10:00 PM
I have a question: What is the extent of a cube?

@WillHunting When I multiply it out it doesn't turn into a differenceo f two cubes

@Argon Or Charlon?

@RavenDreamer what do you mean by extent?

@Charlie Sounds like Charlatan

@OldJohn See page 5 on this PDF: google.com/…

user19161
10:01 PM
@Jordan $(a-b)(a^2+ab+b^2)=a^3+a^2b+ab^2-a^2b-ab^2-b^3$.

what are morphisms in a category of CW complexes?

@RavenDreamer can't you explain it here?

@Argon So it is Aarlie

$-a^3 b - a^2 b^2 -a b^3$

are these just continuous mappings that take cells to cells?

10:02 PM
oh Dave Eberly's C++ library - cool!

oh
I suck at math and I forgot how to multiply

user19161
@RavenDreamer Maybe the vertices?

@Jordan $1\times 1 = ?$

this will be a short round 2 of calculus 2, probably drop out in the first month
fun

user19161
10:03 PM
@Jordan That's because you haven't understood multiplication. I told you, more haste, less speed.

Some men are created for math, others for cleaning toilets
The choice is yours.

@RavenDreamer OK - which bit of that definition is the real problem?

I know I will never be good at math no matter how hard I try

@RavenDreamer, where does it mention 'cubes'?

@N3buchadnezzar Hahaha, I love how those are the only choices!!

10:04 PM
but it is just a means to an end,something the college is forcing me to do to further their own profits

@PeterSheldrick bounding "box".

I apologize; rectangular prism would have been more correct

@Argon There are only ten kinds of people in this world, those who understand binary and those who dont.
@Charlie Well there are toilets out there, and some need to clean them..

@OldJohn The formula for the vertices.

10:04 PM
@RavenDreamer, nah a cube is a rectangular box where each side is the same length

he is just defining a box with $C$ as centre and $\pm a_i$ for the sides

here the sides have different lengths! those are the 'extents'...

when was factoring ever taught in school?

10:05 PM
extents = lengths of the sides

But you say "There are 10 kinds of people in this world..."

Q. What's purple and commutes?

@PeterSheldrick So the extents are 1/2 width, 1/2 height, 1/2 depth ?

@Argon my programming prof liked to do these jokes :P

A. An Abelian grape

10:06 PM
@RavenDreamer no - the sides are of lenght $2a_i$

@Charlie Hahaha!

@Argon very funny!

Why did the prof. name his dog Cauchy?
Because he left a residue at every pole!

user19161
@RavenDreamer Seems that they are half the lengths of each of the three sides of the cuboid.

where he says $|\sigma_i|=1$, it would have been clearer if he had said $\sigma_i = \pm 1$

10:07 PM
You're losing me at the dollar signs.

@RavenDreamer ChatJax

@WillHunting Thank you.

see use plaintext

It will parse the Tex

@RavenDreamer you need chatjax

10:07 PM
the latex support in the chat isn't good enough!
oh

how would I factor something like $3x^{3/2} - 9x^{1/2} + 6x ^{-1/2}$?

user19161
@RavenDreamer Imagine going from the centre of the cuboid to each of the eight vertices of a cuboid. One can go forward or backward in each of the three directions to get the eight points.

@Jordan Multiply all by $x^{1/2}$

@Charlie $$\lim_{x \to 8^+}\frac{1}{x-8} = \infty \ \Rightarrow \lim_{x \to 3^+}\frac{1}{x-3} = \omega$$

doesnt that change the value?

10:08 PM
@WillHunting yes. That makes sense.

@Jordan Yes it would.
Sorry, I thought you were solving it

just factoring
pull out a -1/2 I guess?

@N3buchadnezzar If you took a contour integral over Western Europe, what would its value be?
0, because all the Poles are in Eastern Europe.

Hahaha

user19161

10:10 PM
for example, if you have a cuboid with centre at (1,2,3) and sides 4,6,20, then the vertices will be at (1+/-2,2+/-3,3+/-10)
that would look better with LaTeX :)

@WillHunting Cleaning toilets is very important

user19161
@N3buchadnezzar The choice is often not ours to make. Life is unfair. People are born different, we must admit that.

user19161
@N3buchadnezzar Yes, Will cleans the toilets on the MIT campus.

@WillHunting :)

@WillHunting Will is doing a great job then!
My point is not everyone is cut out for math, why force them. Other jobs are equally important.

10:12 PM
I got that one on my own, math confidence + 1/2

user19161
Yes, only stupid people say cleaners are not important.

@Jordan mathConfidence++;

user19161
Nonetheless I hope to see more equality in this world. I think ten per cent of people own ninety per cent of the money.

user19161
There are people eating delicacies every day while others are starving.

$$\frac{64}{16} \, = \, \frac{6\!\!\!\backslash4}{16\!\!\!\backslash} \,=\, \frac{4}{1} \,=\, 4$$

10:14 PM
Yep

user19161
There are politicians who get million dollar salaries while homeless people sleep on the streets.

@Argon Nooo, this is wrong! :p

@WillHunting and people here throwing away food every day which would keep people alive in some parts of the world :(

user19161
@OldJohn I try not to waste food, but sometimes I can't finish it though.

10:15 PM

@N3buchadnezzar Well, this is how I've been doing division... OH NOES! :)

@WillHunting me too

I love jokes like these

user19161
@PeterSheldrick See the link near the top right.

10:15 PM
thanks...

$$\frac{\mathrm{d}}{\mathrm{d}x} (x) = \frac{\mathrm{d}\!\!\!\backslash}{\mathrm{d}\!\!\!\backslash x} = \frac{1}{x} \cdot x = 1$$

user19161
@n3b Much analysis is geometrically intuitive. Just visualise graphs of functions which often help you in proofs or counterexamples.

user19161
Algebra however often lacks that geometrical intuition.

@WillHunting but beware of relying too much on the picture - it can mislead :)

@WillHunting Indeed

user19161
10:17 PM
@OldJohn Yes, just as a first step.

Like giving sets structure and geometric properties

user19161
Mathematics is motivated by intuition, but after that becomes independent of that intuition.

Well this vectorspace is orthogonal to this vectorspace

user19161
Which girl will be my orthogonal complement?

10:18 PM
@WillHunting XXX

that is orthogonal to the discussion!

user19161
@Charlie Hmm.

@Charlie But it gives the right answer!

paralel talk

@WillHunting Justin Bieber will be your girl

10:19 PM

what is the method implemented in simplifying $\frac{x^2 + 3x + 2}{x^2 - x -2}$

user19161
@Jordan Factorise top and bottom.

One can roughly divide mathematical education into three stages:

1. The “pre-rigorous” stage, in which mathematics is taught in an informal, intuitive manner, based on examples, fuzzy notions, and hand-waving. (For instance, calculus is usually first introduced in terms of slopes, areas, rates of change, and so forth.) The emphasis is more on computation than on theory. This stage generally lasts until the early undergraduate years.

2. The “rigorous” stage, in which one is now taught that in order to do maths “properly”, one needs to work and think in a much more precise and formal m

@Jordan Factor top and bottom, cancel stuffs

it didnt work when I tried it, guess I need to factor harder

@Jordan Factor harder, stronger, better, faster!

oh I got it
thanks

factor early, factor often

10:23 PM
@OldJohn Its factor day, factorday, factorday. Party and party and yay

that explanation of how math is taught seems to dismiss, or lump it into college math, how poorly math is taught in elementary, junior high and high school

user19161
@Argon I wonder what XXX thinks of me...

@N3buchadnezzar that summarises my experience perfectly :)

@WillHunting I wonder what XXX thinks of XXX....

Hey, if someone asks me again what does a mathematician do... I will get seriously mad....

10:24 PM
math in the US at least is purely taught on memorization of formulas, no understanding is ever required or reinforced. I hated math until college, now I just suck at it but appreciate it

@Charlie Math. $\blacksquare$

user19161
@Argon What are you saying?

@WillHunting Nothing

@Argon yup!

user19161
@Argon You mean what one thinks of oneself?

10:25 PM
@WillHunting Well does XXX know who is XXX?

@Argon makes sense....

@OldJohn Indeed?

user19161
@Argon I think not. Anyway, I am going to share some secrets with XXX soon...

Terrence Tao's blag is very good
He writes words, and I read them.

wut blag?

10:27 PM
@argon

@N3buchadnezzar yep - I felt that it was pretty much exactly like the diagrams show - reaching the boundary, pushing it by a tiny amount, and seeing very little outside of the area you are actually researching in ...

@Charlie

check out the last post on timothy gowers blag

@OldJohn Well I do not want to grow up, nor specialize myself. I want to learn it all

@Argon Do I disturb you?

10:28 PM
@Charlie Nope.

@Argon hmm

@N3buchadnezzar you will soon realise that is impossible - and if you want to do some research that extends the extent of human knowledge, then you have to specialise to the extent that only a few people in the world care about what you are proving

@Charlie hmmmm

@Argon hmmmm

10:29 PM
@OldJohn I know.. I know.. But I am going to be a teacher, not a postdoc.

23 hours ago, by Charlie
@Argon hmmmm...........................................

So I could learn a lot about nothing

28 secs ago, by Argon
23 hours ago, by Charlie
@Argon hmmmm...........................................

here you go here's a link gowers.wordpress.com/2012/11/20/…

user19161
I think I have shared my secrets with Jonas, Jayesh, Pedro, Benjamin, Aaron, Marilia, Old John, Gustavo and Limitless John.

10:30 PM
@N3buchadnezzar OK - then you need to restrict to a smaller circle in that diagram - and try to understand all of it :)

@Charlie Recursion:

how do I use algebraic division if I don't know what a possible factor could be? it seems too time consuming to start at x-1 and work to x-infinity

57 secs ago, by Charlie
28 secs ago, by Argon
23 hours ago, by Charlie
@Argon hmmmm...........................................

@Jordan, you guess the factor... that's what i wrote ages ago...

10:31 PM
@Argon we better stop it before people start to complain :P

user19161
@Jordan Look at the factors of the constant when trying to factor a quadratic.

@Argon what time is it?

@Charlie 17:33

@Jordan, you guess and then you do polynomial division, or you guess the factor and the factorization and just verify by multiplcation...

@OldJohn i think I will just take most of the introductory courses, and see what I fancy the most.

10:32 PM
@Argon oh... 20h33 here

user19161
So @jordan give me a quadratic you wanna factor and I show you how.

@PeterSheldrick But guess how? I mean starting at just 1 and working my way through everything seems tedious

@Charlie Late!

@Jordan, or you guess all the factors

10:33 PM
@Argon a little

$2x^3 - 5x^2 - 4x -3$
x-1 doesnt work

Complex analysis, abstract algebra, topology, quantum physics, algebraic topology, functional analysis, real analysis etc

@Jordan, in exam question like these the roots are usually (small) integers... hence you just look if any of the integers fits -6,-5,...+5,+6
simple as that

@N3buchadnezzar I have a superficial understanding of quite a lot of maths - but only a deep understanding of stuff that very few people (8-10?) have any interest in :)

everybody does it, nobody bothers to make it explicit

user19161
10:34 PM
@Jordan That's a cubic not a quadratic.

@PeterSheldrick Why did you say -6, -5 or are those just random?

@WillHunting No idea what that means

Suppose I am tossing coins. What is the probability that I will get a tails for the first time on the 5th flip?

@OldJohn That is what will be remembered for the future though..

10:34 PM
they are small integers

@Argon DST's fault

@csss (1/2)^5

user19161
@Jordan A cubic is of degree 3 and a quadratic of degree 2.

@Jordan Quadratic =2nd degree polynomial; cubic = 3rd degree; quartic = 4th degree, etc
@Charlie DST?

10:35 PM

Not in the future perhaps

ty

@Argon daylight saving time.

quad sounds like 4, but I guess quads are in your legs and you have two legs

@OldJohn 10 people per generation = $\infty$ people
:)

user19161
10:36 PM
@Jordan To factor a cubic use the remainder and factor theorem to guess a linear factor and then factorise the resulting quadratic if possible.

@OldJohn What should one research then? The hot and cool things, something that interests you, or something you can actually make progress in ?

@N3buchadnezzar I don't think my area is ever going to be of interest to more than a few people - even in any future

@WillHunting I don't know those words

user19161
@jordan Just post more questions on the main site if you need help.

Ok, but people usually get mad at my questions

10:37 PM
@N3buchadnezzar I chose the last 2 - interested me and I felt I might make progress - so my area was very far from "hot" or "cool" ... more like "neglected" :)))

user19161
@Jordan You really need to bombard your instructors with questions.

user19161
@jordan You must learn things step by step. Did you learn how to factorise a quadratic or cubic in class? How was it taught?

@OldJohn What was popular then? =)

@Jordan , @will is right

@OldJohn, harmonic functions? isn't that a major field of math? it's not obscure or anything is it

user19161
10:38 PM
There's no point practising a million questions when you don't know the method!

@WillHunting I was never taught factoring in school

user19161
All that shit about practice, practice, practice is BULLSHIT.

@WillHunting why?

user19161
@Charlie In our context of discussion of course.

@WillHunting ok

user19161
10:39 PM
I just don't wanna give Jordan the wrong impression.

@WillHunting, maybe it is bullshit for the bigger picture, but it isn't bullshit for exams at all
exams are bullshit maybe
you gotta fight bullshit with bullshit

user19161
@PeterSheldrick Well if that's how one learns math, one won't get very far.

@PeterSheldrick harmonic functions are quite active - but my research was into the boundary behaviour of fine continuous functions - and that was not a popular area at all - not "cool" and no prospects of implications in other areas - but I found it very interesting indeed

@Argon it's funny.... in portuguese DST is an Acronym to STD...

I don't need to get far in math really, I just need to finish the university's requirements

user19161
10:41 PM
I am also speaking from my heart here. That's what many teachers here do: make their students practise, practise, practise when they themselves don't understand the math.

@Charlie :)

user19161
@Jordan Ah, then I have nothing more to say to you.

@WillHunting I had that teacher last year. Awful stuff.

@Argon :)
@WillHunting unfortunately

I have too many things to learn to focus on just one

10:42 PM
@WillHunting, it is obviously bullshit, since any CAS is a top student like that, but that is what teachers put on their test - because it is easy to check!

I have been working on amth all day today and I have worked through about 12 problems of pre-algebra

user19161
You are right, exams are bullshit. I say this not because I do badly on them myself.

that is why we still write exams on paper, and that is why you don't have a CAS to help you on the exam
this all changes some time in the future, but fuck knows when, so at this point in time the rules of the game are still set
it doesn't help when the CEOs of mathematica make pushes to get into school, since they are a private company! it doesn't help at all...
it looks nice but it is actually making the whole thing more entrenched

Isn't there a chemical element called darmstadtium?

hello all!

10:48 PM
yeah it was discovered in the town i live in ;)

@PeterSheldrick Yeah! Nice! I knew that this name was familiar....

A biased coin has 0.6 chance of landing on heads. What is the probability that we get the 3rd head on the 7th flip?

@smackcrane Hello you!

Biig booty females!

@csss isn't it geometric?

10:50 PM
I think it is negative binomial

@csss ah, yeah yeah
are you sure?

@Charlie Here<3

@will look! a 2X2 blue square!

user19161
@Charlie Where Marilia?

just look at the faq computerbasedmath.org/faq.html
" If, in a Computer-Based Math™ world, "...

10:53 PM
@WillHunting users. disappeared.... you rarely call me marilia....

so they trade marked that term... wtf? is that a joke?

@Charlie its funny!

that's a great way to convince educators to support you

@Charlie Marilia!

10:54 PM
@Argon Aaron!

user19161
@Charlie Hmm, why not. I just say whatever I feel like...

@WillHunting Good

quick q for you guys too short for a proper thread
hello

that's what the chat is for...

@Argon

10:56 PM
m^4 +4nm^2 + 16 = 0. Thus, we see that m must be even. why is this true. sorry if its stupidly simple, its too late for maths.

@Mar

and also for talking random crap :)

that just happens...

@Argon funny!

user19161
@TessaDangerBamkin The last two terms are even, and odd times odd is odd, so m must be even.

10:57 PM
why incorrect ellipsis. too much cynicism :)

@Argon why @Mar?

ah ok
i was close

@Charlie I don't know! :)

hooray for Computer Modern 8)

thankyou

10:58 PM
$\LaTeX$

please do our exam for us

@Argon Listen to this.

@mr.FS Do you dig Computer Modern as much as I do? :3

@AlexeiAverchenko yes but did you accidentally reply to the wrong person?

i prefer mono spaced fonts