/sci/ - Science & Math

I work with polynomials in [math] {\mathbb F}_p [/math] (p=2 is the case I'm most interested in) and would like to read up one results in that direction. For polynomials, a large corpus of information surrounds the algebraic geometry situation and there e.g. with Hilberts Nullstellensatz, sadly they want polynomials over an algebraically closed field.

Now since I don't work in the rationals or the reals, and ans my finite field isn't algebraically closed, I'd like to know in which direction to go or where to read. Can I find the closure of [math] {\mathbb F}_2 [/math] to make such theorems apply and what is it?
I know there are those tasks of counting solutions over finite fields, the Weil theorems and such. Can you give me some pointers? Much appreciated.

>>9690931
[eqn]\bar{\mathbb F}_{p^n}=\bigcup_{i\in\mathbb N} \mathbb F_{p^i}[/eqn]

For elliptic curves over finite fields, you have Hasse's bound of the cardinality[eqn]|p+1-\mathrm{card}(E(\mathbb F_p))|\leq 2\sqrt p[/eqn]

>>9690987
To prove this you need the Weil pairing and more theory on elliptic curves

>>9690987
Mhm, so you say the the closure of F_2 is the union of all fields of order 2^n? Naive question: What's a union of fields?

I think reasoning of elliptic curves isn't relevant to me, I work with polynomials over hundreds of variables.

>>9690999
Note that any two finite fields of characteristic p, say of order p^n and p^m, then they both will be contained in the field p^nm I believe (or at least in a bigger one), so addition and multiplication etc still make sense. Of course, taking the union of arbitrary fields is not a field in general, and if the specific union i mentioned is not infinite, then it cannot be a field either.

And desu idk much about polynomials in many variables. Maybe you can reduce it to an elliptic curve through projective transformations?

How do I use the fact that the Sylow subgroups are Abelian? Also a general approach would help.

>>9691009
fyi I found there's a weaker zero-existence condition which is required for what's called a quasi-algebracally closed field, and finite fields fulfill it. In any case, that doesn't help me much.

https://en.wikipedia.org/wiki/Quasi-algebraically_closed_field

>>9690914

>>9691117
I split the integral into two parts, from 0 to t and t to t+1. Then I have to somehow integrate s with respect to dBs from t to t+1?

>>9691117
if you tell me what integral i have to compute, i can give it a try, but i have 0 knowledge of probability

i need to put together a
>math related application in C#
for my programming class

what should i make? im a brainlet undergrad so keep it simple pls

>>9691207
I (>>9690931) am in need of a high performing framework for polynomials, multiplication over [math] {\mathbb Z}_2 [/math] (i.e. x^n = x for n>0). I imagine a polynomial class which hold exponent vectors (e.g. if the variables are x,y,z,w,u, the exponent vector {1,0,1,0,0} represents x+1+z+1+1=1+x+z and you have e.g. multiplication alla (x+y)·(1+x+z) = 1*x + x*x + y + x*y + x z + y z = y + x*y + x z + y z). I work in several hundred variables, which is an issue since if you consdier monomials of total degree 3, you already have about 100^3 possibilities.

I currently work in Mathematica and have some drafts in Python, and I did a tiny bit of some C#/Cpp before, so contact me if you're interested in that. Relating to that, I previously today ask this question >>>/g/65636032

when I was 5 I had an accident that gave me permanent brain damage. School did not go well for me and I never bothered to learn any math (assuming that I even could).
I want to start learning calculus but I am very confused about integrating 'perfect' curves. Will there always be a tiny and insignificant loss when integrating?

t. literal brainlet with 88 IQ

Do genes play a role in the blood brain barrier? Are some people more vulnerable to chemicals leaking into the brain?, like: drugs, car polution, vaccines?

>>9691357
you should contact this man, he will show you the way to do Calculus and how to properly deal with those tiny losses

>>9690914
I am so fucking bad at math i want to kill myself

>>9691357
In practical cases where you can't know the exact description of a curve, your intuition is absolutely right. Then, the precision depends on how good your numerical method is.

When we're talking about something exact like [math]\int_{0}^{5}x^2 dx[/math], though, there's no loss whatsoever, because we've "removed" the loss analytically using limits.

>>9690914
can someone tell me how i got the +35? im so fucking confused. everything was going perfect until the 35

>>9691380
What about the integrals that have at least one boundary set to infinity? How far do people calculate to have a reasonable approximation?
I dont really understand the infinity concept

>>9691387
-5 * -7 = 35

>>9691401
holy shit thank u so much

>>9691387
2 (4 - 3x) + 12 = 7x - 5 (2x -7)
8 - 6x + 12 = 7x - 10x - ( -35)
20 - 6x = -3x + 35
-6x = -3x + 15
0 = 3x + 15
3(x + 5) = 0
how to solve? im lost

Is there a method for finding the indefinite integral of the reciprocal of a function?

>>9691421
um .... stop pretending to be me

>>9691387

>>9691428
never mind, just found out

>>9691433
im doing another algebra equation now... i know this is probably not completely right cus i suck at algebra and i'm retarded

can someone give solution?

>>9691433
thank u this helps a lot btw.

>>9691438
4*-7=-28
Not -3
Also you don't "cancel" on the same side of the equals sign, you combine.

>>9691433
wait no that has to be wrong

what

its -15 no?

>>9691433
i literally did that equation with my maths teacher and it was -15 at the end?

>>9691434
You cunt, hahaha

Someone please answer >>9691428, I didn't say I found out.

>>9691448
would someone be able to give a demonstration would help a lot

>>9691438

>>9691207
If you are interested in doing numerics there are a lot of things you can do.

If you like linear algebra you could write a few solver for Linear systems, that can be as hard/easy as you want.

>>9691428
take the log and use integration by parts


>retards can't figure out simple addition and multiplication itt

>>9691428
Wouldn't you just take the antiderivative like normal, just of the reciprocal?

>>9691469
i'm really confused because firstly. how does the 7 disappear on the second line, only to appear on the third again? plus how does 35x+14+32-28 give 46

>>9691487
like i get how u got it

but i just dont understand how the third line looks like that

>>9691489
Here's a more in depth look:

>>9691489
oh my god i think i get it so its like .... 35 - 28 = 7 and then 14+32?

guys this is stupid question thread, not retarded question thread

>>9691505
i was abandoned by my parents as a child thats why i cant do algebra

>>9691501
Yup. Can't forget to distribute

>>9691505
Show us where the x touched you

>>9691508
ok now im on the third part and i get that 14 goes into 7 twice but where does it come from..


its just 60 - 46 yes

but.. the 7 part confuses me,,,,

is it 14 divided by 2 if so that makes sense

so its like 14 divided by 2 then 60 - 46

i think i get this now ill try to do some other and if i get stuck ill post it

genuinely just trying to understand algebra but i dont have math brain

>>9691532
Did you see the guide I posted above?

>>9691538
yeah

i have to know maths really well within 6 weeks and doing it by myself seems like a lost cause do u think i should pay for a tutor

like i cant even do something as simple as this wtf is wrong with me. you might find it hard to believe but i actually am fine at every other subject i do but i'm borderline retarded when it comes to math. seriously actually hurts to be this bad because everyone calls me smart yet i cant even do simple algebra. what the fuck..

>>9691568
I'm not sure if you need a tutor, but I'd be happy to help you as I have time. I'm in school to be an Algebra/Calculus teacher so it doesn't phase me.

>>9691568
No one but you has an issue with you struggling on these problems. As long as you're putting forth an honest effort, not giving up just because you don't immediately get the right answer, then people will be willing to help.
The geniuses of Rome struggled with calculus ideas, but they still kept trying.

>>9691595
Ik I could call you a brainlet for trying to be a teacher instead of pursuing PhD in pure math, but I'm curious, what makes you want to be a teacher? Is it because you love teaching more than math? I've always wondered how high school math teachers can be satisfied by one day just stop learning even all the undergrad math. Hell most of my high school math and physics teachers stopped at or before linear algebra and only one teacher took the real analysis sequence. It's just sort of confusing how people who supposedly like math would become content with how little they know. I'm sorry if this offends you, I've always been a little curious.

am i doing pic related right or is there an easier way?
let [math] f(z)=4e^z\cos(e^z) [/math]. basically i argued by cauchy-goursat that [eqn] \int_C f(z) \d z +\int_{C_1}f(z)\d z+\int_{C_2}f(z)\d z =0\,, [/eqn]where [math] C_1 [/math] and [math] C_2 [/math] are the lines parametrised by [math] \gamma_1(t)=\log\pi-t\,,\quad 0\leq t\leq \log\pi [/math] and [math] \gamma_2(t)=it\,,\quad 0\leq t\leq 1 [/math], respectively.
then evaluating the integrals over c1 and c2 i eventually found [math] \displaystyle\int_C f(z)\d z=-4\sin(e^i) [/math]

i ask since theres no answers provided and it's difficult to check on wolframalpha.

>>9691613
Well, to begin, my degree requires me to take Linear, Diff Equations, and Discrete, so it's not too shabby in terms of content.

To answer your first question, I do love teaching, and math is a decent sized passion in my life, but not my only one. The other third of my passion in life is writing novels and poetry. Being a teacher allows for upward movement in the future (graduate degree and moving to the university level teaching) and also offers excellent job security with half decent pay and benefits (at least here in Colorado).

>>9691612
>>9691595
I honestly can't do something as simple as this. I know the answer is -2 but i cant get my head around as to where that goes or how you get it. it's truly over i need to kill myself

>>9691635
There are a lot of things worse then being bad at math.

Try to focus first on the things without an x try to bring them on one side and then the things with an x and bring them on the other.

Honestly, it is just practice, nobody is good at that by nature.

>>9691641
im literally trying. im too stupid to comprehend it at all

i get A+ grades in art, i'm relatively good at languages and history and english


Legit why can't I do math at all if that's the case? makes no sense. I don't get it and neither does anyone else. i must be mentally inpaired

>>9691635

He ( >>9691641 )'s right. If you can't get it just by reading the equation and the textbook, the solution of to grind out ton of problems until you finally "click". You'll have to look at solution manual often but assuming you aren't retarded, your brain will eventually realize the pattern and remember it.

>>9691635
It's all about using strategies and practicing until it "clicks" for you. For instance here, the strategy is always to isolate the x's, and that automatically isolates the rest of the equation (in this case, just a couple of regular numbers). From there, you always want to focus on making x completely by itself, which usually involves using what you can loosely refer to as the principle of equality to allow yourself to divide on one side and do so on the other as well. Doing that yields the x by itself, and the equation solved.

>>9691656
impaired*

see what i mean haha... :)))

>>9691656
>i get A+ grades in art, i'm relatively good at languages and history and english
Great, I am awful at art and languages.

>Legit why can't I do math at all if that's the case?
Because different people have different talents.

>I don't get it and neither does anyone else
Maybe everyone is shit at something?

>>9691656
Saying i should kms, I'm retarded won't help you. Just practice practice practice grind grind grind. The feeling of satisfaction when it finally clicks will be fantastic.
Start with this worksheet.

https://cdn.kutasoftware.com/Worksheets/Alg1/One-Step%20Equations.pdf

Then if you get it, go to this one.
If not, look for more worksheets.

https://cdn.kutasoftware.com/Worksheets/Alg1/Multi-Step%20Equations.pdf

>>9691615
no poles inside or on (or outside) the contour so integral is 0 by cauchy's theorem

>>9691669
ever notice how some people get math without trying as hard as I do to understand it?

thats what makes me want to die because it wont click in my brain yet it does so simply for almost everyone on this board.

but yeah, maybe everyone is shit at something. I want to devote all my time and energy into understanding math but fucking lol, i bet i could do math all day today and i still wouldnt understand it

i'm going to do that anyway. I can decide if I need to hang myself if this doesn't come easy to me after a lot of practice today

>>9691672
ill try this out

>>9691679
which integral? [math] \displaystyle\int_C 4e^z\cos(e^z)\d z\ ? [/math]

>>9691690
Again, I'd be happy to give you a throwaway email address to shoot questions to. I can Skype on occasion, too.

>>9691690
>ever notice how some people get math without trying as hard as I do to understand it?
Certainly, I know a lot of people who have an easier time then me.

>thats what makes me want to die because it wont click in my brain yet it does so simply for almost everyone on this board.
Sample bias.

>all day
Trying too hard is a bad Idea, take breaks.

>if I need to hang myself
You don't.

>>9691697
maybe
what would your email be?

im doing the sheet

x−7=13

this is where i get stuck.
i keep doing -6-7=-13 but i need 13 not -13

what is the name of this sytem? it's not in equilibrium clearly, and it can't just be a couple.

>>9691721
nvm i got it
20-7=13

lmao!!! wow

>>9691679
>>9691695
well, if you read the statement of cauchy's theorem, it says that the integral has to be closed...

>>9691726
i know but idk what other integral he/you could be talking about

>>9691721
I get the feeling that you're trying to logic your way to an answer, but the better bet it to follow the strategy of isolation, and let the answer come to you.

In this case, you want to add 7 to both sides, that yields x=20. If we check,

(20)-7=13 is a true statement, so the answer is verified.

I'll make an email here in a minute and post it. Anyone else is welcome to send questions, but I can only really help up to Calc 1.

>>9691735
ok but im doing n+16=9

and 9+16+9 is not working

>>9691754
16+9-16=9? still dont get it is this right?

>>9691754
>>9691758
You're almost there. You're on the right track to isolate n (the variable) by subtracting 16. Always remember that the principle of equality tells us if you do something to one side, you must do it to the other side as well. So:

n+16=9 becomes:

n+16-16=9-16 So:

n=-7

>>9691769
im so fucking stupid loooool

>>9691769
holy fuckkkk. im so bad

>>9691791

>>9691791
ok i know its 8(-13)=-104, however i solved it out logically rather than adding it to both sides because im still retarded with that formula.

>>9691807
are you still here? i will try to explain it to you

>>9691807
That can work in some cases, but usually "logicing" it out only works on simple equations. You wouldn't want to try to solve (see pic) because the answer is + or - 3/2. Not easy to logic through, which is why we use standardized strategies.

>>9691825
>>9691791
>>9691754
can someone explain what is happening?

Does it take more circles of area A, to fill a square of area 1? Or more squares of area A, to fill a circle of area 1?

as you probably know that a number of the form [math]2^n - 1[/math] is a mersenne number.
now do this [math] 5 * 2^{n + 1} - 1[/math] you will get the mersenne number with a digit of nine on its right
my question is this common knowlege?

I want to disprove that there exists natural numbers (excluding 0) n and m that n^4 + n^2 +1 is m^2. I've done some equation manipulation to make the left hand side, ((n+1)^2 - n)((n+1)^2+n). so this would be (n+1)^4 - n^2. How can I prove or disprove that this is a perfect square? (m^2)

>>9691841

>>9691807
By the way, the email is:

uccsalgebrahelp@hotmail.com

Again, anyone and everyone is welcome to send questions at or below the Calc 1 level.

>>9691870
dude this is /sqt/ come on now

>>9691880
True but come on now he is asking if it is common knowledge that multiples of 10 end in 0

>>9691888
Jesus Christ, I had no idea.
Also trips of truth.

>>9691888
yeah i was retarded for not noticing it in first glance

>>9691841
>>9691870
I dont get it what the issue?

>>9691117
The way you usually do this is by using Ito's lemma and seeing that the dt-part vanishes

>>9691910
see >>9691888

14b = −56 I CANT DO THIS???!??

>>9691930
-56/14 = b

>>9691940
i got 42? no idea what to do with it

wtfff

>>9691729
there's only one integral youre talking about, and its the one that goes around the contour, the rest are your lame attempts attempts at answering a trick question

i'm reading this passage in a book regarding

>numerical integration using gauss-legendre method

and this is supposed to be a coded example.

am i missing something or is that result just wrong? wolfram says the integral of exp(-xx) from 1 to 2 is approximately 0.135

>>9691791
>>9691794
LOST

>>9691943
When you have multiplication, 14b = 28 then you divide both sides, you will get: 14b/14 = 28/14, b = 2

When you have addition/subtraction then you subtract/divide: 14b + 2 = 16, 14b + 2 - 2 = 16 -2, 14b = 14, now you do the thing from the first paragraph: 14b/14 = 14/14, b = 1

Let me just ask you, are you from the USA? I live in europe and I learned this level of math in elementary school when I was 12

>>9691955
>addition/subtraction then you subtract/divide
typo, what I meant was:
>addition/subtraction then you subtract/add

>>9691955
No need to be smug, it doesn't make you look good. We for instance could now attack your typo and accuse you of having a poor education, but let's focus on helping, alright?

>>9691918
I still dont understand what is so special with that question I ask the same all the time

guess I'm just retarded

>>9691961
Not sure how typos equal a bad education since I'm sure some of the smartest men in history have made typos, but I wasn't trying to sound smug, I'm honestly wondering since I always heard american education is really bad(https://www.youtube.com/watch?v=M2fHQ9eULzk))

>>9691970
I am American, and I have a good education. The world is a complex place. And anything trivial can be attacked as a example of poor education (you accuse him of having a poor education because of his lack of understand of Algebra, I may accuse you of not developing patience enough to proofread your writing).
Also, Man on the Streets style interviews are some of the worst, cherry-picking, one-sided drama pieces possible. I strongly recommend finding some data that is more objective.

>>9691947
sorry, im genuinely not following you. can you write out which integral youre talking about?
in >>9691679 you say there are no poles in or on the contour so the integral(?) is 0. i presumed you did not mean the integral [math] \displaystyle \int_{C+C_1+C_2} 4e^z\cos(e^z)\, dz [/math] (although the only integral in my post on a closed contour) because i already said it was 0 and i'm not sure why you would repeat that back to me. the only other integrals you couldve meant is the one in >>9691695 or the two along the line, which are not on closed contours

and why is it a trick question?

>>9691950
>am i missing something or is that result just wrong?
It seems like that result is wrong, although I have no Idea what causes it.

It might just be falsely implemented, exp(-x*x) shouldn't really be a problem to integrate numerically.

>>9691997
well fuck, the theory behind it is a complete shitfest to me so I don't think i'll be able to find what's wrong in the code either

>>9692004
It has been nearly two years since my course in numerics, if you post the code I can give it a look though.

>>9691913
I think Martingale implies no dt term, not the other way around. Appreciate the insight though. I'm still stuck on it after 2 hours...

I have a function f(x, y), that is defined piecewise only by the condition that x > y. Is there a name for this kind of function? Or in higher dimensions? Trying to see if there are any techniques for handling these.

>>9692017
please do take a look

paste2.org/xH0aAPGH

>>9692055
i've just found out that when I manually tell the program to use a legrende polynomial of degree 5

i.e.
>((63 * x * x * x * x * x) - (70 * x * x * x) + (15 * x)) / 8.0;

then it seems to work so far, so the problem should be with the Legrende function, which generates the legrende polynomial of degree n.

any input is still appreciated though man

>>9692055
>>9692070
I dont see anything inherently wrong with the code but the issue is that I dont know what legendre stuff is so my suggestion is use ConsoleWriteline as a means of debugging and check each pass

>>9692088
okay, thank you anyway, you're kind

>>9692095
oh wait why is n initialized as n = 1?
You do realize you only make 4 cycles?

So you do legendre(double whatever, 5)
and your n is 1
what do you think happens in the cycle when you start from 1?
right
1,2,3,4 - four passed
you need to use <= or start from 0

>>9692102
You are also returning P1 when you have a polynomial of degree 0, is that right?

>>9692044
It's not clear what you're asking. Is this a map
f: A x A -> {true, false}
into the Booleans or do you say that only for x > y a return value is defined? In the first case, that's a characteristic function and in the second case, it's not a function at all but rather a dependent function (or, if you want something weaker, a partial function)

>>9692102
I am also not sure about your recursive calculation (it differs in form from the formula I found, but still might be entirely correct) , if you continue to have problems maybe try the explicit version?
And not the recursive?

>>9692109
For x>y, it returns a value b, and for x <y it returns a value c.I guess that would be closer to the former?

>>9692102
Also
for (int i = 0; i < (n + 1) / 2; i++)
Seems like a bad idea in general, although I have no idea whether there are some guarantees about rounding.

>>9692130
No I'm talking about his Legendre() function where he uses while cycle as a means to do 5 passes. He is not using cycle var anywhere else in there.
I dont know how that polynomial formula works but if he needs 5 proper passes he shoud start with 0 or change the comparison flag

>>9692120
It's just a constant plus a step function, then. You can write it as

[math] f(x,y) := b \cdot H(x-y) + c \cdot H(-(x-y)) [/math]

or, assuming b<c, as

[math] f(x,y) := b + (c-b) \cdot H(y-x) [/math]

where H is

https://en.wikipedia.org/wiki/Heaviside_step_function

>>9692131
>No I'm talking about his Legendre() function where he uses while cycle as a means to do 5 passes.
I know that, that's why the "Also", just another note for him probably replied to the wrong person.

>I dont know how that polynomial formula works but if he needs 5 proper passes he shoud start with 0 or change the comparison flag
I think that fits.

For a given "n" he wants a polynomial of degree n, for deg = 1 his polynomial has degree 1 and is returned as such.
For deg = 2, there is exactly one pass in the recursive loop, so he gets a polynomial of degree 2.
And so on, or am I missing something?

The formula is here: https://en.wikipedia.org/wiki/Legendre_polynomials, he is using the recursive version, although I am not entirely sure if his implementation is correct.

>>9692095
>>9692102
>>9692106
>>9692116
>>9692130
>>9692131
>>9692141

I got it to work.
Thank you again.

>>9692149
The Legrende() function was a mess, it works now.

>>9692149
Good job.
Have a nice day/night.

>>9692149
>>9692151
4chan keeps eating my picture fuck

>>9692141
>The formula is here
I'm on middleschool level anon it is kinda hard for me to understand it

>>9692138
Thanks, I can't believe I forgot about those.

How do I get the old youtube layout back?

>>9692183
I said "assuming b<c", but under the shower I realized that the expression is just as valid for c>b.

>>9692172
It doesn't really matter that there are fewer passes of the cycle than user calls for since it's an approximation anyway. You'll just end up with a slightly larger error which gets more and more negligible for large n.

Where can I learn mathematical language?
Sure, there are many different fields and some symbols have different meanings in some areas but, Is there a book with all the symbols used in math and how to use them?

>>9692213
you wouldn't fare well learning it that way as a lot of symbols get reused and depend entirely on the context on which they are used in. You'll find different notation in different textbooks because there isn't a single convention set in stone.

>>9692213
>a book with all the symbols used in math and how to use them?
no. notation varies from author to author. if you want a brief overview of "standard" uses, check wikipedia
though i'm not entirely sure why you'd want to learn the notation without the theory

I haven't come across these two symbols in my lectures. I found that the the circle with cross is a direct sum though from my understanding that's an operation between vector spaces but in this example it's used for elements of a vector space i.e. vectors. For the circled dot I can't find anything mathematically relevant online. Is it the same the outer product or just simply scalar multiplaction'

>>9692304
they just represent addition and scalar multiplication in the vector space. the author could have equivalently wrote "let [math] (V,+,\cdot) [/math] be a vector space"

I need help guys.

I told myself I would need to learn Calculus AP in order be ready for higher levels of Physics/Chemistry. Currently a NEET, i want to be good at this shit to be ready for college, except I don't want to wait too long doing this. It's a time waster.

How much do you need to be good at these subjects. Do you need to at least learn Algebra 2 or 1? Trigonometry?

>>9692306
>>9692304
My teacher would use those symbols whenever we had a vector space with a nonstandard operation

>>9692317
actually it was just any set. Cause I remember proving that lots of sets vector spaces lots of nonstandard operations

Not sure this is the correct board, but I have a question on how to hire a programmer.

I will be needing to hire someone to make me a working automated device and program that delivers nutrients to a hydroponic system. I have everything set up except the programming, because I can't figure that shit out to save my business.

There will be more involvement on this, but they will need to know how to make and set up a working device, program it, and have it work wirelessly/bluetooth with external devices for easy access, if they choose not to push buttons on the actual unit itself.

Where can I go to find programmers that can do this? Is there a specific website to look into or will linkedin/indeed/career buuilder, etc work fine? What would you expect your pay to be and for how long?

>>9692319
that makes more sense. i imagine the lecturer in >>9692304 just used them to stress they may be any internal binary operation rather than "traditional" addition and scalar multiplication

>>9692304
it's just to emphasize that those are arbitrary operations and not + and . in the traditional sense

>>9692324
Depends on where you are if you want on site, otherwise you can look for someone remote but you'll need to structure the task in the cleanest and most precise way. Since you won't hire for long you should be looking at contractors, a skilled one will easily demand 100/200$ a hour in most civilized places, otherwise you could look for a highschooler or University pothead, try maker spaces or college job platforms. Even if you find someone cheap like that It's either hit or miss with the quality, more likely miss.
DESU I'd just try to do the most possible myself (learn it) and hire someone to wrap it up

Just started Munkres, and I'm already running into some problems. Why exactly are the collection of sets in the pic not topologies? I feel like I'm missing something really dumb here.

>>9691615
[math]d(e^z) = e^z dz[/math] so [eqn]4\oint_C dz e^z \cos(e^z) = 4\oint_{\ln(C)}d(e^z)\cos(e^z) = 4\oint_{w(C)}dw \cos(w)[/eqn]
where [math]w:\mathbb{C}\rightarrow \mathbb{C}[/math] is the homomorphism on cycles [math]C_1(\mathbb{C},\mathbb{Z})[/math] induced by the conformal mapping [math]z\mapsto e^z[/math].
>>9692304
[math]\otimes[/math] is tensor product, and [math]\odot[/math] is symmetrized tensor product. [eqn]X\odot Y = \frac{1}{2}\left(X\otimes Y + Y\otimes X\right)[/eqn]
>>9692377
Complements of open sets are supposed to be closed, but in the first example the complement [math]U^c = \emptyset[/math] of the neighborhood [math]U \ni c[/math] of [math]c[/math] is open.
For the second example try taking the complement of the union of the intersections of the three neighborhoods.

>>9691400
Well it depends again on whether you're doing a numerical integral or an analytic one

If it's analytic, you'll have something like

[eqn]\int_1^\infty\frac{1}{x^2}dx=lim_{a\rightarrow\infty}[-\frac{1}{x}]_{x=1}^{x=a}=lim_{a\rightarrow\infty}-\frac{1}{a} + 1 = 1[/eqn]

Where in the last step we take the limit so that the integral converges

Meanwhile, in the numeric case you really do always have an error margin. There are tools to estimate how big it is, though.

>>9692410
Got it, thanks a bunch.

>>9692341
>DESU I'd just try to do the most possible myself (learn it) and hire someone to wrap it up
Yea, I'm just having such a hard time figuring it out. I've been trying for months now with no luck.

I'll check with the places you suggest. How long does a job like that sound like it should take? I'd like to pay for the job, and then hire them again once I expand on the concept down the road.

You mentioned it will cost 100-200 bucks an hour. How many hours would you think that takes? Phone app, PC/Mac software (same functionality as phone app), and hardware set up? I already have an idea as to what hardware I will be using. I simply need it to be programmed to work together. But additional hardware suggestions would be considered if they know a better way.

I want to learn the following math subjects, ordering the ones I want to learn the most to the ones I want to learn the least:

1. Set theory
2. Linear Álgebra
3. Topology
4. Calculus
5. Formal logic

What is the best course of action? What are the pre-requisites?

Do you know of any subscription based service I can subscribe to in order to learn math? I noticed subscribing to stuff makes me more motivated to work towards it. If not, other good sources are welcome.

>>9692570
>Do you know of any subscription based service I can subscribe to in order to learn math?
I don't know what you mean by subscription but maybe
https://www.coursera.org/browse/math-and-logic
https://www.edx.org/course/subject/math

>>9692035
Someone please help

>>9692377
a u b is not in the first one a n c is not in the second one, where u and n are union and intersection

>>9692570
I would go in this order

http://4chan-science.wikia.com/wiki/Mathematics#Proofs_and_Mathematical_Reasoning
http://4chan-science.wikia.com/wiki/Mathematics#Matrix_Algebra
http://4chan-science.wikia.com/wiki/Mathematics#Introductory_Set_Theory
http://4chan-science.wikia.com/wiki/Mathematics#Calculus
http://4chan-science.wikia.com/wiki/Mathematics#Finite_Vector_Spaces
http://4chan-science.wikia.com/wiki/Mathematics#Point-set_Topology
http://4chan-science.wikia.com/wiki/Mathematics#Introductory_Logic

Has anyone heard of the following? Imagine you want to find prime numbers that are only made of prime numbers within them. A slow method is to apply the Sieve of Eratosthenes to the digits within prime numbers. Let me show you what I mean from primes [2, 113]:
2, 3, 5, 7, 11, 13, 17, 23, 31, 37, 53, 71, 73, 113
You will notice that this is a much smaller group of primes than normal primes. Nothing with the number 9 is allowed, and even numbers are no longer allowed at all. Even 101, 103, and 107 aren't allowed because 10 isn't prime. You see what I'm doing now? What's the name of this pattern? I can't find it on OEIS. Other than my question, does this pattern have anything written about it?
I found it interesting to think about. I can't tell if it's a closed set or not. As prime numbers become larger, the chances of them having composites within their digits rises. However, there might be very large "prime-prime" numbers.

>>9693420
> Imagine you want to find prime numbers that are only made of prime numbers within them.
What exactly do you mean by this?

>Nothing with the number 9 is allowed, and even numbers are no longer allowed at all.
But 2 is in your list.

>>9693420
It's unclear what you mean, shouldn't 11,13,17,31,71,113 all be excluded since they contain a '1' which is not prime?

I'm doing some practice problems learning Taylor polynomials and series and I'm having trouble understanding a certain problem:

Use the first four nonzero terms of the Taylor series [math]\sqrt[4]{1+x}[/math] to approximate [math]\sqrt[4]{1.12}[/math]
Round your answer to 5 decimal places

Am I suppose to use [math]\sqrt[4]{1.12}[/math] as my center or am I suppose to approximate using a taylor polynomial and if I'm suppose to use a taylor polynomial what should my center be?

My inital thought was to use a maclaurin polynomial to approximate the value, but that didn't work. My polynomial ended up being [math]1+x+\frac{1}{4*2!}(x^2)-\frac{3}{16*3!}(x^3)[/math].

Maybe one of you could provide a tip or two. Currently trying to prove that every automorphism h of the structure (R, +, *, <) is the identity map. What I don't get is how you are supposed to show that the automorphism is the identity on the rational numbers (ik you extend it to the reals afterwards using density) without the division operatior defined. How would you show h(m/n) = m/n?

>>9693423
I know it's difficult for me to explain. 2 and 23 are special they're prime to start and don't have compisites around them. 211
223 not included: it has 22
227 not included: 22
229 not included: 22 and 9
233 not included: 33
239 not included: 9 and 39
241 not included: 4 and 24
251 not included: 25 and 51
257 not included: 25 and 57
263 not included: 6, 26, and 63
269 not inlcuded: 26, 6, 9, 69
271 not included: 27
277 not included: 27, 77
281 not included: 28, 8, 81
283 not included: 28, 8
293 not included: 29, 9, 93

>>9693436
ah, neat. I forgot. Thanks. Let's exclude them too. It's a smaller group [2, 73]: 2, 3, 5, 7, 23, 31, 37, 53, 73. I'm just messing with the numbers.

>>9693444
I still included 31. Remove this: 2, 3, 5, 7, 23, 37, 53, 73

>>9693445
https://oeis.org/A019546 "Primes whose digits are primes."
I found it. Thanks everyone who questioned my method.

>>9693448
Even this list doesn't follow the rules I want though. I'll keep trying

>>9693449
>>9693444
Do you mean for a number with decimal representation [math] \sum_{i=0}^n a_i 10^i [/math], that whenever [math] 0\leq j\leq k \leq n[/math], you then have that [math] \sum_{i=0}^{k-j} a_{j+i} 10^i [/math] is prime?

https://oeis.org/A085823
This might be it. It's only 2, 3, 5, 7, 23, 37, 53, 73, 373. I will try to find "Numbers in which all substrings are primes" bigger than 373 but it might not be possible.

>>9693454
I'm so math illiterate that's it difficult for me to read what you have there. It might be the mathematical representation of the rules I'm trying to create.

>>9693459
>I will try to find "Numbers in which all substrings are primes" bigger than 373 but it might not be possible.
There's an alleged proof that there are no bigger ones on that page (in the comments, "From Jean-Marc Falcoz, Jan 11 2009: (Start)...").

>>9693461
Yeah, and it shows me all the reasoning *why* it isn't possible. Well, that's all for now. Thanks.

>>9690914
Does anyone else lose subscriber access to New Scientist when they change from wifi to 4g (or vice versa) on the same device?

Maybe my uni has some sort of shit subscription with them?

I need to learn Chemistry, particularly I want to specialize in organic chemistry. What's a good path to take, I have been looking at Chang's Chemistry, are there any other books you'd recommend for someone who only took a rather bad intro course in college?

its been 8 years since i studied linear algebra at school, and now i need to know trig. what should i read to go from "what is pythagoras again?" to knowing how to find the closest point along a vector to a given point, and how long will it take me if i have nothing else to do with my time but study math?

Anyone here studying at Delft?

>>9691039
I don't know how you'd prove (a) but (b) follows from (a):
If [math] Q = P^x [/math] is the subgroup in (a), then the normalizer [math] H[/math] of [math]P [/math] in [math] Q[/math] is [math] \{1\} [/math], because otherwise [math] |HP| [/math] would be [math] \gt |P|[/math] [math] [/math] as [math] HP / P \approx H / H \cap P [/math]. So [math] Q [/math] acts (by conjugation) faithfully on the set of [math] Q[/math]-conjugates of [math]P [/math]. So the number of [math] p[/math]-Sylow subgroups, [math] k[/math], is [math] \geq p^n [/math]. As [math] k[/math] is [math] \equiv 1 \mod p [/math], this means [math] k \geq p^n + 1[/math]. Now it's almost trivial that [math] |G| \geq p^n(p^n + 1) [/math] as [math] |G| = |N(P)| \cdot k [/math].

I'm helping my little cousin with her AP calc homework and I cannot for the life of me figure out part C. The rest of the problem seems trivial but part C does not make any sense to me. I do not see how you could find the volume of this sculpture without doing some sort of revolution that involves pi, yet there is no pi in the solution.

>>9691791

In a partially filled set of orbitals, (let's say those on 2p), is it possible to leave out 3 electrons with mixed spin, or will electrons be always removed in such a way that when three are left, they all have the same spin?

>>9695223
Not a revolution solid. Think of h(x) as the location of the point in the R surface along the Z axis. This effectively leaves you a pyramid with nigh-infinite sides along the curve, effectively giving you a volume of (Given H as the highest value of h, and R as its surface) V= 1/3xHxR.

I want to improve my math.
May you guys give some good books to start with?

>>9695223
Basically it tells you to find the volume of that area which will be revolving around the x-axis.
By the disk method.

Integral from 0 to 4 of (Pi*radius^2)dx
Radius is given by the fuction so, (4-x)^2

Why the fuck are you doing that idiots homework. The teachers has showed him enough for him to do it by himself.

>>9695275
like what subject? this shit usually goes on a crescendo way. Start with basic algebra once you are done go with trigonometry, or jump to pre-calculus and then jump to Calculus

>>9695275
>>9695288
Like the starting point.
Algebra and then moving to calculus, that kind of stuff

>>9695294
But I need some good books, you know

>>9695279

First, that is not the correct answer or method for part C.

Second, your reading skills are very poor because I said "she " not "he".

Third, I'm helping my cousin because she's family and I love her. Sorry you do not understand that.

I think you might be the idiot here.

>>9695270
Thanks, I now see that the height was actually into the Z-axis. Before, I thought that the height was a value in the Y-axis. That makes much more sense and I would like the blame the wording of that one haha.

>>9695294
Yes start with Algebra because there are little tricks that will show later in calculus, especially when having to simplify, transform, cancel terms or find the zeros(factoring).

Pre-algebra.
Algebra.
Pre-calculus
Calculus I
Calculus II
Linear Algebra
Calculus III

After that its mostly proofs and pure/Applied mathematics stuff youll touch in Uni.
Like Real Analysis, Complex Analysis,etc.

Id recommend you to start with youtube as the begging part is fairly easy to cover. Look for Professor Leonard, he has complete series on most of these subjects.

What are some things mathematicians have proved in all bases? What does that even mean?

>>9695270
>In a partially filled set of orbitals, (let's say those on 2p), is it possible to leave out 3 electrons with mixed spin, or will electrons be always removed in such a way that when three are left, they all have the same spin?

It depends on how the electrons are removed/added.

Say you have nitrogen. In it's ground state (that is to say there are an equal number of electrons as there are protons) all the electrons will have the same spin direction (i.e. +1/2).

Now let's say you add an electron to nitrogen (N-) then remove it. The three electrons will have the same spin direction.

Now let's say you have carbon, and you ionize it (C+). The electron removed from one of the pairs could be of any direction, meaning that 50% of the time you will be left with one electron with -1/2 spin and the other two at +1/2.

>>9695309
Thanks man, appreciate it.

>>9695299
oh sweetheart...

>>9695299
you just multiply by pi for that question. i always assume that question was supposed to be an introduction for calc 3 because if you were to put an angle in there and integrate it you would just get pi too

>>9695270
>>9695323
Let me expand a bit (from wikipedia):

>Hund's rule: every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin.

>This rule deals with reducing the repulsion between electrons. It can be understood from the classical picture that if all electrons are orbiting in the same direction (higher orbital angular momentum) they meet less often than if some of them orbit in opposite directions. In the latter case the repulsive force increases, which separates electrons. This adds potential energy to them, so their energy level is higher.

When you ionize atoms, you essentially emit a strong electromagnetic field on the particles until the electrons break away. When this happens, any of the electrons (regardless of spin) can be removed.

>>9695323
>>9695336
Thanks anon.

>>9695336
Actually I meant to copy and paste rule 1 not rule 2 from wikipedia.

Is this a solid undergraduate mathematics curriculum if I'm undecided in what I want to go into, but am looking at finance, data science, or teaching?
I'm minoring in TESOL and pursuing a teaching license so I can move to and work in Taiwan, after learning the language and seeing if I like TESOL I may decide to get a masters in a field related to stats, maths, or finance at a Taiwanese uni.

Calc 1 (done)

calc 2 (done)

calc 3

discrete maths

linear algebra (self studied, will be easy)

geometry

abstract algebra

math w/ MATLAB

probability, mathematical modelling

applied statistics

applied regression modelling w/ R 3cr.

combinatorics and graph theory 3cr.

Why is brush shifting done in the direction opposite to the direction of motor rotation in case DC motors?

Is there such thing as a periodic function whose period increases in time? Or are parabolic functions only capable of this?

>>9695959
if the "period" increases with time it's not a periodic function by definition you retard. It can (probably) be modelled as an infinite sum of periodic functions - see fourier series.

What does it mean to use a "conditional discharge" in the context proof? Lets say you are asked to proof that set A = set B. And you have something like

Step 1: x is an element of A (this is our premise we assumed)
.
.
.
Step 9: x is an element of B
Step 10: x is an element of A → x is an element of B (Conditional Discharge on 1 and 9)

The reason I'm asking this question is that many texts on logic use this term as understood by the reader and don't take the time to adequately explain the technical sense in which they are using it. As far as I can tell is related to the conditional (→) logic operator.

I understand when I read something like "we get this because we used this definition or this logical identity" but the world discharge is what confuses me.

Is there any truth whatsoever to this post? I mean, there’s no way onions is actually good for muscles, right?
>>>/ck/10503334

>>9696511
onions is very good for your body. it is an excellent source of protein. all the essential amino acids.

>>9695223
C) each cross section parallel to the y-z plane is a rectangle, with base g(x) and height 4-h(x). The area of each cross section is base times height, which you integrate from x=0 to x=4.

>>9696511
based

setting aside obvious physical challlenges: if you put a bunch of protons neutrons and electrons together to make an atom that is so big you can see it, what the fuck would it look like??

Anyone familiar with plastic injection? I've had a low level lab on it where I was told that short shots can be caused by high temperature given everything else set correctly. Why would this be? My intuition is that high temp would mean lower viscosity and longer cooling time. Is there a breakpoint at which another phenomena makes heat detrimental?

Can someone explain to me why the [math]k[/math]th de Rham cohomology of an [math]n[/math]-sphere is 0, for [math]k > n[/math]? I can see why for [math]k < n[/math] but every proof I've seen just says it's trivial for [math]k > n[/math], but it's not trivial for me.

>>9698328
You can't have k forms on n dim space for k>n, since there will necessarily be dependencies, thus it is space of closed forms is trivial so the de rham cohomology is trivial.

>>9698346
Oh, right. Christ, I completely forgot about the whole point of dR comohology being on the space of differential forms. Thanks anon.

>>9698360
I mean if you want to think about about it topologically, the n-sphere is a CW-complex with one 0-cell and one n-cell. The cohomology is obvious from that.

>>9698373
We haven't studied CW complexes (yet?) in class but I'll give it a look.

>>9698381
An n-cell attachment is the gluing of a topological space to an n-disc along the boundary (n-1)-sphere of the disc.

A CW-complex is a space built inductively from such n-cell attachments, starting with a discrete set.

does steam make clams soft enough to eat without deleting your teeth

>>9691865
You'll want to do a proof by contradiction.
n even implies the l.h.s is odd. So m^2 is odd so m is odd.

Then fix n,m in the form 2k and 2j+1 and see what happens. You should get a contradiction that n,m are naturals.
Do the same thing for n odd and m even and you're done.

I have 10 cards of which 2 are aces. Selecting 5 cards at random, what is the prob of getting both aces?

>>9698373
but you need to know that de rham cohomology is isomorphic to cellular cohomology. this is not trivial (at least for me)

>>9690914
.47 KB
I'm doing simulations in Mathematica for my bachelor thesis but due to the adaptive nature of Mathematica's NDSolve function, my professor wants me to write my own (much slower and uch less accurate) code. Does Mathematica really not have an option to "log" its precise numerical techniques, so they can be re-used everywhere else (and I won't run into trouble with peer reviewers checking the data)? It strikes me as odd that this isn't a feature phycisists run into all the time.

>>9698980

Physicists don't use mathematica that much. Tends to be matlab with python.

>>9698980
I guess he's got a point there. In all fairness, it shouldn't be too hard to pick another solver (netlib) and check the results against your Mathematica output. Sure, it'll take a while to get it all set up, but you could then just pop your code on github for peer review.

>>9698980
>Does Mathematica really not have an option to "log" its precise numerical techniques, so they can be re-used everywhere else
So that people can steal your code?
The point of creating closed source software is that people CAN'T re use the things you do.
It probably isn't even written in mathematica itself, but something like C/C++.

It is the same for e.g. MATLAB, if they told you what the backslash operator (and all their other stuff) does their product would become significantly less valuable.

I´m too lazy to watch youtube videos until I come through it and everyone else in my environment doesn´t care.
Variables like a are pronounced "a", how are Variables like a' pronounced?

Anybody else noticing this board becoming more and more reddit

>>9699350
Depends.

>>9691479
I mean yeah. I think he was wondering if there is a direct relationship between the two results obtained. I'd say generally no, because it depends too much on which function you're integrating.

>>9699119
I don't mean their algorithms but the result of it. I can easily find out what the step sizes are, and constrain it with MaxStepSize if I want, I just want to be able to re-use those specific parameters on other computers, and call upon the right technique at the right time. But I get your point on secrecy, and I respect that f that is indeed the reason for this shortage.

>>9699350
"a prime"
mostly if you're doing calculus

>>9699426
You could have a look at different, open source, software and see what they use.

I would be surprised if Octave wouldn't have the algorithms you need already implemented, they might not be *as good* but certainly better then nothing.

hey sci I am an EE undegrad im going to start a diplomate in advanced math. (I asked whether or not I should take the offer to do this on the last /sqt/ and ive decided to go for it)

I basically need to take 4 courses from the math career my uni offers and ill graduate with an EE degree and a math mention.

since /sci/ is full of mathfags im sure someone will have no problem helping pic the most interesting and useful courses to take so ill list the options and a basic summary of the contents of each course.

please note that my uni works on a trimester regime, so each course lasts 3 months not 5/6 like in a semester regime thats usually the norm.

options:

> analysis 1
-set theory
-the real numbers system
-topology of the real numbers system
-limits and continuity
-differentiation
-series
-function series
>analysis 2
-the [math] \R ^n [/math] space
-limits and continuity for multivariable functions
-differentiabillity
-varieties
-minima and maxima
>analysis 3
-the Riemann integral
-vector analysis
-measure theory
-the Lebesgue integral
>analysis 4
-the Lebesgue integral on [math] IR [/math]
-metric space [math] L^2 [a,b] [/math]
-Fourier analysis
>linear algebra
-vectorial space
-linear transforms
-numerical linear algebra
>abstract algebra 1
-groups
-rings
-polynomial rings
-bodies
>abstract algebra 2
-vectorial spaces
-linear transforms
-dual space
-ortogonal space?
>diff equations 1
-existence theory
-first order equations models
-recolection
-ED systems
>diff equations 2
-stability of linear and almost linear systems
-stability of non linear systems
-discrete dynamic systems

I have some other options but those are in statistics and I dont like that shit so im definitely not taking those.

im translating all names from my native language so be aware of that.

>>9699572
The analysis stuff certainly won't be a bad choice, it is practically the basis for everything you do in EE, especially 1-3.
Neither will be the differential equations class, that will be relevant when it comes to the Maxwell equations in differential form.
Linear algebra might come in handy if you want to focus more on numeric simulations.
Abstract algebra is interesting but less relevant to EE.

Analysis 1-3 seem to be extremely relevant to everything that you will be doing in EE, same for 4, but to a lesser degree.

>>9699581
Abstract algebra is one of the topics that most interest me, is it a very bad choice for EE?

>>9699572
>bodies
Assuming you're german, you probably mean "fields"

>>9699593
>is it a very bad choice for EE?
It won't be very relevant to what else you will be doing.
Most of electrical engineering is basically analysis, have a look at the Maxwell equations they are at the core of everything you will be doing.

Not that abstract algebra is a bad choice, it is an interesting subject and it isn't a bad Idea to take something because you think you will enjoy it, but from a purely "rational" standpoint it isn't optimal.

>>9699599
There are Universities with trimesters in Germany?

>>9699602
the bundeswehr universities are on trimesters afaik.
whatever, maybe there are more languages that use this word for "field"

>>9699599
Haha not german my friend
>>9699602
Makes sense, rigth now im thinkf analysis 1 to 3 and abs. Alg

Studying for a college entry test and theres only one question I cant figure out how Im supposed to solve it. (Probably is something simple but Ive been out of school for 6 years)

If 3x^2 - 2x + 7 = 0
Then (x - (1/3))^2 = ?

I already know the answer is -20/9 but I have no idea how to reach it. The first equation doesnt factor into integers since 7 is a prime number and 1 and 7 will never make -2 no matter which is negative / positive. Trying to solve it with the quadratic formula gets me (2 +- sqrt(-80))/6 which seems to complicate things more since there is no "i" in the the answer.

Im not even sure what to look up to learn how to do it since it doesnt seem to be simple factoring or using the quadratic formula

>>9699572
Depends on what you want. Doubt any of it will be very applicable to EE anyways, other than possibly Linear algebra or DEs. What I would choose as a mathematician (pure math phd student here) is, in order:

>Linear algebra
Literally essential for every math and physical science and CS
>analysis 1-3, maybe 4 if you like it
Analysis is pretty important, albeit slightly boring and uninteresting.
>algebra 1-2
I would have put it over analysis (i am an algebrafag) but it looks like you dont cover much of the intersting stuff. In a 3 month course, you can't properly cover any single one of those topics (groups, rings, bodies/fields),let alone all 3. I don't see how algebra 2 comes after 1 either, since it seems like it should follow from linear algebra
>DEs
probably pretty useful for EE, but I once took a PDEs course and i couldnt believe how boring it was. Literally I could not give a fuck about any of the topics.

>>9699887
look up "completing the square". If you still dont know, ill try it

>>9699887
pq formula
x=1/3 +- sqrt(1/9 - 7/3) = 1/3 +- sqrt(-20/9)
->(x-1/3)^2=-20/9

>>9699901
>>9699905
Thank you anons

>>9699895
You can cover much more than you would think in three months.
I posted the name of the units withing each course, not the fully detailed study plan as that would be just too fucking long.
Either way, why do you see analysis as not useful for an EE? I wouldve thought it to be very, very useful to formalize and further deepen one's calculus knowledge.

is there any reason why [math] \varphi(0)=0 [/math] is included in this definition or is it just stylistic?

Egsplain that last equality pls
Anon said it was a change of variable and it makes sense for r and dr but not for the integration limits

>>9699963
>subtract 1x from the integration limits
>in turn, add 1x everywhere the integration symbol (here "r") occurs
How does it not make sense? The only thing that doesn't make sense is renaming "r" to "s", it just makes the step seem more complicated than it is

is there a way to do this without using the axioms in the following orders
commutativity ... associativity ... commutativity
associativity ... commutativity ... associativity

>>9699929
Not in an introductory course that doesn't even require linear algebra.

And what do you think extra rigorous calculus will do to you as an EE? If you have a sum you have to evaluate or an integral, you're most likely not going to use any analysis techniques and just use the standard calculus ones. Maybe complex analysis would help on the other hand but then again you need analysis

>>9699955
It's superfluous actually, and you can show it directly from the def of homomorphism: f(0)=f(0+0)=f(0)+f(0) so by cancellation f(0) must be 0.

>>9699963
r=s+x change of variables


>>9700060
why would you do it any other way?

>>9700086
>It's superfluous actually, and you can show it directly from the def of homomorphism: f(0)=f(0+0)=f(0)+f(0) so by cancellation f(0) must be 0.
that's kind of what i thought... but i know with rings sometimes you see [math] f(1)=1 [/math] imposed, which i believe does make a difference. i just wondered if something similar was going on.

>why would you do it any other way?
it seemed a bit awkward doing it that way and i was curious if there was a quicker way

thanks

>>9700086
Analysis requires you to have taken calc 3.
And theres more than 1 analysis course. I need to take 4 courses bro.

Also, analysis / pure math stuff interests me, thats the main reason I want to do the diplomate, usefulness to EE is considered, albeit secondarily.

Youre also not considering the fact that taking math courses that forces you to start thinking deeply and rigorously as a mathematitian can greatly improve my ability as a future engineer. Regardless of the contents of the aforementioned courses.

>>9700106
in practice you do most steps at the same time.

note that the condition f(1)=1 is necessary for rings (since multiplication is not a group). Replicating my proof, try to see where it goes wrong if you don't assume it, and why it is important. That condition is usually eliminated when you consider rings without a unit (obviously).

>>9700108
not gonna lie, the progression your school offers is pretty shit. Analysis 3 should go before analysis 2. Why would you teach multivariate before integration??

Anyways, analysis looks interesting until you try it. Also, any course other than probably DEs should be mentally stimulating if that's what you want. The most abstract and hence hardest could be algebra, although a lot of people tend to struggle with analysis (although the arguments tend to be more intuitive and hence easier to understand)

>>9700124
In multivariable anylisis you do see integration, in analysis 3 you just go deeper into it.
as I said, I outlined the content units without specifying what [math] exactly [/math] you study in said units. That may be causing some confusion.
Regardless, ill take analysis 1 to 3 and abstract algebra. may take a 5th course but not sure.

>>9700172
nigga in the course descriptions you didnt mention integrals up to anal3, and there you mentioned Riemann integral which is the beginners integral?? you sure?

Also, not sure how youre gonna do algebra without linear algebra, usually every other example is matrices, unless youve done matrix stuff before, which gives no problem then

>>9700177
forgot to mention

multivariable anal is calculus+linear algebra, so you gonna be fucked for anal2 without LA

Is there a proper method for determining R/S configuration?

I know you're supposed to give priorities to groups and then draw arcs (clockwise-R, anticlockwise - S)

But what does one do when the 4th priority group isn't going behind the plain. Or in molecules like pic related

>>9700177
>>9700180
To be 100% honest in might be a mix up in the published course description. Ive seen it before in other courses. But anal1 course description does mention integration.
Ive done a lot of shit with matrixes in calc. Linear algebra just formalizes what ive already seen and delves a bit deeper.

Let [math]F[/math] be a field, and let [math]g(x)[/math] be an irreducible polynomial over [math]F[x][/math]. Is it true that [math]F[x]/(g(x)) = F(\alpha)[/math] where [math]\alpha[/math] is a root of [math]g(x)[/math]?
If so, why?
Morandi's Field and Gallois theory seems to state this fact as obvious, but it is not so obvious to me.

>>9700353
it's not equal to, it's just isomorphic, sorry.

How often do you guys study? I never study, get drunk everyday and I feel like a brainlet that I cant exel in my classes while doing the minimalist amount of work.

>>9699999
get

For biologists: what is the superfamily taxon of the golden lion tamarin (Leontopithecus rosalia)? I've tried looking online at various websites, but none of them have shown me what the superfamily is. This is my first time coming to /sci/, so I apologize for my lack of intelligence.

Is it a bad practice to write my number one as a stick instead of pic related?

UKfag here read this and help.

The GCSEs are in 4 weeks and I have covered the foundation tier so now I am moving on to the higher tier, is 4 weeks enough to get the grade I want? I want grade 6 or higher

>>9700692
bump

does this graph have a hamiltonian cycle? i'm pretty sure it doesn't since i think i've tried everything possible but how do i prove that it doesnt have one?

>>9700972
>i'm pretty sure it doesn't since i think i've tried everything possible but how do i prove that it doesnt have one?
By exhaustion.

>>9700353
let [math]\alpha[/math] be a root of g(x), the irreducible polynomial. Assume deg g>1 (otherwise [math]\alpha[/math] is contained in F trivially, and [math]F=F(\alpha)[/math]). Note that the ideal (g) in the polynomial ring F[x] is maximal due to irreducibility, and in particular, the quotient F[x]/(g) is a field, which also contains the field F. Now consider the evaluation at [math]\alpha[/math] homomorphism [math]F[x]/(g)\to F(\alpha)[/math] defined by [math]f(x)+(g)\mapsto f(\alpha)[/math]. The linear polynomial h(x)=x is mapped to [math]\alpha[/math], since we know deg g>1 so h must exist in the quotient field.

The homomorphism is injective since g is irreducible, since if f([math]\alpha[/math]) evaluates to 0, then it must be divisible by g and hence 0 in the quotient field. It is surjective on the field F because the contstant polynomial j(x)=a maps to a in [math]F(\alpha)[/math], and we know [math]\alpha[/math] is also in the image.

>>9701101
>let α be a root of g(x), the irreducible polynomial. Assume deg g>1 (otherwise α is contained in F trivially, and F=F(α)). Note that the ideal (g) in the polynomial ring F[x] is maximal due to irreducibility, and in particular, the quotient F[x]/(g) is a field, which also contains the field F. Now consider the evaluation at α homomorphism F[x]/(g)→F(α) defined by f(x)+(g)↦f(α). The linear polynomial h(x)=x is mapped to α, since we know deg g>1 so h must exist in the quotient field.
>The homomorphism is injective since g is irreducible, since if f(α) evaluates to 0, then it must be divisible by g and hence 0 in the quotient field. It is surjective on the field F because the contstant polynomial j(x)=a maps to a in F(α), and we know α is also in the image.
nerd

>>9701101
>>9700353
Also note that it can be any root, since there is a trivial isomorphism between, say, F[math](\alpha)[/math] and F(>>9701103)

>>9700692
fuck off

>>9700353
Yep.
Let a be a root of g(x). Then g(x) is the minimal polynomial of a (just normalize it) and its degree n is the degree of F(a). So for every x in F(a), x = b0 + b1a + b2a^2 + ... + b_n-1 a^(n-1) for some bi in F.
But for each coset X in F[x]/(g(x)), there is precisely one polynomial of degree < n in the coset X (divide your representative by g(x)). So there's a natural isomorphism between the two by taking that unique representative in F(x)/(g(x)) and evaluating at a to get an element of F(a).

>>9700353
Ok just found an easier proof actually: Let E be an algebraic extension of F that contains a root [math]\alpha[/math] of g. Consider The evaluation at [math]\alpha[/math] homomorphism [math]F[x]\to E[/math]. The kernel of this polynomial is (g(x)), since g is irreduible and [math]\alpha[/math] is a root. If we can show that the image of this homomorphism is [math]F(\alpha)[/math], then the first isomorphism theorem gives you the desired isomorphism. Clearly the whole of F and [math]\alpha[/math] is in the image as before. If any other root [math]\beta[/math] is in the image, then that means some polynomial h(x) evaluated at [math]\alpha[/math] gave you [math]\beta[/math]. In particular, [math]\beta [/math] is a linear combination of elements in [math]F[/math] and [math]\alpha[/math], hence [math]\beta\in F(\alpha)[/math].

>>9701142
not a *linear* combination actually, if anything should be an F-linear combination of [math]\{1,\alpha,\alpha^2,...,\alpha^d\}[/math] for some d

I need a motor to turn a shaft with a bit of weight at a constant torque (say 0.5 N*m) until reaching a certain speed. The weight and dimensions of this shaft can be adjusted accordingly to accommodate whatever brushless motor is most practical


How can I produce constant torque? Is it really just a matter of providing constant current?


And how do I calculate the torque value of a brushless motor to achieve the desired strength accurately?


Finally, How could this be done with an arduino?, I'll tip whoever helps most

>>9701215
> How can I produce constant torque? Is it really just a matter of providing constant current?
More or less. Torque is very closely related to current until you start saturating the core. If you need to control the torque more accurately than that, you can either measure the current-torque curve or use a torque sensor.

> And how do I calculate the torque value of a brushless motor to achieve the desired strength accurately?
The torque constant (Kt) is usually documented.

> Finally, How could this be done with an arduino?, I'll tip whoever helps most
Are you using an external motor controller or is the Arduino supposed to be driving the motor directly? If you're using an external controller, you'd measure the current draw with a sense resistor and ADC and use a feedback loop (e.g. PID control) to vary the control signal.

If you're using the Arduino as the controller, motor control isn't rocket surgery but it's not trivial enough to describe here.

I'll leave all the soppy context out.

An Introduction to Statistical Learning
Elements of Statistical Learning
Probability with Applications in Engineering, Science, and Technology

Are these three textbooks enough to get me into, and understanding. the latest and greatest in ML/AI?

Are there any good textbooks which explain the ins and outs of 'newer' things like Conventional Neural Networks? Or am I left to sifting through some research papers and understanding that language?

>>9701312
A PID controller and those other parts sound really expensive though, and arduinos can only supply like 30mA max

And okay, the torque is directly proportional to the current. But how does the voltage play into this? If speed is related to voltage, does the voltage have to be the one manipulated until desired speed?


Is there any way to build this project without spending hundreds on tools?

I just registered for my Fall courses and I'm wondering if I'm overkilling it and possibly hurting myself.

Currently registered for:
Calc 3
Linear Algebra
Applied Regression Analysis
Sampling Methods

I got a B+ in Calc 2 and a C in Calc 1. I've taken Discrete Math and got a B- in it. However, the problems with Calc 1 and Discrete Math revolve around myself having a horrible work method during that time.

>>9701470
I've only taken up to Calc 2, it's a bit of work usually but there're tonnnns of resources online for whatever you could possibly need to know.

I never took Linear Algebra because they said that through doing Math 1 and Math 2 at my Uni I'd already completed everything that's in there plus some.

Regression analysis is pretty interesting, did a unit in it last semester. The basics are pretty simple once you wrap your head around it; just a 'line of best fit' over many dimensions. Logistic regression is a bit of a different beast. A lot of the cool stuff is the methods of variable reductions such as Partial Least Squares and LASSO. As too many variables (and not a lot of data) will almost always lead to over fitting; a model which isn't robust enough and fails given some new, unseen, 'strange' data.

Sampling methods sounds similar to a unit I'll be taking next semester, but probably just involves a fair bit of probability theory (different discrete/continuous distributions etc), paired with experimental design - shouldn't be too hard.

From what I can tell it's a really nice mix and it all ties together quite nicely. It really will come down to how heavy the workload is by your unit coordinators though - best of luck.

Sounds like a Data Science based curriculum you've got there? Applied math/statistics of some sort at least?

>>9700972
If there was a hamiltonian cycle it would contain edges ae,ac.
Then it cannot contain both bc,be or dc,de or gc,ge but it must contain two edges adjacent to b,d,g so by pigeonhole it contains all of bf,df,gf.
Contradiction as there would be three edges adjacent to f.

>>9701457
> A PID controller and those other parts sound really expensive though
A PID controller is 10 lines of code running on the Arduino.

> and arduinos can only supply like 30mA max
Something has to control the current to the motor. If the current is substantial, the bulk of the cost is going to be the power transistors, regardless of whether they're part of a separate ESC or driven directly from the Arduino.

> And okay, the torque is directly proportional to the current. But how does the voltage play into this?
Voltage affects maximum speed.

> If speed is related to voltage, does the voltage have to be the one manipulated until desired speed?
For a brushless motor, you'd typically have two nested feedback loops. The inner loop would vary the PWM duty cycle to achieve a desired current (this might be simple hysteresis), the outer loop (typically PID) would vary the current to achieve the desired speed or acceleration.

If you're using an external ESC, it would take a control signal (which might be voltage, PWM or PPM) and vary the speed accordingly.

> Is there any way to build this project without spending hundreds on tools?
Tools (as in, things you need to build the project which aren't themselves part of the finished project) aren't necessarily that expensive. If you need a torque transducer to calibrate the motor; that would probably cost a few hundred dollars if you can't borrow one. Otherwise you'll just have to rely upon the stated Kt (or current-torque curves) from the motor's manufacturer. If you're using the Arduino for motor control, you'll need the use of a scope if it doesn't Just Work.

>>9701534
Yeah, I'm a stats major, math minor, actuarial and data science certificate guy. I'm planning on taking the P exam in about a year. The data science stuff is just from personal interest.

>>9701568
BTW, I should also point out that using a brushless motor will increase the complexity and/or cost of the project compared to using a brushed DC motor.

A "brushless DC" motor needs (usually) 3-phase AC, which needs to be generated with a motor controller (aka electronic speed controller or ESC), which will either add cost (if you buy it) or complexity (if you use the Arduino).

>>9701570
Ahh thought so, I'm a Data Science major; actually in the first group of students at my uni that can be doing it.

It's interesting because the way the degree feels at the moment is a bit of a dumbed down Statistics major with some added Computer Science mixed in where the Stats bits have been cut out.

I really am starting to love the Statistical theory, and probably might have been better suited just doing the Statistics major. But the Computer Science bits (databases, fundamentals of programming, Python, R, data structures & algorithms) are really essential for the whole 'pipeline' and I definitely would've missed out on those if I did the pure Statistics major. To compensate though I'm pretty much going out of my way to fill all my electives with pure Statistics and Actuary units to 'fill that gap.' What's this P exam?

I'm from Perth, Australia though and there's not really too many opportunities it seems for graduate/junior data scientists - where as all over the rest of the world it seems companies are begging for them. Managed to land some work experience but it's within essentially a medical research institution, where there's not actually an established analytics team so I'm pretty lost and useless without any sort of guidance or direction - always FUN. Where're you studying?

>>9701585
The P-exam is an exam that is a requirement to become an Actuary in the US. It's a test over probability theory and applications, along with a ton of statistics.
https://www.soa.org/education/exam-req/edu-exam-p-detail.aspx

I came into university as a CS major, ended up hating it and switched to Statistics. Now, I kinda wish I would've done pure math but it is what it is. Pure stat-based jobs are pretty rare in the US, or they don't pay what you'd expect. Actuaries are paid phenomenally here, so I plan on passing that exam and living in EZ mode while I save money. Insurance industry here is bogus and is always hiring. I am actually doing an internship with a data science based risk management company over the summer.

>>9701589
Sounds like you've got it all planned out, good man. I actually started doing a semester as a CS major too, and hated it and switched too ahahah.

Our University offers an Actuarial Science major and I'm starting to wish I'd done that. One of my lecturers who's from the Finance side of thing said he'd heard of companies in America hiring Physicists to make finance models (be a quant), because they were more hands on and used to data compared to a pure Mathematics major - and understood stats unlike most Finance majors.

In Western Australia though our whole industry is mining based. Some of these resource companies are beginning to form analytics/data driven teams - but we're 10 years behind the rest of the world in an industry sense; tried and tested, not fond of change.

Hard to find opportunities, especially as a junior with not a lot to offer. Might have to put my American citizenship to work soon enough ey?

>>9701579
Thank you that's a ton of help


Do you have a discord or something I can contact for any additional questions?

Any organic chemistry guys around?
Is this a trick question?

"During a chemical reaction one flourine atom replaces one hydrogen in the compound C8h18, draw the skeletal formula for all the possible isomers of this new compound.".

Won't the skeletal formulas for C8H17F look exactly the same as those of C8H18?

>>9701692
Bump

>>9700684
who cares?
writing it like that is probably more likely to be mistaken for 7, especially if you're not careful. if you do want to write it like that, personally i'd make sure i added the line at the bottom as well

how to get good at Work problems in Calculus 2? Stuff like draining water out of a conical shape or trough, or lifting rope up a building. I've done extremely well at the pure calc 2 problems but I'm pretty abysmal at this stuff

Ok so i'm starting to learn analysis from myself as my uni is garbage. I don't understand why there is a = instead of a < on this pic, i'm a brainlet.

Is learning python worth it if I already know matlab? what sort of things can python offer that matlab does not?

>>9702140
Because y^2+ x - y^2=x

>>9702150
Ok i'm retarded, i thought the notation meant that (y + e)^2 = x, i thought that every = or < sign was corresponding directly to (y + e)^2.
It was just me being a fucking brainlet.
>>9702147
Yes because matlab is not a real programming language.
Python is a general purpose programming language, you can literally do everything, it's free software, the only real downside is the performance. If you only want to do math don't bother because you can already do the same thing in matlab without having to relearn everything.

>>9701692
When drawing a skeletal structure, anything that isn't a carbon or hydrogen needs to be explicitly drawn. C8H17F (fluorooctane) has four isomers: 1-fluorooctane, 2-fluorooctane, 3-fluorooctane, and 4-fluorooctane. (Note: 5-fluorooctane is the same as 4-fluorooctane)

Chemfags help me please.
[math]Fe + CuSO_4 \longrightarrow Cu + FeSO_4[/math]
I know it's a redox reaction because Fe and Cu changed their oxidation states ([math]Fe^0 \longrightarrow Fe^{+2}[/math] and [math]Cu^{+2} \longrightarrow Cu^0[/math]).
Why do the electrons relocate from Fe to Cu? Is there any atomic property to explain this electron transfer?

>>9702197
>atomic property to explain this electron transfer?
Cu is (Cu)ter than Fe therefore the electrons relocate from Fe to Cu. Don't try to overthink when doing chemistry.

how do i do pic related without using the matrix of T?
so far ive got :
[math] \lambda [/math] is an eigenvalue if for non-zero [math] v\in V [/math] we have [math] T(v)=\lambda v [/math].
so [math] \begin{pmatrix}x+y\\x+y\end{pmatrix}=\lambda\begin{pmatrix}x\\y\end{pmatrix} [/math] and [math] \begin{pmatrix}x-\lambda x+y\\x+y-\lambda y\end{pmatrix}=\begin{pmatrix} 0\\ 0\end{pmatrix} [/math].
hence [math]
(1-\lambda)x+y=0\,;\ x+(1-\lambda)y=0 [/math]
but i have literally no idea how to proceed from there. if i subtract one equation from the other i find [math] \lambda=0 [/math] (which is wrong) so clearly i'm not getting something

Alright guys, help me out.
There is the 'Dr Fox effect'.
>Lecturing in a charismatic way benefits more than speaking in a monotone boring voice.

But there is another psychological phenomenon that looks like the above, but it's like:
>An amateur like me writes something for a science magazine.
>It gets rejected.
>I publish it again, but under the name of a well-known scientist.
>It gets published and has good reviews.

How is that called again? Cause I forgot it.

Second one:
In typing down words on a paper, I 'brainwash' the reader in thinking that this paper is poor written, so that they are more biased to think that it is actually poor written.

How do you know to use washer or shells method for volume of solids of revolution?

>>9702222
>Don't try to overthink when doing chemistry.
Ok, I just wanted to know if there was some underlying mechanism that explained why Fe displaced Cu but I'll just assume that the answer is either non-existant or too hard to understand.

Chemistry General? Chemistry General

>>9702230
Why is lambda = 0 wrong? Isn't that the eigenvalue of (x, -x)?

'sup /sci/ I accidentally bullshitted my way into a job that I'm not even remotely qualified for (I've been NEET since I left highschool 8 years ago) and now I spend all day watching bugs and writing down what they do. My boss seems to think that they "exhibit ritual behaviours and signs of greater intelligence" but I think he's full of shit since he hired me just because I told him that one day bugs would inherit the earth (lol). Is there any truth to what he's saying, outside of mating rituals which can't require much thought if aboriginals can perform them, or is he just wasting his money?

Can someone help me with this, X,Y are standard normaly distributed and independent, what is E[X|X>Y]

>>9690914
any medical doctors in the house? I have a ICD-10 question.

>>9702197
HSAB theory. Iron is harder than copper. Sulfate ions aren't necessarily hard or soft, but because it is binding as a salt it will prefer a harder metal.

>>9700181
>But what does one do when the 4th priority group isn't going behind the plain.

When the 4th group is on the wedge you have to rotate the molecule 180 degrees like in pic related.

I don't understand cantor's diagonalization argument. Why can't S occur in the sequence?

>>9697543
It would be invisible to us. The energies associated with electron transition levels at very large radii would be far beyond the visible light range in the electromagnetic spectrum.

In order to see matter, an electron in the valence band needs to excite itself to an empty orbital of a slightly higher energy. When light is absorbed by matter (exciting an electron to a higher energy state) the color you see is all the light that didn't get absorbed (light that gets reflected back to you). As you get bigger and bigger, the differences in energy between orbitals increases, and thus so does the energy you need to excite an electron.

So you would need extremely powerful light rays for any energy to even be absorbed, and even then it would only be visible on ultra high frequency radiation detectors.

When you see the color black, what you are seeing is matter which is reflecting back all the light shown on it because it isn't exciting any of its valence electrons. In this case, we wouldn't even see black (say against a white background) because the only part of the atom that can reflect light is the nucleus, which would still be incredibly tiny compared to an atom the size of a room (i.e. even when the electrons orbit at the distance of a few meters, the nuclei would still be impossibly small to see).

If the nuclei was huge, you would see a star.

>>9702674
Is HSAB really related? I just found out about reactivity series and they don't correlate to the chemical hardness of some elements (for example Lithium has a high reactivity but low chemical hardness).
I'm literally on the first semester of ChemE so I might be wrong.

>>9702731
>>9702731
nvm I understand it now,

>>9697543
It would be invisible to us. The energies associated with electron transition levels at very large radii would be far beyond the visible light range in the electromagnetic spectrum.

In order to see matter, an electron in the valence band needs to excite itself to an empty orbital of a slightly higher energy. When light is absorbed by matter (exciting an electron to a higher energy state) the color you see is all the light that didn't get absorbed (light that gets reflected back to you). As you get bigger and bigger, the differences in energy between orbitals increases, and thus so does the energy you need to excite an electron.

So you would need extremely powerful light rays for any energy to even be absorbed, and even then it would only be visible on ultra high frequency radiation detectors.

When you see the color white, what you are seeing is matter which is reflecting back all the light shown on it because it isn't exciting any of its valence electrons. In this case, we wouldn't even see white because the only part of the atom that can reflect light is the nucleus, which would still be incredibly tiny compared to an atom the size of a room (i.e. even when the electrons orbit at the distance of a few meters, the nuclei would still be impossibly small to see).

If the nuclei was huge, you would see a star.

>>9702770
The reactivity series is an over-simplification of chemistry, though I can't say I'd expect any different from engineers.

How reactive a metal ion is will only depend on what the other ion is in the solution. There is no general 'cheat sheet' formula you can use to simply this fact.

Delete the reactivity series from your memory. Now.

>>9702793
Ok, I'll forget about reactivity series.
Thanks for answering my question.

I don't understand this. She later uses u_0 = 100x/l as a boundary condition.
If she's letting x = l, why is she writing it that way?

>>9702693

just visualize it as a 3rd molecule the F OH and CH3 form a wheel that then goes clockwise

>>9702847
>If she's letting x = l, why is she writing it that way?
She's not, re-read that sentence and the previous one.

>>9702230
why is 0 wrong? The only thing that can't be the zero (vector) is the eigenvector, not the eigenvalue

In Rosen's book "Number theory in function fields" there is the exercise to show that if [math]B,D [/math] are divisors with [math] B + D [/math] being in the canonical class then [math] | l(B) - l(D) | \leq \frac{1}{2} | \deg(B) - \deg(D) | [/math].
But using Riemann-Roch, I get that
[math] l(B) - l(D) = \deg(B) + 1-g [/math]
and
[math] l(D) - l(B) = \deg(D) + 1-g [/math]
([math] D = C-B [/math], because [math] B + D [/math] is canonical). To clarify: [math] l(D) [/math] is the length of a divisor of a function field, [math] \deg [/math] its degree. Furthermore, [math] g [/math] is the genus of the function field and [math] C [/math] a suitable canonical divisor.
If I subtract the equations by one another, I even get the equality
[math] l(B) - l(D) = \frac{1}{2} (\deg(B) - \deg(D)) [/math].
Have I done something wrong or is the conclusion correct, and the conclusion of the exercise is just weaker?

>>9999999