/sci/ - Science & Math

Are all the non-trivial zeros of the Riemann Zeta function REALLY on the line 1/2 + ib or is that an old wives' tale?

>>6490565
Can you solve triple integrals?

What is the deal with 1/r^2

what is the derivative of uranus

Can your write a proof for me?
<span class="math"> \forall x,y \in \mathbb{F}, (xy>0) \Longrightarrow (x>0 \wedge y>0) \vee ( x<0 \wedge y<0) [/spoiler]

fuck he is stuck on the Riemann question.

>>6490567
"Trivial" is subjective. With an IQ as high as mine finding all the zeros is trivial. For an undergrad student it might be harder.

>>6490577
Nobody can. Triple integrals are currently being researched by the most talented mathematicians and the new tools we develop to tackle the problem are inspiring new and exciting areas of math. A solution to triple integrals however hasn't been found yet.

>>6490595
Everytime these threads pop up I hope someone will be able to solve them. Next time I guess.

>>6490595
OK let me rephrase

Are all the non-integer zeros of the Riemann Zeta function REALLY on the line 1/2 + ib or is that an old wives' tale?

>>6490577
>>6490595
Alright, I see this pop up every now and then: What the fuck is a triple integral? It sounds like a troll/meme thing...

>>6490611
<span class="math"> \iiint f \, \mathrm{d} V [/spoiler]
It's a meme that they are hard.
It's part of multivariate calc which in STEM is usually taken second year.

Give me a thesis topic in machine learning, data mining, kdd for a computer science bachelors degree

>>6490619
What's so special about them that no one has solved them yet? If an integral is finding how much a line bends downwards, what's a triple one?

>>6490565
>Math PhD here taking your calculus questions.

What is the most generalized mathematical structure that captures the basic concepts of differentiation?

Like how "modules" generalize vector spaces.

>>6490630
That's a derivative.
An integral is the area taken under a curve.
Triple integrals aren't much more unsolvable than normal integrals.
I've used them (and solved them) in incompressible flow.
I'm pretty sure they are useful in E&M as well.

>>6490623
"how much data is big data".

>>6490645
You can solve them approximately numerically, but because it's a three-body problems, it's not possible to find a general solution to any but the most asymptotic of triple integrals.

>>6490658
> but because it's a three-body problems,
wat.
there are plenty of triple integrals that aren't many-body problems.

>>6490671
>TRIPLE integral
>not THREE body problem

Stop talking out off your ass.

>>6490602
Sure they are. I proved it. If you don't believe me, post a counter-example.

>>6490623
Construct an algorithm that makes a machine learn how to come up with new BSc thesis topics for CS students.

>>6490634
derivations in differential Galois theory

>>6490650
about tree fiddy

>>6490696
>post a counter-example.
0.49999....+ik where k is the imaginary part of a zero on the critical line
rekt

>>6490681
Wat.

>>6490717
>mfw anon solves the Riemann hypothesis

today was a glorious day

>>6490595
uhh do i not know them right?
even i can solve tripple integrals, dependent on such as castesian coordinates. rendering software also make use of tripple integral solutions

srsly, can't we solve this step by step?

>>6490787
There's single integrals that are unsolvable.

>>6490591
plz.
I can only think of doing it case by case.

>>6490824
You didn't even bother telling us what F is.

>>6490787
>i can solve tripple integrals
You need to get published right the fuck now.

>>6490834
F is a field you mongoloid

Not TECHNICALLY a calc question, but first year undergrad student here. Studying for a mathematics major. Any advice? just finished Calc II.

>>6490845
Not every field is ordered, you braindead simpleton.

>>6490845
>Implying > is implied by a field

>>6490846
Pre-upper math such as calculus is absolutely nothing like what you'll be doing later on for your degree. Grab an abstract algebra textbook and work through that.

>>6490845
Try to prove in the case where <span class="math">\bf{F} = \frac {\mathbb {Z}}{2 \mathbb{Z}}[/spoiler].

>>6490853
>>6490856
>>6490866
well no shit, why would you even ask this question unless you were using ordered fields?

i thought /sci/ was above baseless nitpicking

>>6490888
>above baseless nitpicking
>anywhere on the internet

>>6490888
Don't ask a math question then complain about people wanting specificity.

>>6490681
you're a fucking idiot

Is it okay if I ask a non-calc related question?

So right now in math class, we're learning about arithmetic and geometric series. I was wondering if given a finite number of points to define a pattern for, is it possible to find multiple patterns for that set of points?

For example, given the points { 2, 4}
couldn't you conclude that the pattern of the series could recursively be (previous term) * 2
or
(previous term) + 2
?

if so, is there a formula to brute force a pattern given a finite set of numbers?

I drew a rough picture of what I'm talking about. Basically, I'm asking for a formula that will graph a function that connects a finite set of numbers.

>>6490824
sorry.
F is an ordered field.
I wrote at the beginning of the section and didn't specify it ever again.

>>6491390
Image

I had made a thread regarding this ( >>6491349 ), but I'll ask a tangental question here:

Where specifically should I start learning about the math behind digital audio/video compression?

I watched the Xiph videos, but I'm simply not familiar enough with mathematics to understand them*, and I'd like to learn more.


* I'm only in Calc 1 in uni.

>>6491392
Or, prove the contrapositive of the quantified part and make it look way less gross.

Thm: For all x,y in F: xy > 0 implies (x,y > 0 or x,y < 0)

Proof:
Let x,y in F. Suppose WOLOG that x < 0 and y >= 0.

If y = 0, xy = 0 because 0 is fucking 0.
If y > 0, xy < 0 because of whatever that axiom is that says multiplying by positives (x) preserves inequality signs.

>>6491432
> WOLOG
Thanks I needed that a while back.

>>6490696
you mean the formal derivative of an element of a polynomial ring?

I'm in galois theory right now graduating this spring, going to a PhD program in the fall I started typing out the name of the school but then realized maybe I ought not.

What are you research interests OP?

>>6490565
What's the story behind the gif?

>>6491443
>you mean the formal derivative of an element of a polynomial ring?
a few steps up the abstraction ladder and coming from a more analytic perspective (DEs) though the formal derivative is an example of a derivation.

>>6491421
I'm not sure if this is what you're asking, but there is always a "best" polynomial to hit a number of arbitrary points. If you have n points, then you'll need at most a polynomial of degree (n-1), I'm pretty sure.

>>6491485
so, galois theory in the realm of lie groups instead of symmetric groups? that's about the only way I can imagine bringing differentiability into things, but that doesn't smack of abstraction. You must climb a very different ladder when it comes to thinking about abstraction than I do. We'd be talking category theory if you stepped up two rungs on my ladder.

Prove that every real symmetric nxn matrix has a real eigenvalue.

>>6491508
>so, galois theory in the realm of lie groups instead of symmetric groups?
yep.

>>6490565
Does P=NP?

>>6491610

>computer science questions

>>6491610
Only when N=1 or P=0

>>6491637
Computer science is a branch of math.

Current College Student
This university UH
Offers partial differential equations
How hard is that shit compare to ordinary differential equations?
Also do you know what in the blue fuck vector analysis is?
I am taking Calc 3 and ordinary differential equations

>>6490778
claim $1000000

Please help

>>6491649
C

Yeah I hate parametrics and series

>>6491643
huh, another UH student. PDE is easy enough if you understand stuff, but if you are in calc III and wondering what vector analysis is you might want to take a step back. I can't help much though with ought knowing your major - because if you take any physics courses that deal in PDE or vectors you'll basically figure things out as you go and honestly makes it more conceptual when you take the actual courses later.

>>6491643
huh, another UH student. PDE here is easy enough if you understand stuff, but if you are in calc III and wondering what vector analysis is you might want to take a step back. I can't help much though with out knowing your major - because if you take any physics courses that deal in PDE or vectors you'll basically figure things out as you go and honestly makes it more conceptual when you take the actual courses later.

Who the faak decided to invert derivation to make hellfeelgiving integration?

>>6490787
What is this thing?
Why this thread is killing me?
What is going on?

>>6491637
>you will never be as bright a mathematician as Turing, the father of computer science

>>6492229
Turing was a mathematician. If instead of studying math he studied a modern CS curriculum, he would have never made the discoveries he's known for. He would probably turn around in his grave if he knew how CS is taught nowadays.

>>6491392
I know this is late, but this might help you in the future.

Whenever you have a statement of the form
>A or B
It is equivalent to the statement
>not A => B
So you can try proving that instead.

Which books did you read? I wanna go for Zorich. Fuck that trivial bullshit for Down'ses.

>>6492233
butthurt community college dropout who thinks his half complete associate degree in IT compares to CS courses at university detected

>>6492271
Keep projecting. I'm studying at an elite university.

P =NP ?

>>6492274
>community college
>elite university

>>6492278
I don't even know what a community college is. Protip: Not everyone is from burger land.

>>6490565

Can you explain variational calculus on manifolds to me. I'm just finishing my undergrad in physics, so keep it on that level.

>>6492286
don't feel bad. Therapy can help you get over your insecurities.

>>6490567
lol'd

>>6492310
Why would I take therapy for YOUR mental illness?

>>6491724

Write the whole thing in polar form and then use polar integration; not hard

>>6491539
Watch the MIT videos on symmetric matrices; they're really useful and usually contain proofs like this

>>6491812
Major is in engineering
Why step down?

>>6490565
what is the limit as x approaches 2 of x=cos(y)

>>6491812
Same guy
Major in engineering
I have to take math courses to raise my GPA or some shit so I decide to take PDE and Vectors analysis
Ok so how hard is that going to be
Also how much linear algebra do I need to know. More conceptual? Elaborate please
And thank you

>>6490585
infinty LOL

>>6492321
He clearly said "your" insecurities. I don't know how his mental illness is of any relevance.

>>6492844
What insecurities?

>>6492848
I think it is stocks stuff

I find the OP's gif very humorous

>>6492234
still helpful.
Going through real analysis is my first exposure to proofs since high school.

>why do you hate me Pugh

>>6493011
But that's wrong.

>>6490866
0 element of integer multiplication and negation rule of multiplication of integers?

>>6493011
That sounds wonderful, what textbook is it?

>>6493682
Fucking search the name that's right fucking there holy shit

>>6490565
let <span class="math">(a_n)_{n \in \mathbb{N} }[/spoiler] be a strictly increasing sequence of streactly positive real numbers. Show that <span class="math">\sum_{k=1}^{+\infty}1-\frac{a_k}{a_{k+1}}=+\infty[/spoiler]

>>6494079
let <span class="math"> a_{n+1}=a_{n} / (1-2^{-k}) [/spoiler] and <span class="math"> a_0 = 1 [/spoiler]
then <span class="math"> a_{n+1} > a_n > 0[/spoiler] for all n and <span class="math"> a_{n} / a_{n+1} =1-2^-n[/spoiler]
therefore <span class="math"> \sum 1-a_{n+1} / a_n =2[/spoiler]

>>6493682
It's Pugh - Real Mathematical Analysis.

>>6492233
>He would probably turn around in his grave if he knew how CS is taught nowadays.

Probably not because, unlike you, he'd be smart enough to specialize in theory (not software engineering, or some other piece of cake bullshit copout) in a top 10 school to boot.

What are some uses of non-integer derivatives ?

Is there an analogue of Taylor's formula involving these ?

>>6490787
how would you solve one like this where limits are arbitrary functions of the shit you're integrating by

<span class="math"> \int_0^{f(x,y,z)} \int_0^{g(x,y,z)} \int_{h(x,y,z)}^0 k(x,y,z) dy dz dx [/spoiler]

im an undergraduate student. how to find myself to be more interested into maths?

>>6495627
Stop sucking so many engineering penii.

If you could help me out here >>6495611

that'd be nice

>>6492722
>What is the limit as x approaches 2 of x = cos(y)

What is the limit as x approaches 2 of y = arccos(x)?

>>6490645
>an integral is the area taken under a curve

Holy shit. Do they really teach these kids that?

>>6496303
Next you're going to tell us that a derivative isn't the instantaneous slope of the curve.

>>6496328
That is a geometric interpretation m8

>>6496303
he mentioned the geometric interpretation in
> If an integral is finding how much a line bends downwards, what's a triple one?

>>6496330
what's a book that doesn't geometric interpetation?
I was going through apostol and suddenly area.

>>6496303
could you seriously be more of a giant fucking faggot

why

picked sin(t) for f A=-1, B=1, C=2, a=1 and y0=2
Supposed to use Euler's method, improved Euler's method and Runge-Kutta method for 10,20 and 40 steps. The problem is I can't figure out how to get "h" or at least the "b" in h=b-a/n so I'm stuck. Any help would be greatly appreciated.

>>6495627
I personally enjoy abstract courses a lot more than just computational shit. I've been taking Abstract Algebra this semester and it's pretty fun.

>>6496381
What do you mean? H is just the step size. Surely the rest of the text in the problem tells you what step size to use?

>>6496386
nope everything you see is whats given, ill attach the rest.

>>6496386
a wait i think i see now y(b) is y(a+1) which depends on whatever a you pick, feel like an idiot now

>>6496402
Yeah, I saw that just now too. This is a lot of grinding to do for no real reason though.

>>6496381
Why doesn't my diff eq. homework look like this?

I just get straight problems for the most part, sometimes it's an IVP or non-homogeneous but I very seldom have a WORDS WORDS WORDS problem like that.

Is that a bad thing?

>>6496406
Yea, but this way we don't have to do this in an exam.

>>6496414
No, my homework looks like that as well this was just something my professor came up with.

>>6496414
>That rote computation

I feel for you

This is a precalc question and pretty simple from what I understand, But I for the life of me cannot understand how to tell if two vectors have the "same" radian number. How do I tell if these vectors are going the same direction

>>6496414
>having anime paused in the background

My ODE book is wordy as hell. If it were just straight problems, my homework wouldn't take nearly as long.

>>6496419
forgot pic

>>6496419
>>6496423
Just think about your unit circle. A full circle is 2*pi. Anyways, those vectors are pointing in different directions so they obviously aren't going in the same direction. However, they are going in perfectly opposite directions (180 degrees=pi) so you can clearly see that 8pi/5 is exactly 1 pi greater than 3pi/5.

>>6496421
>having anime paused in the background
Not quite.

My homework doesn't really take that long. I don't know if that's bad or not. Is there any benefit to solving these wordy problems or am I pretty much getting the same understanding from grinding straight problems.

Please OP
I just need help finding the critical points. I took derivatives with regard to X and Y but am getting convoluted answers for what the critical points are

>>6496452
I guess it just depends on you, but for me, doing straight problems is easy as shit and I don't learn much. You just plug in the formula, do the method or whatever it is. Wordy problems force you to interpret the situation and pull out equations that describe the situation. It's much harder and requires more thinking, in my opinion and thus, you learn more.

>>6496454
OP hasn't been here for three days.

>>6496457
Well can someone help? Sorry to beg but this question is basic calculus so I assum plenty of people could figure out at least the first part out regarding the crit. points

>>6496460
>Anonymous ## Mod 11/20/13(Wed)16:47 No.6171689▶
>Reminder: /sci/ is for discussing topics pertaining to science and mathematics, not for helping you with your homework. See the rules page for details.

>>6496465
>Had a question about a basic calculus problem that is not homework, I am just trying to learn it
>Post in a thread asking for questions about Calculus
Not that it matters, I won't bother posting again

>>6490565
Explain the connection between Vandermonde Matrices, the Discrete Fourier Transform, and Polynomials over Fields. We use a Vandermonde matrix to solve for roots of polynomials, why can't we use a DFT or just FT to compute roots of larger, stronger polynomials? Perhaps it doesn't give all roots, but wouldn't this cause a real upset in cryptography?

Can U help me on >>6496459
TNX!

>>6496427
Thanks so much!

>>6490565
Ok so this is a weird question. We can define non-integer derivatives such as the half derivative and so on, I had the random thought a week or two ago about whether or not one can define a complex ordered derivative?

>>6496529
You can always take the derivative with respect to x^(1/2) rather than x. Change of variables makes this notion rather useless though.

>>6491610
They already proved that it doesn't for non-trivial cases

>>6496380
(30-8)*4=92 because 4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4+4=92

>>6490565
If OP is still looking at this thread...

Can you explain absolutely convergent and conditionally convergent?

>>6496529
Not OP, but it seems to me you could do this with the Fourier transform. Something like
<span class="math"> F\Big( d^w f \Big) = (2\pi i z)^w F(f)[/spoiler], then transform back.

>>6496529
(I'm not OP)
Here's an idea:
If you treat functions as elements of a (complex) vector space,
then what you're looking for is an operator <span class="math">A[/spoiler], such that
<span class="math">A^{2} f = (\frac{d}{dx})^{-1} f[/spoiler],
where we can define the "inverse derivative" of a function by integrating the function from 0 to <span class="math">x[/spoiler] or something.

I think you could use this: >>6498237
to find the matrix elements of the operator, if you use <span class="math">e^{ikx}[/spoiler] as your basis.

I have math aphasia and it takes me far longer than most people to learn and execute mathematics

how can I learn calc II finally using alternative learning methods

at what age should i give up studying math?

>>6490565
I keep clicking of the gif

What is the lim c->0 of (f(x+c) - f(x))/c if f(x)=x? My homework is due tomorrow please respond

>>6490565

curlG = <xyz, -yz^2, zy^2>

does G(x,y,z) exist? if so, what is it.

can you please graph x=-0.025x^2+1.125x and tell me the y coordinate when x=40, my calculator has fucked up.

also a pic of the graph would be great.

>>6498840
>operating under the assumption that trolling doesn't occur on /sci/..

f'(x)

>>6498810
Once you get past arithmetic and basic algebra so 10

>>6498978
So i can be 25 and start college with thr intention of getting a phd in math?

>>6498810
>at what age should i give up studying math?
If you haven't derived the basics of calculus by the time you hit puberty, then you should give up.

Please prove <span class="math"> \oint_C { \bar r \times \frac{d}{{dt}}} \bar B \cdot d\ell = - \frac{d}{{dt}}} \bar B \int_S dS [/spoiler]

Where the closed curve C is the countour of surface S and r is the curve.

Do you consider the extremities to be a local max or min over a defined domain?

Please prove <span class="math"> \oint_C { \bar r \times \frac{d}{dt} \bar B \cdot d\ell = - \frac{d}{dt} \bar B \int_S dS [/spoiler]

Where the closed curve C is the countour of surface S and r is the curve.

Please prove <span class="math"> \oint_C \bar r \times \frac{d}{dt} \bar B \cdot d\ell = - \frac{d}{dt} \bar B \int_S dS [/spoiler]

Where the closed curve C is the countour of surface S and r is the curve.

>>6500079
99% of humanity is inelegible but people still do it
Why?

So what's a set that doesn't have this property?

>>6490565

I want to be an EE. I have my CS Associates degree. should I get a math or physics degree?

>>6502231
Q of example 1.9(a)

>>6502231
errr it gives you an example anon: the rationals

>>6502243
can you give another example?
he keeps referring back and i'm out of heap memory in my brain.

>>6502246
got it.
i'm just being dumb apparently.

>>6490565
so not exactly calculus, but im about to graduate, and im applying for grad school in applied math

im applying to a masters program at a state school with a 2nd tier math program, i have no job so i really need to get in, i double majored with a 3.6 overall but only have a 3.3 in math, i have an almost perfect GRE but no jobs or research and im not sure how good my recs are

do you know if im likely to get rejected by this? its a masters and i dont need funding since its in state and not that great a program (top 100, not top 50) so i really should get in but oh my god the fucking anxiety is killing me i cant study for exams

i applied to a few other related programs at other schools, berkely, nyu poly and a couple 2nd tiers, but im pretty sure i cant get into berkeley and im not too worried about the others

sorry to shitpost but im really stressed out and maybe someone here will know

>>6500056

yeah obviously

f I do synthetic division by -3
I get: x^3 - 3x^2 + 7x -5
If I do synthetic division by 1
I get: x^3 - x^2 +15x

neither of those polynomials have solutions
I tried entering "none", but it doesn't work
so what am I missing?

Let u, v and w be three vectors in R^3 such that: u + v = w.

Using the geometric meaning of vector addition and cross product, explain the statement of u x v = w x v = u x w. geometrically. Make sure that all the cases are covered.

>>6502302
draw some pictures anon
u x v will be perpendicular to u and v

>>6502315

I figured that out, just not sure how to answer the question

>>6502318
if all those cross products are the same then what does that say about the relationship between u, v and w?

>>6502302
>>6502318
>Let u, v and w be three vectors in R^3 such that: u + v = w.
>Using the geometric meaning of vector addition and cross product, explain the statement of u x v = w x v = u x w. geometrically. Make sure that all the cases are covered.

There are only 3 possible cases.

Case 1: At least 2 of the vectors are the zero vector.
Case 2: Exactly 1 of the vectors is the zero vector, and the other 2 are parallel to each other.
Case 3: All three vectors are not the zero vector, and they all lie in the same plane.
In case 3, there's one more thing you need to figure out. I'll leave it to you.