/sci/ - Science & Math » Thread #13276478

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/mg/ - math general

El Arcón Mon 14 Jun 08:41:26 2021 No.13276478 View Reply Original Report

Quoted By: >>13276640 >>13276648 >>13276934 >>13281972 >>13282333 >>13282596 >>13282677 >>13286446 >>13287432 >>13287440 >>13293768 >>13296543 >>13302085 >>13302252 >>13311506

previous >>13245710

previous thread died edition

talk about mathematics here
don't shit up the thread

Anonymous

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Anonymous Mon 14 Jun 2021 08:44:43 No.13276489 Report

Quoted By: >>13276584 >>13276635 >>13279400 >>13303551

$S_t = S_0\cdot \exp\left( (\mu - \frac{\sigma^2}{2} )\,t + \sigma\,W_t\right)$

Anonymous

Anonymous Mon 14 Jun 2021 09:18:43 No.13276573 Report

Quoted By: >>13296418

I read calculus by salas.
what now?

Anonymous

Anonymous Mon 14 Jun 2021 09:21:03 No.13276584 Report

Quoted By: >>13276628

>>13276489
Excuse me miss you seem to have a shitcoin logo attached to your behind.

Anonymous

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Anonymous Mon 14 Jun 2021 09:34:15 No.13276628 Report

Quoted By:

>>13276584
I was okay with it since I don't even know the shitcoin

$(\mathbf d + \mathbf{d^*})^2$

Anonymous

Anonymous Mon 14 Jun 2021 09:38:26 No.13276635 Report

Quoted By: >>13276652 >>13276663 >>13286528 >>13287948 >>13292971 >>13298848

>>13276489
it should be illegal for women to dress like this

Anonymous

Anonymous Mon 14 Jun 2021 09:38:55 No.13276638 Report

Quoted By: >>13276644 >>13276663 >>13298806 >>13307801 >>13307825

do you guys also get depressed and lose the will to live if you can't solve a problem in the textbook you are going through?

Anonymous

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Anonymous Mon 14 Jun 2021 09:39:20 No.13276640 Report

Quoted By: >>13276663 >>13276796

>>13276478
how do i do c)
i proved that it's invertible and that it has an oblique asymptote towards +inf but idk how to do c)
does the add 1 and subtract 1 trick work for 0^inf?

Anonymous

Anonymous Mon 14 Jun 2021 09:41:47 No.13276644 Report

Quoted By:

>>13276638
No, I merely feel moderate amounts of sadness and frustration

Anonymous

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Anonymous Mon 14 Jun 2021 09:43:43 No.13276648 Report

Quoted By: >>13276663

>>13276478
what math will get me most women?

Anonymous

Anonymous Mon 14 Jun 2021 09:44:50 No.13276652 Report

Quoted By: >>13292971

>>13276635
it should be compulsory

Anonymous

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Anonymous Mon 14 Jun 2021 09:49:15 No.13276663 Report

Quoted By: >>13276671

>>13276638
No, it just means you lack background or it's just hard

>>13276640
I can't imagine the +1 be relevant with those monotonous functions

>>13276648
either, it's not about what you study

>>13276635
go back to your calculus text Elliot

Anonymous

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Anonymous Mon 14 Jun 2021 09:53:50 No.13276669 Report

Quoted By: >>13276809 >>13303551

How do you get fY(y)=1/y?

Anonymous

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Anonymous Mon 14 Jun 2021 09:54:38 No.13276671 Report

Quoted By: >>13303551

>>13276663
yeah, it doesn't work
i thought of writing the function as e^ln(...) but idk if it's worth the effort
I didn't really understand what the answers say either

Anonymous

Anonymous Mon 14 Jun 2021 11:01:48 No.13276796 Report

Quoted By: >>13276831 >>13276836 >>13277047

>>13276640
You just write down the composition.
On the numerator you get 2^(1/x) e^3 --> e^3.
Now, turning the focus to the denominator, you can write it down as
1/x log(exp(2x) +1) =
= 1/x log(exp(2x) * (1 + exp(-2x))
= (1/x * 2x) + (1/x * log(1 + exp(-2x))
--> 2 + 1/Infinity * 0 = 2

So, the entire limit is e^3 / 2

Anonymous

Anonymous Mon 14 Jun 2021 11:09:04 No.13276809 Report

Quoted By: >>13282970

>>13276669
Basically change of variables. By definition, $\int_A f_Y(y) dy = P_Y(A) = P_X(r^{-1}(A)) = \int_{r^{-1}(A)} f_X(x)dx$ As r is increasing, we can change variables by setting $x = r^{-1}(y)$ in the last integral to get $\int_A f_X(r^{-1}(y)) \frac{dr^{-1}(y)}{dy}\ dy$ so we must have $f_Y(y) = f_X(r^{-1}(y)) \frac{dr^{-1}(y)}{dy}$ .

Anonymous

Anonymous Mon 14 Jun 2021 11:19:00 No.13276831 Report

Quoted By: >>13276836

>>13276796
Oops I messed up at the denominator.
Here the correct calculation:

(exp(2x) + 1) ^ (1/x) =
= exp( 1/x log(exp(2x) + 1) )
= exp( 1/x (log(exp(2x) * (1 + exp(-2x)) )
= exp( 2 + log(1 + exp(-2x)) / x)
--> exp(2)

So the answer is e^3 / e^2 = e

Anonymous

Anonymous Mon 14 Jun 2021 11:21:16 No.13276836 Report

Quoted By: >>13276845

>>13276796
>>13276831
ooooooooooooooooooooooooooooooooooooooooooooooohhhhh
wow i'm retarded
thanks anon

Anonymous

Anonymous Mon 14 Jun 2021 11:24:39 No.13276845 Report

Quoted By:

>>13276836
No worries. These are just tricks that you learn by practicing. It's not really about being smart.

Anonymous

Anonymous Mon 14 Jun 2021 12:01:11 No.13276934 Report

Quoted By: >>13276965

>>13276478
HELP /mg/
my textbook says if you have a polynomial ring K[t], a Vectorspace V and an endomorphism f in V, then
*: K[t] x V -> V, (p, v) -> p(f) (v) , where p(f) = a*id + b*f + c* f^2 + ...
defines a module on V
But that does not seem to be the case as far as I can tell since the associative law is not upheld:
p1 * (p2 * v) = p1(f) (p2(f) (v)) != (p1*p2)(f) (v) = (p1*p2) * v
What is my mistake?

Anonymous

Anonymous Mon 14 Jun 2021 12:13:56 No.13276965 Report

Quoted By: >>13276976

>>13276934
What does p1*p2 mean? p2 is not an element of V.

Anonymous

Anonymous Mon 14 Jun 2021 12:17:55 No.13276976 Report

Quoted By: >>13276992 >>13277007

>>13276965
well p1,p2 are in K[t] and multiplication on a polynomial ring is usally defined "pointwise":
(p1*p2) (t) = p1(t)*p2(t)

Anonymous

Anonymous Mon 14 Jun 2021 12:24:58 No.13276992 Report

Quoted By: >>13277010

>>13276976
Yes but you are using the same symbol (*) for two different operations.
*: K[t] x V --> V being associative makes no sense:
p1 * (p2 * v) makes sense, but (p1 * p2) * v doesn't since the defined * is not an operation of K[t] x K[t]

Anonymous

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Anonymous Mon 14 Jun 2021 12:31:36 No.13277007 Report

Quoted By: >>13277010

>>13276976
>>13276976
Maybe you meant property 3 in pic?

Anonymous

Anonymous Mon 14 Jun 2021 12:33:43 No.13277010 Report

Quoted By:

>>13277007
>>13276992
yes associativity is what thats called in my textbook

Anonymous

Anonymous Mon 14 Jun 2021 12:37:11 No.13277022 Report

Quoted By: >>13277026

I'm being a major retard here, but what's the simplest argument to see that $\lim_{x \to \infty} \log (e^{x k} + 1) = k$ for some positive k? I don't see a simple way to get rid of that $+1$ in the log.

Anonymous

Anonymous Mon 14 Jun 2021 12:38:25 No.13277026 Report

Quoted By: >>13277047 >>13303551

>>13277022
fuck I mean $\lim_{x \to \infty} \log (e^{x k} + 1)/x = k$

Anonymous

Anonymous Mon 14 Jun 2021 12:48:04 No.13277047 Report

Quoted By:

>>13277026
1/x log(exp(kx+ 1)) =
= 1/x log( exp(kx) * (1 + exp(-kx)) )
= 1/x kx + log(1+exp(-kx))/x
--> k + log(1)/infinity
= k

See also >>13276796

Anonymous

Anonymous Mon 14 Jun 2021 17:52:13 No.13277795 Report

Quoted By: >>13277809 >>13277940 >>13277957

>one exam left to get my bachelor
>have 0 (zero) motivation to study after three years of continuous studying
mathematically speaking, is there a way out of this

Bismarck

Bismarck Mon 14 Jun 2021 17:58:36 No.13277809 Report

Quoted By:

>>13277795
Not getting the bachelor

Anonymous

Anonymous Mon 14 Jun 2021 18:45:00 No.13277940 Report

Quoted By:

>>13277795
yeah, learn knot theory so you can make a knot to hang yourself

Anonymous

Anonymous Mon 14 Jun 2021 18:52:16 No.13277957 Report

Quoted By:

>>13277795
Alternatively
>one more exam before finally done
>find the motivation to do it one more time for that sweet release afterward

Anonymous

Anonymous Mon 14 Jun 2021 20:02:38 No.13278150 Report

Quoted By: >>13278353 >>13278801 >>13279236 >>13279808

I just came up with the following:
Let $X$ be a topological space. We define a path-covering of $X$ as a set $\mathcal{P}$ of continuous paths $[0,1] \longrightarrow X$ with the following properties:
(i) all paths are non-constant
(ii) the images of two paths do not intersect
(iii) every $x \in X$ lies in the image of some path.

$[0,1]^d$ has a path covering. So does $S^1$ . But what about $S^2$ or $D^2$ ? I think they don't. I also think $(0,1)$ SHOULD not have a path covering but it does - you can keep adding tiny paths to fill out everything. Maybe we can add a new axiom to fix this?
Furthermore:
We say that two path coverings $\mathcal{P}$ and $\mathcal{Q}$ of $X$ are equivalent if there exists a homeomorphism $f: X \longrightarrow X$ so that $f$ becomes a bijection of paths from $\mathcal{P}$ to $\mathcal{Q}$ , up to reparametrization.
The obvious questions are: How many non-equivalent path coverings does a topological space contain? Does $[0,1] \times \R$ have two? Vertical stripes and horizontal stripes?

Anonymous

Anonymous Mon 14 Jun 2021 21:11:46 No.13278353 Report

Quoted By: >>13278362 >>13278393 >>13279343

>>13278150
For the sphere/ball just dilate and rotate your covering for the circle.

Anonymous

Anonymous Mon 14 Jun 2021 21:13:41 No.13278362 Report

Quoted By: >>13278393

>>13278353
Oh nevermind. You need to put a line through the z axis for the ball then surround it with copies of the one for the circle. Not sure about the sphere yet.

Anonymous

Anonymous Mon 14 Jun 2021 21:20:49 No.13278393 Report

Quoted By:

>>13278362
>>13278353
can you draw a picture? my issue was that you will always have a middle point left out - sort of.
At the moment you can always do these weird tricts where you write D^2 for example as an uncountable sum of disjoint tiny line segments - that's probably possible, right?
One should find an axiom which makes it impossible to just fill out the space with tiny line segments. Perhaps every point must have an open neighbourhood that does not fully contain any path?

Anonymous

Anonymous Tue 15 Jun 2021 00:25:54 No.13278801 Report

Quoted By:

>>13278150
Every disk D has a path-covering, since the inclusion of a small cube Q is isotopic to the homeomorphism Q=D. It's true for spheres too, since they're a union of two disks. It's probably true for any CW complex, but I'm too lazy to think through the details.

Anonymous

Anonymous Tue 15 Jun 2021 02:52:49 No.13279236 Report

Quoted By:

>>13278150
do the paths have to be injective?

Anonymous

Anonymous Tue 15 Jun 2021 03:22:33 No.13279343 Report

Quoted By:

>>13278353
Could we just use the Hahn–Mazurkiewicz theorem? Admittedly such a proof would be useless for finding nonequivalent path-coverings.

Anonymous

Anonymous Tue 15 Jun 2021 03:40:04 No.13279393 Report

Quoted By: >>13280970

>>13236860
This was recommended to me by a philosophy graduate student who specializes in logic: https://www.logicmatters.net/tyl/

Looks like a decent annotated bibliography.

Anonymous

Anonymous Tue 15 Jun 2021 03:43:10 No.13279400 Report

Quoted By: >>13292221

>>13276489
kill all women inshallah

Anonymous

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Anonymous Tue 15 Jun 2021 05:55:18 No.13279686 Report

Quoted By: >>13280358 >>13280515 >>13283654

>hey read this book to learn Calculus lmao
>what do you mean its easier to learn from Khan Academy!? Fucking BRAINLET LMAO
Tell me why its better to learn from some old book

Anonymous

Anonymous Tue 15 Jun 2021 07:10:26 No.13279808 Report

Quoted By:

>>13278150
If you are talking about a regular surfaces inside $\mathbb{R}^d<script type="math/tex"> you could just cover them with some local maps from <script type="math/tex"> [0,1]^d$ that don't intersect eachother. By definitions they are injective, so no intersection of paths and the non-constant axiom is still valid, and they would cover all the points on your surface.
So for a sphere you can just map each hemisphere, minus the equator, to a plane by a simple projection and then map the equator to the line.
I'm not really getting the restriction on an interval $[0,1] [\math] instead of a general <script type="math/tex"> [a,b] [\math], since you could always reparametrize your curves to match the interval you want, and get some nice tools from differential geometry too, like Frenet coordinates, embedding in surfaces or just an easier definition of your paths$

Anonymous

Anonymous Tue 15 Jun 2021 11:50:10 No.13280358 Report

Quoted By:

>>13279686
dumb spic

Anonymous

Anonymous Tue 15 Jun 2021 12:55:29 No.13280515 Report

Quoted By:

>>13279686
Up to the end of undergrad stuff it's not the book that matters, it's doing exercises in an analog format such as pen and paper. Your brain cells don't get used as effectively in other methods.

Anonymous

Anonymous Tue 15 Jun 2021 13:11:34 No.13280582 Report

Quoted By: >>13280635 >>13280926

Fellas how the fuck do I survive my PDEs course. The exam is in a week and I have totally lost motivation. It feels like an endless, mindnumbing catalogue of canonical forms, formulas, such dumb shit. They won't really even examine theory and I wouldn't have time for it anyways. It's all so boring and exhausting

Anonymous

Anonymous Tue 15 Jun 2021 13:27:02 No.13280635 Report

Quoted By:

>>13280582
kek

Anonymous

Anonymous Tue 15 Jun 2021 15:08:27 No.13280852 Report

Quoted By: >>13280926

The Lagrangian multiplier method says you can turn a constrained optimization problem into an unconstrained optimization by subtracting the objective by the constraints scaled by Lagrange multipliers. Why does this work? Every textbook and resource I've read glosses over why the constrained optimization problem and the Lagrangian are equivalent.

Anonymous

Anonymous Tue 15 Jun 2021 15:33:28 No.13280926 Report

Quoted By:

>>13280582
Plough through it anon, the nightmare will end soon.

>>13280852
Have you looked at the wiki page for Lagrangian multipliers? I'm pretty sure there must be some resources there. Anyway, letting x denote a tuple of real variables, if $f(x)$ is what you want to minimize subject to $g(x) = 0$ , then what you're asking for is the minimum of f restricted to the hypersurface g = 0 so if p is a point on this surface where the restriction of f attains its minimum, then by the first derivative test and the chain rule, you must have that $\nabla f(p)$ is orthogonal to every tangent vector on the surface i.e. it is perpendicular to the surface, but $\nabla g$ is also perpendicular to the hypersurface, so these two vectors must be proportional: $\nabla f(p) - \lambda \nabla g(p) = 0$ . So basically, you just need to find critical points of $f - \lambda g$ where $\lambda$ is a real parameter.

Anonymous

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Anonymous Tue 15 Jun 2021 15:52:21 No.13280970 Report

Quoted By: >>13281007

>>13279393
This text is really helpful, but I usually don't record it because the Prof is a convicted pedophile

https://www.tcs.cam.ac.uk/cambridge-university-silent-over-pervert-don/

I read his Gödel book and he also made a dismissive remark about constructivists.
This is unexcusable.

Anonymous

Anonymous Tue 15 Jun 2021 16:05:38 No.13281007 Report

Quoted By:

>>13280970
>makes dismissive remark about constructivists
The next step up from being a serial pedophile, according to /sci/.

Anonymous

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Anonymous Tue 15 Jun 2021 22:01:40 No.13281972 Report

Quoted By:

>>13276478
Pine cone appeal on YouTube
https://youtu.be/adnuB9lrjHE

Anonymous

Anonymous Tue 15 Jun 2021 22:38:09 No.13282060 Report

Quoted By: >>13283971

Greetings, I have a non-standard disclamer ultimately related to the topic of this thread and ultimately helpful in regard to far reach.
Some time ago I have completed a book, mostly in Russian
https://www.mediafire.com/file/qyvynvm4pm62c1i
https://www.mediafire.com/view/ubnigki01zr4b1u
consisting of 6 works total. Relevant here is only the first, ???. The first part of that long-story, ??c??a????o??y?a/lettersfromnowhere is concerned with a book I localized as progenitor of both mathematical formalism and modern algebra, Ruffini's 1799 Teoria Generale delle Equazioni, consisting of more than 500 pages.
I don't know Italian and it was written somewhat freeform, so I opted for visual skims and associations concerned, something started coming together off those associations floating up, ??? deals with that.
It's a very intense read, which has two points of import to here. First one is the text file 09, dealing with more or less conceptual culmination of what came together having floated up from the book.
The second one is text file zz, dealing with what I saw as crucial fallacy in what came together regarding the book, formalism as such being extension, it contains a reference to one of the last texts from the file 17.
In the MIDDLE of previous text file, z, I have provided correction to what I ingested in 09 regarding high-level narrative of the book, having mirrored this argument in the style of my part of the writings preceding.
This concerns organization of text, formulae considered abbreviations...

Anonymous

Anonymous Tue 15 Jun 2021 22:39:14 No.13282062 Report

Quoted By: >>13283971

IN THE MIDDLE OF z.txt THERE IS A TEXT BLOCK WITH KEYWORDS "a????y?o?ec??e??oe ?po???e?e??e" / "antiartistical work" EXPANDING OVER 09 WHICH CAN BE FORMALIZED IF NEED BE AS A FIXTURE TO BOOK AS A WHOLE.
THIS PARTICULAR TEXT CAN BE TRANSLATED INTO MATHEMATICAL METHODS COMPATIBLE WITH RUFFINI'S AND NOT MIRRORED BY HIM WHICH CAN PROVIDE FIXTURES WHERE NEED BE.
THIS IS IMPORTANT. THIS IS THE CORRECTION I CAME UP WITH WHILE EMPLOYING MY READING METHODS. RUFFINI'S FORMULAIC LANGUAGE HAS TO BE MAPPED TO HIS PART 09, THEN IT WILL BECOME CLEARER HOW TO FORMALIZE THE CORRECTION.
First, formalization of what he says in 09 with the formulaic language he develops, then formalization of what I say in 09 retorting, then formalization of the development mid-z.txt. The point is this last one.
Good luck. Nevermind, I'm off.

Anonymous

Anonymous Tue 15 Jun 2021 23:44:05 No.13282256 Report

Quoted By: >>13282287

Lang fucking sucks.

Anonymous

Anonymous Tue 15 Jun 2021 23:53:31 No.13282287 Report

Quoted By:

>>13282256
What did you say about my penis?

Anonymous

Anonymous Wed 16 Jun 2021 00:06:14 No.13282333 Report

Quoted By:

>>13276478
Is Topics in Algebra by Herstein and Mathematical Analysis good books to self learn algebra and analysis?

Anonymous

Anonymous Wed 16 Jun 2021 01:35:28 No.13282577 Report

Quoted By: >>13282612 >>13282870

>First order logic using "sets" to define itself (e.g. defining a formal language as a triplet of sets themselves) even though ZF set theory is based on FOL is not redundant since FOL is able to prove equality, this is, the existence of something, and the only thing set theory is doing is giving a semantic intention to that which exists calling it "set"

am I right?

Anonymous

Anonymous Wed 16 Jun 2021 01:41:52 No.13282596 Report

Quoted By: >>13282615 >>13283505 >>13288064 >>13305117 >>13305280

>>13276478
>Be mathematician
>Spend life writing obscure proofs for nonsense that isn't applicable to anything in real life
>Essentially just mentally masturbate all day
>Don't even write anything of vague interest to anyone other than mathematicians, unlike all other sciences and even humanities
>Can't write to save your life
>Can't appreciate art that isn't perfectly symmetrical or describable through calculus
>Can't appreciate poetry
>Can't appreciate literature
>Can't appreciate opera
>Smugly think yourself superior to other humanities (because math, as a subfield of logic, as a subfield of philosophy, is a humanities subject)
>Verbal IQ 95 at best
>No wife
>No kids
>No hobbies
>No personality
>Insufferable in all social settings by everyone, even other mathematicians
>Sit alone and miserable on a mountain of dollar bills that can never buy you happiness
>Wonder why people don't respect you or like you

Anonymous

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Anonymous Wed 16 Jun 2021 01:46:31 No.13282612 Report

Quoted By:

>>13282577
You sure it's not just "What do you mean 'it's circular hence incorrect', do you not understand how primitives fucking work?"

Anonymous

Anonymous Wed 16 Jun 2021 01:47:28 No.13282615 Report

Quoted By: >>13282653

>>13282596
Yeah those people and their mountains of money. They have a hard and sad and lonely life. I prefer it here on the streets with my pookie pipe. No sir, you could keep your mountain of money and the problems that come with it.

Anonymous

Anonymous Wed 16 Jun 2021 01:59:03 No.13282653 Report

Quoted By: >>13300569

>>13282615
Or you could earn a decent wage? It's not like you either earn $400,000/year or $0/year. You can live a comfortable life in my state with an income of $28,000/year or so.

Anonymous

Anonymous Wed 16 Jun 2021 02:06:23 No.13282677 Report

Quoted By: >>13282695 >>13283574 >>13284122

>>13276478
Let "Nonsense" be a value of a function in tri-valued propositional calculus (True, False, Nonsense). In your linguistic intuition:

1) Is the negation of a Nonsensical proposition True or Nonsensical?

2) A conjunction of a True and Nonsensical proposition?

3) A non-exclusive alternative of True and Nonsensical proposition?

Anonymous

Anonymous Wed 16 Jun 2021 02:14:43 No.13282695 Report

Quoted By: >>13284122

>>13282677
Nonsensical.
Nonsensical.
True.

Anonymous

Anonymous Wed 16 Jun 2021 03:28:40 No.13282870 Report

Quoted By:

>>13282577
Forget it, I just found an overflow answer that satisfies me

https://math.stackexchange.com/questions/173735/how-to-avoid-perceived-circularity-when-defining-a-formal-language

good luck people searching in the archives :)

Anonymous

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Anonymous Wed 16 Jun 2021 04:12:36 No.13282970 Report

Quoted By:

>>13276809

Anonymous

Anonymous Wed 16 Jun 2021 04:34:23 No.13282996 Report

Quoted By:

>>13273187
>I like the author but I don't think there's much physics in the book.
So you didn't even read the book and yet you find yourself in a position to make a commentary about it. Modern /mg/, everyone.

Anonymous

Anonymous Wed 16 Jun 2021 04:41:37 No.13283009 Report

Quoted By: >>13283496

How to relearn mathematics?

Anonymous

Anonymous Wed 16 Jun 2021 06:12:19 No.13283264 Report

Quoted By: >>13283495 >>13283496 >>13305126

Self-loathing NEET who only graduated high school. Please post any one book so that get into mathematics again?

Anonymous

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Anonymous Wed 16 Jun 2021 07:28:35 No.13283490 Report

Quoted By:

I'm thinking based

Anonymous

Anonymous Wed 16 Jun 2021 07:31:29 No.13283495 Report

Quoted By: >>13283501

>>13283264
fuck you

Anonymous

Anonymous Wed 16 Jun 2021 07:31:36 No.13283496 Report

Quoted By: >>13283501

>>13283009
>>13283264
Lang Basic Mathematics

Anonymous

Anonymous Wed 16 Jun 2021 07:33:33 No.13283501 Report

Quoted By: >>13283508

>>13283495
Why?
>>13283496
Thank you.

Anonymous

Anonymous Wed 16 Jun 2021 07:35:34 No.13283505 Report

Quoted By: >>13287537

>>13282596
This was good bait until the mountain of dollar bills part.

Anonymous

Anonymous Wed 16 Jun 2021 07:36:36 No.13283508 Report

Quoted By: >>13283515

>>13283501
because this "spam" gets far too common now

Anonymous

Anonymous Wed 16 Jun 2021 07:39:24 No.13283515 Report

Quoted By:

>>13283508
I'm new to this board. Sorry, if I annoyed you.

Anonymous

Anonymous Wed 16 Jun 2021 08:11:31 No.13283574 Report

Quoted By:

>>13282677
>>13282677
These are my intuitions too. What's interesting is when you redefine functions according to old rules, you'll see that these intuitions cannot all be satisfied. Either functions need to be adjusted or intuitions abandoned.

Anonymous

Anonymous Wed 16 Jun 2021 08:56:36 No.13283637 Report

Quoted By: >>13283662 >>13288642 >>13296837

Basic arithmetic survey for mg users:
Could you, in theory, multiply two 50-digit numbers if all you had was a pen and paper?

Anonymous

Anonymous Wed 16 Jun 2021 09:03:00 No.13283654 Report

Quoted By:

>>13279686
For basic undergraduate stuff khan academy is good but you will not be learning the esoteric parts from videos

Anonymous

Anonymous Wed 16 Jun 2021 09:05:25 No.13283662 Report

Quoted By:

>>13283637
yes

Anonymous

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Anonymous Wed 16 Jun 2021 09:10:50 No.13283674 Report

Quoted By: >>13302233

should a solid background in multivariable calc, partial differential equations, complex analysis, and a decent understanding of linear algebra be enough to get into the meat of quantum mechanics? Already took an undergrad course in QM but they simplified a lot of maths for the mathlets in the class.
What else should I get into in my own time?

Anonymous

Anonymous Wed 16 Jun 2021 09:45:18 No.13283751 Report

Quoted By: >>13283767

What is the intuition behind the definition of Compact sets which says "Every open cover has a finite subcover"?

Anonymous

Anonymous Wed 16 Jun 2021 09:56:51 No.13283767 Report

Quoted By:

>>13283751
I always imagined open sets scattered in space. If these are everywhere of course it somehow must be spread out, and if there's a particular spot where we have a lot of them it should be compact

Anonymous

Anonymous Wed 16 Jun 2021 10:37:16 No.13283835 Report

Quoted By: >>13283925 >>13288248

Why does iterating f(x) = 1 + 1/x with initial value in (-1, 1)\{0} converge (to ?)?

Is it a contraction in that interval?

Anonymous

Anonymous Wed 16 Jun 2021 11:15:09 No.13283925 Report

Quoted By: >>13283939

>>13283835
Assume it converges and solve for a fixed point.

Anonymous

Anonymous Wed 16 Jun 2021 11:21:35 No.13283939 Report

Quoted By:

>>13283925
f(x) = x having a solution doesn't imply that f^n (x) converges.

Anonymous

Anonymous Wed 16 Jun 2021 11:38:23 No.13283971 Report

Quoted By:

>>13282060 >>13282062
Algebraical corrects are thus: 1) Distributivity associates, 2) Associativity associates, 3) Zero sum comprises Zero.
Zero is redefined into the center of subjective coordinate systems used in personal understanding of physics, which can be called Mechanical Zero and thus cannot possibly be expanded onto I.
Summation is impossible without 1, you have to sequence the summants.
1x(0+0)=1x0
(0+0)x1=1x(0+0)=1x0=0x1
What does this substitute in Ruffini's work.
1 either ends up self-contradictory (there ending up several different 1-s) or it doesn't, Summation presupposes its integrity, it may end up wrong.
In (0+0)x1=1x(0+0)=1x0=0x1, 1 is strictly the same 1, say 1a.
In other words one have to keep an eye in regard of possible substitution of 1-s.
One is Self-Integral strictly supplants One is Commonspread.
Zero now having definite object, is thus Self-Integral strictly supplanting Zero is Commonspread.
Strict de facto supplant Commonspread -> Self-Integrity is a forced-reinterpretation of the book I call Anti-Purity.
Good luck, never mind.

Anonymous

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Anonymous Wed 16 Jun 2021 12:38:01 No.13284122 Report

Quoted By: >>13284188

>>13282677
>>13282695
If both negation and conjunction of "Nonsensical" propositions result in Nonsensical again, then your logic won't prove non-contradiction schema
not(P and non(P)).
which holds via Modus ponens if False is bottom. This in turn raises the question what rules on inference you can trust/use in that system
Without you having provided more rules, your "Nonsense" seems to work as a falser false.

The Heytng algebras modeling intuitionstic logics prove this (pic related for the smallest semantics).

Anonymous

Anonymous Wed 16 Jun 2021 13:05:24 No.13284188 Report

Quoted By: >>13284588

>>13284122
>This in turn raises the question what rules on inference you can trust/use in that system
I'm having fun with it as a way of exploring the intuitions surrounding nonsense. I seem to have a very clear intuition about conjunction and alternative and almost as strong one about negation. I thought this would help me construct an implication, of which I have no clear intuitions, but it turns out you run into contradictions if you try to define implication in terms of the other functions. This is either interesting for intuition exploring or trivial for some reason I haven't realized yet.
>Without you having provided more rules, your "Nonsense" seems to work as a falser false.
I'll think about it some more when I have a minute, but I think it's possible there might be some intuitive allure of this understanding of the term ("It's not even false!"). I'll also check out if setting the negation of Nonsense as True will fix things. Might be simply that the level of analysis is too broad, as there are different kinds of nonsense (contradictions in terms, empty terms, meaningless statements etc).

Anonymous

Anonymous Wed 16 Jun 2021 14:25:02 No.13284365 Report

Quoted By:

Mathematics is a young man's game. It was over for me before I even started.

Anonymous

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Anonymous Wed 16 Jun 2021 15:52:56 No.13284588 Report

Quoted By:

>>13284188
>but it turns out you run into contradictions if you try to define implication in terms of the other functions
There's implications that break with the one with the simple two valued boolean algebra, see e.g.
https://en.wikipedia.org/wiki/Relevance_logic

The semantics get complicated quickly

Anonymous

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Anonymous Wed 16 Jun 2021 21:47:15 No.13285738 Report

Quoted By: >>13285778

I literally don't even remember how to solve a quadratic equation any more, unless it neatly factorizes

Anonymous

Anonymous Wed 16 Jun 2021 21:57:01 No.13285778 Report

Quoted By:

>>13285738
https://www.youtube.com/watch?v=XKBX0r3J-9Y

Anonymous

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Anonymous Wed 16 Jun 2021 22:52:05 No.13285978 Report

Quoted By:

Anonymous

Anonymous Wed 16 Jun 2021 23:14:32 No.13286062 Report

Quoted By:

>First good mg thread in a month
>All it took was having Tooker as OP

Anonymous

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Anonymous Thu 17 Jun 2021 00:48:59 No.13286446 Report

Quoted By:

>>13276478
How hard should I go into the problems? They are all just really hard, and i am still in the first chapters.

Anonymous

Anonymous Thu 17 Jun 2021 01:10:42 No.13286528 Report

Quoted By:

>>13276635
Inshallah

Anonymous

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Anonymous Thu 17 Jun 2021 05:33:28 No.13287432 Report

Quoted By: >>13287442 >>13287534

>>13276478
Visit my YouTube for math videos!
https://youtu.be/adnuB9lrjHE

Anonymous

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Anonymous Thu 17 Jun 2021 05:35:10 No.13287440 Report

Quoted By:

>>13276478
PineConeappeal.org

Anonymous

Anonymous Thu 17 Jun 2021 05:35:33 No.13287442 Report

Quoted By:

>>13287432
no. fuck off

Anonymous

Anonymous Thu 17 Jun 2021 05:40:39 No.13287456 Report

Quoted By: >>13287460 >>13287471

>bombed an exam
>final year of undergrad
Well, it looks like grad school is not happening. I bought a lot of textbooks on sale, which is now a waste of money. What should I do now?

Anonymous

Anonymous Thu 17 Jun 2021 05:41:32 No.13287460 Report

Quoted By: >>13287476

>>13287456
read the textbooks. They're nice whether or not you're continuing

Anonymous

Anonymous Thu 17 Jun 2021 05:45:36 No.13287471 Report

Quoted By: >>13287476

>>13287456
Also was it a final or just a midterm? I got like straight 65s on my algebraic topology homeworks (no midterms), but I did well (80%) on my final and also everyone else did pretty shit so it was graded on a curve and I ended with an A. Keep you head up king

Anonymous

Anonymous Thu 17 Jun 2021 05:50:16 No.13287476 Report

Quoted By:

>>13287460
Yeah, I guess I’ll be a hobbyist
>>13287471
It was a final exam for my representation theory class. I’m pretty sure I did badly relative to my peers because they’re mostly a pretty smart bunch. It’s nice to hear that you did well, though. Thank you for the encouragement.

Anonymous

Anonymous Thu 17 Jun 2021 06:20:38 No.13287534 Report

Quoted By:

>>13287432
kys

Anonymous

Anonymous Thu 17 Jun 2021 06:21:42 No.13287537 Report

Quoted By:

>>13283505
But it’s true.

Anonymous

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Anonymous Thu 17 Jun 2021 09:23:21 No.13287948 Report

Quoted By:

>>13276635
Ok Abdul

Anonymous

Anonymous Thu 17 Jun 2021 10:24:19 No.13288064 Report

Quoted By: >>13288661 >>13310177

>>13282596
>be mathematician
>your work is being used to detect prion diseases
>essentially just mentally masturbate all day
>only 160+ IQ geniuses can understand your work, ignore the plebs
>Can't write to save your life, just like 99.9% of other humans
>spend 3-4 hours every day working through the canon of western literature, genuine appreciation for art
>finished music school
>Know yourself to be superior to humanities
>Verbal IQ tested to be 140 when I was a child, higher even than non-verbal
>No Wife, can't settle for just one hoe
>No Kids (lmao)
>No need to rationalize useless pathologies as hobbies or irrational tendencies as personality.
>Insufferable in all social settings by everyone, even other mathematicians, don't crave for social approval
>Sit alone on a mountain of dollar bills that can never buy you happiness
>Know that people don't respect you, don't give a shit, because I am not an oversocialized faggot who thinks social approval is what redeems human beings

Anonymous

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Anonymous Thu 17 Jun 2021 10:32:57 No.13288092 Report

Quoted By: >>13288124 >>13288154

Brainlet here, I'm writing a program and I need an equation that can describe a curve like this.
f(x) = ???????

Anonymous

Anonymous Thu 17 Jun 2021 10:50:20 No.13288124 Report

Quoted By: >>13292199

>>13288092
the integral of exp (-x^2)

Anonymous

Anonymous Thu 17 Jun 2021 11:08:42 No.13288154 Report

Quoted By: >>13292199

>>13288092
https://en.wikipedia.org/wiki/Sigmoid_function
https://youtu.be/X1mo7Uwvzn8

Anonymous

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Anonymous Thu 17 Jun 2021 11:33:45 No.13288212 Report

Quoted By:

I don't know what I just figured out but
0=P?N

Anonymous

Anonymous Thu 17 Jun 2021 11:56:21 No.13288248 Report

Quoted By: >>13288408 >>13288454 >>13288464

>>13283835
Anyone?

Anonymous

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Anonymous Thu 17 Jun 2021 12:51:07 No.13288408 Report

Quoted By: >>13288464

>>13288248
Empirically I say yes

https://www.wolframalpha.com/input/?i=NestList%5B%281%2B1%2F%23%29%26%2C+-0.3%2C+20%5D

Where the thing down as under x=f(x) fixed point assumption and solve for it, to see if it makes sense.
If so, check the books for the requirements (convexity or whatever) in your intervsl

Anonymous

Anonymous Thu 17 Jun 2021 12:55:47 No.13288425 Report

Quoted By:

write*

Anonymous

Anonymous Thu 17 Jun 2021 13:10:16 No.13288454 Report

Quoted By: >>13288464 >>13288485

>>13288248
Let $x_0 \in (-1, 1)/\{0\}$ and define $x_{n+1} = f(x_n)$ . If $x_0 \in (0, 1)$ , then it's not hard to see that $x_n \in [3/2, 2]$ , for all $n \geq 4$ and f is a contraction mapping there so the sequence converges. If $x_0 \in (-1, 0)$ and is the negative of the quotient of two consecutive Fibonacci numbers, then you eventually reach $x_n = 0$ , so you should exclude such points. Assuming you've done that, if $x_n \in (-\infty, -1 + \epsilon) \cup (-\epsilon, 0)$ for some small epsilon, then after a few more iterations, you eventually reach a positive number and the sequence converges as before. On the other hand, if $x_n, x_{n+1} \in [-1 + \epsilon, -\epsilon]$ , then as |f'| is bounded below by some quantity strictly greater than 1 on that interval, $x_{n+1} and x_{n+2}$ will be even further apart. I think it shouldn't be hard to then show that the sequence eventually escapes this compact interval so that it also eventually becomes positive and converges. Disclaimer: I haven't checked any of this in detail.

Anonymous

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Anonymous Thu 17 Jun 2021 13:16:37 No.13288464 Report

Quoted By: >>13288485

>>13288248
>>13288408
>>13288454
I just went through the steps I outlined in >>13288408 myself and turns out that $\frac{1-\sqrt{5}}{2} = --0.618034\dots$ is an isolated fixed point. I say isolated in that trying to deviate by $\pm 10^{-4}$ makes it go back to phi.

Anonymous

Anonymous Thu 17 Jun 2021 13:28:24 No.13288485 Report

Quoted By: >>13288573

>>13288464
That's probably related to the fact that the initial point shouldn't be any of -1, -1/2, -2/3, -3/5, etc. that I pointed out here >>13288454. The limit point of this sequence is exactly 1 - phi, the other fixed point of this function. As long as you don't start with these numbers, the sequence should converge to phi I think.

Anonymous

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Anonymous Thu 17 Jun 2021 14:06:11 No.13288573 Report

Quoted By: >>13288618

>>13288485
Okay I just saw that, explicitly,

$f^n(x/y) = \frac{s(n)}{s(n-1)}$

with

$s(n) = x\, F_{n+1} + y\, F_{n}$

which explains the eventual zero for consecutive F_n's.

As
$\varphi\, F_{k+1} + 1\, F_{k} = \varphi^{k+1}$
this would mean
$f^n(x) = \frac{\varphi^{n+1} + (x-\varphi)\,F_{n+1}}{\varphi^{n} + (x-\varphi)\,F_{n}} \approx \varphi$

and maybe the other fixed pint can also be explained algebraically, by expressing $-\varphi^{-1}=-0.6...$ as a power series in the fibs indeed

Anonymous

Anonymous Thu 17 Jun 2021 14:25:11 No.13288618 Report

Quoted By: >>13288622

>>13288573
The only way to reach the other fixed point 1 - phi = -1/phi would be to start at it, if my proof sketch in that earlier post is right.

Anonymous

Anonymous Thu 17 Jun 2021 14:26:36 No.13288622 Report

Quoted By:

>>13288618
*By reach I mean converge. The only way to actually reach it in a finite number of iterations is obviously by starting with it.

Anonymous

Anonymous Thu 17 Jun 2021 14:40:04 No.13288642 Report

Quoted By:

>>13283637
Give me two such numbers. I'll do it and post the picture of the piece of paper.

Anonymous

Anonymous Thu 17 Jun 2021 14:47:56 No.13288661 Report

Quoted By: >>13288728

>>13288064
then why do you post here

Anonymous

Anonymous Thu 17 Jun 2021 15:13:09 No.13288728 Report

Quoted By:

>>13288661
Because I have a very immature sense of humour

Anonymous

Anonymous Thu 17 Jun 2021 17:19:24 No.13289263 Report

Quoted By: >>13289801

how do i understand any of this shit

Anonymous

Anonymous Thu 17 Jun 2021 18:04:58 No.13289464 Report

Quoted By: >>13289857 >>13292344 >>13292648 >>13303551

Let $X=\mathbb{R}^{\mathbb{R}}=\{f:\mathbb{R} \rightarrow \mathbb{R}: f \text{ is continuous}\}$ with the product topology (a.k.a the topology of pointwise convergence or point-open topology).
How can I show that $X$ is not locally compact. I was given the following hint: check pre-image of any neighborhood under the canonical projection.
what can I do with that?

Anonymous

Anonymous Thu 17 Jun 2021 19:26:33 No.13289801 Report

Quoted By:

>>13289263
Study math for a few years.

Anonymous

Anonymous Thu 17 Jun 2021 19:42:04 No.13289857 Report

Quoted By: >>13289984

>>13289464
Sounds like a "compact set can't continuously surject onto non-compact set" argument.
>>>/sci/sqt for further assistance/spoonfeeding.

Anonymous

Anonymous Thu 17 Jun 2021 20:17:35 No.13289984 Report

Quoted By:

>>13289857
Shut up.

Anonymous

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Anonymous Thu 17 Jun 2021 20:27:08 No.13290025 Report

Quoted By: >>13290077 >>13290212

Hi I'm a noob pls no bully. Just starting Velleman. For question 1C, my solution is on top and Velleman's is on the bottom. Are they equivalent? If not, what did I fuck up? Thanks. No this isn't homework, I'm a musician.

Anonymous

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Anonymous Thu 17 Jun 2021 20:43:45 No.13290077 Report

Quoted By: >>13290359 >>13291066

>>13290025
Your solution is false because, firstly, y isn't bound.
Basically the book uses a constant term m to avoid the open y.

If we do add $\forall y$ , then it leads to wrong conclusions.
$\forall x[P(x)\land Q(x)]$
implies
$\forall x[P(x)]$
(right projection, categorically speaking)
So your solution
$\forall x\forall y[L(x,y)\land \neg M(y)]$
implies
$\forall x\forall y[L(x,y)]$
but that's false since Mary doesn't like herself.

Your M(y) is of course also just y=m.

You can get an equivalent solution to the book solution that looks similar to yours.
Namely $P\lor Q$ implies $\neg P\implies Q$ and classically you can turn that around to get
$\forall x[(x=m)\lor L(x,m)]$
"for everybody holds that they either are Mary or like her"

That said, the book solution is also wrong, since it doesn't prove that Mary dislikes herself, which is implied by the text.

>I'm a musician.
lel
https://youtu.be/1sVQ4QhU4fg

Anonymous

Anonymous Thu 17 Jun 2021 21:21:21 No.13290212 Report

Quoted By: >>13290359

>>13290025
As I understand it, your solution doesn't say anything about Mary. It just says that every person likes the Y person and that Mary is not Y. Who is Y though?

Anonymous

Anonymous Thu 17 Jun 2021 22:05:02 No.13290359 Report

Quoted By:

>>13290077
>>13290212
Thanks a lot

Anonymous

Anonymous Fri 18 Jun 2021 02:37:47 No.13291066 Report

Quoted By: >>13292271 >>13292291

>>13290077
What does right projection mean?

Anonymous

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Anonymous Fri 18 Jun 2021 04:45:29 No.13291448 Report

Quoted By: >>13292271 >>13292291 >>13292319 >>13292682

I understand the intersection/ union of a family of sets, but I do not understand these definitions at all. Perhaps the brackets are throwing me off. Would the intersection of family F be translated into something like "the sets of values of x such that all sets A are elements of family F in which x is an element of A" ? Please correct me if I'm wrong, I'm trying to understand the formal definitions, not just the concept. It seems that there's an element of literacy that needs to be practiced here.

Anonymous

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Anonymous Fri 18 Jun 2021 09:09:12 No.13292116 Report

Quoted By:

Give nerd bf

Anonymous

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Anonymous Fri 18 Jun 2021 09:58:19 No.13292199 Report

Quoted By: >>13292468

>>13288154
>>13288124
This is definitely what I'm looking for, thanks.
I've done some thinking and realized that going forwards, I'm going to need to relearn calculus (haven't used it since high school) and learn the math/physics behind things like orbits and time dilation for a game I eventually plan on making.

What are some good resources to pick up that kind of stuff?

Anonymous

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Anonymous Fri 18 Jun 2021 10:16:17 No.13292221 Report

Quoted By: >>13304254

>>13279400

Anonymous

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Anonymous Fri 18 Jun 2021 10:44:55 No.13292271 Report

Quoted By:

>>13291066
Left projection rather, in this case.
Under left and right Conjunction Elimination here
https://en.m.wikipedia.org/wiki/List_of_rules_of_inference

>>13291448
F is an already fixed set of sets (say there are 5 such sets A1, A2, ... A5 in F.
The intersection here is a set obtained by collecting all x that are in each of those five sets.
B:={x | forall (A in F). (x in A)}
is
>B denotes the class of all x (taken from the universe of sets, our domain of discourse, the sets) for which the following property holds: For all sets A in the set F, x belongs to A.

For any x that's provably in all the A's, this property is true and so it's taken to be part of B. Otherwise, not.

The axiom of Union says B is a set itself (meaning it is now also part of the domain of discourse)

Anonymous

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Anonymous Fri 18 Jun 2021 10:55:08 No.13292291 Report

Quoted By:

>>13291066
Left projection rather, in this case.
Under left and right Conjunction Elimination here

https://en.m.wikipedia.org/wiki/List_of_rules_of_inference

>If it's the case that I'm tall and bald, then it's also the case that I'm bald

In terms of provability, if you have a proof for "P and Q", then the rule claims you also have a proof for P.
This is "projecting the left component". Or you could say it eliminates the right side/omponent

>>13291448 #
F is an already fixed set of sets (say there are 5 such sets A1, A2, ... A5 in F.
The intersection here is a set obtained by collecting all x that are in each of those five sets.
B:={x | forall (A in F). (x in A)}
is
>B denotes the class of all x (taken from the universe of sets, our domain of discourse, the sets) for which the following property holds: For all sets A in the set F, x belongs to A.

For any x that's provably in all the A's, this property is true and so it's taken to be part of B. Otherwise, not.

Similar for union. The axiom of Union says B is a set itself (meaning it is now also part of the domain of discourse)

Anonymous

Anonymous Fri 18 Jun 2021 11:13:25 No.13292319 Report

Quoted By:

>>13291448
the union of the set F := (by definition) the union of all elements of F = the set of all x such that x is a member of at least one f ? F = the set of all x such that there exists f ? F such that x ? f
the intersection of the set F := (by definition) the intersection of all elements of F = the set of all x such that x is a member of all f ? F = the set of all x such that there for all f ? F we have x ? f

Anonymous

Anonymous Fri 18 Jun 2021 11:25:23 No.13292344 Report

Quoted By:

>>13289464
If it were locally compact, then there would be a basic neighborhood U of the form product A_i where all but finitely many i's have A_i = R and for others A_i=(a_i, b_i), whose closure is compact. But the projection functions are continuous, and the image under a continuous map of a compact set is compact, so taking i such that A_i=R, the i'th projection is R, which contradicts the fact that R is not compact.

Anonymous

Anonymous Fri 18 Jun 2021 12:40:14 No.13292468 Report

Quoted By: >>13292495 >>13295901 >>13296588

>>13292199
Basic Mathematics, Lang
then:
any good Calculus book
any good Linear Algebra book
University Physics with Modern Physics, Young and Friedman

If you want to make a Kerbal Space Program or Planetary Annihilation ripoff and can do the necessary programming and 3d modelling already those books are all you need. You might need more physics knowledge if you want to ape something like Children of a Dead Earth or C:MANO though.

Anonymous

Anonymous Fri 18 Jun 2021 12:56:14 No.13292495 Report

Quoted By:

>>13292468
CMANO is amazing, nice to see it in /mg/

Anonymous

Anonymous Fri 18 Jun 2021 14:17:49 No.13292648 Report

Quoted By:

>>13289464
Not to be pedantic or anything, but $\mathbb{R}^{\mathbb{R}}$ isn't a good notation for continuous real functions, since that is the notation for general functions from R to R. Use $\mathcal{C}^{0}(\mathbb{R})$ instead, that's the standard notation.

Anonymous

Anonymous Fri 18 Jun 2021 14:35:46 No.13292682 Report

Quoted By: >>13292726

>>13291448
I understand the definition on the right, but what the fuck does $\mathcal{F}(x \in A)[\math] mean? Never seen that notation. Also, what book is that?$

Anonymous

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Anonymous Fri 18 Jun 2021 14:53:19 No.13292726 Report

Quoted By:

>>13292682
It's bad kerning.

$\forall (A \in F).\ (x \in A)$

Anonymous

Anonymous Fri 18 Jun 2021 16:13:45 No.13292971 Report

Quoted By:

>>13276635
>>13276652
not sure which one is more based

Anonymous

Anonymous Fri 18 Jun 2021 18:56:33 No.13293555 Report

Quoted By: >>13295721 >>13310180

>GPA in the high 3.6's
>major GPA much lower

If I have good letters of recommendation, do I have any shot at a top 20 university? I'm in Burgerland.

Anonymous

Anonymous Fri 18 Jun 2021 19:55:40 No.13293768 Report

Quoted By: >>13293995

>>13276478
Today I thought about killing myself because I can't comprehend basic twelve grade math manipulation to which I've been studying harduously for the past couple of months.

Anonymous

Anonymous Fri 18 Jun 2021 21:04:39 No.13293985 Report

Quoted By: >>13304170 >>13308078

What textbooks do you recommend to learn differential geometry?

I'm learning it to lean on to general Relativity, but I'd also just like to understand the subject more completely, beyond just it's application to GR. What's the best book(s) to start with?

Anonymous

Anonymous Fri 18 Jun 2021 21:07:34 No.13293995 Report

Quoted By: >>13294733

>>13293768
What are you struggling with specifically? Honestly everything up to and including multivariable calculus you just learn by doing many problems and learn shit through repetition, and fully grasp the topic after you can actually use it.

Anonymous

Anonymous Sat 19 Jun 2021 00:11:56 No.13294640 Report

Quoted By:

>teacher leaves homework
>exercise is not anywhere on books or the internet
I hate complex analysis so much

Anonymous

Anonymous Sat 19 Jun 2021 00:34:29 No.13294733 Report

Quoted By: >>13295685 >>13302241

>>13293995
Im struggling with limits. The manuals I have don't seem to cover all of the intricacies related to the resolution of the problems that appear on the exams.

Anonymous

Anonymous Sat 19 Jun 2021 00:45:59 No.13294766 Report

Quoted By: >>13296356 >>13296374

Nature had an article on software theorem provers (Lean).
https://tinyurl
.com/a2xtk4ms

Anonymous

Anonymous Sat 19 Jun 2021 04:24:10 No.13295685 Report

Quoted By:

>>13294733
Can you give an example problem?

Honestly, limits is a really good example of something you understand better after you've done some higher level math (namely calculus and analysis) so don't get too put out if you don't grasp it all entirely when you first meet it.

Anonymous

Anonymous Sat 19 Jun 2021 04:42:07 No.13295721 Report

Quoted By:

>>13293555
None honestly, sorry.

Anonymous

View Same Google iqdb SauceNAO learn maffs.png, 3MiB, 4125x2400

Anonymous Sat 19 Jun 2021 06:30:52 No.13295901 Report

Quoted By: >>13296350

>>13292468
I'll look into this stuff, thanks.
There's also this pic I've seen posted around in /g/ for reading material, what's /sci/'s take on it?

Anonymous

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Anonymous Sat 19 Jun 2021 07:12:56 No.13296015 Report

Quoted By: >>13296349 >>13296444

How would I go about showing that this is the case?

Anonymous

Anonymous Sat 19 Jun 2021 09:35:14 No.13296349 Report

Quoted By: >>13296412

>>13296015
by writing both sides in expanded form?

Anonymous

Anonymous Sat 19 Jun 2021 09:35:35 No.13296350 Report

Quoted By: >>13296577

>>13295901
The order is fucked, and there's stuff you don't need. How much do you already know?

Anonymous

Anonymous Sat 19 Jun 2021 09:40:01 No.13296356 Report

Quoted By:

>>13294766
thx for sharing

Anonymous

Anonymous Sat 19 Jun 2021 09:46:27 No.13296369 Report

Quoted By:

Trigonometry doesn't even work!
https://www.youtube.com/watch?v=eXlHHZjNy_I&t=0s

Anonymous

Anonymous Sat 19 Jun 2021 09:48:12 No.13296374 Report

Quoted By:

>>13294766
Did they ever rename coq due to it being insensitive to people who have to say the name?

Anonymous

Anonymous Sat 19 Jun 2021 10:14:05 No.13296412 Report

Quoted By: >>13296416

>>13296349
but isn't there some more efficient way? doing this would take quite a bit of time, no?

Anonymous

View Same Google iqdb SauceNAO unknown-13.png, 58KiB, 413x508

Anonymous Sat 19 Jun 2021 10:15:29 No.13296415 Report

Quoted By: >>13297117

Is this a good guide?

Anonymous

Anonymous Sat 19 Jun 2021 10:15:30 No.13296416 Report

Quoted By:

>>13296412
If there is wouldn't it be in whatever book this is from?

Anonymous

Anonymous Sat 19 Jun 2021 10:18:08 No.13296418 Report

Quoted By:

>>13276573
Linear algebra

Anonymous

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Anonymous Sat 19 Jun 2021 10:21:30 No.13296422 Report

Quoted By: >>13296444 >>13296461

do you guys know the banach-tarski paradox? could you explain it in layman’s terms?

Anonymous

Anonymous Sat 19 Jun 2021 10:30:56 No.13296444 Report

Quoted By: >>13296502

>>13296422
Watch this vsauce video: https://www.youtube.com/watch?v=s86-Z-CbaHA

>>13296015
If you replace B and C by -1, this is just the multiplicativity of the usual norm for quaternions, so that's where you can look.

Anonymous

Anonymous Sat 19 Jun 2021 10:38:04 No.13296461 Report

Quoted By:

>>13296422
consider this procedure: take a shape, decompose it into finitely many pieces, rotate each piece, then move the pieces to assemble a new shape. intuition says that the volume of the original shape and the new shape should be the same. the banach-tarski construction shows that it's not true: it's possible to decompose a solid ball into 5 pieces and rotate them such that they can be assembled to form two solid balls, each of the same volume you've started with.

Anonymous

Anonymous Sat 19 Jun 2021 10:56:57 No.13296502 Report

Quoted By: >>13296550

>>13296444
if i don't know what quaternions are, i have to go about it the usual way?

Anonymous

Anonymous Sat 19 Jun 2021 11:12:42 No.13296543 Report

Quoted By: >>13310254

>>13276478
Time series forecasting Chads,
I need some of your guidance to how to approach this problem.
I have one time series that i need to predict but its probably dependent on several other variables that are also dependent on time. What would be the name of this problem on time series forecasting?
The theory is vast and im new to this, never done time dependent analysis before.
In summary- one variable dependent on time to predict that is also dependent on some other time dependent variables.
I guess you could always use convolutional neural nets to approach this but id rather start with something less elaborate with more theory built around it.

Anonymous

Anonymous Sat 19 Jun 2021 11:16:21 No.13296550 Report

Quoted By:

>>13296502
No idea, there might be much more simple proofs too. You could also prove it using some basic properties of 2 by 2 matrices and determinants if you know about those.

Anonymous

Anonymous Sat 19 Jun 2021 11:36:09 No.13296577 Report

Quoted By: >>13296588

>>13296350
I reckon I can comfortably pick up geometry, algebra, and quadratic equations easily, but everything beyond that such as calculus and vectors are concepts I haven't even thought about in the last 10 years, so I'm going to be pretty rusty there.

Anonymous

Anonymous Sat 19 Jun 2021 11:43:37 No.13296588 Report

Quoted By: >>13296823

>>13296577
That chart says 'foundational approach'. So unless you're into the foundations of mathematics like logic and sets and all that it's a bad idea. Another anon suggested stuff to you here:
>>13292468
That's fine. You can look at MIT OCW if you want calculus and linear algebra and intro physics lectures to go along with it.
Don't fret too much over the right books, just do it as the saying goes.

Anonymous

Anonymous Sat 19 Jun 2021 13:18:47 No.13296823 Report

Quoted By:

>>13296588
Trust me, I'd rather not have to read a dozen books just to program a game. Thanks for the recommendations.

Anonymous

Anonymous Sat 19 Jun 2021 13:25:08 No.13296837 Report

Quoted By:

>>13283637
Yes, indeed. I worked with the Trachtenberg
method and, following basic rules of multiplying
certain numbers (not rote-memorization) the
answer can be found within five minutes--
or three minutes if one is quick of mind.

Anonymous

Anonymous Sat 19 Jun 2021 15:24:19 No.13297117 Report

Quoted By:

>>13296415
basic math lang is a meme the errata for that book is another book
the best fill in the gaps is to go through a book that interests you and is reasonably hard and when you meet something you don't remember / feel shaky with, just google and learn

Anonymous

Anonymous Sat 19 Jun 2021 16:54:37 No.13297360 Report

Quoted By: >>13297523 >>13297548 >>13303551

Is there a term for functions $g$ such that
$\lim_{x \to \infty} \frac{\log g ( f( x ))}{x} = \lim_{x \to \infty} \frac{\log f( x )}{x}$ for any f,
that is, the function g is "asymptotically irrelevant"? This holds for linear functions but not sure what else.

Anonymous

View Same Google iqdb SauceNAO vulkan.gif, 3MiB, 498x280

Anonymous Sat 19 Jun 2021 17:55:28 No.13297523 Report

Quoted By:

>>13297360
>This holds for linear functions but not sure what else.

$\frac{\log(c\cdot f(x))}{x} = \frac{\log\, f(x)}{x} + \frac{\log\,c}{x}$
so it holds for linear functions because c loses out against c.

I was first reminded of
https://en.wikipedia.org/wiki/Logarithmically_convex_function
but I don't think the class of functions is so interesting.
I note that it already breaks for $g(x):=x^{1+\varepsilon}$ , for small finite $\varepsilon$ , by a similar analysis.
$\frac{ f(x)^{ 1+\varepsilon } } { x } = (1+\varepsilon) \frac{ f(x) }{ x } \neq \frac{ f(x) }{ x }$
so I don't expect much.

I suppose it holds whenever application by g is effectively a multiplication by a function h that grows less strongly than exp, as
$\dfrac{\log(h(x)\cdot f(x))}{x} = \frac{\log\, f(x)}{x} + \dfrac{\log\,h(x)}{x}$
although in that case we don't speak of g as a function on R anymore.

Anonymous

Anonymous Sat 19 Jun 2021 18:02:47 No.13297548 Report

Quoted By:

>>13297360
f(x) = Theta(x)?

Anonymous

View Same Google iqdb SauceNAO Screen Shot 2021-06-19 at 14.35.43.jpg, 52KiB, 540x568

Anonymous Sat 19 Jun 2021 19:46:25 No.13297918 Report

Quoted By: >>13297970

Math brainlet here studying basic linguistics for grad school, finishing a semantics book as I type this. I got exposed for the first time to a bunch of concepts all at once while reading:

> Frege's sense and reference
> predicate logic
> lambda functions
> set theory

Gotta admit, my asshole's torn out from this stuff. I can wrap my head around most of it, but I couldn't really apply what I knew to specific problems after my first reading. Took some notes, and hopefully it makes more sense if I encounter it again

Anonymous

View Same Google iqdb SauceNAO 1623504422876.jpg, 66KiB, 750x717

Anonymous Sat 19 Jun 2021 19:59:11 No.13297970 Report

Quoted By: >>13298013

>>13297918
How can I subscribe to your blog?

Anonymous

Anonymous Sat 19 Jun 2021 20:06:20 No.13298013 Report

Quoted By: >>13298094

>>13297970

Simple, DM my Grindr account, and I'll tell you everything after some morning eggs

Anonymous

Anonymous Sat 19 Jun 2021 20:23:37 No.13298094 Report

Quoted By: >>13298109

>>13298013
do I have to eat the whole bowl?

Anonymous

Anonymous Sat 19 Jun 2021 20:27:51 No.13298109 Report

Quoted By: >>13298841

>>13298094

Just enough of 'em
they're over medium, just the way we like them :)

Anonymous

Anonymous Sat 19 Jun 2021 23:30:14 No.13298746 Report

Quoted By: >>13298841 >>13299194 >>13299963

I'm doing a PhD in algebraic number theory, AMA.
I just finished my first year and my thesis will probably be on p-adic Hodge theory and Shimura varieties.

Anonymous

Anonymous Sat 19 Jun 2021 23:46:32 No.13298806 Report

Quoted By:

>>13276638
how can you come here with your feelings and not post one of the problems you can't solve?!?!
just get it off your chest already!!

Anonymous

Anonymous Sat 19 Jun 2021 23:59:26 No.13298841 Report

Quoted By: >>13299063

>>13298746
>AMA
Did >>13298109 recognize the reference and then pretend he didn't or did he just not recognize the reference?

Anonymous

Anonymous Sun 20 Jun 2021 00:01:24 No.13298848 Report

Quoted By:

>>13276635
mashallah

Anonymous

Anonymous Sun 20 Jun 2021 01:35:39 No.13299063 Report

Quoted By:

>>13298841

Of course, and I really like my eggs over medium, with runny yolks

Anonymous

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Anonymous Sun 20 Jun 2021 02:23:19 No.13299194 Report

Quoted By: >>13301030

>>13298746
Please tell me you aren't this faggot.

Anonymous

Anonymous Sun 20 Jun 2021 02:56:53 No.13299287 Report

Quoted By: >>13299293 >>13299313

given a positive integer k, what's the probability that neither 6k -1 nor 6k + 1 is prime?

Anonymous

Anonymous Sun 20 Jun 2021 03:00:58 No.13299293 Report

Quoted By: >>13299340

>>13299287
It tends to 1 as k increases.

Anonymous

Anonymous Sun 20 Jun 2021 03:07:49 No.13299313 Report

Quoted By:

>>13299287
Either zero or one.

Anonymous

Anonymous Sun 20 Jun 2021 03:12:09 No.13299324 Report

Quoted By: >>13299331 >>13299888

Mathematicians try to disassociate themselves from physics and physicists try to pretend physics is purely intuitional in an attempt to disassociate themselves from mathematics. Why? Everything is connected. Math is useless without physics and physics is useless without math and here I define usefulness in the only way possible: to learn the truth.

Anonymous

Anonymous Sun 20 Jun 2021 03:14:09 No.13299331 Report

Quoted By: >>13299364

>>13299324
>Math is useless without physics
Math would still be very much useful without physics, Arnold-chan.
Accounting, computer science, biomathematics, economics, statistics, etc.

Anonymous

Anonymous Sun 20 Jun 2021 03:16:21 No.13299340 Report

Quoted By: >>13299352

>>13299293
You don't know that. If we assume the Riemann Hypothesis and some other stronger conjectures we know that statement is true for primes separated by 6, but not 2.

Anonymous

Anonymous Sun 20 Jun 2021 03:18:47 No.13299352 Report

Quoted By: >>13299947 >>13300056 >>13310262

>>13299340
what's so special about 6 such that {6k-1,6k+1} generates all prime numbers? is it that {2,3} are the first {2} primes, and hence 2x3 generates all primes? any salience to this?

Anonymous

Anonymous Sun 20 Jun 2021 03:20:56 No.13299364 Report

Quoted By:

>>13299331
Are you blind? Did you not see the way I defined usefulness right after the part you quoted? The things you mentioned are "useful" for a society, nothing else. True usefulness relates to the truth.

Anonymous

Anonymous Sun 20 Jun 2021 06:54:25 No.13299888 Report

Quoted By:

>>13299324
>truth
lol

Anonymous

View Same Google iqdb SauceNAO riddler.png, 549KiB, 1920x3532

Anonymous Sun 20 Jun 2021 07:12:00 No.13299932 Report

Quoted By:

I want to know how to do the math.

Anonymous

Anonymous Sun 20 Jun 2021 07:16:22 No.13299947 Report

Quoted By:

>>13299352
just that 1 and 5 are the only 0 < k < 6 which are relatively prime to 6

Anonymous

Anonymous Sun 20 Jun 2021 07:24:23 No.13299963 Report

Quoted By:

>>13298746
Have you passed your quals yet?

Anonymous

View Same Google iqdb SauceNAO 8bce661fcffa894de078045cb51c4cb0 (...).gif, 5KiB, 345x480

Anonymous Sun 20 Jun 2021 07:26:05 No.13299968 Report

Quoted By: >>13300051 >>13300460

Hi guys, I really your help for this one.

Let's say you have an oblique cone with the same height and width x. The cone is special in that it has no rotational shear strength whatsoever. You draw a straight line down from its tip to the edge of its base. Then you roll the cone exactly one time.

Because the cone has no rotational shear strength, each infinitesimal "slice" rotates at a different speed, approaching infinity at the tip. The cone rolled in a straight line, but the line you drew is now wrapped around the cone.

What is the equation for the the elevation of the line? I think it should look something like this. Please help me :(

Anonymous

Anonymous Sun 20 Jun 2021 08:09:05 No.13300051 Report

Quoted By: >>13300075

>>13299968
Is there a right angle between the base and the shortest line along the slope from the base to the apex?

Anonymous

Anonymous Sun 20 Jun 2021 08:10:37 No.13300056 Report

Quoted By:

>>13299352
Because 6 is a perfect number for which the non-unitary divisors are prime.

Anonymous

Anonymous Sun 20 Jun 2021 08:26:26 No.13300075 Report

Quoted By: >>13300312

>>13300051
No it would be 45 degrees because the line take the "long way" down to the apex, if that makes sense

Anonymous

Anonymous Sun 20 Jun 2021 10:39:33 No.13300312 Report

Quoted By: >>13301268

>>13300075
Then why is there a small square in that pseudo-corner?

Anonymous

Anonymous Sun 20 Jun 2021 11:39:30 No.13300446 Report

Quoted By:

How do l prove that all convex Jordan curves with no cusps are infinitely differentiable?

Anonymous

Anonymous Sun 20 Jun 2021 11:44:17 No.13300460 Report

Quoted By:

>>13299968
I can't give you a proof method but it's easy to compute if you unroll the cone around it's shortest generatrix and turn the line the cone rolls on into a curve on the flattened sector.

Anonymous

Anonymous Sun 20 Jun 2021 12:31:31 No.13300569 Report

Quoted By:

>>13282653
I might not be an american, but i'm sure that's not enough to have a wife and 2-4 kids. I mean, you want to have a big family right?

Anonymous

Anonymous Sun 20 Jun 2021 12:43:48 No.13300604 Report

Quoted By: >>13300621

is every compact subset of R^n the intersection of a nested sequence of finite unions of compact convex subsets?

Anonymous

Anonymous Sun 20 Jun 2021 12:49:32 No.13300621 Report

Quoted By: >>13300631 >>13300641

>>13300604
Yes. Let X be compact. For each n, cover X with closed balls of radius 1/n centered at points of X. By compactness we can take such cover to be finite. The only problem is that such a sequence n-> cover may not be nested. You fix that by making the radius possibly smaller than 1/n, such that each ball in the cover is contained in an open ball of the previous cover, since the union of the open balls in the previous cover is open. To prove that the intersection of such covers is X, take a point y outside of x and let d be the distance from y to X, which exists since X is compact. Once the balls in the covers get smaller than d, y will be outside of the cover. Hence we're done.

Anonymous

Anonymous Sun 20 Jun 2021 12:53:35 No.13300631 Report

Quoted By:

>>13300621
very good, thanks

Anonymous

Anonymous Sun 20 Jun 2021 12:58:54 No.13300641 Report

Quoted By:

>>13300621
>which exists since X is compact
Mean to say "which is >0 since X is compact". The distance always exists.

Anonymous

Anonymous Sun 20 Jun 2021 15:14:56 No.13301030 Report

Quoted By:

>>13299194
I'm pretty sure Mark Sweeney is in at least his second year of grad school, but idr what he's studying.

Anonymous

Anonymous Sun 20 Jun 2021 15:48:56 No.13301142 Report

Quoted By: >>13301174

Wiktionary defines a supercube as the union of ${0,1}^{n}$ and the $n-1$ dimensional balls joining every $2^{n-1}$ vertices that share a coordinate.
I can't visualise this. For a 3-supercube, is it a cube with 6 disks attached at the faces?

Anonymous

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Anonymous Sun 20 Jun 2021 15:56:53 No.13301174 Report

Quoted By:

>>13301142

...it's just a cube, dude. A cube with a bunch of fancy little points on the ends, chill

Once you start getting laid, these types of revelations will come to you.

Anonymous

Anonymous Sun 20 Jun 2021 16:20:33 No.13301268 Report

Quoted By:

>>13300312
Oh yeah you're right. I thought you were asking something else.

Anonymous

Anonymous Sun 20 Jun 2021 19:40:39 No.13302038 Report

Quoted By: >>13302316

If you have a probability of something happening, say .03, how do you figure out how many times on average it would take for that .03 to happen? Eg wheel spin with 3% chance of winning something. How many wheel spins on average before you win?

Anonymous

Anonymous Sun 20 Jun 2021 19:54:49 No.13302085 Report

Quoted By: >>13302316

>>13276478
so, in the Peano Axioms, the formula for induction can be a second order logic formula? and if not how to show that induction implies that natural numbers are well-ordered?

Anonymous

Anonymous Sun 20 Jun 2021 20:32:56 No.13302233 Report

Quoted By:

>>13283674
Yes, it would. Get yourself some knowledge on fourier transforms and bessel functions and you will have covered everything necessary for QM (undergrad, that is--QFT is a bit more)
What QM class did you take, chemistry? A normal QM class is not dumbed down in the slightest.

Anonymous

Anonymous Sun 20 Jun 2021 20:36:26 No.13302241 Report

Quoted By:

>>13294733
Since you said 12th grade math and limits I assume you mean the first part of calculus class? Honestly, if you're stuck on that, skip it. Since calc 1, I've never heard one person say the word "limit". Just start doing derivatives and do a LOT (especially the trig properties)
t. Physics grad

Anonymous

Anonymous Sun 20 Jun 2021 20:38:49 No.13302252 Report

Quoted By: >>13302316

>>13276478
How can I get a intuitive understanding behind formulae derivations?
For example, I completely understand how to derive the quadratic formula, but I have no idea why one gets what one gets. I obviously understand that -b/2a is the axis of symmetry and that sqrt(b^2-4ac) is the distance from the axis of symmetry to the zeros.
But why? Why would -b/2a give the axis of symmetry for example? Could it be purely derived intuitively (what is the reason that the formula is as it is, beyond its derivation)?

Anonymous

Anonymous Sun 20 Jun 2021 20:54:11 No.13302316 Report

Quoted By: >>13302496 >>13304610

>>13302038
I think
E[N] = 1 + (1-p) * E[N]
where p is the chance of winning. So
E[N] = 1/p

>>13302085
Giuseppe initially worked in the second order logic where you quantify over formulas, but when people say Peano Axioms today, they mean the first order variant where the axiom is a schema.
I.e. for every formula, the scheme is an axiom. But this "for every" is not part of the language. E.g. you can't prove negations of statements involving universal quantification over predicates, etc., in first order logic. The only tool you have is the rule that if you got a well-formed predicate, then you can instantiate the induction formula for that predicate as an axiom.
First order and second order Peano arithmetic are thus different formual theories of arithmetic. Indeed, they model situation is completely different - second order PA is categorical, while first order PA suffers from Gödel and thus has big models.

If you mean well-order in terms of smallest elements of sets, then I suppose it's not a sentence in the language?
Of course you'll be able to prove nice things about "<" itself

>>13302252
Yes I think you can "see" those things geometrically by just looking at the graphs of a generic example.

Anonymous

Anonymous Sun 20 Jun 2021 21:28:13 No.13302496 Report

Quoted By: >>13302618

>>13302316
>Yes I think you can "see" those things geometrically by just looking at the graphs of a generic example.
But that doesn't explain why -b/2a for example as said is the axis of symmetry, it just shows that it works

Anonymous

Anonymous Sun 20 Jun 2021 21:59:49 No.13302618 Report

Quoted By:

>>13302496
I have a problem with parsing the reply in context with the sentence.
No, I think you can geometrically see why it should be true, not just that it works out.

Anonymous

Anonymous Sun 20 Jun 2021 22:09:54 No.13302660 Report

Quoted By: >>13302701 >>13302744 >>13302775 >>13303712 >>13304265 >>13305234

look at all these posers
quick, post a number
bet you can't

Anonymous

Anonymous Sun 20 Jun 2021 22:19:13 No.13302701 Report

Quoted By:

>>13302660
1 if there is a cardinality between $\aleph_0$ and $2^{\aleph_0}$ and 0 otherwise.

Anonymous

Anonymous Sun 20 Jun 2021 22:28:33 No.13302744 Report

Quoted By: >>13302764

>>13302660
13302660

Anonymous

Anonymous Sun 20 Jun 2021 22:36:05 No.13302764 Report

Quoted By: >>13302779

>>13302744
Prove that's an actual number by showing me 13302660 of something.

Anonymous

Anonymous Sun 20 Jun 2021 22:40:16 No.13302775 Report

Quoted By:

>>13302660
i

Anonymous

View Same Google iqdb SauceNAO square.gif, 1MiB, 3686x3686

Anonymous Sun 20 Jun 2021 22:41:49 No.13302779 Report

Quoted By: >>13302784

>>13302764
have fun counting pixels

Anonymous

Anonymous Sun 20 Jun 2021 22:43:48 No.13302784 Report

Quoted By: >>13302790

>>13302779
>3686x3686

anon, I...

Anonymous

Anonymous Sun 20 Jun 2021 22:45:39 No.13302790 Report

Quoted By: >>13303149

>>13302784
you got some extra pixels for free, dont complain

Anonymous

Anonymous Mon 21 Jun 2021 01:08:03 No.13303149 Report

Quoted By:

>>13302790
lee mao

Anonymous

Anonymous Mon 21 Jun 2021 02:33:28 No.13303374 Report

Quoted By: >>13303378

What are some good books on Complex Analysis?

Anonymous

Anonymous Mon 21 Jun 2021 02:34:20 No.13303378 Report

Quoted By:

>>13303374
Ahlfors

Anonymous

Anonymous Mon 21 Jun 2021 03:17:24 No.13303551 Report

Quoted By: >>13308551

>>13276489
>>13276669
>>13276671
>>13277026
>>13289464
>>13297360
Are these university tier questions? If so I'm fucked. I picked to go into Math and have been studycelling from no math knowledge to something because I want to do a good degree.

Anonymous

Anonymous Mon 21 Jun 2021 04:05:27 No.13303712 Report

Quoted By:

>>13302660
Checkem

Anonymous

Anonymous Mon 21 Jun 2021 06:54:22 No.13304170 Report

Quoted By:

>>13293985
Lee smooth manifolds. If you don't have the point set and rigorous calculus background you should start there, otherwise the prerequisites are very minimal.

Anonymous

Anonymous Mon 21 Jun 2021 07:37:32 No.13304251 Report

Quoted By:

I haven't taken the vaxx and might not do so as long as those vaccinated still have to go through the same measures in public anyway.

But realistically, I don't think the vaccine, even if there's an issue, is worse than drinking a cola every day. And in any case, I kinda feel that if 70% of people in the nation see side effects, I'm somehow less affected practically. If there's big side effects, they'd be so severe on the nation that we cope together

Anonymous

Anonymous Mon 21 Jun 2021 07:38:46 No.13304254 Report

Quoted By: >>13311533

>>13292221
I'll keep the cow that you call "mother" as my sex slave

Anonymous

Anonymous Mon 21 Jun 2021 07:42:44 No.13304265 Report

Quoted By: >>13304275 >>13304286

>>13302660
1,179,832,395,293,178,259,148,587,778,443,982,767,423,908,163,629,667,689,799,210,969,550,884,231,351,169,347,804,766,799,500,510,294,050,388,349,696,532,084,729,374,087,533,384,204,019,322,892,961,178,819,464,698,121,263,533,012,685,335,273,004,294,789,382,652,477,324,465,427,001,701,326,230,145,911,466,316,029,644,714,371,748,823,861,128,004,214,806,081,770,714,277,374,544,632,880,180,009,063,325,310,867,611,466,814,559,562,175,609,414,340,177,417,478,580,290,981,292,661,586,700,768,075,544,788,360,242,053,436,899,439,186,009,859,147,147,653,878,644,064,667,799,709,427,693,731,208,035,920,284,052,203,131,022,083,688,425,805,265,631,534,978,481,761,954,009,800,546,844,281,261,649,619,610,291,306,374,918,025,956,972,209,823,833,523,561,696,079,181,976,208,783,662,818,235,613,615,149,296,343,931,089,295,234,402,130,043,253,489,826,928,097,199,211,074,340,929,916,161,625,854,705,227,595,565,090,740,962,113,793,308,742,649,598,603,963,747,960,941,063,835,474,664,306,971,892,700,806,057,422,478,626,083,960,243,385,932,102,946,293,048,920,279,760,860,198,799,159,782,580,284,293,120,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Anonymous

Anonymous Mon 21 Jun 2021 07:47:52 No.13304275 Report

Quoted By: >>13304280

>>13304265
That's numberwang!

Anonymous

Anonymous Mon 21 Jun 2021 07:50:10 No.13304280 Report

Quoted By:

>>13304275
For some reason the line breaking is really odd, I'm trying again without commas
1179832395293178259148587778443982767423908163629667689799210969550884231351169347804766799500510294050388349696532084729374087533384204019322892961178819464698121263533012685335273004294789382652477324465427001701326230145911466316029644714371748823861128004214806081770714277374544632880180009063325310867611466814559562175609414340177417478580290981292661586700768075544788360242053436899439186009859147147653878644064667799709427693731208035920284052203131022083688425805265631534978481761954009800546844281261649619610291306374918025956972209823833523561696079181976208783662818235613615149296343931089295234402130043253489826928097199211074340929916161625854705227595565090740962113793308742649598603963747960941063835474664306971892700806057422478626083960243385932102946293048920279760860198799159782580284293120000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Anonymous

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Anonymous Mon 21 Jun 2021 07:53:26 No.13304286 Report

Quoted By:

>>13304265
I'm guessing that's some factorial?
The 0's at the end indicate it's some simple product

Anonymous

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Anonymous Mon 21 Jun 2021 09:08:50 No.13304433 Report

Quoted By: >>13304487

Why do physicists do this?

Anonymous

Anonymous Mon 21 Jun 2021 09:35:58 No.13304487 Report

Quoted By:

>>13304433
It's a humorous remark. And he's simplifying the expression to something informal that still expresses relevant dependencies and functional behaviour.

Anonymous

Anonymous Mon 21 Jun 2021 10:15:47 No.13304610 Report

Quoted By: >>13304742

>>13302316

thank you, obviously, stupid me, it was, in fact, enough to google Peano Axioms and read Wikipedia but that is more and more true about anything so one could stop communicating directly with anyone

saying this, thank you again for your kind answer

Anonymous

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Anonymous Mon 21 Jun 2021 11:02:45 No.13304742 Report

Quoted By:

>>13304610

Anonymous

Anonymous Mon 21 Jun 2021 13:36:14 No.13305117 Report

Quoted By:

>>13282596
> implying mathematicians make money
yeah right

Anonymous

Anonymous Mon 21 Jun 2021 13:38:47 No.13305126 Report

Quoted By:

>>13283264
Mathematics Made Difficult by Carl E. Linderholm.

Anonymous

Anonymous Mon 21 Jun 2021 14:20:15 No.13305234 Report

Quoted By: >>13305399

>>13302660
$\{\varnothing, \{varnothing\}\}$

Anonymous

Anonymous Mon 21 Jun 2021 14:36:11 No.13305280 Report

Quoted By:

>>13282596
mathematics is an art

Anonymous

Anonymous Mon 21 Jun 2021 14:58:06 No.13305327 Report

Quoted By: >>13305470

Bros, is it possible to be self taught into algebra? I have to take algebra courses in Uni, but i want to be prepared.

it's fucking nothing

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it's fucking nothing Mon 21 Jun 2021 15:28:23 No.13305399 Report

Quoted By:

>>13305234
>can't even count to two

Anonymous

Anonymous Mon 21 Jun 2021 15:50:42 No.13305470 Report

Quoted By:

>>13305327
why not?

Anonymous

Anonymous Mon 21 Jun 2021 16:16:06 No.13305564 Report

Quoted By: >>13305572

This thread is worthless, there's not a single intelligent person here.

Anonymous

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Anonymous Mon 21 Jun 2021 16:18:36 No.13305572 Report

Quoted By:

>>13305564

Anonymous

Anonymous Mon 21 Jun 2021 16:27:33 No.13305624 Report

Quoted By: >>13305654 >>13305664

What's your favorite field?

Anonymous

Anonymous Mon 21 Jun 2021 16:32:13 No.13305654 Report

Quoted By:

>>13305624
The Elysian Fields.

Anonymous

Anonymous Mon 21 Jun 2021 16:34:57 No.13305664 Report

Quoted By: >>13305731 >>13307274 >>13307334

>>13305624
besides Q, R, C and the finite fields is there anything else?

Anonymous

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Anonymous Mon 21 Jun 2021 16:49:32 No.13305731 Report

Quoted By:

>>13305664
If you're asking whether there are more fields that those, then yes, there's many more and very different kinds of fields. I think if you look alone under the field extensions of Q and R, there are more than the cardinality of R many such extensions. Someone can fill in the technicalities. I suppose the surreals are a field, but in ZF they are too big to be a set

Anonymous

Anonymous Mon 21 Jun 2021 21:11:52 No.13307274 Report

Quoted By: >>13307308 >>13307380

>>13305664
quaternions, many -ions, extensions fields for $\mathbb{Q}(\sqrt(x))$

Anonymous

Anonymous Mon 21 Jun 2021 21:20:32 No.13307308 Report

Quoted By:

>>13307274
>quaternions
>a field
Grandpa, this isn't the nineteenth century anymore, only the commutative ones are fields.

Anonymous

Anonymous Mon 21 Jun 2021 21:27:39 No.13307332 Report

Quoted By: >>13307783

What's your favorite magma?

Anonymous

Anonymous Mon 21 Jun 2021 21:28:00 No.13307334 Report

Quoted By:

>>13305664
kummer extensions

Anonymous

Anonymous Mon 21 Jun 2021 21:38:31 No.13307380 Report

Quoted By: >>13307392

>>13307274
Why nobody is mentioning the p-fucking-adic numbers?

Anonymous

Anonymous Mon 21 Jun 2021 21:41:05 No.13307392 Report

Quoted By:

>>13307380
They are so obvious as to not be worth mentioning.

Anonymous

Anonymous Mon 21 Jun 2021 21:53:14 No.13307432 Report

Quoted By: >>13307466

This thread: people mentally masturbating themselves and beginners asking stupid questions.

Anonymous

Anonymous Mon 21 Jun 2021 22:00:49 No.13307466 Report

Quoted By: >>13307510

>>13307432
is there a way around this?

Anonymous

Anonymous Mon 21 Jun 2021 22:12:39 No.13307510 Report

Quoted By:

>>13307466
No.

Anonymous

Anonymous Mon 21 Jun 2021 22:15:56 No.13307528 Report

Quoted By: >>13307543 >>13307552

Why does approximation exist within mathematics? Derivatives and integrals—the basis of calculus—are both approximates.

I get that it's more "practical" but it's not pure mathematics, is it?

Anonymous

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Anonymous Mon 21 Jun 2021 22:19:55 No.13307543 Report

Quoted By:

>>13307528

Anonymous

Anonymous Mon 21 Jun 2021 22:22:32 No.13307552 Report

Quoted By:

>>13307528
Nice bait, 8/10.

Anonymous

Anonymous Mon 21 Jun 2021 23:32:04 No.13307783 Report

Quoted By:

>>13307332
Felsic magma is pretty based.

Anonymous

Anonymous Mon 21 Jun 2021 23:39:03 No.13307801 Report

Quoted By: >>13307825

>>13276638
I do fren

Anonymous

Anonymous Mon 21 Jun 2021 23:41:58 No.13307808 Report

Quoted By: >>13307830 >>13307955

someone post a flow chart for set theory please

Anonymous

Anonymous Mon 21 Jun 2021 23:47:21 No.13307825 Report

Quoted By: >>13307843

>>13276638
>>13307801
You have weak minds.

Anonymous

Anonymous Mon 21 Jun 2021 23:47:43 No.13307830 Report

Quoted By:

>>13307808
There are only two and they were both made by the same person.

Anonymous

Anonymous Mon 21 Jun 2021 23:52:33 No.13307843 Report

Quoted By:

>>13307825
Indeed

Anonymous

Anonymous Tue 22 Jun 2021 00:37:33 No.13307955 Report

Quoted By:

>>13307808
Just use Enderton's books. If you need logic he has a good introduction (A Mathematical Introduction to Logic), and then his Elements of Set Theory book. I think there's even a lecture series on youtube that uses them (thanks to this pandemic), I haven't watched it though.
After that just get Jech, or Kunen or something. You'll probably have a good idea of what you'd like.

Anonymous

Anonymous Tue 22 Jun 2021 01:05:25 No.13308039 Report

Quoted By: >>13309107

Why would anyone want to learn Set Theory? It's useless, just learn Naive Set Theory and move on.

Anonymous

Anonymous Tue 22 Jun 2021 01:19:21 No.13308078 Report

Quoted By:

>>13293985
Lee's "manifolds and differential geometry" is a good textbook for learning diff geo stuff

Anonymous

Anonymous Tue 22 Jun 2021 03:36:31 No.13308551 Report

Quoted By: >>13308585

>>13303551
Math has a way of looking intimidating, and no matter how far you go there's always some random subject you've never seen before that will look like moonrunes. Just keep doing your best and everything will sort itself out

Anonymous

Anonymous Tue 22 Jun 2021 03:50:20 No.13308585 Report

Quoted By:

>>13308551
Thanks anon, I appreciate it. I will keep trying my best, I remember back in school when I was around 15/16 algebra always came easily for me and it just made sense to me logically, I struggled with geometry the most and it's proving to be my enemy this time around too at 23. Although I'm finding everything more difficult because I haven't been learning math at all during all these years.

Anonymous

Anonymous Tue 22 Jun 2021 06:49:25 No.13309107 Report

Quoted By: >>13310195

>>13308039
To learn set theory.
If you want "useful", study electrical engineering or something. This line of thought is capitalist subversion of the subject

Anonymous

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Anonymous Tue 22 Jun 2021 11:01:23 No.13309699 Report

Quoted By: >>13309743

FOURIER SUPREMACY ALERT
Have you heard the Riemann Hypothesis news?
https://arxiv.org/abs/2106.01715
>This fact is tested numerically by reproducing the first thirty one zeros of the Riemann zeta function from our spectral side, and estimate the probability of having obtained this agreement at random, as a very small number whose first fifty decimal places are all zero. The theoretical concept which emerges is that of zeta cycle and our main result establishes its relation with the critical zeros of the Riemann zeta function and with the spectral realization of these zeros obtained by the first author.
https://www.youtube.com/watch?v=kNXPe1u81pA&t=1s
Why to take this somewhat seriously:
>It's not like a full proof hacky piece of shit
>It's a numerical argument for the first 31 zeros
>So really it's like RH has been chipped away at just a little bit
Also first author credentials: https://alainconnes.org/
Second author credentials: https://math.jhu.edu/~kc/

Anonymous

Anonymous Tue 22 Jun 2021 11:17:08 No.13309743 Report

Quoted By: >>13309747 >>13309795

>>13309699
This is a nothingburger. Connes is a hack.

Anonymous

Anonymous Tue 22 Jun 2021 11:17:47 No.13309747 Report

Quoted By: >>13309849

>>13309743
>Connes is a hack
Prove it. He has impressive credentials.

Anonymous

Anonymous Tue 22 Jun 2021 11:38:01 No.13309795 Report

Quoted By: >>13309849

>>13309743
is this what youre referring to?
https://www.quantamagazine.org/landmark-computer-science-proof-cascades-through-physics-and-math-20200304/
who cares if his conjecture is false, that is just knowledge gained

Anonymous

Anonymous Tue 22 Jun 2021 11:53:08 No.13309849 Report

Quoted By: >>13309861

>>13309795
>>13309747
He's a crank.

Anonymous

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Anonymous Tue 22 Jun 2021 11:55:37 No.13309861 Report

Quoted By: >>13310141 >>13310391

>>13309849
No, pic related is a crank.
Any other reason as to why you think Connes is a crank?

Anonymous

Anonymous Tue 22 Jun 2021 13:42:42 No.13310141 Report

Quoted By:

>>13309861
Both are cranks. Stop defending either of them.

Anonymous

Anonymous Tue 22 Jun 2021 13:56:58 No.13310177 Report

Quoted By: >>13310275

>>13288064
>>No Kids (lmao)
Ruins the rest of the post

Anonymous

Anonymous Tue 22 Jun 2021 13:59:27 No.13310180 Report

Quoted By:

>>13293555
Research research research

Anonymous

Anonymous Tue 22 Jun 2021 14:07:10 No.13310195 Report

Quoted By:

>>13309107
Based, let people enjoy things for the sake of it anon

Anonymous

Anonymous Tue 22 Jun 2021 14:25:18 No.13310254 Report

Quoted By:

>>13296543
Sounds like you're just talking about a dynamical system

Anonymous

Anonymous Tue 22 Jun 2021 14:27:43 No.13310262 Report

Quoted By:

>>13299352
Theres nothing deep about the association. It has to do with the factorization of numbers divisible by 6. It's a triviality, not something profound

Anonymous

Anonymous Tue 22 Jun 2021 14:32:40 No.13310275 Report

Quoted By:

>>13310177
To pass my superior genes I am planning to spend the millions of dollars I have earned doing mathematics to pay poorfag southeast asian women to carry my children. I will be like Genghis Khan crossedover with Euler.

Anonymous

Anonymous Tue 22 Jun 2021 15:14:27 No.13310391 Report

Quoted By:

>>13309861
mirin those shizo arms

Anonymous

Anonymous Tue 22 Jun 2021 16:03:29 No.13310538 Report

Quoted By: >>13310546

Suppose a limit diverges and so is undefined in IR. Let's call it a function, f(x) evaluated at a.

Is there a way to "store" this expression and suspend evaluation? Like how a fraction is of the form a/b, a suspension of division.

Multiplying the limit with 0 should yield 0 regardless if it diverges. So is f(a) a valid expression in some context? Do I need a new number system?

Anonymous

Anonymous Tue 22 Jun 2021 16:08:10 No.13310546 Report

Quoted By: >>13310581

>>13310538
Yes, you can consider a nonprincipal ultrafilter U over the naturals N and the ultraproduct R^N / U where (a_i) ~ (b_i) iff {i: a_i = b_i} is in U. These are the hyperreals. For sequences that converge there is iirc the shadow function which returns the real number to which it converges, but it makes sense for nonzero sequences too. This structure also forms a field, and has a lot of very nice properties.
Take a look at the book Lectures on the Hyperreals by Goldblatt.

Anonymous

Anonymous Tue 22 Jun 2021 16:24:07 No.13310581 Report

Quoted By:

>>13310546
Interesting, thanks for the pointer.

Anonymous

Anonymous Tue 22 Jun 2021 16:52:19 No.13310661 Report

Quoted By:

Amy good books and material on FWER, Bonferroni/Holm, etc?

Anonymous

Anonymous Tue 22 Jun 2021 18:12:29 No.13310889 Report

Quoted By: >>13310966

>Prove that for any compact simple gauge group G, a non-trivial Yang-Mills theory exists on R4 and has a mass gap ?>0.

All modern set theory is based on the Zermelo-Fraenkel axioms. One fundamental property of these axioma is that they guarantee the existence of a set. If we throw away this assumption, we get a theory that does not allow for sets. If all gauge groups are sets, this means we cannot construct gauge groups, hence Yang-Mills becomes trivial.

Anonymous

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Anonymous Tue 22 Jun 2021 18:45:55 No.13310966 Report

Quoted By:

>>13310889
Okay, I'll take the shizo bait.

>If we throw away this assumption, we get a theory that does not allow for sets.
No, even if you don't adopt Emptyset or Infinity, this doesn't mean they aren't permitted.

>If all gauge groups are sets, this means we cannot construct gauge groups, hence Yang-Mills becomes trivial.
If you prove it's consistent with Z, I'd say it counts as proof or at least an achievement worth the price.

(Would be disappointing though, if it's e.g. a mere ZF existence statement without hint on what it is)

>If all gauge groups are sets, this means we cannot construct gauge groups
For better or worse, mathematicians don't care about what can be constructed.

Anonymous

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Anonymous Tue 22 Jun 2021 19:09:36 No.13311070 Report

Quoted By:

>tfw professor won't let us use latex for assignments, wants everything handwritten
>it's a online course
Why would anyone ever do this

Anonymous

Anonymous Tue 22 Jun 2021 21:17:20 No.13311506 Report

Quoted By: >>13311618 >>13311625

>>13276478
I'm getting an engineering degree but I like math. Does it make sense to look more into pure math for me?

Anonymous

Anonymous Tue 22 Jun 2021 21:22:53 No.13311533 Report

Quoted By:

>>13304254
Cow is a good animal. Friendly, peaceful, gives a lot of milk.

Anonymous

Anonymous Tue 22 Jun 2021 21:42:53 No.13311618 Report

Quoted By:

>>13311506
>I'm a carpenter but I like music. Does it make sense to listen to music for me?
What a stupid fucking question is that

Anonymous

Anonymous Tue 22 Jun 2021 21:44:24 No.13311625 Report

Quoted By:

>>13311506
Stick to engineering.

Anonymous

Anonymous Tue 22 Jun 2021 21:48:50 No.13311645 Report

Quoted By: >>13311787

What are some really cool topics in algebraic topology that I could explore? I've taken a graduate level course at the level of May/van Dieck

Anonymous

Anonymous Tue 22 Jun 2021 22:20:04 No.13311787 Report

Quoted By:

>>13311645
Spectral sequences.

El Arcón

El Arcón Tue 22 Jun 2021 22:59:32 No.13311918 Report

Quoted By: >>13311940

>>13311913

Anonymous

Anonymous Tue 22 Jun 2021 23:05:55 No.13311940 Report

Quoted By:

>>13311918
seems we have 30 more posts

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