components, every connected component must be a path component.

iwriteonbananas

@DanielFischer i see

are the path-components closed subsets of the space?

they should be by continuity of sin, no?

Daniel Fischer

@iwriteonbananas Not necessarily. Consider the topologist's sine curve.

That is pretty much, the thing you have together with $\{0\}\times [-1,1]$.

iwriteonbananas

@DanielFischer does the topologists sine curve also have two path-components btw?

Daniel Fischer

The closure of the path component $\{(x,\sin \frac{1}{x}) : x > 0\}$ contains $\{0\} \times [-1,1]$.

iwriteonbananas

1:33 PM

oh yeah dang it

Daniel Fischer

@iwriteonbananas Usually, one considers only $x\geqslant 0$ in the top. s.c., so then you have two path components. If you also have negative $x$, then three.

iwriteonbananas

@DanielFischer right, yea i meant the one where we only consider nonneg. x

is $\{(x,\sin \frac{1}{x}) : x > 0\}$ homeomorphic to $(0,1)$?

Daniel Fischer

Guess?

iwriteonbananas

i guess it is

but not sure why

which is usually a bad sign

Daniel Fischer

@iwriteonbananas If you're sure, it's no longer a guess.

iwriteonbananas

1:38 PM

tru dat

Daniel Fischer

Can you give a bijection between the two and its inverse?

iwriteonbananas

jeez...i thought people in topology dont do that

Daniel Fischer

@iwriteonbananas Don't do what?

iwriteonbananas

give explicit homeomorphisms

:D

Daniel Fischer

@iwriteonbananas Sometimes, that's the easiest way to show two spaces are homeomorphic.

iwriteonbananas

1:42 PM

well we just map $x\mapsto (x,\sin(1/x))$

Pedro Tamaroff

@iwriteonbananas The homeomorphism is easy to visuzalise: flatten the wave injectively onto $(0,\infty)$, then use $(0,\infty)\sim (1,\infty)\sim (0,1)$.

iwriteonbananas

@PedroTamaroff yeah you're right

Daniel Fischer

@iwriteonbananas Okay. Then the next questions are: Is it continuous? What is the inverse? Is that continuous?

iwriteonbananas

@DanielFischer yeah its continuous bc each component is. inverse i guess is $(x,\sin(1/x))\mapsto x$ which is also continuous

1 sec

Daniel Fischer

Right. Why is $(x,\sin(1/x)) \mapsto x$ continuous?

iwriteonbananas

1:46 PM

it's trivial to check continuity using sequences

Daniel Fischer

@iwriteonbananas Can you give a higher-level argument?

iwriteonbananas

:D

hmm

its just the projection onto the 1st coordinate

Daniel Fischer

@iwriteonbananas Good. And what do we know about coordinate projections in general?

iwriteonbananas

they're quotient maps which are always continuous

Daniel Fischer

I'd rather think of the initial topology (wrt the projections) on the product, but okay.

robjohn

1:56 PM

@evinda look... which is bigger: $\frac{\log(n)}{\log(a)}$ or $\frac{\log(n)}{\log(b)}$ if $a\gt b$?

evinda

@robjohn The second is bigger

robjohn

@evinda what if $\log(n)\lt0$?

evinda

@robjohn Then the first is bigger... It is $\log(n)\lt0$ when $n<1$, right?

robjohn

@evinda yes

evinda

$$\log_a n< \log_b n \Rightarrow \frac{\log_n a}{ \log_n n}< \frac{\log_n b}{\log_n n}$$
Is this right, @robjohn ?

Pedro Tamaroff

2:14 PM

Nevermind.

Daniel Fischer

@PedroTamaroff No. Apparently something looks similar to something else.

Pedro Tamaroff

@DanielFischer The amount of "data" was off-putting but it was well received in MO.

Could you do me a favour and migrate my question on flat $\mathcal O(D)$-modules to MO?

robjohn

@PedroTamaroff wow... the only property of the zeta function used in that first limit is $\lim\limits_{s\to1}\zeta(s)(s-1)=1$.

@PedroTamaroff That is one long post.

Pedro Tamaroff

@robjohn Yes. Unnecessarily long in fact.

John Doe

Hi everyone.

Daniel Fischer

2:21 PM

@PedroTamaroff I have no idea whether it would be suitable for MO. Ask Mariano? Or some other moderator with an MO account?

John Doe

Anyone watching the snooker?

robjohn

@PedroTamaroff gratuitous mention of $\zeta(s)$... I would have simply used $\frac1{s-1}$

Pedro Tamaroff

@DanielFischer Yes, Mariano said it could be moved.

Secret Name

Hello.

robjohn

@JohnDoe never watched snooker.

Secret Name

2:23 PM

Can I ask you? What is the best way for division?

Daniel Fischer

@robjohn You should some time, it's awesome. Best TV sport ever.

Secret Name

I want to hear your opinion.

John Doe

@robjohn It's the current world champion vs the snooker player regarded as the greatest of all time.

And the defending champion of the tournament.

Daniel Fischer

@PedroTamaroff And gone.

Pedro Tamaroff

Hope MO guys aren't too mean to me. =)

Daniel Fischer

2:24 PM

@JohnDoe Stephen Hendry, or Steve Davis?

@PedroTamaroff You'll find out.

robjohn

@PedroTamaroff Mariano will pound on you :-)

2

John Doe

@DanielFischer :Ronnie O Sullivan vs Neil Roberston, but yeah Hendry might still arguably be regarded as the best.

Daniel Fischer

Right, Ronnie is also one of the candidates for all time best.

user136984

I had a dream about elliptic curves...

skullpatrol

Get out!

NOW

user136984

2:35 PM

Pedro Tamaroff

@skullpatrol What?

skullpatrol

The elliptic dreamer.

user136984

I have no idea why there is a full stop at the end of that equation though...

Daniel Fischer

@Toroidal Perhaps that equation is the final part of a sentence?

user136984

Perhaps...

Daniel Fischer

2:37 PM

We next consider the elliptic curve with the equation $$y^2 = x(x-a^p)(x+b^p).$$

Jasper Loy

@Toroidal Please do not troll. I think you are trolling from what you have posted in both rooms.

user136984

Both rooms?

skullpatrol

Yes.

user136984

I am definitely not large enough to be a troll.

user136984

Anyway what is wrong about talking about elliptic curves? I do not see how that is trolling.

skullpatrol

2:39 PM

What does size have to do with it?

Troll.

user136984

Trolls are big and fat and carry big log things to hit people on the head with...

skullpatrol

Do not feed^

user136984

DO NOT FEED THE TROLLS, there should be a sign like that.

John Doe

Does anyone know how to manipulate line spacing in latex in the preamble when you are working in the 'book' document class?

user136984

Does anyone happen to know where I could find the 200-page paper by Andrew Wiles where he attempts to prove Fermat's Last Theorem using parts of the Taniyama conjecture?

skullpatrol

2:42 PM

Let's go back to the English room @Toroidal I'll show you how I handle trolls like you pal.

Alessandro

@JohnDoe no, but I know where to find people who know! tex.stackexchange.com

John Doe

Okay thanks. I was trying to avoid that :)

Alessandro

@JohnDoe well, maybe you'll find somewhere here as well, but if you don't there's always this alternative :)

user136984

Seriously, I am trying to find that 200-page paper. Does anyone know where I can find it? :)

user136984

I read about it in a good book and would like to read it myself, but I am just having some trouble tracking the actual thing down...

John Doe

3:03 PM

Current world number one, not current world champion.

teadawg1337

3:47 PM

Hello, @TedShifrin

You'll be glad to know that I'm taking Calc I this semester instead of Pre-Calc

Pedro Tamaroff

@teadawg1337 What will you be learning?

teadawg1337

@Pedro It's a course on single variable calculus. Which is something I've already done, but at least I'm getting college credit for it this time

It also means I can spend more time doing independent work :D

evinda

4:07 PM

@DanielFischer The topological sort of a graph can be considered as an order of its nodes along a horizontal line so that all the directed edges go from the left to the right.

How could we show that all the directed edges go fom the left to the right?

We suppose that it is:

Then it holds that $[d(w),f(w)] \subset [d(u),f(u)]$. How can we find a contradiction?

Chris's sis

4:19 PM

yahoo.com/parenting/…

(it just appeared in my mail box - interesting)

Ramanewbie

4:47 PM

hi

is there anyone here ?

Arkamis

Nope

Ramanewbie

^^

I've a question

I'ld like a concrete example for the résolution of a polynomial

A second-degree one

A situation that could apply in always life

Arkamis

Sorry, I don't know what the resolution of a polynomial is

Ramanewbie

what do you mean ? Maybe I'm not saying it properly

I'm a begginer ^^

Arkamis

I am not familiar with the term "resolution of a polynomial."

Ramanewbie

4:55 PM

What's wrong with it ?

Arkamis

Nothing -- I've never heard it before!

Ramanewbie

so what's a polynomial for you ? just a function ?

Arkamis

I know what a polynomial is

I don't know what the "resolution" is

Do you mean finding the roots of a polynomial?

Like computing $x$ when $P(x) = 0$?

Ramanewbie

erm wait no

well maybe

It depends what you mean :

I would like an exercice where you must solve that type of equation :

$x^2+x+5$

for instance

Arkamis

Ok

That occurs many places

Ramanewbie

5:00 PM

what do you mean ?

Arkamis

The term for a second order polynomial like that is sometimes known as a "quadratic equation"

In general, you have $ax^2+bx+c$

Ramanewbie

yes

Arkamis

So you want to know where they are used?

Ramanewbie

you can put coefficients if you want to

Arkamis

What are you asking?

Ramanewbie

5:01 PM

well, I'ld like an exercice where it has an use in real life

for instance :

500 hands are shaked at a party. How many people were at this party ?

Arkamis

Ok

Ramanewbie

Then you have to resolve $\dfrac{x^2-x}{2}-500=0$

Arkamis

Here is an example from real life

Ramanewbie

so $\dfrac{x^2-x-1000}{2}=0$

Arkamis

The force of drag on a car is proportional to the square of its velocity, and the resisting force due to friction is proportional to its velocity. What is the terminal velocity of a car rolling down a hill with a constant slope?

So you sum the forces:

$F_{\text{drag}} + F_{\text{friction}} + F_{\text{gravity}} = 0$

Ramanewbie

5:05 PM

yes

Arkamis

This becomes $dv^2 + fv + g = 0$

Ramanewbie

that's great

but don't you have sth more explicit, for begginners ?

really noob begginners

Arkamis

Real world problems are rarely beginner level.

I don't understand what you're looking for

Ramanewbie

An exercice where you have to resolve a second degree polynomial, but sth conrete and easy to understand for begginers

Arkamis

Compute $x$ when $3x^2 + 10x + 3 = 0$.

Or better yet

here's one

The drag on a toy car is given by $3.5v^2$. The friction is given by $3v$. If the toy car is rolling down a hill where the force of gravity is $-0.5$, what is the terminal velocity of the toy car?

Ramanewbie

5:16 PM

what's v

iwriteonbananas

@DanielFischer can u give me an example of a space that's first countable but not 2nd countable?

Arkamis

$v$ is its velocity

Ramanewbie

ok

Arkamis

So you need to find the velocity when the sum of its forces balances out

Ramanewbie

ok tks

Bill Dubuque

5:58 PM

@robjohn Yet more data!

robjohn

@BillDubuque Ah

Arkamis

Boy, am I sure glad this four year old post was bumped back to the main page.

Nothing says "improved readability" than changing an H to an $H$ in an answer that contains a 23-line polynomial.

evinda

Hey @Arkamis!!! Could I ask you something?

@Arkamis We want to find for which $p$, the equation $x^2+y^2=3z^2$ has a rational root in $\mathbb{Q}_p$.

For $p=3$:

Let $(x, y, z)$ a root in $\mathbb{Z}_3$ and not all of $x, y, z$ are divisible by $3$.

$\Rightarrow x^2+y^2 \equiv 0 \pmod 3$ in $\mathbb{Z}_3$

$\Rightarrow x \equiv 0 \pmod 3 \text{ and } y \equiv 0 \pmod 3$

$\Rightarrow z \equiv 0 \pmod 3$, a contradiction.

So, there is no solution in $\mathbb{Q}_3$.

How do we conclude that $z \equiv 0 \pmod 3$ ?

Arkamis

@evinda I am literally the worst person here to answer such a question.

evinda

A ok @Arkamis

Arkamis

6:12 PM

It has been at least 4 years since I've looked at any of that kind of material, and I promptly forgot it all when the class was over.

but, I can take a stab

Since $x^2+y^2 = 3z^2$, it is obvious that $x^2+y^2 \equiv 0\bmod 3$

evinda

So we know that $3z^2 \equiv 0 \mod 3$.. How do we conclude that $z \equiv 0 \mod 3$ ? @Arkamis

Arkamis

I'm getting there, hang on!

Then, suppose that we had $x \not \equiv 0 \bmod 3$ and $y\not \equiv 0\bmod 3$, then we have $x^2 \equiv 1 \bmod 3, y^2 \equiv 1 \bmod 3$, so their sum cannot be equivalent to 0.

And... hm. I'm not seeing that next step either.

yeah, got nothing. I don't think that's a valid conclusion at all.

Ted Shifrin

@teadawg: Yes!! Glad you went and made your polite fuss!

Arkamis

Ah wait

I think I have it @evinda

Ted Shifrin

@teadawg: Most college courses try to put a bit more emphasis on word problem skills than high school courses.

Arkamis

6:20 PM

Since $x \equiv 0 \bmod 3$ and likewise for $y$, we can write $x = 3m$ and $y = 3n$ for some $m,n$.

Now, throw that into the equation: $(3m)^2 + (3n)^2 = 3z^2$. Now, we have $3m^2 + 3n^2 = z^2$. Therefore, $z^2 \equiv 0 \bmod 3$, hence so much $z$ be.

argh

These trivial formatting edits are starting to irritate me,

@evinda Do you see now?

Daniel Fischer

@iwriteonbananas Any non-separable metric space. For example an uncountable discrete space.

Ted Shifrin

heya @DanielF and bananas

Daniel Fischer

Heya @Ted and oranges

Kevin Driscoll

@TedShifrin I know that math majors study groups usually in Abstract Algebra. Is there a separate math class for infinite Lie groups and representation theory, or do they leave all that to the physicists?

user159870

6:37 PM

Heya @DanielFischer and fishes

HAHAHAHHAHAH

Alessandro

Good evening (or day/night based on your timezone) to everyone

Arkamis

@KevinDriscoll Such a math class exists, but it is disguised to keep the filthy physicists from registering.

evinda

@Arkamis I see!!!! Thank you very much!!!

Good evening @Alessandro

teadawg1337

I'm going to be taking calculus-based physics this semester, so I should be able to determine whether or not I should become a mathematical physicist AND a mathematician

Arkamis

@teadawg1337 Calc-based physics is easy. Just remember, F=ma and you can't push with a rope.

Kevin Driscoll

6:47 PM

@Arkamis Yes, I know we stink of computation and calculation. Suppose you were to name such a class though, what would you name it?

@teadawg1337 I wouldn't try and put too much stock in an introductory physics class. It's usually not taught in a way that would be representative of what mathematical physicists do. If you're interested, you should talk to a mathematical physicist at your school if you can, or if there aren't any at least a strong theorist.

teadawg1337

@KevinDriscoll I took AP Physics B in high school, and I enjoyed the living hell out of it. Got a 4 on the AP Exam without studying.

I also don't think Physics 2110 would be an introductory course :P

Alessandro

Do you have any suggestion for an introductory book to logic and set theory? I have a copy of Shoenfield's mathematical logic but it's a bit harsh...

Kevin Driscoll

@teadawg1337 The intro courses here are numbered 2211 and 2212.

But ya if you have AP Physics B credit, maybe you're in a more advanced E&M class

Ah wait, no B is the one that does mechanics and E&M

So the next course int eh series would be...... Intermediate Classical mechanics. Or a first course in Quantum mechanics.

teadawg1337

AP Physics B is algebra-based, not calc-based. Also, I'm only in a community college right now. 2120 is the most advanced physics course I can take there, which is calculus-based E&M, optics, quantum, modern, and waves

I'll be taking 2120 next semester

(I'm a first-semester freshman right now)

Kevin Driscoll

7:09 PM

Ah, I see. I think it's a bit unfortunate the state of trying to be a physics or math student at a community college for 2 years and then transfer

At a 4 year school by the end of your 2nd year you'd have already taken at least 4 and probably 5 physics courses. But at most community college you can only take 2 or sometimes 3.

I imagine math is similar because they're unlikely to have any pure math courses. Just engineering type stuff through Diff Eq.

iwriteonbananas

@TedShifrin well well well, tedster is back!

Kevin Driscoll

I started at a community college myself, but that was dual-enrollment in High School

teadawg1337

My high school GPA limited my options, so I'm going to community college for two years to make up for it

Regaining lost ground, if you will.

Chris's sis

7:34 PM

$$\lim_{n\to\infty} \sum_{k=n+1}^{2n} \frac{\frac{1}{2} \log ^{\frac{1}{k \log (2)}-1}(2) (-k \log (2)+\log (k \log (2))-1) k^{\frac{1}{k \log (2)}}+\frac{1}{3} \log ^{\frac{1}{k \log (3)}-1}(3) (k \log (3)-\log (k \log (3))+1) k^{\frac{1}{k \log (3)}}}{k}=?$$

$$\log (2) \left(\frac{1}{3\log (3)}-\frac{1}{2\log (2) \log (\log (2))}\right)$$

Transcript for

$Mathematics$ Mathematics