/sqt/ - Stupid Questions Thread: Saturday Night Edition

I tried to learn calculus but didn't get it - so I self harmed. Should I give up?

>>8871113
give up on self-harm and pick up a friendlier calculus book

>>8871108
Have any of you have to retake a class? Does that make you a brainlet?

Honestly I'm having a really hard time learning calc as well, is there anywhere other than college where I can learn it.

>>8871113
>>8871118
It only gets worse

File: Student.jpg (492KB, 849x565px) Image search: [Google]

492KB, 849x565px

Somebody here has a good source to study linear algebra (specifically linear transformations)?

How the fuck do you study for Latex functions and Matrices?

File: 6.jpg (556KB, 940x959px) Image search: [Google]

556KB, 940x959px

What the fuck are modular forms?

File: 1493514542125.jpg (86KB, 576x1024px) Image search: [Google]

86KB, 576x1024px

Can you guys help a brainlet with this. I have done it correctly?
p1 of 2.

File: 1493514658831.jpg (71KB, 576x1024px) Image search: [Google]

71KB, 576x1024px

>>8871144
*have I done it correctly
p2 of 2.

File: 51AhCLii+UL._SX398_BO1,204,203,200_.jpg (40KB, 400x500px) Image search: [Google]

40KB, 400x500px

>>8871124
>Somebody here has a good source to study linear algebra (specifically linear transformations)?
I first learned from Poole's book, but almost every linear algebra textbook covers the same topics

>>8871133
>What the fuck are modular forms?
any specific question you have about them? their main draw is that they're holomorphic and satisfy a nice functional equation in terms of matrices in [math] SL_2(\mathbb{Z}[/math]

>>8871144
>open wolframalpha.com
>type in (your answer)^5=-1
>see if it says True

>>8871108
can anyone please tell me what ferrugination is from a perspective of soil and phosphorus? Thanks peeps, google is being a shitheap

File: Untitled.png (15KB, 699x542px) Image search: [Google]

15KB, 699x542px

>>8871159
>>open wolframalpha.com
>>type in (your answer)^5=-1
>>see if it says True
It's not giving me an answer in the notation I've used.

Heard the latest Waking Up podcast with Sam
Harris and Charles Murray recently and it got
me interested in the book The Bell Curve.

Is there a decent updated version of this book
which adds interesting new discovery/research
to complement the book itself in an introduction
chapter or something?

File: Capture.png (30KB, 781x432px) Image search: [Google]

30KB, 781x432px

>>8871177

>>8871183
Thanks man, I've had like 3 hours sleep and I need to hand this soon, so I'm zombified.

Shouldn't the equation be set to = 1 and not = -1?. Since the modulus of -1 is 1?

File: Capture.png (15KB, 276x45px) Image search: [Google]

15KB, 276x45px

>>8871190
>Shouldn't the equation be set to = 1 and not = -1?
well you wrote pic related, so your five answers should satisfy that equality

z^5=-1 isn't the same as z^5=1

>>8871191
I'm not sure where I've gone wrong.

>>8871190
https://answers.yahoo.com/question/index?qid=20100210062758AA2xyf0

>>8871199
[math]z^5=-1 \\
z^5 = |r|(\cos(\theta)+i*\sin(\theta))\\
-1=1(-1+0i) \\
\theta=\pi [/math]

>>8871204
Ah, crap. I think I understand where I went wrong. The principal argument of - 1 is not 0, but pi. Should have drawn a complex plane. Thanks friend.

File: curve fitting.png (350KB, 1620x943px) Image search: [Google]

350KB, 1620x943px

I have some noisey data, but I want a nice curve fit in there. How would I do it in MATLAB? Already tried least squares.

modelFun = @(p, theta)(p(1) + p(2) * cos(theta - p(3)));
p = nlinfit(x, solar_rad, modelFun, [1 1 0]);
yFit = modelFun(p, x);

>>8871118
KKKhan academy or just go through a good book yourself

>>8871259
Is there something similar to Khan academy but less Islamic?

>>8871271
Get engineering mathematics by KA Stroud or Open University MST124 textbooks.

Is the open source computer science github worth doing? I'm interested in changing jobs from menial labour and would really like to avoid goign to uni if at all possible.

The coursework there for the most part looks pretty reputable but I don't know if I'd just be wasting my time.

File: black-macro-wallpaper-3.jpg (143KB, 1280x1024px) Image search: [Google]

143KB, 1280x1024px

find a, b and c such that the vector equation:
\vec{r} = a*sin(t)i + bj + c*cos(t)k
form a parabolic helix

>>8871352
crap, forgot to wrap it up
[math] \vec{r} = a*sin(t)i + bj + c*cos(t)k [/math]

>>8871284
Yes, most unis have open lectures now https://functionalcs.github.io/curriculum/

can get most of the books on libgen.io

In three valued logic, A entails B, if for every valuation of A that has a value in the set of designated truth values, the valuation of B also has a value in the set of designed truth values.

Is this correct? For some reason I can't find any where that mentions this plainly.

>>8871360
Thinking specifically of this:

https://github.com/open-source-society/computer-science

I believe I can get it done in approximately 1.5 years if I work at it. I just dont want to get there and discovere I've wasted 18 months of my life.

>>8871362
There are multiple versions of three-valued logic floating around, which means that the "correct" definition will depend on the context in which you intend to use that logic for.
Note that
>has a value in the set of designated truth values
needs to be defined as well; for example, if "false" is a designated truth-value then you probably don't want to say that A entails B if every valuation of B is "false" (i.e., B is a contradiction).

>>8871352
>>8871355
bump

>>8871352
What are the restriction on a,b,c, because if they have to be constants, it's just a circle or ellipse in space.

>>8871471
I've just found a definition of validity hidden in my book.
It says that [math] \Sigma \vDash A [/math] iff every valuation v is such that if [math]v(B) \in D[/math] for all [math]B \in \Sigma[/math] then [math]v(A) \in D[/math].

I feel the urge to simply see whether the overall valuation [math]v(\Sigma) \in D[/math] and [math]v(A) \in D[/math], but the wording in these definitions is making me doubt myself.


I've yet to encounter a logic with false as a designated truth value, so I didn't think of that!

File: 20170430_062331.jpg (1011KB, 2120x825px) Image search: [Google]

1011KB, 2120x825px

I'm unsure as to how to solve this or proceed.
I need to determine the complex number. Could you please point me in the right direction?

>>8871514
no restrictions

File: helpwithb.png (74KB, 1091x545px) Image search: [Google]

74KB, 1091x545px

How would I complete part b? It's seems too easy, but perhaps I'm overlooking how to find the average in a multi variable function? If you could post the formula for finding it I'd be grateful.

As an example, the average for single variable:
average change [math] = \frac{f(a) - f(b)}{a - b}[math]

>>8871553
latex correction
[math] = \frac{f(a) - f(b)}{a - b}[/math]

>>8871534
what are you having trouble with? it looks like you just need to factor.

>>8871516
>definition of validity
<mild rant>
You should be wary of any book that tries to [math]formally[/math] define first-order (and zero-order) logic in terms of set theory. This is because set theory is itself defined in terms of first-order logic (in that ZFC, or whatever variant of set theory you're using, is justified on the basis of the completeness theorems for FOL) and it is EXTREMELY easy to get caught up in circular reasoning and end up with a mess of unsound arguments. I see this every time someone comes up with a "breakthrough" proof of P=NP, the Riemann hypothesis or the Collatz conjecture. Sometimes these are advanced by credentialed mathematicians, demonstrating that not even they are immune to logical fallacies.
</mild rant>

Anyway, in response to your question, B and Σ are of different types so the definition of your valuation v is going to require some way of "gluing" the two cases together (what would the domain of v be, if you think of it as a function)? How you perform this gluing will determine if v(B), for all B in Σ, entails v(Σ).

>I've yet to encounter a logic with false as a designated truth value, so I didn't think of that!
The conventional definition of a truth-value is simply a Boolean (true or false), and it is known that any many-valued logic is logically equivalent to a two-valued one. See e.g., https://plato.stanford.edu/entries/truth-values/suszko-thesis.html

>>8871557
>what are you having trouble with? it looks like you just need to factor.
I'm not even sure how to proceed.
Do I multiply it all bracket by bracket like I would do with a second degree polynomial?

>>8871565
Ok, those are z's not 2's right? If so, factor it out like
[math]z^5 + 1 = z(-\frac{\pi}{5})(-\frac{3 \pi}{5}) ... (-\frac{9 \pi}{5}) [/math]

multiply all those values for pi, the you should arrive at
[math] z^5 + 1 = z \cdot (some constant)[/math]

File: 800px-Fourier_unit_pulse.svg.png (34KB, 800x600px) Image search: [Google]

34KB, 800x600px

For the "Re" function on the top right. What's an actual function f(x)=? that looks like that? I can't think of a function with a big spike in the middle and gets smaller on either side off the top of my head.

>>8871580
Yes all z's.

>>8871587
ok, then you should be where I arrived at. You should then multiply all your values for pi, divide both sides by z, subtract 1 from both sides to obtain
[math]z^4=(some \ constant) - 1 [/math]
at which point you can just take the fourth root of both sides to find what z is equal to

>>8871580
>>8871590
Wow, how didn't I consider taking the z's out. Holyshit. Thanks man!!!

File: 4563454513.jpg (274KB, 3000x1688px) Image search: [Google]

274KB, 3000x1688px

Is fate real? If so should that affect any of the choices i make? I believe it's real so how do i help others to prove that all things are predestined?

File: help.png (18KB, 1057x399px) Image search: [Google]

18KB, 1057x399px

Did I do these right? My answers are:
a) no point of intersection. It is a circle on xy, and will never contact the plane z=2

b) [math] x^2 + y^2 =2 [/math], so the point <1,0,0> is on the curve. Since it supposedly intersects [math] x-2z=2 \to x=2+2z[/math], I know z must be zero when they intersect. Setting z to 0 yields x=2, so the point (2,0,0).

Converting the equations to parametric [math] \vec{r} = r_2 + t(r_2-r_1) \to \vec{r} = <1,0,0> + t<-1,0,0>[/math]

I don't know, I feel like my thoughts are all over the place.

>>8871607
give me an example of a point [math](x,y,z)[/math] satisfying [math]x^2 + y^2 = 2[/math]

>>8871611
..(1,1,0)

I've got to change my first point I see

>>8871607

[math] \color{YellowGreen}{>not \ \ using \ \ \langle \ \ \rangle} [/math]

>>8871618
You asked for a point, not a direction vector..

Can you help me, oh wise anon?

>>8871617
clearly for any other z, (1,1,z) is also okay

File: 20170430_073853.jpg (2MB, 2120x1640px) Image search: [Google]

2MB, 2120x1640px

>>8871590
I have messed something up as I can't evaluate the answer with my calculator.

>>8871607

ok ok

the first one actually does have a non empty solution, if you consider the circle to actually be a cylinder, which is what the condition actually describes in 3 space, z can range over all values, but as long as the x and y are on the cylinder of radius 2 the condition is satisfied, so the answer is something like

(r*cost,r*sint,2) where r is root two or whatever

for the second one

just do the math, I got it to work with a trig substitution for the cylinder.

What's the difference between "popsci" and non-popsci?

>>8871640
I think I've just realised where I went wrong.
I didn't put the full solutions of z^5 = -1 into the brackets, just the angle, instead of the cos and isin.

>>8871684
"popsci" is science without mathematics, where people (usually with only a little knowledge about the subject) try to educate the public about various things in science by using very broad (and usually wrong) analogies or just try to break down recent discoveries to make them digestible for the public.

Point [math]P(-1,3)[/math] is reflected in relation to line [math]x+2y-2=0[/math]. What point is the reflection point of [math]P[/math]?

Doing some exercises and this got me stumped

How can I design a minimal-phase lowpass filter?

Mathematica seems very poorly documented in this regard. I would probably need some sort of tailored software like ScopeDSP but I don't feel like spending $999 on it just to find out that it doesn't do what I want it to do.

>>8871801
And I'm looking to design a digital filter in software, not circuitry.

>>8871803
And it's not "continuous time", I'm dealing with discrete samples.

Fucking hell, all this DSP crap online is so fucking vague and poorly explained.

Since evwry subset of a well-ordered set is well-ordered, is it possible to form a 'smallest non-well-orderable set' in ZF set theory without choice, similar to how you can form the smallest uncountable ordinal?

>>8871580
>>8871590
What are you talking about anon that's not how you factor things. You obviously have a fifth degree polynomial on both sides.

>>8871640
This is wrong you need to factor the left side using the roots you found and it will simplify.

I'm working on a neural network to compare image patches. This might be a question more suitable for /g/, but I don't think anyone on there has done any serious deep learning work.

Basically, no matter what I try my loss just won't go below 0.69 and the accuracy won't go above 0.5. My network is as follows:
>Input - first image patch in red channel, second image patch in blue channel
>Split - divide into two separate images
>For each image: 5 convolutional layers with 96 convolutions in each layer, each followed by a ReLU layer
>Concatenate layer - concatenate the output of the convolutional layers together
>3 fully connected layers, each followed by a ReLU layer
>Sigmoid cross-entropy loss function at the end

Labels are 0 for a pair that don't match and 1 for a pair that do. Can anyone think of any reasons why my network isn't training? I ran it for 10000 iterations with 128 pairs in each batch which is about 1/10th of an epoch, but I didn't see any change besides converging on the 0.69 loss.

File: series.png (2KB, 137x50px) Image search: [Google]

2KB, 137x50px

what convergence test works with pic related?

>>8871914
Your question is retarded and /sci/ isn't for homework help, so I'm not gonna give you the answer.

>>8871914
limit lol

File: IMG_8457.jpg (42KB, 217x346px) Image search: [Google]

42KB, 217x346px

please show me that i'm not retarded and confirm that this is badly worded or something, maybe i'm missing something obvious

>two people are testing how much bungee cord is required for a safe vertical jump towards a river below.
>person one drops a boulder from the bridge, and uses a stopwatch to time how long it takes before he sees the splash in the river. it takes 4.2 seconds.
>person 2 times how long it takes before he hears the splash. he times 4.5 seconds.
>the relationship between the distance the boulder has fallen and the time taken is d=4.9t^2
>the speed of sound in air is 344 m/s
>the two people make their calculations independently amd without knowing what each other's stopwatch shows.
>their final estimate of a safe distance is the mean of their estimates, less a 5m safety margin.
>calculate this distance

as far as i know it uses quadratics

File: Capture.png (39KB, 549x313px) Image search: [Google]

39KB, 549x313px

Resolution principle. I hope I translated it well:
>Three people live in Dreadbury Mansion: aunt Agatha, uncle Charlie and the Butler
>One of the inhabitants killed aunt Agatha (she could've killed herself)
>Killer always hates and is poorer than their victim
>Uncle Charlie doesn't hate anyone who is hated by aunt Agatha
>Aunt Agatha hates every inhabitant except the Butler
>The Butler hates anyone who is hated by Agatha and is poorer then her
>No Dreadbury Mansion inhabitant hates all inhabitants
>Who killed aunt Agatha?

Pic related is what I came up with. Removing existential qualifier from say, alpha_{4} will introduce a new [Skolem] constant.

What do I do then? Can I unify a skolem constant and a regular constant?

>>8871949
It took 4.2 seconds for them to SEE the splash but 4.5 seconds for them to HEAR the splash.

That means it took 0.3 seconds for the sound to reach them. You know the speed of sound and the time it was travelling, so to get person two's distance estimate solve for distance travelled.
Person one's distance estimate is just plugging 4.2 into the equation given.
Then you take the mean and subtract 5.

They're pretty retarded people though, person one's estimate is gonna be way more accurate than person two's.

>>8871962
my problem wih the question is when it says they calculated it independently, then gives the speed of sound, implying that person two used that to figure out the amount that his time was out, it makes me second guess myself

>>8871919
which college or uni is setting homework like that this late in the year? and i know its retarded which is why im posting it itt.
>>8871929
this one http://mathworld.wolfram.com/LimitTest.html? but [math]
(-1)^n\frac{\sin n +1}{n}\to 0 [/math] and if you meant the limit comparison test, that wont work either because its not true that [math] (-1)^n\frac{\sin n +1}{n}\geq 0 [/math] for all n.

>>8871949
person two's estimate depends on how far away he is, otherwise the speed of sound alone doesn't tell you much

File: 1483874302087.jpg (18KB, 451x451px) Image search: [Google]

18KB, 451x451px

Can you invent/improve vaccines/medication with a microbiology degree? What's the "endgame" for someone with a virology PhD? Could he/she lead a team of scientists? Is it even a safe career to head towards (in terms of job stability and pay)

>>8871739
think of a rectangle, with 1 vertex on the P, 2 vertices on the line, and another vertex on the reflection point
thus
x=-1 will give you the y of the reflection point
y=3 will give you the x of the reflection point


[math]
P(-1,3) \\
x+2y-2=0 \\
x=-1 \rightarrow -1+2y-2=0\rightarrow y=3/2 \\
y=3 \rightarrow x+2(3)-2=0 \rightarrow x=-4 \\
P'(-4,\frac{3}{2})[/math]

Should I learn analysis first before differential geometry?

File: Untitled (2).png (22KB, 591x196px) Image search: [Google]

22KB, 591x196px

Does this look correct? Specifically the restrictions on h.

>>8872440
It is correct but it looks weird as fuck. Anyways, let me explain the constraints.

[math] h \neq 0 [/math] because in the limit you want to consider only points around 0. Here it just so happens that h=0 is not defined but even if the function was defined at h=0, you really do not care about that value, only values around h=0.

[math] b - a < h [/math]
This is just to keep [math] f(a + h)[/math] inside the interval (b,c). Notice that if you had h be smaller than b - a then:
[math] a + h < a + b - a = b[/math]
So a + h < b and then f(a+h) would not be defined, given that f is only defined in (b,c).

The same goes for the restriction h < c - a. If you take an h such that h > c - a then a + h > a + c - a = c. So a + h would be bigger than c and thus f(a+h) would not be defined.

>>8871871
>This is wrong you need to factor the left side using the roots you found and it will simplify

I don't know how to do that.

So I've been trying to find a parametric equation for the radial coordinates of a satellite in an elliptical orbit around the earth as a function of t.

I have:
u + (f/a)sin (u) = 2pi × (t - t_p)/T + pi, and
r = a + fcos (u)
where
f = focal radius = sqrt (mu^2 + 2BC)/abs (2C)
a = semi-major axis = mu/abs (2C)
t_p = time of first perigee after t=0
T = orbital period = 2pi*mu/abs (2C)^(3/2)
C (constant) = (K + U)/m = 1/2*v^2 - mu/r (<0 since orbit is elliptical)
and finally
mu = G*M_earth ~ 400,000 km^3/s^2

Which all boils down to:
u + (f/a)*sin (u) = x
r = a + f*cos (u)
Solve for r in terms of x.

Since f/a < 1, the first equation is strictly increasing, which seems to imply that the inverse exists, but I haven't been able to find it.

I am doing the exercise in question. I proved part a) and then part b) but the weird thing is that I did not apply the result of part a) while proving b) which confuses me. Am I doing something unrigorous here?

Proof of b):
To prove that for prime powers, h*g equals the identity function I consider the computation:
[eqn] h(p^k)*g(p^k) = f(p^k)*g(p^k) = g^{-1}(p^k)*g(p^k) = I(p^k) [/eqn]
Now, consider an arbitrary integer [math] n = \prod_{k=1}^{s} p_k ^{a_k}[/math]. Then:
[eqn] h(n)*g(n) = \sum\limits_{d|n}^{} g(d)h\left(\frac{n}{d}\right) = \sum\limits_{d|\prod_{k=1}^{s} p_k ^{a_k}}^{} g(d)h\left(\frac{\prod_{k=1}^{s} p_k ^{a_k}}{d}\right) [/eqn]
But both h and g are multiplicative, which means their dirichlet product is also multiplicative. So that is equal to:
[eqn] \prod_{k=1}^{s} \sum\limits_{d|p_k ^{a_k}}^{} g(d)h\left( \frac{ p_k ^{a_k}}{d} \right) = \prod_{k=1}^{s} g(p_k ^{a_k})*h(p_k ^{a_k}) = \prod_{k=1}^{s} I( p_k ^{a_k}) [/eqn]
And I is multiplicative so that just equals [math] I(n) [/math] and that proves the theorem, right? No need to use that other formula in a)

File: weird.png (116KB, 961x383px) Image search: [Google]

116KB, 961x383px

>>8872576
Fuck. The exercise is pic related.

>>8871617
>>8871651
I didn't consider that [math]- \frac{x^2}{5} + \frac{y^2}{2}=2[/math] is not a 2D circle, but a 3D cylinder. Thanks boys

>>8871514
bump, there are no restrictions on what a, b and c must be

What do analysts do and what do I have to study to become one?

File: 2017-04-30 19_48_16-book 2.pdf - SumatraPDF.png (4KB, 247x82px) Image search: [Google]

4KB, 247x82px

Supposed to find out if this diverges or converges.
Since its alternating i basically got 2 options divergence test or alternating series test
the alternating test dont think it would work since it looks to me like the numerator will increase more than the denomenator so one of the conditions wont be met.
still with the divergence test I dont know how to do the limit of that its just a bunch of infinites
someone help how do i continue?

>>8871553
bumping this as well

Can someone recommend a good book on Linear Algebra.

I'd like a more in depth treatment that is analogous to what Analysis is to Calculus.

File: help111.png (20KB, 925x204px) Image search: [Google]

20KB, 925x204px

completely lost, I understand multiplication rule and induction, but not sure how to prove it for these primes and integers

>>8872722
check the /sci/ wiki

http://4chan-science.wikia.com/wiki/Math_Textbook_Recommendations

and this
http://4chan-science.wikia.com/wiki/Mathematics
scroll down and they talk about it more in depth on the second link

>>8872739
Great resource

Cheers

>>8872688
if a series [math]\sum_{n>0}a_n[/math] converges, then [math] a_n\to 0 [/math]. as you said the numerator "outgrows" the denominator so [math] a_n \not\to 0[/math]. hence the series diverges.

>>8872733
and here anon:
http://linear.ups.edu/fcla/index.html
https://www.youtube.com/watch?v=kjBOesZCoqc&feature=youtu.be&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

personally I'm going with this book, but I don't know anything about linear algebra:
http://www.springer.com/gp/book/9780387940991
the supposed focus on geometric intuition should be comfy

>>8872733
Clearly each of the given distinct primes is a divisor of N. Now think of how their powers can combine to form other divisors.

Try an example. 60 = 2^2 + 3 + 5 and 60 has 12 divisors

>>8872763
Ok, this is where I just arrived at on scratch paper actually. I understand that each prime would become a divisor of a later number, but how do you take into account the divisibility of the integers, and the multiplication of the entire thing?

>>8872776
>>8872763
Because I'm certain the answer isn't simply equal to the number of primes..

>>8872763
>>8872776
>>8872782
>>8872733
OH, I think I've misrepresented the exponent sign as an AND sign... Ok, this simplifies it a bit :) Thanks anon-san

>>8871204
z=exp( (1 + 2 k)/5 pi i )
where k=0,1,2,3,4.

>>8872745
also this short section in this guide on linear / abstract algebra
https://functionalcs.github.io/curriculum/#org8994b70

File: inductor.jpg (21KB, 298x285px) Image search: [Google]

21KB, 298x285px

Why does current flow through inductors following the spiral of the wire if the conductor is in contact with other coils?
Current takes the path of least resistance, and the copper is un-insulated and in contact with the rest of the coils. Why doesn't it just take the pic-related path?

>>8872958
They are not fully exposed wires. They are coated in a bit of insulating material.

>>8872958
>>8872968
Forgot link

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

>>8872969
>>8872968
Cool, I never knew that. Thanks anon.

>>8871116
Science and mathematics are only useful when understood, if you don't understand a formula or problem, it doesn't necessarily mean that you're a beainlet. Such subjects either click or they don't, there is a very slim middle ground but it's so minuscule that it shouldn't even count.

File: kosovska-bitka.jpg (251KB, 1200x800px) Image search: [Google]

251KB, 1200x800px

How do I even check whether this polynomial is irreducible when Eisenstein's criterion fails? W T F REEEEEEE

File: still working.png (5KB, 647x67px) Image search: [Google]

5KB, 647x67px

>>8873006
good fucking thing I even failed to add the right picture, because Eisenstein's criterion does actually show that it is irreducible over Q[x], hehe, feels good to be fucking retarded and forgetting that 2 is a prime innit lads lmao xd

ty for the help

>>8873010

Just learned about this criterion. Is is fair to say that if 'p' exists and FAILS all three conditions that Q is not irreducible (reducible) over the rationals?

>>8872733
bumping this, so far I'm able to come up with that the the divisors of N is
[math] \sum_{1}^{m} (m+1)+m+2)+...+(m+m-1)+(m+m) [/math]

not sure how to move forward and present it using induction and multiplication rule in a neat forumula, pls halp

File: brankd.png (4KB, 429x46px) Image search: [Google]

4KB, 429x46px

>>8873023
No. It's not an if and only if statement.

>>8873029

alright, thanks. The source I was reading from wasn't entirely clear

>>8873027
>>8872733
wrong formula, here's better one
[math] \sum_{1}^{m} (1+2) + (1+2) +...+ (1+(m-1)) + (1+m)

>>8873039
>>8873027

fuuuck, again:
[math] \sum_{1}^{m} (1+2) + (1+2) +...+ (1+(m-1)) + (1+m)[/math]

>>8872733
This is trivial

It is
[eqn] (a_1 + 1)(a_2+1)(a_3+1)\cdots(a_m+1) [/eqn]

>>8873048
I don't know how to show it using the multiplication rule and induction though

>>8873048
>>8873053
and I believe you would want to sum them, not multiply

example, take am=2, then [math]2^1(3^2) =18[/math], which has 5 factors: 18, 9, 3, 2, 1. This would be the sum of [math](a_1+1) + (a_2+1)[/math], not the product

File: limit.png (11KB, 495x159px) Image search: [Google]

11KB, 495x159px

how do i find (c) in pic related without the squeeze rule? i think the limit's zero because [eqn] 0\leq\frac{(1+x)^{\frac{x}{x+1}}\cos^4 x}{e^x}\leq\frac{(1+x)}{e^x} [/eqn] and [math] \frac{(1+x)}{e^x}\to 0 [/math] right? but i think there's a cleverer way to find it using part (b) and exp(something)

>>8873063

Let 'y' equal the limit and play around with logarithm laws.

>>8871232
Fourier transform.

File: proof.png (12KB, 535x89px) Image search: [Google]

12KB, 535x89px

>>8873122
Can any analyst point me to a proof of pic related?

Does this proof seem correct:
˫~∃x(Fx→P)↔~(∀xFx→P)
1 (1) ~∃x(Fx→P) A
1 (2) ~(∀xFx→P) 1 Conf
(3) ~∃x(Fx→P) →~(∀xFx→P) 2 →I (1)
4 (4) ~(∀xFx→P) A
4 (5) ~∃x(Fx→P) 4 Conf
(6) ~(∀xFx→P) →~∃x(Fx→P) 5 →I (4)
(7) ~∃x(Fx→P)↔~(∀xFx→P) 3, 6 ↔I

>>8872688

I would assume that you can't yet prove that the limit goes to infinity, so just use the ratio test.

>>8872524
Every polynomial can be written in the form on the right with a different root ih each bracket.
For example if a quadratic polynomial has roots 1 and 2 it can be factored as (x-1)(x-2) times a constant. You can therefore just write yours as z-pi/5 times z-3pi/5 etc

>>8873209
I fucked up it should be exp(i pi/5) exp(i 3pi/5) etc

>>8873136
Euler–Mascheroni constant should lead you in the right direction

>>8873057
[eqn] 2^1 3^2 = 18 [/eqn] has factors [math] 1,2,3,6,9,18 [/math] which equals [math] (1+1)(2+1)=6 [/math].

This doesn't require induction. It is trivial.
The number of divisors is all the ways you can choose permutations of the powers.
The first power has [math] a_1 +1 [/math] possibilities ([math] 1 [/math] for the possibility [math] a_1 = 0 [/math]. Similarly for [math] a_2 [/math] and so on.

>>8873273
divisors, not factors

>>8873273
Oh ok, I see. Thanks. and it does require induction because that's what the assignment calls for. I'm still unsure how to apply multiplication rule and induction, but I can probably get it from here. thanks wise anon

>>8873273
what if you have an extraordinarily large [math]a_m[/math] ? Is there a more concise way to arrive at the answer, say if the set of integer exponents is 1-1,000?

File: 1493589727904-1828858919.jpg (2MB, 2144x3808px) Image search: [Google]

2MB, 2144x3808px

Could someone check my work? I'm supposed to find c

File: IMAG0331.jpg (703KB, 3808x2144px) Image search: [Google]

703KB, 3808x2144px

>>8873348
Damn, not sure why I multiplied by 2 on that last step; should be c = 1/15

>>8873348
>>8873369
nevermind i'm an idiot, its 21

File: average_defn.jpg (10KB, 776x224px) Image search: [Google]

10KB, 776x224px

How do you find the "average change" in a function of two variables?

For reference, the formula for single variable functions in pic related

>>8873467
take norm of top and bottom, that's it

>>8873477
define "norm"?

>>8873500
if you can't google for 5 seconds then don't bother asking anything

>>8873505
I did google, but wanted to make sure you weren't referring to a normal vector or anything. I haven't ever heard that term used, or done anything involving it in class, so wanted to be sure, anon-san

>>8873522
the idea is a norm measures "size" and the average change is just "change in function" divided by "change in argument"

a function of 2 variables is just a function of a pair, so if you want to see change in f(x,y) from (x0,y0) to (x1,y1) that's just the change between f(x1,y1) and f(x0,y0) divided by the change between (x1, y1) and (x0,y0). you just need a way to measure this "distance", and in fairly general terms it's a norm that does that. read up a bit, the "euclidean norm" is the usual distance on the plane and works just fine for this purpose

>>8873531
ty

>>8873554
>>8873531
Ok, what I don't understand though is lets say we want to find [math]\delta h = \frac{f(1,0) - f(1,1)}{(1,0)-(1,1)} = \frac{9-8}{(1,0)-(1,1)}[/math], how would I compute the denominator?

In the meantime, I am reading up on Euclidean Norm, but I know this computation has to be so bloody simple.

>>8873467
If you have a path from one point to the other and a means of measuring path length, then you could get change per unit length.

>>8873566
Eucledian norm is bloody simple. It's the standard way we measure distance between two points in space.

How to find magnitude of [math]\langle 1, 2t, 0 \rangle [/math]

>>8873682
I get stuck at:
[math] \sqrt{1+4t^2}[/math]

Alright autists

Suppose X is a compact Hausdorff space, and E is some rank n vector bundle, we can assume it's real for argument's sake.

Show there exists some E' such that E + E' is trivial.

I figured compactness means that this bundle is determined by a finite number of maps F_i,j into GL(R) so we just need to find corresponding maps F'_i,j into GL(R) such that the direct sums of their images F_i,j (x), F'_i,j(x) is homotopic to the identity.

In the case where intersections of local charts is contractible, this isn't so difficult, but that's not the case in general.

>>8873682
>>8873687
You've found it... assuming r(t) is defined parametrically as the vector you posted. Just plug in a value at a particular time t into the magnitude function in your second post and that will give you ||r(t)|| at time t.

>>8873737
>In the case where intersections of local charts is contractible,

you can always arrange for this to be the case; it's called a "Good open cover"

Is Elon Musk promising too much too soon?

About 1-2 years ago, Springer publishing released a massive dump of graduate level mathematics texts. Does anyone have an active seed of this vintage torrent?

File: P70501-124253.jpg (161KB, 841x624px) Image search: [Google]

161KB, 841x624px

Can someone help with this? I'm not sure what it means by over 0:0.1:60 seconds. What interval is it wanting me to use? T=0.1 to T=60? i'm new to matlab.

>>8873785
>massive dump

lol

>>8873788
that 0:0.1:60 expression creates a vector from 0 to 60 in 0.1 intervals

>>8871914
Well, sin(n+1)/n is smaller than 1/n, isn't it?

(-1)^n * 1/n is convergent, and you can use the Leibniz method to prove it. This is enough to say that the first function is also convergent.

>>8873797
Ah, that makes sense. Thanks

File: BigO.png (11KB, 425x103px) Image search: [Google]

11KB, 425x103px

Can someone tell me what happened in pic related? Why is that true? Specifically what happened with the Big O part. To be quite honest I don't really understand the algebraic properties of the Big O thing.

Also, what does the Big O thing actually represent? I kinda get that if you have a non-dominant term then you can put it as the Big O of something simpler but then why? How is that helpful?

Just watched the Expanse and was positively surprised by the improved realism regarding science in this science fiction show.
can anyone recommend me similar movies/tv shows?

Is electrical engineering a dying field? Should I major in it if I want a good salary?

>>8873815
Can somebody explain big O in a nutshell, or give a source that defines it rigorously?

>>8873831
I know the definition. I a using a textbook that just defined it. The problem I have is that without giving a single exercise or example it then moved to prove really series identities about the Riemann Zeta function and other functions and it has been abusing that Big O thing leaving me almost clueless.

I just want to know why is it useful to replace the full expansion of a function with some simplied Big O thing, and what happened in my example.

>>8873312
>>8873318
Not sure what multiplication rule means. To do induction just start with one prime factor, move up to 2 prime factors, until you get to m prime factors

>>8873838
>>8873815
Big O means order

You might write O(dx^2) as in it is of the order dx^2. Order general means that there is a finite difference between that term and similar terms.
So for instance, O(x+1) = O(x) because there is always a finite difference between them.

O(x^2) however is not the O(x) because x^2 - x goes to infinity.

[eqn] \sum 1 = x [/eqn] that's why its okay to pull the O out of the sum

>>8873838
The reason we use O is because we often want to only look at the function or series in question as it goes to infinity. At this point the rest of the terms of a lower order being arbitrarily less significant.

File: definition.png (89KB, 991x245px) Image search: [Google]

89KB, 991x245px

>>8873846
>O(x^2) however is not the O(x) because x^2 - x goes to infinity.

But I can prove that [math] x = O(x^2) [/math] right? Because in the interval [math] [1,\infty) [/math]
[eqn] \frac{|x|}{x^2} = \frac{x}{x^2} = \frac{1}{x} \leq 1 [/eqn]

Right?

>>8873848
I see. I guess that makes sense but when I see it in practice it looks pretty arbitrary. There was a theorem in which the author literally put an entire integral inside a big O.

>>8873846
Please don't try to explain things unless you actually know what you're talking about. You're not being helpful. You clearly don't understand big O notation.

>>8873846
this is not correct

for example, 2x^2-x^2 goes to infinity, but any quantity that is O(2x^2) is also O(x^2) and vice versa

see the definition in>>8873872

>>8873892
So [math] x = O(x^2) [/math] is correct? But what does it mean? That x grows like [math] x^2[/math] ?

>>8873899
yes x=O(x^2) is correct. it means that x grows no faster than x^2.

>>8873908
Oh, that does make sense.

>>8873899
To be totally correct, you would not use the equality symbol, as x is a member of the class O(x^2); it is not *equal* to O(x^2).

>>8873908
>>8873915
Okay, I have a question for you.

Is [math]\frac{x^{\alpha + 1}}{\alpha + 1} O(x^{-\alpha - 1}) [/math] equal to [math]O(1)[/math] ?

File: 5.png (7KB, 356x239px) Image search: [Google]

7KB, 356x239px

I have a nomenclature question.
I don't understand when they use the dot between the water and the metal/ligands. Is H2O still acting as a ligand?
I tried to google the structure in 3 dimension but I'm still uncertain.

>>8873929
I think this is my first time seeing O notation used in mutliplication

File: part.png (40KB, 841x253px) Image search: [Google]

40KB, 841x253px

>>8873988
Pic related is a part of proof. Notice that below almost the entire thing turns into a bunch of O's and I am trying to guess which part turned into which O.

I assume that [math] \frac{ x^{\alpha + 1}}{\alpha + 1} O(x^{-\alpha - 1}) [/math] turned into [math] O(1) [/math] because [math] \frac{ x^{\alpha + 1}}{\alpha + 1} O(x^{-\alpha - 1}) = O( \frac{ x^{\alpha + 1}}{\alpha + 1}x^{-\alpha - 1}) = O(\frac{1}{\alpha + 1}) = O(1) [/math]

I am using those equals sign carelessly though because as I said, I am trying to guess. If my computation is "correct" then I suppose that would be the case.

File: asjkfkja.png (33KB, 761x493px) Image search: [Google]

33KB, 761x493px

why is Vx = 20/s?
is it because there's no current going through the 5 ohm resistor? I am a brainlet

File: 20090319.png (119KB, 700x276px) Image search: [Google]

119KB, 700x276px

Asking again.

Anyone knows a good anatomy and biomedical engineering intro textbook?

I am a software engineering brainlet who need a basic understanding of the human body's mechanical aspects.

File: IMG_20170430_224013.jpg (1MB, 3264x2448px) Image search: [Google]

1MB, 3264x2448px

Diff eq final coming up and I remembered this problem I fucked up on an exam a while back. I'm trying to redo it so I know if it ever shows up again, did I set this up right? Answers supposed to be 9e^tsin(t) if that helps.

>>8874039
Hoppenfeld - Physical Examination of the Spine and Extremities
I got this book to diagnose muscular-skeletal injuries after I fractured my forearm.

Nettler's Atlas is one of the usual recommended atlases on anatmony

>>8874063
That second one looks pretty complete, thank you, however, it's fucking $350. I guess that I can pirate it.

>>8874051
Woah man, you don't even need Laplace transform to solve that

>>8874105
I know, but she's testing on whether we know how to do it. But I'm a brainlet and can't remember partial fractions.

>>8874120
As you can see by my eloquent use of "but" twice.

I need a quick rundown on recognizable matrices and Jacoboian equations

>>8874120
kek i don't ever remember learning them growing up, and was able to get through calc 2 and 3 without ever learning them, but in differential equations i finally sat down and took the time learn it. I recommend you do the same, its a nice tool to have in your back pocket

>>8874175
That's basically the spot I'm in haha. You have any recommendations for learning it quick? Kinda pressed for time.

>>8873839
I did this, but don't really know how to move on to the next step.

Basically I have my base case, so now I'm trying n+1, and I'm not sure what to do here

File: helpmesci.png (20KB, 892x181px) Image search: [Google]

20KB, 892x181px

So in pic related I've got the formula for the divisors of N:
[math]N_d = (a_1 + 1) \cdot (a_2 + 1) \cdot ... \cdot (a_{m-1} +1) \cdot (a_{m} +1) [/math]

But how do I prove it using induction? Other than the base case step. I don't know how to concisely prove it for n+1:
[math]N_d &= (1 + 1) \cdot (2 + 1) \cdot .. \cdot ((n-1) + 1 \cdot (n+1)[/math]

>>8874227
Not sure what happened to the Tex
[math] N_d = (1 + 1) \cdot (2 + 1) \cdot .. \cdot ((n-1) + 1 \cdot (n+1) [/math]

Furthermore, on this corrected step for my induction, I don't believe I've done it right at all. I don't think I could safely start at 1 + 1 as I have.

>>8874235
try induction on m

Is there a blood or DNA test to see if me and my friend belong to the same paternal or maternal lineage? That is, that we are related

Not an American by the way, so don't bother convincing me otherwise (we Korean). Serious answers please, we are really serious about this

>>8874247
..I thought I was? I mean I called it n, but it was basically equal to m? What do you mean?

I'm trying to remember the name of a guy.
>Avoided being published
>Researched at MIT
>Stupid good at math
>Only got an associate's degree
I think one of his name's started with a P

how do i get good at equilibrium in chemistry? i have an exam on thursday that will consist of some equilibrium stuff, plus some orbitals stuff and covalent bonds. The latter is easy and intersting to me, but the equilibrium stuff isn't as easy.

I just don't like chemistry at all and this is a required course so I'm just trying to get a basic understanding of it to pass this exam.

why is the dot product of unit vector and itself 0?

>>8874014
looks basically right. it's not a problem here, but one thing that can trip you up with big O is not being careful about what variables you're considering. as an example of what i mean, you write O((a+1)^{-1})=O(1), and similarly we would have O((a+1)^{-2})=O(1), because (a+1)^{-2} is a constant that does not depend on x. But if a were the independent variable, then O((a+1)^{-2}) would not equal O((a+1)^{-1}). Like I said, your proof looks fine, but this is just a warning about a common pitfall in these types of proofs.

>>8874382
it's 1 not 0

Hey guys, I'd like to learn about Sequences an Series of Real Numbers. Recommend books please. Undergrad here.

>>8874413
Oh yeah. Why is that?

>>8874428
the dot product gives you the product of the magnitudes times the cosine of the angle between the vectors

since the magnitude is 1, you have 1^2 = 1, and since they're the same vector, the angle is 0, and cos(0) is 1, so you have 1*1 = 1

algebraically, for example the dot product of the unit vector (1, 0, 0) with itself would be 1*1 + 0*0 + 0*0 = 1

>>8872255
Biomedical is probably one of the safest research paths to go down. Microbiology/virology tend to find mechanisms of actions that medicinal chemists and biochemists can then target using drug design.

Why are quasars always depicted as emitting most of their light as a beam that passes straight through its center? If it's part of an accretion disk, shouldn't the light and matter just kind of spiral all over the place with no distinct direction?

File: deform.png (18KB, 521x132px) Image search: [Google]

18KB, 521x132px

Aren't "plastic" and "permanent" the same, hence circular logic?

Prove

n/(n+1) < 1 for all natural numbers n greater than or equal to 2.

>>8874586
>Prove
> n/(n+1) < 1 for all natural numbers n greater than or equal to 2.
By definition [math]n<n+1[/math] for [math]n\in \mathbb{N}[/math]
Q.E.D.

>>8873986
No, it's not the same. The water is in the second sphere of coordination. You can have the same complex without the water. Or with a different number of molecule of water.

Also, the first one I think it's wrong, the right one should be the second, but with the dot. (which is not low, but in the middle as the multiplication)

>>8874255
Well, you can do the DNA test to see of it matches your father one and check if it's really your father, so I guess you might do the same and check the grade of relationship.
Just guessing, though.

>>8874593
rekt

File: IMG_20170501_114230.jpg (3MB, 3120x4160px) Image search: [Google]

3MB, 3120x4160px

How the fuck do you solve this ?

>>8874669
first you should try rotating it so you can read it

File: IMG_20170501_115439.jpg (3MB, 3120x4160px) Image search: [Google]

3MB, 3120x4160px

>>8874683
Of course how can I be so stupid

how do i show that [math] x^3-x [/math] is injective on [math] \left[-\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}\right] [/math] ? i know it's clear from the graph but i cant get past [math] x(x+1)(x-1)=x'(x'+1)(x'-1) [/math]

>>8874758
use calculus

>>8874586
Are you sure that's the problem? "n >= 2" sounds suspicious since it also works for "n>=0"

>>8874801
thanks i didnt know you could do that. is there a way to show it without derivatives though because this part of the course was before that

How do prove that [math] \sup_{n\in\mathbb{N}}L(f;P_n)\leq \sup_{P}L(f;P) [/math] or is it trivial?

>>8871113
I failed calc the first time I took it. I aced it the second time. Same teacher. Dont worry anon, youll get it.

>>8875296
Don't give him false hope. When I took Calc, my class was filled with people taking it for the 3rd+ time.

>>8874688
I don't understand the notation. What does [T]_B mean?

>>8875307
the coordinates of T wrt to the basis B id imagine

>>8874758
Show it's monotonic

A rather odd request but... I need a chemical that smells really fucking bad. My first thought was skunk oil but I don't know how long it'll last in an open area.

Requirements
>non-toxic (vomiting, headache etc. is perfectly acceptable but no permanent damage)
>"invisible"
>should last for several hours in an open area
>must be purchasable by anyone
>bonus points for something you can mix together yourself (inb4 mustard gas)

If I have a number [math] n = p_1 ^{a_1} p_2 ^{a_2} ... p_n^{a_n} [/math]

Such that:
[math]p_1 ^{a_1} < p_2^{a_2} < ... < p_n^{a_n}[/math]

Is there an easy way to prove that the number [math] k = p_1^{a_1} + (p_2^{a_2} p_3^{a_3} ... p_n^{a_n}) - 1 [/math] does not divide the original number?

If I know the entropy of two distributions X1 and X2, how do I calculate the entropy of a distribution that's X1 with probability a and X2 with probability 1-a?

>>8875660
>Is there an easy way to prove that the number k=pa11+(pa22pa33...pann)−1 does not divide the original number?
why do you think k shouldn't divide n in the first place?

>>8875674
>why do you think k shouldn't divide n in the first place?

Because I've been doing a lot of examples and the resulting k never divides n.

Do you have a counter example? I'd appreciate that too.

>>8875677
>>8875674
Oh. Another thing is that n must have at least two prime factors.

>>8875680
>Oh. Another thing is that n must have at least two prime factors.
it sounds like you've left out some context of what you're trying to do

what is k not dividing n supposed to give you?

>>8875687
Okay, let me type out the entire problem:

Find all the pairs of positive integers (x,y) such that if [math]\alpha[/math] and [math]\beta[/math] are relative primes and divisors of the number [math] x^3 + y^3 [/math] then [math] \alpha + \beta - 1 [/math] is also a divisor of [math] x^3 + y^3 [/math].

I conjectured that the answer is the pairs (x,y) such that [math]x^3 + y^3[/math] is a power of a prime number.

I already proved that these numbers have the property, so now I am trying to prove that numbers that are not like this do not have the property.

In other words, I am trying to prove that if [math] x^3 + y^3 [/math] is not the power of a prime (and thus has at least two prime factors) then the property fails.

And my choice of [math] \alpha [/math] and [math] \beta [/math] that I think will prove to be the counter example is the one in >>8875660

>>8875733
>2 and 7 are relatively prime and both divide 28 but 2+7-1=8 does not

That's right. That is because 28 is not a prime power. 28 = 2*2*7

File: aaa.png (6KB, 567x38px) Image search: [Google]

6KB, 567x38px

Where alpha is sqrt(2) + i.

I don't know mang, playing around with it algebraically just gives me x^2 -2*ix -3, which isn't even in Q[x].

>>8875842
look at the roots of the polynomial you found and add the rest of their galois conjugates

>>8874669
apply t to each given vector

>>8875856
We haven't learned about galois conjugates yet. I just multiplied (sqrt(2) + i) with itself. Got (sqrt(2) + i)^4 which gave me an expression with only (sqrt(2) + i) +/* constant terms. Replace with x, and badda bing, badda boom. Gonna work on proving that my polynomial is irreducible now, thanks senpai.

>>8871914
>>8873808
>>8871929
>>8871987
>>8871919
ALTERNATING SERIES TEST YOU NIGGERS

File: series2.png (7KB, 846x59px) Image search: [Google]

7KB, 846x59px

>>8875921

Is it scientifically possible to be a sissy bitch (google deepslutpuppy as an example) and an alpha male of the group at the same time? I want to be that popular guy, but I can't help what I'm into.

Pop quiz for the thread on chemical nomenclature. English spellings of the elements' full names are assumed throughout.

1) There is EXACTLY ONE element whose symbol can be described in the following way: it has two letters, the second of which does not occur anywhere in the spelling of the element's full name. Name this element.

2) Name the ten elements for which the first letter of their symbol is not the same as the first letter of their word, or full name (hint: these are mostly well-known, moderately to quite important metals).

3) Name the fourteen elements whose symbol is given by exactly one letter.

4) There are exactly two elements belonging to the sets described in 2) and 3). List them.

>>8876113
1)Gold

Do your homeworks yourself.

>>8876125

Not homework mein neger. You score 1/10 on 2).

>>8876113

1) needs to be rephrased to: symbol and name share same first letter, WHILE etc etc.

>>8876113
wtf 1 is clearly false because gold and sodium both work

>>8876158
nvm i missed>>8876134

>>8876167

So now that I've fixed 1)'s phrasing, you are in a position to answer.

What is the easiest way to find f and g such that [eqn] I=\int\sin^3x\cos^2x\,\mathrm{d}x=\int f(g(x))g'(x)\,\mathrm{d}x\,? [/eqn]
I managed to find [math] f(x)=(1-x)\sqrt{x} [/math] and [math] g(x)=\cos^2x [/math] which works if i change I to -2I, but i dont think its the best solution. and also is there a general method to find these functions when 3 and 2 are any integers?

File: ai.png (155KB, 953x237px) Image search: [Google]

155KB, 953x237px

is he really that smart?

tl;dr Why are some scalars invariant under coordinate changes and some aren't?

What does it mean in physics that a quantity is a scalar?
If we define them as quantities that remain unchanged under coordinate system transformations, do then scalars depend on the coordinate transformations we consider?
If so, does that mean that the concept of scalar we talk about in physics is not just 'something that only has magnitude'?
In special relativity we say Lorentz transformations can be seen as a change of coordinates, can we say the same about Galilean transformations? I ask this because in non-relativistic mechanics kinetic energy is invariant under rotations/reflections (I think), but it does change under Galilean transformation.

I came up with this questions because I noticed that despite charge density being a scalar, it does change under Lorentz transformations. Does this happen because in general charge density is a function of a vector (position)? Or is there something more?

What is the standard way to find the integers (a,b) such that [math] \frac{4ab + 1}{a + b} [/math] is an integer.

I am conjecturing based on a polynomial division I did that the solutions are only the integer pairs (a,a+1) but I am not sure if my procedure proves that solution is unique.

How I can easily find all solutions to this equation? (we already know n)
1a+5b+10c+25d+50e=n

>>8876299
I think it should be f'(g(x))? Then it would just be x^3 and sin x and the integral is easy. As you can see it obviously works with x to any n and n-1

>>8871914
Since [math]\sum_{n \ge 1} \frac{(-1)^n}{n}[/math] is an alternating series, it converges, hence we need only check the convergence of [math]\sum_{n \ge 1} \frac{(-1)^n\sin n}[n} = \sum_{n \ge 1} \frac{\sin(n(\pi+1)}{n}[/math]
Now, using partial summation, we get [eqn]\sum_{1 \le n \le N}\frac{\sin(n(\pi+1))}{n} = \sum_{n=1}^N \frac{S_n - S_{n-1}}{n} = \frac{S_N}{N} - \frac{S_1}{2} + \sum_{n=1}^{N-1} \frac{S_n}{n(n+1)}[/eqn]
where [eqn]S_n = \sum_{k=1}^n \sin(k(\pi+1))
= \mathfrak{Im}\left(\sum_{k=1}^n \e^{ik(\pi+1)}\right) = \frac{\sin((n(\pi+1))/2)\sin((n+1)(\pi+1)/2)}{\sin((\pi+1)/2)}[/eqn]
since [math]\pi[/math] is irrational.
Hence, [math](S_n)[/math] is bounded, therefore [math]\frac{S_N}{N}[/math] converges to 0 and the series [math]\sum_{n=1}^{N-1} \frac{S_n}{n(n+1)}[/math] is absolutely convergent, hence the original series converges.

File: sub.png (12KB, 1030x125px) Image search: [Google]

12KB, 1030x125px

>>8876380
thanks but youve lost me. if f(x)=x^3 and g(x)=sinx, then [math]f'(g(x))\cdot g'(x)=(f\circ g)'(x)=(\sin^3x)'=3\sin^2x\cdot \cos x[/math] right?

So taking some number of identical things and figuring out how many ways they can be split into partitions is not so easy. Does it become any easier if you have some number of UNIQUE things and want to figure out the possible partitions? As in, is the formula for figuring this out simpler?

>>8876411
My bad, I confused substitution with the chain rule, your original definition with f(g(x)) is correct.

Can anybody recommend a textbook on electrorefining? I'm running an electrorefining cell and I'd like to better understand some basic concepts - anodic protection, why less noble elements plate onto the cathode at higher currents, that sort of thing.

Thanks!

I just finished a course on ring theory and would like to study an interesting related topic over the summer. Any recommendations? I was thinking NT or AG but am worried about not having covered commutative algebra. Should I just read Atiyah Macdonald instead? Heard it's a bit bland of a subject :/

>>8876453
AM is a pretty dry book, although great for reference. Undergraduate Commutative Algebra by Miles Reid is much more engaging and transparent.

is there any free app that you can put equations and generate the area on chart with all the coords?

>>8876453
Read as much commutative algebra as you need to start AG. Then I would recommend just picking up the rest as you go, that way it is a bit more interesting.

>>8876636
Seems nice as it alludes to the various applications. Wouldn't mind some geometric intuition :)
>>8876647
I'll give this some thought. Usually it's the basics until localization, right?

File: Im_Acoustic.png (64KB, 1667x673px) Image search: [Google]

64KB, 1667x673px

I have no real clue on how to do the following problem, can someone please help?

>>8876733
I posted this problem and I got 0.354025, can someone please confirm or deny this

>>8876453
what did your course on ring theory cover?

>>8876750
Essentially Dummit and Foote chapters on Rings, Modules, Vector Spaces, Fields and Galois. We spent some time doing a bit of category theory. Then last few weeks we had independent reading project in groups where my buddies and I fumbled around with elliptic curves

>>8876786
> independent

> groups

Group reading. Guided reading would be the correct way to put it, I guess. Midway though semester we proposed a general topic and instructor recommended some resources and related topics.

>>8876655
Localization would be included in the basics. It is fundamental in Alg. Geom.

File: Screenshot (8).png (38KB, 826x280px) Image search: [Google]

38KB, 826x280px

How would I give a concrete proof of this? The [math]n[/math]th power of the adjacency matrix gives the number of walks of length [math]n[/math] between two nodes, so it seems obviously true but I dont know how to translate that to a mathematical proof.

>>8876794
>>8876786
lots of directions you could go in then

>theorem about finitely generated abelian group of points on an elliptic curve over a number field
>infinite galois theory
>homological algebra
>representation theory
>basic algebraic number theory: dirichlet's unit theorem (rank of group of units in the ring of integers of a number field), adeles/ideles, dedekind discriminant theorem (ramification of primes in number fields)

>>8876858
induction? a walk of length n+1 between node A and B is a walk of length n from A to a node adjacent to B

>>8876453
Understand localization well. From here, pick an AG text. Read until you realize you don't know an algebra thing. Now you have a reason and a geometric motivation behind learning the algebra thing.

Does anyone know a way to find integers a,b such that
gcd(a,b) > 1
gcd(a,b+1) > 1
gcd(a+1,b) > 1
gcd(a+1,b+1) > 1

I am having a hard time just producing one example.

>>8876859
Thanks for the pointers. In particular mention of representation theory reminds me of the Langlands conjecture. Might make that a goal or something
>>8876988
Not a bad idea. Just hope I don't have too many holes that I spend all my time on algebra

>>8877011
>In particular mention of representation theory reminds me of the Langlands conjecture. Might make that a goal or something
that would be a long term goal for sure, it's an incredibly vast web of conjectures but very interesting and lots of work to still be done. it would be good to learn some basic class field theory and modular forms first for motivation

>>8877006
do you think they exist?

How do you guys keep up with news in math and comp sci

I JUST found out that polymath brought down twin prime bound down to 246

>>8877021
I think so. I was given a problem where I have to prove an upper bound of a property of these numbers.

My first instinct was to find examples so that I could try to conjecture and generalize from there but I have been going for like 30 minutes and I have found no examples.

>>8877023
arxiv
http://www.numbertheory.org/ntw/web.html
tao's blog

>>8876007
you need to stop browsing 4chan yesterday

>>8877025
find any yet?

>>8871585
look at Fourier Transform tables, first. Like spend 5 minutes in Wiki. Seriously. That's all it takes.

>>8871801
Digital filter design is pretty easy to accomplish with Matlab, if you have access to it and the DSP toolbox. I'm sure many anon's here have that so if you want the filter coefficients, just tell them what type of filter you'd like and give some requirements and they'll fart you out some numbers for you.

>>8876113
Chemical nomenclature is not necessary info its just there for normies to feel like they can be smart because they memorized a bunch of labels. Real chemists just use the damn periodic table.

>>8875352
Anything sulfur containing, they all produce the same hydrogen sulfide compound that smells like rotten eggs.

>>8873826
EE is not a dying field. It will probably be a very lucrative field in the next 10 years in the US especially. Our company has many EE's nearing retirement that were trained during the advent of the cold war/nuclear submarine programs who are very talented and will need to be replaced with new blood.

>>8874036
First off, I'm under the assumption that terminals a and b are the terminals that are labeled as Vt+ and Vt- in the picture.

At DC, the impedance of the cap is infinite, making it an open circuit - so no current will flow along the top horizontal wire. Likewise, Vt is an actual open circuit, so no current will flow through it. Using Kirchoff's current law (KCL) on the node shared by Vt+, 1 Ohm, and the cap to know that there cannot be current flowing through the 1 ohm resistor. Now use KCL on the node shared by the cap, the 5ohm resistor and the dependent voltage source to know that there cannot be any current flowing through the 5 ohm resistor. Now that we know all the current amounts (aka - all are zero), we can use Ohm's law and Kirchoff's voltage law (KVL) to determine Vx.

Because there is no current flow in any portion of the circuit, there will be know voltage drops across any of the resistors. KVL then would tell you that 20/s = 0 V [ voltage drop across the 5 ohm resistor] + Vx. So, Vx = 20/s

tl;dr - yes.

>>8874286
Reactions tend to progress in the direction that is most energetically favorable, a condition that is expressed through the equilibrium constant. Everything from there is just le chatlier's principle which is basically if equilibrium is disturbed, the reaction will progress in the direction that reestablishes equilibrium (this includes heat, where exothermic reactions have heat as a product and endothermic have it as a reactant).

File: analysis.png (11KB, 749x101px) Image search: [Google]

11KB, 749x101px

To all the analysts:
I realise that I need to use the intermediate value theorem to solve this, but choosing the interval (0,1) doesn't work. What would be a better interval to choose?

>>8877461
x=1/e

File: whatisthis.png (73KB, 598x545px) Image search: [Google]

73KB, 598x545px

What kind of graph is this

It's from this https://en.wikipedia.org/wiki/Topic_model

I need some help understanding the sign convention on this optics problem.

So i have a person with bad eyesight 2cm from a lens, this person can see 300cm with relaxed eye and 150cm with strained eye.

I'm supposed to find the focal point for both, but I'm not sure if I just use the lens equation 1/f = 1/p + 1/q.

My p is 2cm, but what about my q for either one? Is the q negative for strained eye and positive for relaxed eye?

Is there any resource to seeing all the basic linear algebra theorems and definitions right in front of my face for studying?

It feels like I forgot the stuff I studied for the past exams, now finals are coming up. Anyone recommend a good cheatsheet-y resource?

Any tips and techniques? We're stepping into proofing stuff as well.

Thanks.

is anyone else not seeing latex? i read something about mathjax cdn shutting down but havent seen any posts about it

I want the following :
Start to care about myself
Achieve success
Stay healthy

This is my current situation:
I am out of jobs( getting rejected all the time unless it is about really low class job), clinging on a dead end job.
I am looking at other jobs to finance my student life.
I don't seem to care about my looks, I just let myself go although I still lift.
I am fat and live in a household inhabiting neurotic, toxic people who just mean well, although all it does is just hurt my self esteem.
I am depressed and on pills.
My situation frustrates me, but also I feel like it is too much a hassle to change it and I am too comfortable rotting in my comfort zone.

I don't know what else to add, please ask me questions, let me answer them and help me to help myself.

>>8877718
Good on ya for taking your meds.

Do you have people that you hang out with at school/other activities?

I used to live in a toxic household when I was getting my bachelors degree and what helped me was having a fun hobby where I could meet people. Contrary to what others say, lifting didn't help my mental state so I dropped it and joined my school's salsa/latin dance club, robotics club, and car club. I didn't make any close friends, but I made enough friends to go out clubbing and shit every now and then (which I enjoy as well). Be really nice with people and they might buy you drinks.

I guess my biggest suggestion to you is to get out of the house. Tell your family that you're going to study at school or something. Get your chores out of the way then gtfo of the house. That's what I wish I did when I was in your shoes. Things are better now, but I wish I did that more often.

Success is what you define it to be. My idea of success is living my life according to how I want to -- not my parents, not my siblings. Me. I dictate how I live my life. Sometimes I have days where I don't pick up after myself or skip the dishes and just eat take-out. But you know what? That's my fucking life and I love it. Find the life that you want. It's good that you know that you live in a toxic household, but you need to get out more to experience what more life has to offer.

It's hard to start caring about yourself when you've lived your whole life doing the opposite. But I'm sure you already do care about yourself, seeing as you're taking meds which I presume you got from a doctor. So you do care for yourself. It's hard to recognize, but you're on the right track, man. Treat yo self out every now and then. Leave the house whenever you feel like. Etc.

Good luck, man.

File: 1472674936122.png (3KB, 523x274px) Image search: [Google]

3KB, 523x274px

>>8877586
always use vector notation liek OA, since htey are singed, before using p and q

File: 1467322847183.gif (21KB, 644x225px) Image search: [Google]

21KB, 644x225px

>>8877751

>>8871108
For a quadratic equation is easy to see that the difference of both roots is [math]x_2-x_1=\frac{\sqrt{b^2-4ac}}{2a}[/math]
Is there similar (simple) expressions for the difference of two roots of a cubic equation (of couse x_3-x_2 and x_2-x_1 are usually different)?

>>8877913
For polynomials up to degree 5 there are closed formulas for their roots.
So aside from the "simple" the answer is yes.

Matlab tells me that:
-(27*a^2*(((d/(2*a) + b^3/(27*a^3) - (b*c)/(6*a^2))^2 + (- b^2/(9*a^2) + c/(3*a))^3)^(1/2) - b^3/(27*a^3) - d/(2*a) + (b*c)/(6*a^2))^(2/3) - 9*a*c - 3^(1/2)*b^2*1i + 3*b^2 + 3^(1/2)*a^2*(((d/(2*a) + b^3/(27*a^3) - (b*c)/(6*a^2))^2 + (- b^2/(9*a^2) + c/(3*a))^3)^(1/2) - b^3/(27*a^3) - d/(2*a) + (b*c)/(6*a^2))^(2/3)*9i + 3^(1/2)*a*c*3i)/(18*a^2*(((d/(2*a) + b^3/(27*a^3) - (b*c)/(6*a^2))^2 + (c/(3*a) - b^2/(9*a^2))^3)^(1/2) - b^3/(27*a^3) - d/(2*a) + (b*c)/(6*a^2))^(1/3))
Is the (already simplified), result if you calculate the roots first 3 roots of the polynomial ax^3+bx^2+cx+d and calculate root2-root1.

You should take this with a grain of salt though, I (or even matlab) might have made a mistake

Should a Beer's Law plot always start from the origin?

>>8877937
There has to be an elegant way to write that as a function of the discriminant of the cubic equation, isn't it?

Is it possible that we can't comprehend anything faster than the speed of light and that anything moving faster than the speed of light can't aswell?

>>8877959
Possibly.
I have no Idea how to test that though.

>>8877969
>Is it possible that we can't comprehend anything faster than the speed of light and that anything moving faster than the speed of light can't aswell?
no.

The question is entirely pointless, if there is something that we can not possibly comprehend, then asking if it exist leads to absolutely nothing.

if your inside and can't see the sun, is the sun real, or just a thought with faith that reality is reality..???

File: maxresdefault.jpg (51KB, 1280x720px) Image search: [Google]

51KB, 1280x720px

Morally, what are ordered pairs in set theory?

The obvious answer would be "coordinates of a graph", but set theory has no notion of graph, and you can't put sets on an axis.
Since functions and relations are defined as sets of ordered pairs, is the ordered pair (a,b) supposed to represent the "arrow" from a to b? If so, how is that linked to the coordinate notion?

Is there any way to experimentally determine the resolving power or a grating-based spectrometer using a single laser (ie a single frequency), or is more than one frequency necessary?

>>8878012
The standard definition is that (a,b) := {{a},{a,b}}

It's nicer to think about ordered pairs in the fashion of some sort of "labeling" but this is circular because you need functions to label things, and functions need ordered pairs.

I doing a chemistry question, which was to find the empiracle formulae of an alcohol that has 64.9% carbon, 13.5% hydrogen and 21.6% oxygen by mass.

So far I've done all the calculations and I get:

C= 3.9
H = 9.6
O = 1

The problem is where to go from here. Those aren't intergers and the only interger I can multiply them by is 10, which gives me a silly chemical (C39H96O10 is not an alcohol). Should I just round up and call it C4H10O?

File: 978-613-4-28888-0-full.jpg (188KB, 2000x1462px) Image search: [Google]

188KB, 2000x1462px

>>8878028
Thanks, but I don't think anyone disputes that the standard definition is completely arbitrary, in that there are other possible constructions that are equally consistent.

That's why I asked if there are any particularly [math]moral[/math] definitions, but I'm starting to think that the answer is negative, at least for set theory.
But I'm also currently reading about alternative foundations, and I do think Lawvere was on to something when he defined pic related using ordered pair notation: for example, an object of (f,g) can be interpreted as a formal assignment from an object of f to an object of g. Not sure how much mileage I can get out of this though.

>>8878043
I'm not sure what you want. You need some method of labeling elements 1 and 2 without using the numbers one and two because you haven't defined how to do that.
How would you expect it to not be somewhat arbitrary?

>categoryfaggot
Ah. It makes sense now.

A quiz question asked me to explain why my answer for part a (an ordered pair representing the minimum of a multi-variable function) "could not occur for a continuous function of one variable". My answer was "It is impossible to pass 2 arguments to a single-variable function, so my answer could not be used." I got no credit, with no explanation. How is this incorrect?

File: 1493688530364.png (127KB, 601x508px) Image search: [Google]

127KB, 601x508px

how do I show that

[eqn]\frac{k^{2}}{k^{3}-1} \geq \frac{1}{k} [/eqn]

>>8878371
k^2 >= k^2 - 1/k

>>8877757
so your focal point is always negative?

>>8878041
>Should I just round up and call it C4H10O?
Yes

What topic is a nice intersection of analysis and algebra?

>>8879079
calculus? Calc is elementary analysis, and algebra is a prereq for calc

>>8879098
I mean the abstract algebra kind of algebra.

>>8879099
Howabout discrete mathematics. Plenty of analysis, a good amount of algebra depending on where you look

>>8877404

hence the topic's inclusion in the stupid question thread. Did you forget where we are posting?

Your point is well taken but even you know that it can actually be useful to know certain ones off the top of your head if you use them regularly, my meme questions notwithstanding.

where can I find phase diagram for Fe-Mn-C ?

>>8876361

Let B be an odd integer.
Then (B-1) and (B+1) are even, and so
(B-1)*(B+1) is even. Assume
we can find an odd integer A
that divides (B-1)*(B+1). Set
a = (A+B)/2, b=(A-B)/2 and
k = A-((B-1)*(B+1))/A.
Then a+b = A while
4*a*b+1 = 4*(A+B)/2*(A-B)/2 + 1 =
A^2-B^2+1=A^2-(B-1)*(B+1)
= A* ( A- (B-1)*(B+1)/A )
= (a+b)*k
which is dividble by (a+b).

Example: Take B=13. Then (B-1)*(B+1)=168
=8*21, and we can take A=21. Then
a=(A+B)/2=17, b=(A-B)/2=4,
k=21-8=13. Check:
(4*17*4+1)/(17+4)=13.

>>8879478
Note (B-1)*(B+1) will be divisible by an odd number A>1 unless (B-1)*(B+1) is a power of 2, i.e. unless (B-1) and (B+1) are powers of 2, i.e. unless B=3. If B=3, can take A=1.