/sci/ - Science & Math

Anyone here good in propositional calculus?
I know this is a valid step
[math]x \Rightarrow x \lor y[/math] (weakening the concequent)
is this also valid?
[math]x \Rightarrow x \lor (x \land y)[/math]

>>9320108
add a "union y" at the end

>>9320110
sorry, what?

Yes it is. Implication is incorrect if and only if T==>F. So when x is true you have T ==> T v (whatever), so its true anyway.

>>9320108
Yes. You said you know it (although you obviously don't).
[math] x \implies x \lor (\text{anything}) [/math] is a tautology.

>>9320108
>propositional calculus
not math

How much does it usually take /mg/ to properly work through a textbook? I'm thinking something that would take a 1 (maybe 2) year course load.

>>9320110
x or (x and y) or y

>>9320466
>>9320112

where's the applied math general?

>>9320485
>where's the applied math general?
You're in it

>>9320485
This is the CS general.

[math] computer science \supset math = applied math \cup pure math [/math]

Threadly reminder to work with physicists.

i find that the only mathematics i enjoy doing is that which i investigate and develop on my own. what are some questions i can ask myself to redevelop most of the topics covered in upper-level undergraduate mathematics courses?

>>9320664
>what are some questions i can ask myself to redevelop most of the topics covered in upper-level undergraduate mathematics courses?
'what are necessary and sufficient criteria for a polynomial to be solvable in radicals?'

>>9320729
what are some questions i could ask myself to motivate the notion of "solvability by radicals"?

>>9320758
I suggest you to remove "by radicals" restriction and reinvent theta-functions. That'd be much more fun.
Galois theory is dull and boring, you can complete it by yourself, under 3 months tops.

>>9320458
I would almost never work straight through an entire textbook.

>>9320568
https://arxiv.org/pdf/math/0111082.pdf

>>9320867
Why though?

>>9320880
It takes forever and usually I don't want to know every last thing a textbook has to offer. This doesn't hold for the really short, specialized books, but for larger books I'm usually at this point looking to pick up specific knowledge and then learn something else.

>>9320664
What is a curve ? How do you measure the curvature of a curve ? Why do simple plane curves separate the plane in two regions ? How would you prove this for a convex polygon ?
Compare the length of a simple closed curve and its area.
Why can't R^n be homeomorphic to R^m if m <> n ? Can GL(n,K) be isomorphic to GL(m,K) if m <> n ? How about GL(n,K) and GL(m,L) for different fields ?
Are two compact convex sets with nonempty interior homeomorphic in R^n ?
Does a group with order divisible by d have a subgroup of order d ? What conditions can be put in order for this to be the case ?
Let G be a finite group acting on a finitely generated K-algebra R. Is the algebra R^G of invariants finitely generated ? What if the group G is infinite ?
Is a subalgebra of a finitely generated algebra finitely generated ?

>>9320568
>working with subhuman dog-eaters
I'll pass.

>>9321664
What's wrong with eating dogs?

>>9320458
You don't actually need to work through a whole textbook, usually when trying to learn a new subject if there's enough overlap then you can just skip ahead. In other cases people may only be interested in certain results and so they only look at those. I don't know many people who completely read a textbook since they usually don't need to, at least not in one sitting. Plus all books aren't uniformly great, for example, a lot of people who like Rudin will admit the later chapters on measure theory are just straight up bad. Dummit and Foote while being way too padded out still has some of the best exercises for the subject. I don't think I've ever seen a 'complete' PDE book, point is each book has it's own strengths and weaknesses and you shouldn't limit yourself to one nor exhaust yourself trying to finish.
>>9320664
The field of measure theory was started by asking pretty basic questions about rigorously defining volume and such. Manifolds was developed to understand more abstract spaces. Functional analysis is a pretty straight forward generalization of linear algebra, and complex analysis is so rigid that many of the theorems fall out naturally. I'd suggest looking at some basic definitions and results in the fields and try re-deriving them, most of the elementary results aren't very difficult to prove.

What are amplitudehedrons, /mg/?

>>9321563
Not him, but those are pretty fucking nice questions to ask oneself. I think being able to wonder about these kinds of things is a very important ability. Have any tips for a brainlet?
>>9322334
>most of the elementary results aren't very difficult to prove.
I always found this fascinating. It took so many people so many years to develop alll this stuff and now we can expect a hardworking undergrad to rederive a good chunk of it.

>>9322478
>I always found this fascinating. It took so many people so many years to develop alll this stuff and now we can expect a hardworking undergrad to rederive a good chunk of it.
There's a fundamental difference. A researcher will have to try a lot of things and see which paths lead to anything interesting, etc, but the problems he has solved can then be used as problems in textbooks with the assignment to prove the claims. Instead of using his intuition and reasoning to construct a bridge over a river full of unknown creatures, the student is simply ordered to repair that bridge. Sometimes he is even given hints.

>>9322487
Thank you, I really liked that metaphor.

>>9322723
It's yours my friend. Take care.

what's a good parameterization for a diverse subset of the family of functions that map the unit square to the unit interval and integrate to unity.

>>9322358
Feynman diagrams in the Lagrangian Grassmannian, I think. I'm not a stringer theorist.

>>9322862
Densities associated with bivariate copula functions?

>>9320108

1. only arguments can be valid or invalid, only propositions true or false
2. yes, of course it is also true, you are just instantiating y. y is a variable. that means you can replace it with anything.

>>9319008
Is there a topos of all axioms?

>>9319008
>tfw no known polynomial bijection [math] \mathbb{Q}\times\mathbb{Q} \to \mathbb{Q}[/math]

What is the best brief introduction to Fourier Analysis, for someone who's seen most other parts of analysis at this point.

>>9324283

>>9323450
It is well known that the the category of all axioms is an abelian category.

>>9323450
>>9324896
The fuck are you talking about?
This meme is really pissing me off.

>>9319008
Let A be set of odd numbers
Which axioms should I use to prove that A exists, and that 3 is in A?

>>9325422
1 is in A because 1 = 2x0 + 1
3 is in A because 3 = 2x1 + 1

>>9325428
In first line you show that 1 is odd, not that 1 is in A. Isnt there a missing step from "1 is odd" to "1 is in a set of odd numbers"?

>>9325422
You use
https://en.wikipedia.org/wiki/Axiom_schema_of_replacement
If you know that the set of integers exist then does the set of odd numbers since
[eqn] A = \{ 2 x + 1 : x \in \mathbb{Z} \} [/eqn]

>>9325440
A is a subset of the integers by definition of odd.

Assuming the integers are a set, you can use the axiom schema of replacement (or rather, the axiom schema of restricted comprehension, which is implied by this) to create the set [math]A:=\{x| x\in \mathbb Z\;\; \mathrm{ and }\;\; \exists y\in \mathbb Z : x=2y+1 \}[/math]. The set is non empty because in particular 1 is in the set. And 3 is in the set because 3 = 2x1+1

>>9325460
>>9325454
Ok, I see that it exists. How do you the show that [math](\exists x\in \mathbb{Z} \texttt{ s.t.} 3=2x+1) \implies ()3 \in \{2x+1:x\in \mathbb{Z}\}[/math]

>>9325472
are you literally retarded? I told you twice. It exists because you find it, and it turns out that x is 1

>>9325477
Ok, now I see, thanks.

Do you guys take notes or just go straight to exercises?

>>9325488
Are you asking whether people read a textbook before attempting to do the exercises? Sounds pretty dumb to do exercises without some idea of what's going on.

>>9325460
>Assuming the integers are a set
Which they aren't.

How much is 1+1????!??!!?

>>9325603
I used to take notes, but then I realized it was a waste, I never really went back to them and take a look, it was more just so that I had something to do other than listen to the lecturer. So I don't take notes and just dive into exercises, but if there's something I don't understand I write a little bit of text in a box next to it and arrow pointing to the problem explaining whatever I struggled with. That's the kind of "note" i take, but nothing from books or lecturer.

>>9326311
you take notes to reaffirm learned knowledge during the lecture
i have shit handwriting never re-read notes

>>9319008
Gonna study tonight and tomorrow from Hoffman and Kunze for my final in canonical forms of a matrix and bilinear forms.

Scientifically speaking, how good is this idea? Take in mind that I haven't touched this textbook before. Just gonna pick it up to cover these two topics.

>>9322487
Also we shouldn't downplay the role of notation. Once we have good notation it's often much easier to find the correct way to apply them. If you want a theorem of the type "if object X has property Y then it also has property Z" then this might be straight forward when you have the property Y and Z already defined but if you don't have that then it becomes much harder. Why is Z even a good concept what about the more "intuitive" Z+epsilon (for which the proof doesn't hold)?

Hope that made some sense.

>>9326441
>Z+epsilon
Cringed pretty hard.

Do people actually remember names of these things
My head hurts already when trying to pronounce the name

>>9320868
nice

>>9321664
Is that a Futurama reference?

How can I interact with dark energy/dark matter?

>>9326610
Learn to count in greek first. After that first hurdle, it's easier than you think.

>>9326610
Learn Greek numbers and those names becone trivial. If you are an Amerifat, don't even try pronouncing them, it will go wrong for sure.

well?

>>9326610
I am Greek, so yeah.

>>9327796
0.5 , 0.5 , ...
and
0.49 , 0.499 , ...
are both Cauchy rational sequences and for every rational ε>0 there exists a natural N such for all naturals m and n: if m and n are greater than N, then the m-th term of the first sequence and the n-th term of the other sequence are less than ε distance apart.

ε=p/q
|xm-xn|=1/m<p/q iff m>q/p
take N greater than q/p and it proves it.

This shows that these sequences are equivalent and represent the same real number by definition.

>>9328147
>1/m
meant 1/10^m
this fucks up the rest, but it's easy to fix it

X is uniformly distributed over [10, 20]
Y is uniformly distributed over [10, X]

How can i calculate E(Y)?

WHY IS IT not just (X-10)/2? Does that make (E(X)-10)/2) correct?

Why do I need to use "conditional expectation" at all?

>>9329222
>How can i calculate E(Y)?
E(Y)=E(E(Y|X))

>>9329222
Also,
>WHY IS IT not just (X-10)/2?
Because that's a random variable, not a number.
>(E(X)-10)/2) correct?
Yes.

>>9329251

So E(Y) ends up being 12.5? Or am I retarded

>>9329258
Wait a minute. The expected value of Y given X=x is (10+x)/2, not minus.
So, E(Y) = E((10+X)/2) = (10+E(X))/2.
E(X)= (10+20)/2=15
Therefore, E(Y)=(10+15)/2=12.5.
Yes it ends up being 12.5.

>>9329258

Caught this. Thanks very much.

As for Var(Y), this ends up being

E[Y^2] - [E(Y)]^2

what???? - (12.5^2)

can you explain how I find the expected value of Y squared?

>>9329285
V(Y)= E( V(Y|X) ) + V( E(Y|X) )
Eve's law (EV VE)

https://en.wikipedia.org/wiki/Law_of_total_variance
https://r.amherst.edu/apps/nhorton/Adam-Eve/

>>9329303

any chance of getting some pseudo-math from you...this is quite new to me still

>>9329308
>any chance of getting some pseudo-math from you...
What do you mean?

>>9329312

in programming code that isn't fully written out but is fully outlined is sometimes called pseudo code

E(Y|X) = (10+x)/2 right?

i'm not sure how to get the variance of that

and then im not sure what V(Y|X) is supposed to be either, or how to take an expected value of that

>>9329320
>E(Y|X) = (10+x)/2 right?
Nope. It is (10+X)/2. Capital X.
Consider E(Y|X=x). You put in an x and you get an expression depending on x only. In that expression, replace x with X; this is symbolized by E(Y|X) and it's a random variable.
Similarly for V(Y|X).

V( E(Y|X) ) = 1/4 V(X) = ....

V(Y|X=x) = ....
then replace x with X and take the expected value

>>9329344

i follow up until "Similarly for V(Y|X)" - I only got E(Y|X) by trying to think through the problem logically (expect y to be halfway between 10 and X) and I'm not sure how to represent V(Y|anything)

>V( E(Y|X) ) = 1/4 V(X)

I don't even understand why this is true.

>>9329363
>I only got E(Y|X) by trying to think through the problem logically (expect y to be halfway between 10 and X)
See here >>9329272 . It is (10+X)/2.
The fact that its variance is 1/4 V(X) follows from V(aX+c) = a^2V(X).

>and I'm not sure how to represent V(Y|anything)
Y|X=x is "Y given that we already know the value x of X".
This means that Y|X=x follows Uniform(10,x).
The variance of it is 1/12 (x-10)^2.
Therefore,
V(Y|X=x) = 1/12 (x-10)^2
so
V(Y|X) = 1/12 (X-10)^2 .

And now you have
E( V(Y|X) ) = E( 1/12 (X-10)^2 ) = 1/12 E(X^2 - 20X +100) = 1/12 [ E(X^2) - 20 E(X) +100 ]

To compute E(X^2) you can use this:
E(X^2) = V(X) + (E(X))^2

>>9319008
>universe has been around forever
>universe still hasn't reached thermodynamic equilibrium
Is the second law of thermodynamics wrong?

>>9329513
>>>/sci/sqt/

>>9329513
Universe has not been around forever, Bam problem solved.

>>9329551
What caused the universe to start?

>prof rewrites literally every single proof in the entire class as a "proof by contradiction" for no reason

Can someone give me the /sci/ book guide pictures starting from highschool?

>>9330733

>>9330806
>he/she posted the memelist again

how do you compute zeta function over 2k, k integer?

>>9331518
zeta(0) = -1/2
zeta(2k) = 0, k negative
zeta(2k) can be found using poisson summation + Euler maclaurin; or else by Parseval's theorem, and by Weierstrass factorization for zeta(2)

>>9331537
yes, I think I think I need zeta(4 and 6), I read a formula involving bernoulli numbers(never seen in my life) but was one page of computations involving cotangent, which was a bit random for my standards
do you have any reference for those techniques you said (or care to explain?)

>>9331518
https://en.wikipedia.org/wiki/Particular_values_of_the_Riemann_zeta_function

What do you call this
[eqn]\left(x_1, y_1\right) + \left(x_2, y_2\right) = \left(x_1 + x_2, \sqrt{y_1^2 + y_2^2}\right)[/eqn]

Is it true that every number >11 can be expressed as a sum of a prime and semiprime?

>>9331666
+ is defined on [math]\mathbb{R}\times\left(0,\infty\right)[/math] btw

>>9331666
>What do you call this
What do you mean?

>>9331666
>What do you call this
What do you mean by "this"?

For [math]A,C[/math] simplicial [math]B[/math]-Algebras for some simplicial ring [math]B[/math], how do I prove [math]{\pi _n}\left( {A \otimes _\operatorname{B} ^LC} \right) \cong \operatorname{Tor} _n^\operatorname{B} \left( {A,C} \right)[/math] ?

>>9331848
[math]{\pi _n}\left( {A \otimes _B^LC} \right) \cong \operatorname{Tor} _n^B\left( {A,C} \right )[/math]

>>9331848
>>9331853
nvm this is just Dold-Kan

>>9331853
>>9331848
fucks this?

>>9331518
Logarithmic differentiation.

I'm reading Ratcliffe's Foundations of hyperbolic manifolds, and there it constructs the figure-eight knot complement and proves that it's complete. All fine. But then, in the section on hyperbolic Dehn surgery, it states a theorem on "incomplete hyperbolic 3-manifolds obtained by properly gluing together two ideal tetrahedrons according to the gluing pattern for the figure-eight knot complement". So what gives? How can something like what the theorem states exist if we just proved that such a construction gives a complete manifold? What am I missing?

>>9332320
that would be to relate zeta(2k) and zeta(2k+2)?
mind expanding?

A lot of my proffessors are of the opinion that mathematics degrees have increasingly gotten easier and easier, to the point that we're underprepared and undertrained in a lot of aspects.
Does /mg/ agree? I do, but then again I'm just a fucking undergrad who doesn't know how much mathematics he should know.

>>9332201
Simplicial homotopy group of derived tensor product of simplicial rings.

The equivalence to Tor is one of the fundamental facts behind derived geometry.

The derived tensor product corresponds to the derived fibered product of affine dschemes.

So this shows that a derived intersection of schemes remembers intersections multiplicities (via Serre's intersection formula) while a classical intersection doesn't.

>>9322334
>'complete' PDE book,

There isn't really a true general theory for PDEs. Books just try to study the most important classes of PDEs they can and introduce the most general methods they can.

>>9332516
>derived tensor product
Do you mean derived functors of the tensor product?

What does /mg/ think of stitz and zeager precalculus book?

>>9333625
>What does /mg/ think of stitz and zeager precalculus book?
memebook

>>9333626
Why? It's pretty cool that it's open source.

>>9332516
This seems extremely difficult stuff, how many years am I from doing anything remotely close to it (currently undergrad), 6 years?

>>9333630
Don't acknowledge people who say memebook about anything.

>>9333630
>Why? It's pretty cool that it's open source.
literally a gimmick

Can someone post the proof: think image?

>>9333383
No that anon is referring to the derived tensor product from derived algebraic geometry. In some cases, it coincides with Tor so you can see where the name comes from.

Combinatorial applications of the Hodge-Riemann relations
https://arxiv.org/abs/1711.11176

Why do natural and interesting sequences often turn out to be log-concave? We give one of many possible explanations, from the viewpoint of "standard conjectures". We illustrate with several examples from combinatorics.

>>9333383
Well derived functor in the context of the standard model structure on simplicial modules.

>>9333684
There is a ton of literature on derived algebraic geometry and a lot of it is different. You need to know algebraic geometry (at lvl of Hartshorne) to do any of it. However you also need to be familiar with algebraic topology at varying levels.

I'm learning in terms of simplicial rings, so learning the fundamentals of simplicial homotopy theory suffices.

However if you want to do it Lurie style in terms of E_infinity rings, you should be much stronger in algebraic topology because E_infinity rings are defined as sort of ring-like objects in the (infinity) category of topological spectra. Spectra being a topic of focus in stable homotopy theory, motivated by the study of generalized (co)homology theories.

There is also a lot of category theory. Model categories and infinity categories being of focus. There are various approaches to infinity categories. I'm studying in terms of simplicial enriched categories, because they are the quickest route to get to what I'm interested in. However quasi-categories are a more explicit theory and favored in Lurie's work.

I'm currently reading this https://arxiv.org/pdf/1401.1044.pdf

>>9333986
Huh?

>>9334131
Huh?

>>9333930

Let's see how smart the average /mg/ mathlet is: https://discovermyprofile.com/tag/Intelligence

>>9330714
He's baiting you to contradict him.

Hello /mg/, is this the latest memechart?

>>9335136
I hate these charts. You have people who know nothing more than high school algebra obsessively planning exactly every book they plan to read over the next five years, yet never actually opening one up.

>>9330733
Stop following memelists.

>>9335136
>Tao
>Conway
You should not be reading textbooks from the best in the subject. You should be reading textbooks from the best Teachers of the subject.

Also,
>Rudin
Disgusting.

>>9335136
>no Chapter 0
>no Kunin
>no Jech
absolutely and unequivocally discarded

>>9335377
Tao is actually a really good expositor, go check out the books or his blog, they're excellent.
Conway isn't there until you get further in. At that point you need to be more able to read what's available to you.

>>9335136
Rudin is a meme

>>9335136
If you actually spend time trying to figure out how exactly to approach a hobby (or anything else) you will never start.
Just like a guy spending hours shopping for proper gym clothes instead of just working out with what he got.
If you were genuinely interested you would just pick the top most book which sounds the most interesting and start reading.

There is no "right way" to learn mathematics, all these charts are just the reflections of some peoples experiences, but the only way you will ever learn is by starting.
And you start by looking at the first row and picking the most book which sounds the most interesting to you.

>>9335136
>>9335212
>>9335303
>>9335377
>>9335429
>>9335509
>>9335513
>>9335571
just make a textbooks thread

what the FUCK does a fractional derivative represent geometrically?

>>9335662
geometric intuition is for rich kids
are you a rich kid?

>>9330714
please interrupt every time and say "assuming LEM"

>>9330733

>>9335774
>Jech (optional)
KILL YOURSELF PROMPTLY, INFIDEL

Why is R parametrized as 2sint 4cost?
I'm a retard and can't figure this out.

>>9335970
(2sin(t))^2/4 + (4cos(t))^2/16 = 4sin^2(t)/4+16cos^2(t)/16 =
sin^2(t)+cos^2(t) =
1

>>9335980
I still don't understand. Why isn't it -((cost)^2)/4 + -((sint)^2)/16 ?

>>9336006
Whoops, I meant -2((cost)^2)/4 + -4((sint)^2)/16

>>9335774
this is the worst memebook list I have ever seen, if you don't know shit at least don't put comments on the image

>>9336012
Is it because the curve is clockwise and not counter clockwise? I tried it with R(t) = (2cost, 4sint) and got -4pi

>>9319008
So, anyone doing the Putnam tomorrow?

>>9336012
>-2((cost)^2)/4 + -4((sint)^2)/16
Where are you getting that from?

>>9335303
Why not? the ones at schools are targeted towards future engineers and are mostly boring

Haven't been here on months.
How has this general been?

>>9334452
Huh.

>>9329513
>>universe has been around forever

Stop listening to /reddit/atheism

>>9336582
Pretty shit as you can see. Math is hardly ever mentioned here.

>>9333986
>>9334131
>>9334452
>>9336588
I like Huh. He's just like me. Except Asian. And successful.

>>9329513
>Is the second law of thermodynamics wrong?
You missed the part where the universe is infinite.

inb4 cosmologists and their inane theories about a finite, non-eternal universe
>muh Big Bang

>>9336634
But things are just the way they are. The universe exists because it is the way it is. it makes sense to. it just spawned because it makes sense and there was no force to prevent it from happening. Read Socrates.

>>9336634
>>9336636
>>>/x/

>>9336636
No.
>>9336637
No.

>>9336639
see >>9336637

>>9336256
>mostly boring
And? If you let something being "boring" slow you down instead of trying to be done with it as soon as possible, you are doing it wrong.

>>9336978
Are you retarded? I agree I should try being done with them fast, but how the hell am I doing it "wrong"?
What's fun about a book with 2-line instructions on what a polynomial is followed up by 30 exercises with lots of numbers forcing you to do lot of mental arithmetic, compared to a book by for example Lang who explains deeply in 2-3 pages and builds up intuition and proofs to why and how it works then later become very easy? I don't get your point.
Moving on from HS Algebra to Calculus is often a difficult process because we're almost never taught the intuition and knowledge in equations or things but rather how to compute things

Bump

algebraic geometry or algebraic topology?

>>9339891
Topology so you don't have to play with polynomials.

>>9339891
>algebraic geometry or algebraic topology?
What about them?

what have you be doing today /mg/?
it is nice to think you have been studying instead of shitposting for the last few days

>>9340076
Be in my bed. It's what I always do on the weekends, or more precisely, whenever I'm at my home.

>>9340076
I was shitposting on /c/, /mu/ and /lit/ all day.

>on a flight
>working on a proof
>nothing's working, beginning to doubt that it's true
>plane begins descent
>suddenly realize the crucial step necessary to complete the proof
>everything falls into place
>finish proof just before touchdown
based feeling 2bh bros

>>9340102
What did you prove?

>>9340149
The plane landed safely.

>>9340149
spaces are connected under certain assumptions

>>9340169
lel

>>9340186
If you're not more concrete I won't be able to rob you blind.

> tfw also a topologist
So, why exactly are we all on 4chan?

what kind of pretty pictures can topology make

>>9340241
We only draw pants.

>>9340241

>>9340245
So this is why topologists are overrepresented in /mg/!

>>9339891
Derived Algebraic Geometry

which is pretty much both

>reviewing notes
>on the part where I constructed rows of exact sequences in equivariant cohomology
>have vertical morphisms between them with an s written on the arrows
>flip through notes trying to find out what these s's are
>turned out they're just tildes drawn on the arrows to denote isomorphisms
>mfw

>>9340317
>he can't recognise his own handwriting
Do you write with your feet?

For those interested, I made a video trying to explain Turing machines

https://youtu.be/CAUo5aNmvz8

11:30 - 54:40

>>9340342
lel

>>9340348
kek!

And in 2 weeks I'll start a series on voting theory

>>9339896
You're not going to avoid playing with polynomials in algebraic topology.

>>9340383
No, but you can avoid them a bit better.

>>9340361
You're better off advertising your stuff on >>>/g/ dude.

>>9339896
pleb

>>9340579
:(

>>9340771
well?

https://arxiv.org/abs/1705.09989

>>9340102
Why is doing math on a plane so fun?

>>9340944
Because 2D > 3D.

>>9339896
This

Thoughts?

>>9341155

>>9341155
>>9341188
>>>/g/

>>9341201
Programming is a subset of math.

>>9341246
>subset
>>>/g/
Keep your garbage contained there.

>>9341246
>Programming is a subset of math.
Other way around.

>>9341260
see >>9341258

>>9319008
Probability question here. Suppose i have a sequence of indepenndent random variables and i know that

[math]

X_i \longrightarrow c_n A.S

[\math]

where c is a deterministic constant. Can i use the root test on c_n to determine whether


[math]

\sum_{i=1}^{\infty}X_i = \infty A.S

[\math]

or

[math]
\sum_{i=1}^{\infty}X_i < \infty A.S
[\math]

>>9341400
Probably not.
I can't be arsed to find a counterexample though.

>the
>absolute
>state
>of
>/mg/
And /sci/ in general. Hiromoot should just delete the board at this point.

>>9342400
any takers?

>>9342412
both, by definition and the existence of supremum and infimum for any subset of the reals

>>9342412
>True/false
Neither.

>>9342197
>>the
>>absolute
>>state
>>of
>>/mg/
>And /sci/ in general. Hiromoot should just delete the board at this point.
What do you mean?

>>9342460
>>9342482
b-both?

>>9342611
Isn't it obvious? /sci/ is one of the absolute worst boards on 4chan. /b/ with shitty nerd jokes and the occasional dash of /pol/
It needs to die.

>>9342612
Neither true nor false.

>>9342634
>Isn't it obvious?
No that's why I'm asking what you mean

>>9342612
paraconsistent mathematics when

>>9342640
FUCK math

>>9319008

Reeeee how the fuck do I integrate x!? I am trying to make a formula for cumulative poisson distribution.

>>9342806
Surely you mean [math]\Gamma(x)[/math].

>>9342612
No, it's true.
I meant "both lower bound and upper bound".

I'm having some trouble with this problem. Let M be a compact, orientable m-dimensional manifold. If m is odd, then the euler characteristic of M is 0.

This is a differential topology class with not much algebraic topology content, so we can use for example poincare-hopf and homotopy invariance of degree, but no poincare duality, and only basic results related to the euler characteristic and betti numbers.

>>9342806
Wtf are you integrating? You should be summing.

>>9342848

Show me the way.

>>9342975
by poincare-hopf having a non-vanishing vector field implies euler characteristic 0
you have an orientation and an odd dimensio, do you know how to give such a vector field?

>>9343149
no, that's the problem

>>9329551
There was nothing wrong with my barn in the first place.

>>9343149
>>9343166
p-please respond

>>9343149
>>9343166
anon kun help me

>>9343307
>>9343721
Jesus dude, just fucking think about it yourself for a few hours.

>>9343149
>non-vanishing vector field
It also needs to be continuous (or smooth in smooth manifolds) I believe.

>>9343743
I already thought about it myself for a few hours. The proofs I know use poincare duality. I've tried some techniques related to homotopy to try and simplify the problem, but I'm at a loss for what to do.

>>9343748
That's what vector field implicitly means. In particular, continuous vector fields on smooth manifolds are homotopic to smooth vector fields, so all definitions for smooth vector fields pass well to continuous fields.

Suppose you roll a (fair, 6-sided, perfectly ordinary) die repeatedly until you roll a 6. As is well known, the expected (i.e., long-term average over many trials) number of rolls required is 6.

Now suppose we ask this question conditional on never having rolled any odd numbers. That is, suppose you learn that someone has followed the procedure above, and that they rolled only even numbers up to the point where they rolled that 6. What is the expected number of rolls they took?

(That is: What is the expected number of rolls taken to roll a 6, conditional on having got no odd numbers in the process of rolling that 6? The question is not anything like "what's the expected number of rolls next time, given that you didn't get any odd numbers last time?".)

If you think it's 3, you're wrong.

>>9343790
you sure it's not 3?

>>9343801
Yup. I know the answer, but I'd like an explanation from one of you mathematicians.

Spoiler: the answer is 1/2 * floor(ln(e^2 * pi))

(I expressed it symbolically so that I don't give it away to people who don't want to see the solution)

>>9343811
www.yichijin.com/files/elchanan.pdf

>>9341400
Wait so you have a sequence [math] \{X_i\}_{i=0}^\infty [/math] such that [math] X_i \longrightarrow c_n [/math] a.s. Then what does the n do? This is one limit... Do we have more sequences?

>>9343892
it's probably a typo

give it to me straight /mg/, what prerequisites do I need to start Eisenbud's Commutative algebra

Assume maturity

>>9344260
linear algebra, basic abstract algebra

>>9344260

>>9344308
Kek I read this in his voice

>>9344379
Whose voice?

>>9342634
I blame the crossies.

>>9344390
Eisenbud's

>>9343790
Looks like 1.5

>>9344224
but then the question makes even less sense... How could he use the root test on [math] c_n [/math] then? And what does the information about the variables being independent really tell us? nothing.... Just let [math] X_i [/math] be your fav sequence of numbers that fails the root test.

I'm an ee undergrad student who wants to learm some complex analysis or calculus with complex variables. I have taken calculus 3 and linear algebra. Can /mg/ suggest any good books that focus more on applications and less on mathematical rigor?

>>9345178
>focus more on applications and less on mathematical rigor
>>>/sci/sqt/

>>9345178
> complex analysis
> less rigor
explain why you don't want to have solid foundation on the easiest and most beautiful analysis

>>9345343
>beautiful
>>>/lgbt/

>>9345352
drop dead already you ignorant motherfucker

>>9345362
math is beautiful :333 this proof is so beautiful :3333 euler's identity is a beautiful equation :333

>>9345178
>Can /mg/ suggest any good books that focus more on applications and less on mathematical rigor?
Consider suicide.

>>9345369
is that the extent of your brain little motherfucked
if you are a sad brainlet who struggles with math and can't appreciate its beauty is not our problem

>>9345387
There is nothing beautiful in analysis or complex numbers

>>9345391
well, that's arguable and also depends on what you consider analysis
the concepts of measure theory are fine
complex analysis is the closest thing to classic algebraic geometry, at least have respect for Riemann, he helped during an age of ignorance

>>9345404
Well Riemann is ok, otherwise I can't think of anything nice there

>>9345178
>http://4chan-science.wikia.com/wiki/Mathematics#Complex_Variables

Ablowitz and Fokas

>>9345178
>Can /mg/ suggest any good books that focus more on applications and less on mathematical rigor?

>>9345178
>"""good""" books that focus more on applications and less on mathematical rigor?
Cancer is not welcomed here.

When finding the zeroes of a polynomial function, are the irrational(if any) ones always on the quadratic part?

>>9345757
>When finding the zeroes of a polynomial function, are the irrational(if any) ones always on the quadratic part?
What do you mean?

>>9345766
Say you make a list of possible rational roots using the rational roots theorem but you know there are irrational roots, are you always going to find them when you factor it down to a quadratic function and apply the formula?

>>9345757
if you have an irrational root then the smallest nonzero coefficient must be irrational, and if you are talking about rational polynomials it's quite difficult

>>9345778
>if you have an irrational root then the smallest nonzero coefficient must be irrational
x^2-2 has irrational root and rational coefficients

>>9345773
>Say you make a list of possible rational roots using the rational roots theorem but you know there are irrational roots, are you always going to find them when you factor it down to a quadratic function and apply the formula?
I'm still not totally sure what you're asking but there are polynomials like x^3-2 which has an irrational root 2^(1/3), and you won't find it in a quadratic factor unless you start factoring using some complex numbers

>>9345391
Very much questioning how much complex analysis you've ever studied.

>>9345780
...

>>9345391
complex analysis is by far the most beautiful mathematical subject

>>9346040
>...
?

>>9346042
yeah, interesting how a non-mathematical subject can be the most beautiful mathematical subject

What do the /math/ematicians here think about black holes?

>>9346514
>What do the /math/ematicians here think about black holes?
black holes are like neurons, they're useful for making models and coming up with theoretical ideas but they don't actually exist in practice

>>9346519
>like neurons [...] useful for making models [...] but they don't actually exist
Typo, or do you really believe neurones don't exist?

>>9346521
>Typo, or do you really believe neurones don't exist?
its not a matter of "believe"

>>9346533
I was being serious with my question anon. Please...

>>9346042
Give me one reason why it would be beautiful other than the nice looking pictures one can generate using poles or the notation [math]\oint_{\gamma}[/math] which is "beautiful" when written with a nice handwriting. If you are to say some integral theorem is beautiful, I will call the fact that for any a and b, (a-b)+a+(a+b)=3a, beautiful.

>>9345757
check out the roots of [math]\frac{1}{\sqrt{2}}x-1[/math]

>>9346620
*polynomial function with RATIONAL coefficients
sorry

>>9346071
>non-mathematical subject

>>9346514
Which one? Yours?

>>9346514
>>9346519
>>9346521
>>9346533
>>9346562
Try >>>/x/
This is a mathematics thread.

>mfw reading about the Mason-Stothers theorem

>>9346959
I was asking to checks whether there is something general about my personal experience. From what I've gathered irl with the people I know, mathematicians/math grads tend to be a lot more skeptical about black holes than other STEM folks.

Why is that?

>>9346982
Discuss that somewhere else, I suggest >>>/x/
This is a mathematics thread.

>>9346982
>other STEM folks
The only beings outside of math that are comparable to humans are physicists, and even that is questionable for most of them.

>>9346042
It's one of the dullest mathematical subjects.
>make an incredibly restrictive assumption about our functions
>get "nice" results
I bet you'd love to hear about the beautiful theory of Hölder continuity with [math]\alpha>1[/math]. You don't even need boundedness to assure your function is constant anymore.

>>9347024
>>make an incredibly restrictive assumption about our functions
most of the functions that are commonly used satisfy those restrictions

>>9346600
The fact every holomorphic function is analytic.

>>9347256
This is beautiful how? Because it has all partial derivatives in every point? Or why? How?

>>9347453
It is beautiful relative to real analysis.

In real analysis we have to deal with various classes of differentiability.
i.e. C^k functions, C^infinity functions , Real-Analytic functions


However in complex analysis, a function that is once complex differentiable (holomorphic) is also infinitely complex differentiable. Moreover, a non-trivial fact to prove, holomorphic functions are also analytic.

So every function which is once complex differentiable can be written as a convergent power series.

Giving the idea that holomorphic functions are very close to polynomials.

>>9347522
>a non-trivial fact to prove

The is done via Cauchy's Integral Formula btw

>>9346514
>tfw black hole entropy is related to automorphic representations
https://arxiv.org/pdf/1312.7168.pdf

why x?

>>9347522
yes, one dimensional complex analysis is very easy
multivariable complex analysis instead is way more complex, maybe we should learn it, at least local theory

>>9347813
Greek mistranslation of the Arabic word for "unknown" or something like that.

>>9347825

>>9347825
Dealing with complex manifolds is still usually nicer than dealing with smooth manifolds.

[math]\sum_{n=1}^{\infty} X_n [\math] and [math]\lim \frac{X_{n+1}}{X_n}\rightarrow c}\ [\math] A.S. Then if c<1 can I conclude the sum converges and diverges if c>1

>>9347987
It's /math

>>9343892
>>9345061
[math]\sum_{n=1}^{\infty} X_n [/math] and [math]\lim \frac{X_{n+1}}{X_n}\rightarrow c [/math] A.S. Then if c<1 can I conclude the sum converges and diverges if c>1

>>9344379
eisenbud's voice gives me asmr
he's like the bob ross of mathematics

>>9347522
I just can't see the beauty here. Sorry.

>>9348021
neither in hurwitz theory?

>>9348021
If you want literal beauty, fractals are a good example.

https://math.hse.ru/data/2013/05/27/1298692842/Holomorphic%20dynamics.pdf

>>9348053
that pic gave me cancer, ty

>>9348137
Anything connected to analysis can do that to you.

>>9348454
If you suck at it, yeah.

>>9348467
If you suck at it then you probably won't get cancer.

>>9348454
One day you'll grow up and learn that math cannot be so easily compartmentalized.

>>9348484
>learn math
So I won't be learning any analysis then?

>/mg/ at page 9
the absolute state of /sci/

>>9349634
>Retards on here who don't check the catalog
Agreed

>>9349634
New thread here >>9348310

>>9349663
>bump limit not reached
>new thread not linked in the previous one
Yeah, I am the retard.