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This thread is for questions that don't deserve their own thread.

Tips!
>give context
>describe your thought process if you're stuck
>try wolframalpha.com and stackexchange.com
>How To Ask Questions The Smart Way: http://www.catb.org/~esr/faqs/smart-questions.html
>>
why is the sky blue?
>>
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I'm stumped on how to solve this problem
>>
>>9205966
What have you tried?
>>
>>9205968
For part (a) I was originally confused about notation, but then I realised the root we seek is a coset in F. So I was guessing α=[x], since the coset [math] [x^{4} + x^{3} + x^{2} +x + 1] = [0] [/math], meaning x is a root. Wasn't too sure about b or c.
>>
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Whats the intuition behind solving this stats problem
>>
>>9206001
For this, you gotta know that probability of event 1 AND probability of event 2 = (prob of 1)*(prob of 2)

also,

probability of event 1 OR probability of event 2 = (prob of 1) + (prob of 2)

for some intuition, think of rolling a 6-sided die. Any outcome has probability 1/6. Probability of getting a 2 is 1/6, for example. If you roll the die, and then roll the die again, you're more likely to get a 2 on one of those two rolls. That is you're more likely to get a 2 on either roll 1 OR on roll 2. You add the probabilities, so the actual probability of getting a 2 with 2 rolls is 2/6. Now think of rolling the die twice and insisting that you get a 2 on both rolls. That's a lot less likely to happen. You have to get a 2 on both roll 1 AND roll 2. You multiply the probabilities, and the chance of it happening is 1/36.
>>
>>9206001
>AB is that rare
Damn I really need to start donating.
>>
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If any genius would be willing to give moi a hand with this I'd be forever thankful
>>
>>9206032
wow I screwed up this explanation up so bad. fuck. disregard everything in this post.

you don't roll the die twice and add the probabilities. You expand your acceptable possibilities of the dice roll to add the probabilities. prob of getting 2 OR 3 is 2/6. rolling the dice multiple times creates a binomial distribution.

anyway answers to your problem are:
a) (.46)^2
b) .46
c) (.46)^2 + (.40)^2 + (.10)^2 + (.04)^2
d) you assume people's blood types are independent events. Probability of your partner having a certain blood type isn't affecting the probability of your blood type.
>>
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Struggling to make progress on (a) and (c), any tips.hints/tricks?
>>
is it rude if I resend an email multiple times in a day if it's urgent? A professor simply won't answer my emails. He's being a total retard. What can I do? I need him to answer a question today or tomorrow, I don't have enough time.
>>
>>9206782
Meet in person
>>
>>9206788
shit you're right I guess the only way to do this is to meet in person, otherwise they don't give a shit about you
>>
>>9205960
define why
>>
is flat earth real?
>>
Could it be possible that the universe isn’t actually expanding faster but just rotating around a point?
Could that explain the light shifting in phase?
>>
>>9206190
>>9206095
Is this the new meme?
>>
>>9206806
If you're asking "is the earth actually flat?" then the answer is no.

If you're asking, "do people really believe that the earth is flat?" the answer is yeah, there are probably a few. But a lot of the people who debate it online are just trolls and don't really believe in a flat earth.
>>
>>9206190
a. alpha is just the image of x under the projection Z_3[x] -> Z_3[x] / (f)
b. Can be verified easily
c. Use the division algorithm
>>
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What would be an interpolation function F interpolating f such that
[math] \dfrac{dF}{dx}(k)=\dfrac{1}{2}f(i+1)-\dfrac{1}{2}f(i-1)[/math] ?
>>
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>>9206931
Am I getting close?
>>
Given a list which may contain duplicates, such as {a,b,c,d,a,b}, how can I calculate the number of unique permutations that don't start with, say, a?
>>
>>9206931
that's a second order aproximation for the first derivative [math]\frac{\partial f(x_i)}{\partial x}=\frac{f(x_i+h)-f(x_i-h)}{2h}+\mathcal{O}(h^2) [/math] (in your case h=1)
you can get that by differentiating the quadratic interpolation in [math] x_{i-1},x_i,x_{i+1} [/math]
don't ask me about the g though, I never did interpolation in this weird way with convolutions etc
>>
Why is this class slogging by?
>>
>>9206973
>Given a list which may contain duplicates, such as {a,b,c,d,a,b}, how can I calculate the number of unique permutations that don't start with, say, a?
Inclusion/exclusion principle

Set of words that doesn't start with a=All words - words that start with a=(5!/(2!*2!)-(4!/2!)
>>
[math]9cos^2x+cosx-10[/math]

I am supposed to factor this expression. I am told to "Rewrite the middle term as the sum or difference of two linear factors."

which turns out to be [math]9cos^2x-9cosx+10cosx-10[/math]

What is the sum or difference of two linear factors formula or what does it look like?
>>
I'm trying to find the variation of an anti-symmetric tensor [math] F^{ \mu \nu } [/math] under a Lorentz transformation. So far I've got:[eqn] \delta F^{ \mu \nu } = \delta \left ( \Lambda ^{ \mu } _{ \rho } \Lambda ^ { \nu } _ { \sigma } F^ { \rho \sigma } \right ) \\ \delta F^{ \mu \nu } = -\frac { i } { 2 } \omega _{ \alpha \beta }\left [ \left ( J ^{ \alpha \beta } \right )^{ \mu } _{ \rho } + \left ( J^{ \alpha \beta } \right ) ^{ \nu } _{ \sigma } \right ] \\ \delta F ^{ \mu \nu } = -\frac { i } { 2 } \omega _{ \alpha \beta } \left [ i \left ( \eta ^{ \alpha \mu } \delta ^{ \beta } _{ \rho }- \eta ^{ \beta \mu } \delta ^{ \alpha } _{ \rho } \right ) + i \left ( \eta ^{ \alpha \nu } \delta ^{ \beta } _{ \sigma } - \eta ^{ \beta \nu } \delta ^{ \alpha } _{ \sigma }\right ) \right ] F^{ \rho \sigma }[/eqn]From here I just do the contractions with F and the deltas, but this doesn't look right. Anyone got any feedback?

>>9205960
https://en.wikipedia.org/wiki/Rayleigh_scattering
>>
>>9208669
>9cos2x+cosx−10
> I am supposed to factor this expression. I am told to "Rewrite the middle term as the sum or difference of two linear factors."
> which turns out to be [math]9cos^2x-9cosx+10cosx-10[/math]
> What is the sum or difference of two linear factors formula or what does it look like?
You were nearly there. Notice that
9cos^2x-9cosx=9 cos x (cos x -1)
and
10cosx-10= 10 (cos x-1)

Therefore
9cos^2 x+cos x−10= (9 cos x +10) (cos x -1)
>>
Why don't we make rocket fuel from water?
Why is it not viable to take hydrogen and oxygen out of water and use it as
rocket fuel? Do we not have any efficient way to electrolysis in large scale?
>>
>>9208709
>Do we not have any efficient way to electrolysis in large scale?
That's certainly one problem.
>>
>>9208669
Anon, do you know how factoring polynomials works? Bevause that's a binomial of 9u^2+u-10 with u=cos
>>
>>9208700
Thanks for the reply. I'm really not entirely sure what you can go from [math]9cos2x+cosx−10[/math] to [math]9cos^2x-9cosx+10cosx-10[/math]

I don't know why you can plug in [math]9cosx+10[/math]
>>
>>9208718
>binomial
Ignore that shit
>>
>>9208718
I can factor regular stuff like [math]ax^2+bx+c[/math] but this is the first time I have ever factored trig. There's something pretty basic I'm missing. But I'm not sure what it is.
>>
>>9208724
Literally substitute cos=u then factor and replace when you get it done
>>
>>9208721
>>>9208700 (You)
>Thanks for the reply. I'm really not entirely sure what you can go from 9cos2x+cosx−10 to 9cos2x−9cosx+10cosx−10[/math]Idon′tknowwhyyoucanplugin[math]9cosx+10

cos x= 1*cos x = (10-9)*cos x

It's not so difficult, just do the following:
>>9208726
>Literally substitute cos=u then factor and replace when you get it done

It's just factorizing a second degree polynomial, just writing cos x instead of the usual independent variable.
>>
in mathematica i can do for example
>a + b + c //. m_ + n_ :> {m, n}
>{a, {b, c}}

but what if i have a more complicated expression

how do i get from for example
>If[c, a, b] + x
to
>{c, a, b} + x
>>
>>9208767
nvm i got it

>If[c, a, b] + x /. f_If :> {Delete[f, 0]}
>{c + x, a + x, b + x}
>>
How do you solve math without a calculator
>>
>>9208767
dayum you can even do this
>a + b + c /. m_ + n__ :> {m, n}
>{a, b, c}
>>
>>9208791
There are a number of algorithms for many basic things. If you can't long divide in your head you're retarded, bro
>>
>>9208785
That'll only work if c isn't a boolean, otherwise it will evaluate before Replace has a chance to get it. If you want to stop things from evaluating you have to do stuff like in pic related.
>>
what's a "real function"? is it just shorthand for a real-valued function of a real variable
>>
>>9208947
Yes
>>
hi /sci/
I majored in CS and did some math on the side (not enough to be a math minor). I decided to major in math and I'm starting from scratch, but I'm finding most first courses boring as I know most of the concepts already. However, I don't feel confident yet in my ability to completely forgo studying for those courses. Should I just pace up and study by myself the stuff that I don't know and start more advanced material, should I keep with the pace of the lectures (which is going rather slowly) or should I just start looking into more advanced stuff and learn what I'm missing of the introductory courses on the go?
I feel like I should invest time in the introductory courses, but I also feel I'm wasting time by going over stuff that I'm already comfortable with (sometimes it's hard to tell these two apart), so what should I do?
>>
more of an /r/, does anyone use LabVIEW, and anyone have access to the core 1 class they offer? Its 500 dollars from their website, fuck that shit
>>
>>9209073
wow, just found it on an towelhead site cheers

http://www.mediafire.com/folder/w69s7binv825r/LabVIEW_course
>>
Set A = {"Hello"}
P(A) = 0.05

Set B = {"World"}
P(B) = 0.1

Obviously AUB = {"Hello", "World"}
but what would be the set of {"Hello world", "World Hello"}?
>>
>>9209355
closest with standart operations would be {AxB,BxA} = {{(Hello,World)},{(World,Hello)}}
what kind of measure is P anyways?
>>
>>9209355
It's called the set of permutations
>>
Would it be correct to say that ML-based prediction algorithms are concerned not with the past and future, but only the present because of the law of large numbers?
>>
>>9209375
P is the probability of the word occurring in a theoretical query.
>>9209387
So would it be 2^2?
|AUB| = 2
|Possible outcomes (word can occur)| = 2

Or am I missing something?
>>
I want to build a vacuum chamber so that I can "plasma clean" the oxides off of pure indium and antimony and run some sputtering tests. I have access to some pretty reasonable Edwards vacuum pumps and vacuum lines. I don't know how to go about constructing a cheap vacuum chamber though.

How can I build a safe vacuum chamber? I'm not sure what design I should go for (cylinder capped on either end vs bell jar on a platform) or how thick the vacuum chamber walls should be.
>>
>>9208671
Too hard for /sci/?
>>
>>9210937
I once asked what 7 squared was and got 0 replies if that puts /sci/ into context.
>>
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Why is social welfare a "high demand" major nowadays?
>>
I'm having a hard time understanding the Quine-McCluskey algorithm for minimizing boolean functions.
>>
>>9211130
There's a lot of money in nonprofits
>>
>>9205943
How important are lectures for learning? I'm reading some uni math courses but can't go to the lectures. Will course books and internet resources be sufficient?
>>
>>9211130
>In the modern world you need to have a degree to even get a look in
>Not everyone is smart enough to do study a real subject
>Therefore they have to """"study"""" what is effectively Opinion Studies.
That's the sad truth.
>>
>>9211176
this. corporate douchebags think it looks good to donate to "progressive" causes
>>
>>9210937
I'd love to help if I'd taken a course on QFT. Maybe in a couple of years.

>>9211186
Depends on the quality of the material and the extra effort you're willing to put in. Not impossible, but pretty labour intensive.
>>
>>9211238
I'm not really good at math. Not a total brainlet but not "skilled" so to speak. Is it doomed to fail
>>
in probability, what operations would require all events in the sample space to have equal probability?
>>
>>9211721
Chi squared tests for equal distribution
>>
>>9211736
Nothing else though?
Events wouldn't need to be of the same probability for addition/multiplication?
>>
>>9211741
Not that I can think of. Granted I'm no expert
>>
Do I need to get a Phd to get involved in cutting edge medical research? Or is there a faster way?
>>
>>9211849
Just make significant contributions and some institute will give you an honorary PhD. Good luck finding some place that will hire you
>>
>>9211901
how
>>
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>>9212114
pay a shit ton of money
>>
>>9212114
Good question.
>>
>>9212134
Even if he did rape a bunch of women, Dr. Cosby's contributions to world were vast
>>
Any chemfags that can help me out here? Please tell me this looks familiar to you:

Log Ps = 4.81(1 - Tb/T)
Where Ps is the pressure of a vapor
Tb is the boiling point of the compound(that got turned into the aforementioned vapor)
T is the temperature at which we want to know the pressure of the vapor

With that I'm supposed to get Ps, but I have no idea if it's in atm, Pa, psi, mmHg, or if the temperatures are in celsius, kelvin, fahrenheit or fucking rankine. I've been looking everywhere but can't find this particular formula, and I should have asked the teacher sooner but you know how it is 'you had x amount of time to ask but now it's too late'.
>>
>>9212314

It's the August equation.
>>
>>9212353
Thanks man that one makes the most sense... though I don't see that 4.81 in any chart. And the boiling temperature is in the denominator. Fuck man this is all wrong, I can't get a reasonable result... Could it be another equation? Or should I just roll with it?
>>
Is there any meaningful use for upper and lower bounds of a set that isn't just defining the supremum and infimum?
>>
>>9212856

Let x = Sum of (10^-p) where p is a prime such that p and p + 2 are both prime.

Then x > 0.0010 and x < 0.0011 but to find the exact value of x would require solving the twin prime conjecture.
>>
how the heck do I prove if [math]0\leq x \leq \epsilon[/math] for every [math]\epsilon >0[/math] then [math]x=0[/math]? Seems like a contradiction would work but I'm not sure what do to after I suppose [math]x\neq 0[/math].
>>
>>9212903
you have a severe case of brainletism.

assume x is not zero, therefore by our assumption x>=0 we have x>0

set eps=x/2 and you have your contradiction
>>
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>>9212918
t-thanks
i'm trying to get better anon, this takes time.
>>
Prove to me that if x=1+yz
That y=x-z
>>
>>9212954
trivial
>>
>>9212958
well come on then boy do it
>>
>>9212959
let [math]\Sigma[/math] be the set which contains the answer.
qed
>>
>>9212962
FUCK YOU
>>
>>9212924
Draw stuff anon.
From the drawing your intuition should tell x=0.
Explain your intuition to a friend.
The proof will hopefully comes out of your mouth without you even realizing it.
>>
How can numbers exist? If I have an infinite amount of numbers, how does it makes sense for any given one to exist? How can a number have a finite amount of digits? How can a given number be picked from an infinite amount of numbers, leaving infinite behind?
>>
>>9206001
I've always thought of joint probability of independent events as a proportion. For the first O you have a 46 percent chance now treat the 46 percent as the whole prob space and then take 46 percent of that giving .46*.46=.2116
>>
Are eyebrows genetic? If i have eyebrows that grow into a unibrow, does that mean i have middle eastern genetics?
>>
>>9213037
>How can a number have a finite amount of digits?
you can write 0 as 0.000... just that the trailing zeroes after the decimal point are redundant (except if you're using them to specify how accurate a measurement is for example) since you know what 0 means
>>
Do doors lose more heat if they are open further or not?
Because wouldn't a door that's only slightly open have a bigger difference in pressure so more air would leave?
>>
Any good youtube channels for learning math progressively from basics to something more advanced, i hated and ignored math when i was younger and now want to learn.
>>
>>9213071
>Any good youtube channels for learning math progressively from basics to something more advanced, i hated and ignored math when i was younger and now want to learn.
https://www.youtube.com/user/njwildberger
>>
What's a proof that [math]\binom{n}{2}+\binom{n}{3}+...+\binom{n}{n}=n^2-n-1[/math]
As a related question, how do I search for [math]\binom{n}{m}[/math] on google?
>>
what does this mean? Take example of dice rolling please.
>>
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>>9213100
pic related
>>
>>9213096
>What's a proof that (n2)+(n3)+...+(nn)=n2−n−1
try induction
>>
>>9213096
Search for C(n,m).

Anyway C(n,2)+...= C(n,0)+C(n,1)+C(n,2)+... -C(n,1)-C(n,0)= 2^n -n-1

So you wrote that wrong.
>>
also what's the full-width-half-maximum?
>>
>>9213106
I tried, but I got stuck at [math]\binom{n+1}{2}+\binom{n+1}{3}+...+\binom{n+1}{n}+\binom{n+1}{n+1}=(n+1)(\binom{n}{2}\frac{1}{n-1}+\binom{n}{3}\frac{1}{n-2}+...+\binom{n}{n})+1[/math]
However I searched what >>9213108 said and got it, so thanks.
>>
>>9212954
It does not hold for x=0.5, z=2 though.
>>
>>9212954
It isn't though.
x=1+yz
x-1=yz
y=(x/z)-(1/z)
>>
>>9213096
[math]{n \choose k}[/math] is the number of subsets with k elements of a set with n elements.

Clearly
[math]{n \choose 0} + {n \choose 1} + \ldots + {n \choose n} = 2^n[/math]
since the power set has 2^n elements. Now just subtract the first two terms to get
[math]\binom{n}{2}+\binom{n}{3}+...+\binom{n}{n}=2^n-n-1 [/math]
>>
>>9213138
I solved it already with >>9213108 bringing up C(n,1)+C(n,0), since it's n+1 and that's just the amount missing from the power set, but thank you anyway, your explanation was very easy to understand.
>>
prove: [math]x \in (a-\epsilon, a+\epsilon) \implies |x-a| < \epsilon [/math]

So I can write the interval explicitly as [math]x \in (a-\epsilon, a+\epsilon) = \{x : a-\epsilon < x < a+\epsilon \} [/math]

Do I split this into cases? so first [math]a-\epsilon < x[/math], which equals [math]a-x< \epsilon[/math]. This is just |x-a| for x<0, correct? likewise for case 2, then in both cases it is proven true.
>>
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Am I being really dense?
I've done the first part of this question, and all that's left to do is verify the latter part, but no matter what I do I get
[eqn]
\mathbf{\hat{L}^2} = \mathbf{a}^2 \mathbf{b}^2 -(\mathbf{a \cdot b})^2 - \gamma a_j b_k \delta_{jk} + \gamma a_k b_j \delta_{jk} - \gamma a_j b_k \delta_{jk} - 0 \\
= \mathbf{a}^2 \mathbf{b}^2 -(\mathbf{a \cdot b})^2 -2 \gamma a_j b_j + \gamma a_j b_j
\\ = \mathbf{a}^2 \mathbf{b}^2 -(\mathbf{a \cdot b})^2 -\gamma \mathbf{a \cdot b}
[/eqn]

instead of
[eqn]
\mathbf{\hat{L}^2} = \mathbf{a}^2 \mathbf{b}^2 -(\mathbf{a \cdot b})^2 + \gamma \mathbf{a} \cdot \mathbf{b}[/eqn]
>>
>>9213163
sorry that's confusing [math]\mathbf{\hat{L}^2}[/math] should be [math](\mathbf{a} \times \mathbf{b} )^2[/math]
it's used to prove an identity with the orbital angular momentum operator which I was trying to do before hence the L but it's irrelevant to the algebra.
>>
are the MIT lectures on youtube a good place for a maths undergrad to learn babby codering?
>>
>>9213202
yeah decent-tier at least but afterward you need to pick up a real language like java or C++
>>
>>9213202
https://www.youtube.com/watch?v=2Op3QLzMgSY&list=PL8FE88AA54363BC46
>>
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This "Integrate" command has been running for at least 10 minutes. How much longer can I expect it to take? (Mathematica)
>>
>>9213239
integrate it by hand you lazy fuck
>>
The probability of word1 occurring is 0.05.
The probability of word2 occurring is 0.1.
What is the maximum probability of "word1 word2" occurring, assuming both are independent events?

Is it just W1^W2? Or is there some other way?
>>
If I want to prove that [math]\mathbb{C}[/math] doesn't follow the ordering axioms, is it not enough just to argue that since multiplication isn't closed under [math]\mathbb{C}[/math], it violates part of the axiom and thus can't be ordered?
>>
>>9213239
Might be better to use Monte Carlo integration for that one.
>>
>>9213233
ty

>>9213238
>1986
cool
>>
>>9213202
>>9213233
>java or C++
Ignore this retard.
>>
>>9213304
although I have done some real babby tier graphing in matlab, im not clever enough to do research in maths
its more as an employable skill/hobby
what would you suggest?
>>
>>9213309
>im not clever enough to do research in maths
>what would you suggest?
I heard suicide is a good option.
>>
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>>9213304
>>9213315
>>
>>9213309
>its more as an employable skill/hobby
It doesn't matter, shit languages like C++ or java are cancerous for your brain. You can always get it later if you wish, there's no real need to infect your brain early on.
>>
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Why are word problems in maths so hard?
>>
>>9213341
most likely because you are a subhuman frogposter.
>>
>>9213315
*tips epic morphism*

>>9213327
so just focus on the MIT lectures for now then guess
>>
>>9211287
Keep in mind that the effort you'll need to put in is inversely proportional to your "natural skill". Whether you're doomed to fail is your call.
>>
>>9213161
bump
>>
>>9213341
Practice, anon
>>
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Could someone please explain to me in slow people words how exactly a differential is different from a derivative?

Is the derivative the change in y given a single unit increase in x while the differential is the change in y given an increase in x that is greater than one?

here's a free gif as thanks for an answer
>>
>>9213509
derivative is dy/dx = f'(x)
differential is dy = dy/dx*dx = f'(x)dx
>>
>>9213280
https://math.stackexchange.com/q/487997
>>
How do the mathematics of time dilation work? If I'm travelling at 2/3 the speed of light do I experience subjective time at 1/3 of the objective rate?
>>
>>9213546
yeah but whats the point
>>
>>9213565
dunno, i always hated the dy/dx shit. it's a historical artifact i guess

https://en.wikipedia.org/wiki/Differential_of_a_function#History_and_usage
>>
>>9213546
But dy/dx = f'(x) is the same as dy = f'(x) dx
>>
>>9213509
Differentials are a generalization of derivative. For any differentiable real function, you have the following Taylor expansion:
[eqn]f\left(x\,+\,h\right)\,=\,f\left(x\right)\,+\,f'\left(x\right)\,h\,+\,\underset{h\,\to\,0}{o}\left(h\right)[/eqn]
where [math]\underset{h\,\to\,0}{o}\left(h\right)[/math] denotes a remainder vanishing "faster than" [math]h[/math] when [math]h\,\to\,0[/math].

Now consider a space with fewer assumptions than [math]\mathbf R[/math] (to be more precise, suppose both the definition and target sets of [math]f[/math] are a vector space). The differential of [math]f[/math] is the function which at any point [math]x[/math] of the space outputs a linear application [math]\mathrm df\left(x\right): h\,\longmapsto\, \mathrm df\left(x\right)\left(h\right)[/math] such that
[eqn]f\left(x\,+\,h\right)\,=\,f\left(x\right)\,+\,\mathrm df\left(x\right)\left(h\right)\,+\, \underset{h\,\to\,0}{o}\left(h\right).[/eqn]

With this, you can characterize the differentiation of [math]f[/math] better than with just directional derivatives.
>>
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I need some ideas here. I am currently doing my masters degree in applied statistics and am looking for a project. I got some free time and would like to do a little research on any subject basically.

I know a lot about data analysis, statistics, machine learning, web-scraping etc. and want to apply this for something. Looking for something that doesn't involve me spending money. Anyone got any idea what I could do?

I don't care which subject it is - be it epidemiology, politics whatever. As long as I can do it from home and it involves skills I have, any suggestion is welcome.
>>
When they say that the speed of sound is around 340 m/s at sea level, does that mean this the maximum speed it can possibly travel at ? Or the average speed ?

Because I don't see how the soundwave could always travel at the same speed no matter what created it.
>>
>>9213776
it's the speed you get when you measure the speed of sound (or any pressure wave) in air.
Of course when you take more than one measurement you will get slightly different results, but the average of your measurements will be roughly the same as the accepted value.
speed of sound does depend on temperature, but it doesn't change very much between say 0 and 30 celcius
>>
>>9213711
Sure thing, kid.
>>
>>9213822
>>9213776
I should also say that sound travels much quicker in other media. for instance sound travels at 1,500m/s in water, 5,100m/s in iron
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>>9213163
bumping
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what the h*ck is that??
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>>9213889
Cross section of skin.
>>
Redpill me on fibre and vector bundles.
>What are they intuitively?
>what are they used for?
>what is the intuition for them?
>what are some important theorems regarding them?
>>
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>>9205943
Was the citric acid stem cell theory really faked, or was it covered up by (((RIKEN)))?
>>
>>9206038
If you care about the rarity donate platelets or plasma, not whole blood. AB blood cells can only go to AB recipients.
>>
>>9213827
t. Mr super-duper-thin-rectangles
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>>9213295
I need an analytic answer because I want to take further derivatives of it.

Still has not finished.
>>
>>9213761
Why don't you just choose a subject that interests you?

Or maybe choose a project that'll give you some knowledge on a big controversial issue so you can be an expert on it
>>
I have a bloodflow related phobia (can't give blood or even have my pressure taken without feeling lightheaded or throwing up). To desensitize myself, I want to restrict my blood flow about once a day for 30ish seconds, first by squeezing my arms with my hand, later with a cord or rope. Will this cause long term damage?
>>
I'm 23 with a BS in CS and quit my software job this summer. What should I do with my life?
>>
>>9213940
>not using the inverse of Tai's method
>>
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>>9213952
For something like that, you're going to have to use numerical methods. You can differentiate numerically as well.
>>
>>9205943
what do you call it when a car traveling to the right crashes into a car that is going up so now you have to draw a triangle?
>>
>>9214998
a) go through definition and see where it fails
b) show they are subsets of each other
>>
>>9214391
The thing is I have actually no idea what to do. For example I am interested in epidemiology, but I don't have any theoretical knowledge about the subject, so I don't know where I could start a project.
>>
>>9205943
so my childhood friend killed himself this week, he left this for me and i am too stupid to figure it out can someone help?

indhosjenoftoierer
osndofrirtehejeoni
enshooriniordefejt
tsojnefieidornorhe
erfsoioodennrhejti
>>
>>9215139
can we have more information please?
>>
>>9215140
he was the smarter one, we both had rough times when we were kids (his dad died when he was 4 years old and i never saw mine). he went to engineering and stuff and i went medical school. He has been suffering through some chronic depression for a while but i didn't think it was that serious. Looks like i was wrong. what else do you want to know?
>>
>>9215139
try https://puzzling.stackexchange.com/

i'm not sure what their rules are but you might need to pretend that you have the answer and you're posting it as a puzzle for them to solve
>>
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Can you explain the Heisenberg principle to me concetually and mathematically, /sci/?
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>>9215139
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>>9215335
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>>9215343
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so we've sequenced the human genome, but what does that mean? because surely there is variation in genetic makeup between individuals, so is the genome of a species an 'average'?
>>
>>9213163
no one?
is undergrad QM too hard for /sci/? surely not
>>
>>9215490
I think, I'm not sure but we all largely have the same genes just different numbers of copies and different alleles. So yes "The Human Genome" would be and average, that documents where (generally) each gene is in each chromosome, maybe a range of numbers of copies and common alleles. I'm sure they explain how they do it.
>>
>>9215117
Watch some introductory lectures online or email a professor to get some advice
>>
>>9213163
define a^2
>>
>>9215517
All the commuters are 0, from the definition of the Kronecker delta. Except the second one, which gives: [math] a_j [a_k , b_k ] b_j = \gamma a_j \delta _{ k , k } b_j = \gamma a_j b_j [/math] then use the summation convention (which I'm guessing you're using) so then [math] \gamma a_j b_j = \gamma \vec { a } \cdot \vec { b } [/math]
>>
>>9215541
>all commutators are 0 apart from [math]a_j [a_k , b_k ] b_j = \gamma a_j \delta _{ k , k } b_j = \gamma a_j b_j[/math]
I don't get it.
All all the indices are summed over so the first and third commutator should be
[eqn]a_j[a_j,b_k]b_k = \gamma a_j b_k \delta_{jk} = \gamma a_j b_j = \gamma \mathbf{a} \cdot \mathbf{b} [/eqn]
no?
I don't understand how you can just say only the second commutator is non-zero when j and k are both summed over
>>
>>9215568
Tbh that's what I thought to begin with, then decided if I'm wrong (and do what I did) you end up with the "right" answer, but I don't like my reasoning at all. What book is this? Have you checked the errata?
>>
(Solids of Revolution question)

I have a circle described by the function (x-1)^2 + y^2 = 1/4

If I revolve the circle around x=0 then I'll get a torus.

I need to find the volume, so here's my reasoning.

Given the radius of the circle is 1/2, then the area is pi/4. If I cut the torus through and uncurl it, I'll get a tube with length = the center circumference of the torus. The center circumference is the circumference of the circle with radius 1 (center of the original circle to the origin). So then the tube has length = 2pi.

So then the volume of the tube is 2pi * the area of the circle, so 2pi * pi / 4.

Now it turns out that A. this is the wrong value and B. I'm supposed to approach it from the perspective of a series of inner/outer rings, as though i was looking at cross-sections of the circle from the top down.

I understand why that approach would work, but not why mine doesn't.

Help? My best guess is that my assumption I can deform the torus into a tube without altering its volume is wrong.
>>
>>9215576
it's from Townsend's Modern Approach to Quantum Mechanics page 251 in the first edition and features in both editions it also turns up in the MIT quantum mechanics II course on OCW here: https://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/lecture-notes/MIT8_05F13_Chap_09.pdf (page 5). I've not checked the errata for Townsend but I'll do that now. I suppose it's possible that it's wrong and the MIT lecturer used Townsend for that section and copied the error (if it is an error).
>>
>>9215586
>>9215576
I can't find the errata actually, there doesn't appear to be one on Townsend's website.
>>
>>9215593
Well I'm not sure, unless you can think of a reason to switch the operators in either the second or third commutator, and then use the antisymmetry property. But I'm at a bit of a loss. But I can't think of a good reason to do that. I'd say that you were right and that this is a mistake in the book, but if you want to be sure take it to one of your professors and ask them. Also if you do that post results.
>>
>>9215609
>but if you want to be sure take it to one of your professors and ask them. Also if you do that post results.
I'll do that then, thanks for the help also.
>>
>>9215582
>and uncurl it
here
>>
could crisper editing be used to make human beings toxic to beg bugs? or maybe even some sort of pill? there has to be a way to eradicate those posts once and for all
>>
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question about statistcs
I want to run some kind of analysis across these numbers. specifically, I want to know the difference in the expected and the measured. Would I need to run some kind of anova here? or pearsons? or what?
image related, it's my data set up in what I believe to be a correct manner
so try to explain in plain terms, I want to have a nice chart after all this that shows the variation in the measured value from the expected value. the measured values are scores at different resolutions, the predict values are based off of the percentage of resolution relative to the others, and based off of that score what it could be expected to be. ie. if the score at 2160 was 500, we could expect the score to be 2000 at 1080, as there are 4 times less pixels
please be gentle im retarded and i havent slept in 3 days
>>
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>>9215002
please answer my question
>>
>>9215719
isn't that just a collision?
I mean I guess the triangle you're referring to is the addition of momenta which - because it's a 2 dimensional problem - you have to add as vectors.
>>
>>9215719
impact?
>>
>>9215719
https://en.wikipedia.org/wiki/Impulse_(physics)
>>
Having proven that Ker(f) is a subset of U and Im(f) is a subset of V, with f being a linear map, how do I go on to prove that Graph(f) is a subset of U X V?
Thank you
>>
>>9215789
> how do I go on to prove that Graph(f) is a subset of U X V?
Show that every element of Graph(f) is an element of U X V.
>>
>>9215795
Yeah, I understood that but I have no idea on how Graph of f is formed.
Thank you for your reply
>>
>>9215806
>Yeah, I understood that but I have no idea on how Graph of f is formed.
Look at the definition of a graph.
>>
>>9215823
From what I recall, it is in the definition of a graph that it is a subspace.
Graph(f)=((u,v) belonging to U X V | v = f(u))
I feel so goddamn up
>>
>>9215738
>>9215747
>>9215749
thank you sirs for answering my question and for the tasty (you)s.
>>
>>9215823
>>9215834
Ok I think I did it.
so we can say that all elements in graph(f) are of the form (u,f(u)). But f(u) = v which means that it equals some vector(s) of the V space. Obviously, u belongs to U, therefore Graph is a subspace of UxV.
Am I right?
Thanks
>>
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How tough is Physics I supposed to be? How much am I going to need to be able to solve these retarded as fuck motion/energy problems in later engineering classes?
>>
>>9215789
>subset
subspace*

>how do I go on to prove that Graph(f) is a subspace of U X V?
With the definition of a subspace.
>>
>>9215854
Let (u,f(u)) , (v,f(v)) be two elements of graph(f).
Prove that their their sum is in graph(f).
Prove that (0,0) is in graph(f).
Prove that -(u,f(u)) is in graph(f).
This ensures that graph(f) is a subgroup of UxV with respect to addition. You can condense this by just showing that graph(f) is not empty and (u,f(u)) - (v,f(v)) is in graph(f).
And then:
Prove that λ(u,f(u)) is in graph(f). (this is the extra thing needed to show that it is a subspace)
>>
>>9215941
Or you can also show that graph(f) is the image of the linear map
[math] T : U \to U \times V : u \mapsto (u,f(u) [/math]
>>
For a positive integer n and complex, nonzero y, [math]x^n = y [/math] has n distinct complex roots. However, the nth-root operator [math]\sqrt[n]{y}[/math] is defined to be single valued. Thus nth-root has implicit rules that select one of the roots to be "default". For real y, those rules are, AFAIK:
>If n is odd, then exactly one root is real. [math]\sqrt[n]{y}[/math] is that root, which also has the same sign as y.
>If n is even and y is positive, then there are exactly two real roots, which have equal magnitude but opposite sign. [math]\sqrt[n]{y}[/math] is the positive one.
>If n is even and y is negative, then there are no real roots. [math]\sqrt[n]{y}[/math] is the root which lies on the positive imaginary axis (i.e. is of the form bi, when b is real and positive).

The question, then, is how is the "default" chosen when y is not real? Is it the one with the polar angle divided by n?
>>
>>9216007
when n is even it can be factored n=2k for some k
so for x<0 we know there will always be 2 roots on the imaginary axis, so choosing one of these seems like a sensible choice, limiting the image of the single valued function to the real and imaginary axes

now we can say nthrt(x) = (2k)thrt(-1)*nrt(-x) = i*nthrt(-x)
keeping in mind x<0

someone else could probably explain this better
>>
>>9216007
>Is it the one with the polar angle divided by n?
Yes. It's called the principal square root.

[math] z^{ \frac{1}{n} } = e^{\frac{1}{n} Log z} = e^{\frac{1}{n} (Log |z| + i Arg z)} = |z|^{\frac{1}{n}} e^{i \frac{Arg z}{n}} [/math]

where Log is the principal branch of the logarithm, Arg is the principal argument.
>>
>>9216067
Btw, this root is not more special than the others (and neither is the the principal branch of the logarithm more special that the other branches).
It's just a convention.
>>
>>9215370
>>9215343
>>9215335
what am i looking at here
>>9215310
i really don't know

an anagram maybe? he loved mapping too if this helps, was a big tabletop nerd.
>>
>>9215941
>>9215950
Thanks a lot
>>
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>>9216125
>>
How do I know for an ASU that my number will come out negative or positive? I need to implement this in vhdl.
>>
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>mfw programming class
I fucking hate this stupid shit, I fucking hate software
>>
>>9216086
each row contains the letters defhijnorst and the same quantity of each letter (each row has the letter e 3 times for example). i don't know if there is any pattern besides that.
>>
>>9216140
Undecidable.
>>
>>9216417
maybe I said it wrong, but I'm pretty damn confused on this part.
>>
I need a good book on probability that covers discrete and continious random variables, and the CLT. Any recommendations?.

Some background, if anyone cares:
I attend a very small branch of my college, and the main branch has decided to use us as guinea pigs for a "virtual" course. Basically, each week we get some shittily written pdf, we're supposed to read them and then go do an exam. I can't take this anymore, they don't explain anything, their notation is inconsistent, and the orthography's so bad, you'd think it came straight from a teenage girl's twitter. I've somehow managed to get through the first half of the semester, but I don't want to anymore.
>>
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>>9216442
forgot to upload the image
>>
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What psychological disorder(s) could this poster likely be suffering from?
>>
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>>9215868
REPLY TO ME
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>>9205943
Show that if U and V are subspaces of R3 and U n N = {0} then: V dim(U+V)=dim(U)+dim(V)−dim(U∩V)
>>
>>9216519
She suffers from VDS
"Vaginal Derangement Syndrome"
It's a genetic disorder that affects some 99% of all human females.
They actually think that every single man on Earth actually notices them, and that they have some kind of value, or sexual magnetism/allure. This delusion is widespread, and causes them to think that they actually exist to males, of which 95% have absolutely NO awareness of their existence, unless they are forced to, by outside forces.
See: Liberalism
>>
What are so good texts for a pure mathfag looking into getting physics?
>>
>>9216140
> How do I know for an ASU that my number will come out negative or positive?
You don't. You just perform the calculation and check whether the result /is/ negative or positive.
>>
Can CRISPR make people into genuine transgenders (i.e. change XY to XX or vice versa)?
>>
Help me out anons, on graph theory
https://en.wikipedia.org/wiki/Kosaraju%27s_algorithm
>For each element u of L in order, do Assign(u,u) where Assign(u,root) is the recursive subroutine:
>If u has not been assigned to a component then:
>Assign u as belonging to the component whose root is root.
>For each in-neighbour v of u, do Assign(v,root).
>Otherwise do nothing.
Why the fuck the existence of v->u is enough to justify that v is in the same connected component of root?
>>
Can you recommended a good book that explains the fundamentals of science giving a broad overview on the whole thing. I read A Brief History of Nearly Everything and really enjoyed it, and now want more of the same. I don't know what to read next, maybe Stephen Hawking?
>>
Does anyone have any tips on how to be more confident around people when it comes to math and science?

I can figure things out when I go off on my own and think about them without distractions. But when I'm around people I'm always jumbling up my words and saying really dumb incorrect statements. This is part of why I'm really quiet all of the time and appear like I lack confidence. Do I just need to get over the fear of looking like an idiot and maybe after embarrassing myself a bunch of times it will eventually stop happening? or no?
>>
>>9216962
>But when I'm around people I'm always jumbling up my words and saying really dumb incorrect statements
For example? Do you realize that what you've said is incorrect right away or does it happen afterwards?
>>
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>>9216833
I can't answer your question. But I can tell you that transexuals are mentally ill individuals who need help.
>>
>>9215868
lol, brainlet, you need to put in the effort to understand it, or drop out of engineering
>>
>>9216609
[math] V \to \frac{U+V}{U} : v \mapsto v+U [/math]
This map is linear, it has kernel [math] U \cap V [/math] and image [math] \frac{U+V}{U} [/math] .
(That's essentially the second isomorphism theorem for groups/rings).
>>
at what point in my math undergraduate career can i expect to read the papers of my professors and make sense of them?

my professors often write about p-adic numbers and lie algebras, for example.
>>
>>9217795
take the initiative and find some resources to learn about them yourself
>>
>>9217832
I've tried that, but for each concept i must first understand several others, and going down the rabbit hole seems ultimately not very useful. That might also be because wikipedia is not a great teacher.
>>
>>9217859
find lecture notes, or even youtube videos
they really arent hard to find
>>
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>>9215322
In qm you can determine the position and impulse of things through their wavefunction probabilistically.
That means for example, that there is a certain probability of a particle to be in a given position.
Like any random variable, those properties have a wiggle room/variance (uncertainty) [math] \sigma [/math].

If you are for example able to pin down the position of something very accurately, [math] \sigma_x [/math] will be very small. For [math]\sigma_{x}\sigma_{p}[/math] to still be bigger than [math] \frac{\hbar}{2} [/math], the variance of your impulse [math] \sigma_p [/math] has to be very big, resulting in you not being able to determine it's impule very accurately
>>
Greetings,
I cannot manage to solve this little problem:
there is a 3x3 matrix which has all K on the diagonal and 1 in all other entries. I need to compute the rank but I cannot reduce it to upper triangular form. Can someone help me out?
Thank you
>>
>>9217928
the rank is to computed with respect of the values of K.
>>
>>9217928
first of all you can calculate the determinant of your matrix. If it's equal to zero for a certain K, then it doesn't have full rank.
Now you can check out the values of K, for which the determinant equals 0 and determine if the matrix has rank 2 or 1.
A hint for factoring the determinant: The matrix obviously doesn't have full rank if K = 1, so you can factor (K-1) out
>>
>>9213069
Anyone for this?
>>
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how many skin cells is the width of a finger print groove?
>>
>>9217959
Oh that was very useful.
I found (1-k)(k-2)(k-1) as determinant.
So if k=1 indeed the determinant goes to 0.
Same for k=2.
So now I know for sure that the rank is either 1 or 2. So should I proceed and check how many LI vectors are there?
>>
>>9218009
Actually, I substituted 1 and -2 in my upper triangular matrix.
subbing 1, both row 2 and row 2 got to 0 -> rank 1 if k=1
subbing -2, only row 3 got to 0 -> rank 2 if k=-2

Really thanks a lot.
>>
>>9218018
just wanted to comment that it should be k=-2
glad I could help
>>
I want to edit out irrelevant slides and add annotations/notes/highlight things I'm not sure of from physics/maths lectures. They're all in .pdf form. What's the easiest way to do this? What program?
>>
>>9217996
About 3.50
>>
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I'm stuck on this one. Used almost every technique I could think of, but still not getting anywhere. (It's a commutator between the Poincare group rotation generator and the Pauli-Lubanski pseudovector).
>>
For a lie group G and G-module M, is the group cohomology [math]H_{{\text{grp}}}^k\left( {G,M} \right)[/math] in any way related to the singular cohomology [math]H_{{\text{sing}}}^k\left( {G,M} \right)[/math] ?
>>
What does it mean that the force is "proportional" to the result of two charges? What does "proportional" mean? Proportional by what number?
>>
>>9218117
Done. (samefag)
>>
got a serious excel question about match()
I can find the first instance
but there isn't one damn site out there
that can tell me how to find the second
instance of some string or number in
a match() formula
they all show ways to write a macro to solve
it, but my company does not allow
macros, so how do I do this???
>>
>>9218765
Visual Basic.
>>
>>9218811
forbidden by company policy
they must think we're all malicious hackers or something
>>
>>9218226
> What does it mean that the force is "proportional" to the result of two charges?
If you're referring to Coulomb's law, the force is proportional to the /product/ of the two charges.
>>
what's it mean for an irrational number to exist?
>>
>>9216609
Take a basis for U∩V, extend this to a basis for V and to another basis for U by the replacement theorem. We claim that the first basis and BOTH extensions make a basis for U+V.
Firstly, any vector u+v in U+V is the sum of a linear combination of basis vectors in u and a linear combination of the basis vectors in v, which is just a linear combination of basis vectors in the claimed basis. Therefore, this set spans U+V.
Secondly, set a linear combination of the vectors equal to 0. Move all of the basis vectors in V to the other side, and note that the equality implies that the vector which is a linear combination of the extension of W, and is a linear combination of the basis of V, is in both V and W. Therefore, it is in V∩W. But then all extension basis vectors have coefficient 0, because if they were in V∩W then they would not be independent of the initial basis and would not be added to create an extension to another basis. Finally, we have that a linear combination of the original basis = 0, but of course all of these coefficients are 0 as well! Thus, the set is linearly independent, and a basis for U+V.
Now, we take the number of vectors in each set. There are dim(V∩U) vectors in the initial basis, dim(V) = dim(V∩U) + m vectors in the basis for V, and dim(U) = dim(V∩U) + n vectors in the basis for W. Finally, there are dim(V+U) = dim(V∩U) + m + n vectors in the basis for V+U.
Therefore, dim(V∩U) + m + n= dim(V∩U) + m + dim(V∩U) + n - dim(V∩U)
and dim(V+U) = dim(V) + dim(U) - dim(V∩U) in general for any vector subspaces V and U.
>>
>>9218886

Draw a square. Then draw the diagonal of the square. The diagonal of the square is incommensurable with its side; i.e. there is no length such that both the diagonal and the side are an integer multiple of that length. The diagonal of a square is not a rational multiple of its side. The diagonal of a square is an irrational multiple of its side.
>>
>>9206112
Maybe I'm thinking wrongly here, but shouldn't B be 1 - (1/40 + 1 /10 + 1/4)^2 which equals ~ 86%?
>>
>>9218929
I'm retarded, I meant to write 1 - (.40 + .10 + .4)^2 which equals 70,84%
>>
>>9208671
The hell is i? Why do you have an i outside the brackets and two others inside the brackets?
>>
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New here, how do I get the formula notation to work so I don't see a bunch of [math][/math] everywhere?
>>
>>9219283
Is there a domain I need to add to JS whitelist? cdn.mathjax is already there, is that not the right one?
>>
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>>9218973
i is the imaginary unit, there's one outside from the expansion of the the Lorentz transformations, the two on the inside come from the definition of J.
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>>9219538
Correct image**
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>>9219573

x^2 - 1 - sqrt(3)

To see that it is irreducible, note that (1 - sqrt(3)) (1 + sqrt(3)) = -2 which is not a square.
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>>9219573
x^2 - 1 - sqrt(3)
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Working my way through Artin.

Is there anything to this question other than writing R in terms of [math]1, \alpha[/math]and calculating the addition/multiplication table?
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>>9219267
>>9219538
>>9219612
Fuck off you lazy shit. Do your homework yourself. That shit is easy as fuck.
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Any tips/tricks/hints etc
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>>9219730
a)its the reals, not the rationals
b)look at powers of alpha
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Hi, I need help regarding adjoints of linear operators.
Let [math]V[/math] be a finite vector space with inner product. Then, by using linear functionals, we can show that
there exists a unique [math]w \in V[/math] such that [math]\langle u,w \rangle,\forall u \in V[/math].
Now, we want to define the adjoint. We can define a linear functional [math]f(u) = \langle Tu,w \rangle, \forall u \in V[/math]
where [math]T:V \rightarrow V[/math] is a linear operator. But then, why can we say that
[math]f(u) = \langle Tu,w \rangle = \langle u, w' \rangle[/math] and then define [math]T^*: V \rightarrow V[/math] that
maps [math]w'[/math] to [math]w[/math], giving the definition of adjoint we want?
I mean, there exists a unique [math]w \in V[/math] for the linear functional, then why can I say that there exists another [math]w'[/math]
that satisfies the equation?
I don't get it why we can define the adjoint to be like that.
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>>9219898
My point is, if w is unique and works for every u in V, then why can I say that there exists another w' for that inner product and why Tu = u? Tu is in V just like u is in V. Shouldn't then w = w' and Tu = u?
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>>9219898
>there exists a unique w∈V such that ⟨u,w⟩,∀u∈V⟨u,w⟩,∀u∈V
such that the scalar product is what? are you referring to the riesz representation theorem?
in finite dimensions you can just represent the operator by it's matrix in canonical coordinates and proof that it's transposed matrix indeed has the properties you're looking for.
In infinite dimensions you need the riesz representation theorem to identify the dual space with the original vector space to get unique representants which are needed for T* to be well defined
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>>9219910
I'm talking about this theorem, actually. I'll post the one it uses for the proof.
By the way, the red part is the one I don't really get.
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>>9219910
and the proof for existence works something like this:
If [math] A [/math] is linear and continuous (in finite dimension this is always the case), [math] x \mapsto \left \langle Ax,y \right \rangle [/math] is a continuous linear functional, thus a unique element [math] z [/math] exists, such that [math] \left \langle Ax,y \right \rangle = \left \langle x,z \right \rangle [/math]
Now we can define a mappping [math]A^*: y \mapsto z [/math]
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>>9219921
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>>9219922
I get the z, but why the Ax turns into x?
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>>9205943
Is it possible to prove that proofs make sense ?
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>>9219926
"make sense" in what sense?
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>>9219923
that's indeed riesz
>>9219925
define [math] l(x) = \left \langle Ax,y \right \rangle [/math]
this is a linear functional and according to your theorem, we can represent it through some element [math] \beta [/math] such that [math]l(x) = \left \langle x,\beta \right \rangle [/math]
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>>9219929
DAMN, I'm dumb. I get it now. Thanks, man!
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How can I know if I'm a brainlet? Hass IQ120
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>>9219942
>How can I know if I'm a brainlet?
If you have to ask, you're a brainlet.
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>>9205943
What is energy?
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>>9219898
I don't really understand what you are saying, so I'm just gonna define the adjoint for you.

Every linear functional [math] f:V ]\to F [/math] can be represented as [math] v \mapsto <v,u> [/math] for a unique [math] u \in V [/math] . (That's Riesz's representation theorem)
And every [math] u \mapsto <u,w> [/math] is obviously a linear functional.

Let [math] T:V \to W [/math] be a linear mapping.
Let [math] w \in W [/math] .
Consider the mapping [math] v \mapsto \langle Tv,w \rangle [/math] .
This is a functional of [math] V [/math] .
Since it is a functional of math] V [/math] (just ignore its formula) , there is a unique [math] v_w \in V [/math] with which you can represent the functional as [math] v \mapsto <v,v_w> [/math] .
Consider the mapping [math] W \to V : w \mapsto v_w [/math] .
The previous work shows that it's well defined.
We call this mapping the adjoint of [math] T [/math] and it is denoted by [math] T* [/math] ( [math] T*w := v_w [/math] ).
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>>9219898
>[math]f(u) = \langle Tu,w \rangle, \forall u \in V[/math]
>not "for all [math]u \in V, f(u) = \langle Tu,w \rangle[/math]"
>or at least [math]\forall u \in V :f(u) = \langle Tu,w \rangle[/math]
Cringe.
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>>9219944
How can I know you're not a brainlet too?
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>>9205966

you got part a) which can also be worked out with the classical euler theorem from number theory)

for part b), you have f(b)=0 implies b^5=1, so substitute this into f(b^3).

for part c), g has to be of degree 3. let g=c+dx+ex^2+x^3 and work the calculations out. remember c,d,e belong to Z_3.

too lazy to latex
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I'm in 1st year Mechanical Engineering so I've been getting with what I remember from high school years ago. However I'm currently taking a class on Energy systems that involves thermo dynamics and I don't really understand the theory behind the calculations we do, I just list the variables given and the find the missing variable. While this has been working so far it sure as hell won't later on and my prof isn't really explaining it well. Is there an external resource you guys have found that helps? In first year there is no calculus until 2nd term so we deal with this topic again once we cover it (2nd year earliest).

>p1v1=p2v2
>v1/t1=v2/t2 for constant pressure
>p1/t1=p2/t2 for constant volume
>knowing when a volume is constant instead of pressure or vice versa
>Q=mCv(T2-T1)
>Q=mCp(T2-T1)
>n=Cp/Cv
>open vs closed system
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>>9219953
C'mon, dude. Writing things too formally for such stupid question is a waste of time.
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>>9219945
It's the conserved quantity associated with time translation invariance. In a more classical sense, energy is the capacity to do work.
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>>9219947
Thanks, man!
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>>9219945

what is love?
>baby... don't hurt me.
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>>9219966
Wait. Associated with the time traslation invariance?
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>>9219964
>formally
This has nothing to do with the writing being "formal", the information is the exact same in every sentence. It's just ugly and retarded.
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>>9217517

>using the second isomorphism theorem to solve a freshman tier problem

ok chang
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>>9218083
Re-type the entire thing in [math] \LaTeX [/math]
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>>9216182


you just have terrible instructors, anon.
make sure you get the most of that class, you're gonna need it
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>>9220003
Your point being?
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>>9206038

nope, you need to start selling
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>>9218141
You should ask in the math general, I'm sure someone there knows.
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>>9220003
But, I didn't just used it out of nowhere. I proved it.
dimV/U = V-U and dimKer+dimIm=dimV are standard freshman matterial.
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>>9219983
Yep.
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>>9220019


you truly are asian
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>>9220031
I'm Greek you retard.
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>>9220046


congrats on getting that phd, malakas
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are conic sections important to know? I'm starting multivariable calc now and we skipped that topic in pre-calc.
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If imaginary numbers don't exist, then does the number Zero (0) in particular exist?
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>>9220153
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what is this method of units conversion called ? i need to typeset a me assignment and I want a convenient way to typeset like pic related
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>>9220227
*in latex
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>>9220372
new
>>9220372
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one more for the bump limit
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>>9216067
>>9216007 here

Related:
Let [math]\theta[/math] be a real number.
[eqn]1~= ~e^{2\pi i}
e^{\theta i} ~=~ 1 \cdot e^{\theta i}
=~e^{2\pi i}e^{\theta i}
=~e^{(2\pi + \theta)i}
\sqrt[3]{e^{\theta i}} ~= ~\sqrt [3]{e^{(2\pi + \theta)i}}
e^{\theta i/3}~=~e^{(2\pi + \theta)i/3}
=~e^{2\pi i/3 + \theta i/3}
=~e^{2\pi i/3}e^{\theta i/3}
1~=~e^{2\pi i/3}~=~-\frac{1}{2}+\frac{\sqrt{3}i}{2}[/eqn]
Where is the mistake?
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explain to an engineer the superposition principal in electronics
pls be kind im just an engineer.
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Hi guys, brainlet here forced to take a physics course and struggling hardbody.
Suppose an object with mass m is projected with initial velocity v 0 along the horizontal direction. Assume quadratic air resistance of the form F drag = αv^2 , where F drag is the magnitude of the drag force. Find an expression for the velocity v as a function of time.

Here's what I have so far:
ma = αv^2
m*(dv/dt) = αv^2
(dv/dt) = (αv^2)/m
v(t) = integral of ((αv^2)/m))
Am I even on the right track here?
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Tips/tricks for part (b)?
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Whats the deal with crops and chemicals? Are they as bad as people say? I have a friend that tells me that genetic modification of crops is a ok, fairly harmless.Me and my father have a farm with weath and use some chemicals that literally burn my skin, is this ok or should I use alternatives? Thanks for bearing with my broken english and sq.
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>>9221164
c) Are you fucking retarded or what?
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>>9220984
Just use the universal property of monic irreducibles.
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>>9220963
It's made up garbage.
>>
>>9221083
GMO is controversial. it might be more difficult to sell depending on where you live.




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