Mathematics - 2012-12-02 (page 6 of 7)

@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.

Argon

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

N3buchadnezzar

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

Jordan

doesnt that change the value?

Raven Dreamer

10:08 PM

@WillHunting yes. That makes sense.

Argon

@Jordan Yes it would.

Sorry, I thought you were solving it

Jordan

just factoring

pull out a -1/2 I guess?

Argon

@N3buchadnezzar If you took a contour integral over Western Europe, what would its value be?

0, because all the Poles are in Eastern Europe.

N3buchadnezzar

Hahaha

user19161

@N3buchadnezzar That sounds condescending.

Old John

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 :)

N3buchadnezzar

@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.

Argon

@WillHunting :)

N3buchadnezzar

@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.

Jordan

10:12 PM

I got that one on my own, math confidence + 1/2

user19161

Yes, only stupid people say cleaners are not important.

Argon

@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.

N3buchadnezzar

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

Argon

10:14 PM

Yep

user19161

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

Peter Sheldrick

someone link me to chatjax please

N3buchadnezzar

@Argon Nooo, this is wrong! :p

Old John

@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.

Old John

10:15 PM

@PeterSheldrick link to chatjax is on the right of your screen

Argon

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

N3buchadnezzar

^^

Old John

@WillHunting me too

N3buchadnezzar

I love jokes like these

user19161

@PeterSheldrick See the link near the top right.

Peter Sheldrick

10:15 PM

thanks...

N3buchadnezzar

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

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.

Old John

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

N3buchadnezzar

@WillHunting Indeed

user19161

10:17 PM

@OldJohn Yes, just as a first step.

N3buchadnezzar

Like giving sets structure and geometric properties

Charlie

@N3buchadnezzar classical!!

user19161

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

N3buchadnezzar

Well this vectorspace is orthogonal to this vectorspace

user19161

Which girl will be my orthogonal complement?

Charlie

10:18 PM

@N3buchadnezzar that hurts.....ouch

@WillHunting XXX

Peter Sheldrick

that is orthogonal to the discussion!

user19161

@Charlie Hmm.

N3buchadnezzar

@Charlie But it gives the right answer!

Charlie

paralel talk

@N3buchadnezzar isn't it funny!

N3buchadnezzar

@WillHunting Justin Bieber will be your girl

Argon

10:19 PM

@N3buchadnezzar HAHAH!

Charlie

@N3buchadnezzar hahahahah

Jordan

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

user19161

@Jordan Factorise top and bottom.

N3buchadnezzar

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…

Argon

@Jordan Factor top and bottom, cancel stuffs

N3buchadnezzar

10:21 PM

terrytao.wordpress.com/career-advice/…

Jordan

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

N3buchadnezzar

@Jordan Factor harder, stronger, better, faster!

Jordan

oh I got it

thanks

Charlie

@N3buchadnezzar very good

Old John

factor early, factor often

N3buchadnezzar

10:23 PM

matt.might.net/articles/phd-school-in-pictures

@OldJohn Its factor day, factorday, factorday. Party and party and yay

Jordan

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...

Old John

@N3buchadnezzar that summarises my experience perfectly :)

Argon

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

Charlie

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

Jordan

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

Argon

@Charlie Math. $\blacksquare$

user19161

@Argon What are you saying?

Argon

@WillHunting Nothing

Charlie

@Argon yup!

user19161

@Argon You mean what one thinks of oneself?

Argon

10:25 PM

@WillHunting Well does XXX know who is XXX?

Charlie

@Argon makes sense....

N3buchadnezzar

@OldJohn Indeed?

user19161

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

N3buchadnezzar

Terrence Tao's blag is very good

He writes words, and I read them.

Jordan

wut blag?

Charlie

10:27 PM

@argon

Old John

@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 ...

Argon

@Charlie

Peter Sheldrick

check out the last post on timothy gowers blag

N3buchadnezzar

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

Charlie

@Argon Do I disturb you?

Argon

10:28 PM

@Charlie Nope.

Charlie

@Argon hmm

N3buchadnezzar

@OldJohn Here.. youtube.com/watch?v=1pm4fQRl72k

Old John

@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

Argon

@Charlie hmmmm

Charlie

@Argon hmmmm

N3buchadnezzar

10:29 PM

@OldJohn I know.. I know.. But I am going to be a teacher, not a postdoc.

Argon

23 hours ago, by Charlie

@Argon hmmmm...........................................

N3buchadnezzar

So I could learn a lot about nothing

Charlie

28 secs ago, by Argon

23 hours ago, by Charlie

@Argon hmmmm...........................................

Peter Sheldrick

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.

Old 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 :)

Argon

@Charlie Recursion:

Jordan

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

Argon

57 secs ago, by Charlie

28 secs ago, by Argon

23 hours ago, by Charlie

@Argon hmmmm...........................................

Old John

@N3buchadnezzar Hmm - not sure

Peter Sheldrick

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

Charlie

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.

Charlie

@Argon what time is it?

Argon

@Charlie 17:33

Peter Sheldrick

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

N3buchadnezzar

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

Charlie

10:32 PM

@Argon oh... 20h33 here

user19161

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

Old John

@N3buchadnezzar good approach

Jordan

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

Argon

@Charlie Late!

Peter Sheldrick

@Jordan, or you guess all the factors

Charlie

10:33 PM

@Argon a little

Jordan

$2x^3 - 5x^2 - 4x -3$

x-1 doesnt work

N3buchadnezzar

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

Peter Sheldrick

@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

Old John

@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 :)

Peter Sheldrick

everybody does it, nobody bothers to make it explicit

user19161

10:34 PM

@Jordan That's a cubic not a quadratic.

Jordan

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

Peter Sheldrick

yes

Jordan

@WillHunting No idea what that means

csss

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

N3buchadnezzar

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

Peter Sheldrick

10:34 PM

they are small integers

N3buchadnezzar

=)

Charlie

@Argon DST's fault

N3buchadnezzar

@csss (1/2)^5

user19161

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

Argon

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

@Charlie DST?

Old John

10:35 PM

@N3buchadnezzar But only by about 10 people ! :)

N3buchadnezzar

Not in the future perhaps

csss

ty

Charlie

@Argon daylight saving time.

Jordan

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

Argon

@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.

N3buchadnezzar

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

Old John

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

Jordan

@WillHunting I don't know those words

user19161

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

Jordan

Ok, but people usually get mad at my questions

Old John

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?

N3buchadnezzar

@OldJohn What was popular then? =)

Charlie

@Jordan , @will is right

Peter Sheldrick

@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!

Jordan

@WillHunting I was never taught factoring in school

user19161

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

Charlie

@WillHunting why?

user19161

@Charlie In our context of discussion of course.

Charlie

@WillHunting ok

user19161

10:39 PM

I just don't wanna give Jordan the wrong impression.

Peter Sheldrick

@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.

Old John

@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

Charlie

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

Jordan

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.

Argon

@Charlie :)

user19161

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

Argon

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

Charlie

@Argon :)

@WillHunting unfortunately

Jordan

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

Peter Sheldrick

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!

Jordan

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.

Peter Sheldrick

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...

see further computerbasedmath.org

it looks nice but it is actually making the whole thing more entrenched

Charlie

Isn't there a chemical element called darmstadtium?

smackcrane

hello all!

Peter Sheldrick

10:48 PM

yeah it was discovered in the town i live in ;)

Charlie

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

csss

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?

Charlie

@smackcrane Hello you!

N3buchadnezzar

Biig booty females!

Charlie

@csss isn't it geometric?

@N3buchadnezzar What???

csss

10:50 PM

I think it is negative binomial

Charlie

@csss ah, yeah yeah

are you sure?

N3buchadnezzar

@Charlie Here<3

►

Charlie

@N3buchadnezzar What the F....

@will look! a 2X2 blue square!

user19161

@Charlie Where Marilia?

Peter Sheldrick

just look at the faq computerbasedmath.org/faq.html

" If, in a Computer-Based Math™ world, "...

Charlie

10:53 PM

@WillHunting users. disappeared.... you rarely call me marilia....

Peter Sheldrick

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

N3buchadnezzar

@Charlie its funny!

Peter Sheldrick

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

Charlie

@N3buchadnezzar it's ridiculous

Argon

@Charlie Marilia!

Charlie

10:54 PM

@Argon Aaron!

user19161

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

Charlie

@WillHunting Good

@TessaDangerBamkin Hi

Tessa Danger Bamkin

quick q for you guys too short for a proper thread

hello

Peter Sheldrick

that's what the chat is for...

Charlie

@Argon

Tessa Danger Bamkin

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.

Argon

@Mar

Old John

and also for talking random crap :)

Peter Sheldrick

that just happens...

Charlie

@Argon funny!

user19161

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

Tessa Danger Bamkin

10:57 PM

why incorrect ellipsis. too much cynicism :)

Charlie

@Argon why @Mar?

Tessa Danger Bamkin

ah ok

i was close

Argon

@Charlie I don't know! :)

Alexei Averchenko

hooray for Computer Modern 8)

Tessa Danger Bamkin

thankyou

Alexei Averchenko

10:58 PM

$\LaTeX$

Tessa Danger Bamkin

please do our exam for us

Charlie

@Argon Listen to this.

Alexei Averchenko

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

mr. FS

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

Peter Sheldrick

i prefer mono spaced fonts

Transcript for

$Mathematics$ Mathematics