9:00 PM
well I get paid to go to school, so I would have to get a job if I don't go to school meaning I would have even less time to study
and I am incredibly bad at studying so it takes me a very long time to learn anything
just in this algebra review I can't go 3 questions without getting stuck and having to learn something new

less QQ more pew pew

meh
I get really frustrated at how bad I am and then I do not feel like studying

@Jordan Everybodys life sucks, most people just learn to deal with it.

what is something called that is in the form of $x^3 + 2x^2 + 3x + 12$?

a univariate polynomial of third degree with integer coefficients

9:03 PM
that isnt specific enough
I think factoring is just a lot of memorization of rules asw ell, and I don't remember any

@PeterSheldrick and 4 terms
@Jordan No?

polynomial division works just the same as the usual division algorithm you use in school

well then how do you look at something like a third degree poly and just intuitively think ofa way to do it?
I dont know long division or polynomial division

however, old-school c programmers have a different sort of software division en.wikipedia.org/wiki/Fast_inverse_square_root

@Jordan Gimme one and I will show you

9:07 PM
If I take what classes I am supposed to I am going to fail out of school next semester

then if you fail just apply to a different school

I dont understand when people even learn algebra
I cant get accepted to any schools really

Here is a nice example

I am going across the country to go to a school lol

$$f(x) = x^2 - 3x^2 - x + 3$$

9:08 PM
maybe find one with less of a commute then?

there arent any near me that will accept me
and I am not smart enough to get by without a decent degree

The easiest is just to make a drawing and try some integer values.
IF a polynomial has integer solutions this will always be divisible by the constant term!!!

yup, the constant term is just the product of the roots

So the only possible integer solutions to this polynomial are $-3,-1,1,3$

why?

9:10 PM
@N3buchadnezzar to be precise, that is only true for monic polynomials :)

@nimza hi Alexey!

(x+a)(x+b)(x+c)...=x^n+...+a*b*c...

good to see you @Charlie!

In mathematics, specifically in commutative algebra, the elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial P can be expressed as a polynomial in elementary symmetric polynomials: P can be given by an expression involving only additions and multiplication of constants and elementary symmetric polynomials. There is one elementary symmetric polynomial of degree d in n variables for any d ≤ n, and it is formed by adding together all distinct products of d distinct variables. Definition The el...
uh wall of text sorry about that

@Jordan You can also factor this polynomial by clever factorization!
NO Formulas, you just have to use your brain!

9:12 PM
this sounds like some really advanced math to understand

@Nimza Nice to see you too!

I can work things out with enough time, I am just bad at memorizing algorithms

@Jordan, nah it just works, try it out for small examples

@Charlie :-)

$$\begin{array}{ll} f(x) & = x^3 - 3x^2 - x + 3 \\ & = x^2(x-3) - (x-3) \\ & = (x-3)(x^2-1) \\ & = (x-3)(x+1)(x-1) \end{array}$$

9:13 PM

I always does my monic polynomials this way..

@Jordan, xD

@Jordan I find the wikipedia articles lacking in detail, and I am undergrad..

@Nimza :D

@Jordan, probably :'by math majors (or undergradutes)...'
yeah some are pretty nuts

9:15 PM

@Jordan Just started my second year

what math are you up to? you probably started at calc 2 or something :P

I created some maths pages on wikipedia some years ago ... not sure if they are still there

I don't understand the magic behind that method for factoring

@Jordan Complex analysis, lagrange operators, wave physics, introductory functional analysis, learning about various finite spaces. Banach, Hilbert, R^n..

9:17 PM
What magic?

@Jordan What line is the problem?

@Nimza wassup?

@N3buchadnezzar that is definitely not high school math :P most people start college before college algebra so the first two years of math are college algebra,trig, calc 1, calc 2

@Jordan University...

I guess I get it, I just have to memorize

9:18 PM
@Charlie I have no time for anything :( what about you?

if I have one terms times another terms plus another terms times a term I can takes those terms and just muliply them

@Jordan Able to do this one? $x^3 + x^2 + 8x + 8$

yes but I am not sure why I can make it to be $(x^2 + 8) * (x+1)$

@Nimza i'm good. doing some stuff.

@Jordan It is correct :D Awesome, fantastic. What did you not completely grasp?

9:21 PM
how to factor out an x^2 + 8

$x^3 + x^2 + 8x + 8 = x^2(x+1) + 8(x+1)$

yes not how do you extract those terms without breaking rules?

I take it given, that you was able to do this step. Now the "clue" here is that it is easier to see the algebra if one says Oh what if $a = x+1$

do long division (x^3 + x^2 + 8x + 8)/(x^2 + 8)

@Jordan $$x^2 \cdot a + (x+1) \cdot a$$
From here you could factor out a common term, just like before. It is nothing new. It is exactly the same as when you factored out the $8$.
$a + ab = a(1+b)$

9:24 PM
oh
it is more like I am factoring out the "a" and not the other terms

INDEED =D

I should probably learn long division at some point again

I am looking forward to learning Galois Theory

definitely
do lots of examples until it sticks

crap
now the next one is a fourth degree
$x^4 + 27x$ what is the trick?

9:27 PM
Stop calling it tricks!
A trick is someone pouring water over you at Halloween, if he is able to pull it of consistently it is called a technique.
Hmm, I cant factor this polynomial.. Gosh darn it, let me invent this new branch of mathematics in my diary! Hmm, I must have a gun fight tomorrow, over some lady. Oh well.

@N3buchadnezzar I found Galois theory a really satisfying topic - made all the stuff I had learned about groups and fields come together in a coherent subject

Galois actually died 28 years old, after a gun fight. Most ofhis mathematical work is contained in his diary, which he wrote on the night before he died.
@Charlie Because it is not a trick. It is a technique, which can be used in various cases and application. A trick can be used once, in a very narrow and specific case, not in a general mattter.

hmm

@OldJohn Yeah, looking forward to it. Although I have so much I want to learn, and so little time.

9:30 PM
It is a trick to me because I have never seen a problem like this, having taken calc 1 and 2 3 times
I am pretty experienced in math, four years of math and 8 math credits earned

@N3buchadnezzar same here!! - even at my age I am still learning (and have even less time!)

@Jordan Points at Old John's profile

@argon
@N3buchadnezzar it's so funny when you do that

@OldJohn, didn't you mention somewhere you are mid-twenties or so?

@Charlie makes arm excusing arm movements, and move my arms around like an italian

9:32 PM
@PeterSheldrick definitely not - I can hardly remember my mid-twenties ...

@OldJohn My problem is that I have to take Pedagogy, and Physics, along with my math.

@N3buchadnezzar ugh - pedagogy :(( physics is not that bad, I suppose ...

@Charlie a

9:34 PM
@Charlie Yes?

this is a dirty trick and I doubt I will ever have to know how to do this

(I was making my bed)

$x^4 + 27x$

@Argon hmm nice

@OldJohn Possibly need to cut down on the adult beverages and all the female companions then ;)

user19161
9:34 PM
@Argon I was making tea.

why would you ever want to factor that problem? it is so simple

@Jordan See a common term you can factor out ?

@WillHunting Yums

@N3buchadnezzar so what fun would I have left then?!?!?!

@Argon i just like to disturb people :P

9:34 PM
x(x^3 + 27) doesnt help me

@Charlie Really?

@OldJohn Exellent point

@WillHunting

@Argon yes

@Charlie

9:35 PM
@will i want tea

user19161
@OldJohn You only need 4k more to 10k, go for it!

@argon

@OldJohn I did not have one slow weekend the whole semester, before the exam period began. Out friday, saturday, and most sundays.

user19161
@Charlie I want X, Y and Z.

and then only 10k more to 20k!

9:35 PM
@Charlie Hmmmm......

@Argon hmhhmhmhmhhhhmmmm

@Charlie Hmfffffff

What subjects did you enjoy the most / do you enjoy most, a Old John ?

@Argon pfffff

Points at the Hmming birds

user19161
9:36 PM
I answered several low hanging fruit recently that got me many points.

takes pictures

@Charlie geeezzzz

@Argon yeahh

@WillHunting The queeeessstiiiiiioooooooooon is how looooow caaaaaan youoooooooooo gooooooooo?

user19161

9:37 PM
hmm - different subjects at different stages ...
as an undergrad I most enjoyed number theory, complex analysis and Galois theory
later I really enjoyed potential theory
now I mostly enjoy algebraic number theory

user19161
With some luck I might make it to 10k this year, but probably not.

@WillHunting I must look out for some lhf

@Argon wassup Aaron?

@WillHunting Maybe you could even make it to Isengard.
@Charlie Meh, nothing. I am quite bored :)

user19161
@OldJohn Yes, and you must be ready to type very fast.

9:38 PM
@Argon me too

oh

user19161
@Argon I wonder if I can make it to XXX. =)

@WillHunting currently aiming for my "generalist" badge - I think I just need a couple of answers for something like combinatorics maybe ...

all I had to do was memorize a formula to solve my problem

@OldJohn Never heard about the two last ones

9:39 PM
@Argon will you gain presents next saturday?

user19161

@WillHunting Come on you can go lower than that.

@Charlie Nope :)

@Argon :(

We don't really do that stuff.

9:39 PM
I did enjoy number theory, but I took it to early. My first semester at university

@WillHunting nothing - just seems like an interesting one to get

@Argon oh...

I think that is Christmas influence!

@N3buchadnezzar potential theory is the study of harmonic and subharmonic functions - kept me busy for over 8 years :)

@Argon points at XXX swing You suure you dont do that stuff? ... wink wink

9:40 PM
@Argon hahahah

youtube is pretty terrible for math

user19161
I will change my username in less than 48 hours from now...

@WillHunting The countdown has begun

I need a video on how to factor a fourth degree two term non-perfect square polynomial

user19161
@Argon And then I will also share some secrets with some more people.

9:41 PM
@WillHunting Like me, perhaps?

@Jordan, guess roots and do long division

@OldJohn Yeah, I have had a little about harmonic functions and like. Analytic functions, domains and such. Nothing about subharmonic functions alas.

that handles most exam questions

I don't know long division

time to learn it then...

user19161
9:42 PM
@Argon Hmm, I was thinking of XXX. Well, I think you know the summary already. The rest is in the details.

I only use it like once a year, I always forget it

@Jordan I use the swing all the time

user19161
@Jordan You mean for numbers or polynomials?

then do practice examples to keep it fresh

both
aint nobody got time for that

9:43 PM
well you have time to chat

HAHAHA!

user19161
@PeterSheldrick You are very pro-practice huh?

yes.
that sorts out exams
i'm not suggesting that leads to good math, not at all

user19161
I am not against practice, but it must come after understanding.

but it takes care of exams as a first step

9:44 PM
I fail tests either way

Hey @argon, have you ever watched this movie? this scene is hilarious!

user19161
I think it's not practice that helps in the exams but luck. You just happen to get the right question.

if you have wide practice then your luck increases

@Charlie With Adam Sandler, I saw it a few years ago :)

user19161
@Argon There were times in my life I looked like him.

9:45 PM
@Argon Bam bitty bitty bitty bam bam

@WillHunting HAHAHAHA!

@N3buchadnezzar harmonic functions are fascinating - they are really well behaved inside a region where they are defined, but can get pretty interesting as you approach the boundary :)

@WillHunting in what sense? phisically?

instructors really like to ask trick questions on tests and those always mess me up. Like in my trig class we had to do some manipulation with a clock, but if you failed to realize that the hour hand moves something like 1/360th of a degree when the second hand does you got the question wrong

user19161
@Charlie Yes, I look different every day.

9:47 PM
@WillHunting hmm

it is no longer a trig question but an applications of mechanical clock theory question, you had to know that the hour hand moved steadily with the second hand, and not just at the turn of a minute or hour

user19161
@Charlie You and Jay like to say hmm.

@WillHunting yes..hmmm

@WillHunting hmmm...

@OldJohn What is a function that both has a supremum and infinum on some closed interval I called?

9:48 PM
@Argon Aaron

user19161
@Argon Aaron and I like to say XXX. =)

Is it common to call it a bounded function on the interval I or ?

@Charlie Marilia...!
@WillHunting XXX

@N3buchadnezzar I would call it that, yes

user19161
@N3buchadnezzar We just say it is bounded.

9:49 PM

@Argon Oh, i forgot to tell you that my name comes , somehow, don't ask me how, from "Myriam"

@Charlie Oh, I guess that makes sense then!

well I have already met my limits of understanding of division, why can't I get a factor out of this? $x(x^3 + 27)$

Huh.

@Argon why?

9:51 PM
@Charlie I was wondering what it could have came from

@N3buchadnezzar "When I'm alone I F* myself!"

user19161
@Jordan Well you need to knw that $a^3+b^3=(a+b)(a^2-ab+b^2)$.

Difference of cubes

user19161
@Jordan Similarly, $a^3-b^3=(a-b)(a^2+ab+b^2)$.

@OldJohn I had a misconception about that if $\lim_{x\to a}f(x)$ existed, this implied that the function was well behaved on a small enough interval I around a. Where well behaved implies continuity and boundedness. It was fun finding a counter example ^^

9:52 PM
@Jordan, hint: 3^3=27

@N3buchadnezzar ah yes - limits can exist for some pretty crazy functions :)

user19161
@N3buchadnezzar Of course it is bounded in some interval around $a$, but it is not necessarily continuous at $a$.

Once i was spending a good time trying to prove something.... it happens that it was a false statement.... i realized that when i found a counter example

@Argon Try to find one ;)

9:54 PM
@WillHunting Is that somethingto just memorize?

@WillHunting Does it really have to be bounded? Like John said, there exists some pretty crazy functions.

user19161
@Argon Well just take $f(0)=1$ and $f(x)=0$ otherwise, totally trivial.

user19161
@N3buchadnezzar Like I said, it has to be bounded in some interval around $a$ if the limit exists, this is trivial.

@WillHunting Doesn't $\lim_{x \to 0}f(x) = 0$?

@Jordan, prove it by long division... (a^3+b^3)/(a+b)

user19161
9:56 PM
@Argon Yes, so it is not continuous at $0$.

how do I prove it?

f(x) = 0 if x=0, else $\infty$

by doing long division...

user19161
@Jordan You can prove it by multiplication.

@WillHunting I see now

user19161
9:57 PM

also I don't have a difference of cubes

user19161
@Jordan Sometimes, people experiment and then come up with things. And then you just remember then.

@WillHunting

user19161
@Jordan I gave you the formula above.

@WillHunting $$f_n(x) = \left\{ \begin{array}{lll} 0 & \text{if} & x=0 \\ n & \text{if} & \text{otherwise} \end{array} \right.$$

9:58 PM
@Argon

@Charlie

@WillHunting It doesn't seem to work, I get $-ab^3 - a^2 b^2 + ab^3$

@Argon Charlie+Argon=?

Hello.

user19161
@Jordan The difference of two cubes?

9:59 PM
hello Mr Raven

@Charlie Arlie?