/sci/ - Science & Math

first for brouwerian continuity principles

>>9357573
how does [math]p \lor \neg p[/math] have any possibility of being false? it's a tautology over the inclusive or.

>>9358010
>how does p∨¬p have any possibility of being false?
by not assuming that either p or ¬p has to be true

>>9358020
i don't understand. if p is not true, not p is true, no?

>>9358034
>if p is not true, not p is true, no?
https://en.wikipedia.org/wiki/Law_of_excluded_middle
https://en.wikipedia.org/wiki/Principle_of_bivalence

>>9358038
explain

>>9358044
if you don't assume that either p or ¬p has to be true, then there's no reason p∨¬p has to be true

>>9358048
but if one is false then negation is true and or says it's tautology

>>9358059
>but if one is false then negation is true
Why?

>>9358063
by definition of negation

>>9358068
>by definition of negation
Which definition?

>>9358095
[math]\textit{the}[/math] definition. if something is false, the negation on this something is true and vice versa.

>>9358104
>the definition.
https://en.wikipedia.org/wiki/Negation#Definition

>No agreement exists as to the possibility of defining negation, as to its logical status, function, and meaning, as to its field of applicability..., and as to the interpretation of the negative judgment

>>9358114
so, contrapositive doesn't work? you say negation isn't defined but countless times again it's application in the classical mathematical sense yields practical results

>>9358119
>so, contrapositive doesn't work?
correct

>you say negation isn't defined
I didn't say that, there are multiple definitions.

>>9358127
>correct
you're wrong. what is this, some Wildbergian type philosophy you're arguing with?

>>9358129
>you're wrong.
What do you mean?

>>9358132
tell me, if a sequence is convergence does this imply it is bounded?

>>9358133
>tell me, if a sequence is convergence does this imply it is bounded?
Yes, but what's the relevance?

>>9358138
would you also agree, that if a sequence is unbounded, then it is divergent?

>>9358140
>would you also agree, that if a sequence is unbounded, then it is divergent?
Yes, but what's the relevance?

>>9358149
Do you know what a counter-example is? I just gave you one. That is textbook example of contrapositive.

>>9358153
>Do you know what a counter-example is?
Do you? You don't need contraposition to prove either of those two statements. Assuming that you can't make use of contraposition is not the same as the contrapositive being false for all true statements.

>>9358159
It's not about the proof of the two statements, rather that both of them are logically equivalent via the contrapositive, which you said doesn't work but I just showed you it does.

>>9358160
>rather that both of them are logically equivalent via the contrapositive, which you said doesn't work but I just showed you it does.
Where did you show it works?

>>9358163
>>9358138
>>9358149

>>9358165
You'll have to elaborate on how convergent sequences being bounded and unbounded sequences being divergent implies that given any statement (A -> B), (A -> B) is equivalent to (¬B -> ¬A).

>>9358184
I mean, it's a simple proof by contradiction. If you don't believe in contradiction proof, then all the best but I'll just head on to bed then.

>>9358193
>I mean, it's a simple proof by contradiction.
Feel free to proceed.

>>9358198
https://en.wikipedia.org/wiki/Contraposition#Simple_proof_by_contradiction

>>9358204
>We also know that B is either true or not true

>>9358207
'night anon. Good luck in your studies.

thanks for proving the uselessness of pure math faggotry.

>>9358207
>mfw this thread is too people arguing about the most retarded shit because the first guy did not properly explain that what he meant is that LEM doesn't NEED to work, but we assume it works in our logical system. And the other guy, not knowing this, is posting proofs using our normal logic system and then the first guy dismisses these proofs by simply pointing out that the proofs are on top of normal logic which he is not talking about, but he never properly explained he isn't talking about it.

>>9358215
>too

>>9358215
>because the first guy did not properly explain that what he meant is that LEM doesn't NEED to work
I'm not a "guy".

How could I have been more clear? >>9358048

>>9358219
>mfw this first guy is so embarrassed after noticing he never actually explained himself that the only cover he has is pointing out a typo

I don't want to be mean so just you have something to say I will gift you another typo:

Hey guys, isn't Eminem a good raper?

>>9358224
>Hey guys, isn't Eminem a good raper?
not anymore

>>9358220
>How could I have been more clear?
You were clear to me, but it is clear that the guy you are arguing with did not properly get that. But instead of properly explaining yourself you just followed his rhythm like a little bitch.

>I'm not a "guy".
Mathematically speaking, what do you mean?

>>9358227
>Mathematically speaking, what do you mean?
Guy(me)=0

>>9358227
>Mathematically speaking, what do you mean?
or perhaps keeping in line with the theme of the thread, ¬Guy(me)=1

>>9358228
I don't understand. If Guy an indicator function that gives a 1 whenever the input is a guy or 0 when the input isn't, or is Guy an implicit function that defines the set [math] \{ x \in \mathbb{PEOPLE} : Guy(x) = 0 \} [/math] in the same way you typically implicitly describe a circle? In this sense, wouldn't only guys be roots of the function Guy?

>>9358235
>If Guy an indicator function that gives a 1 whenever the input is a guy or 0 when the input isn't
Quite.

>>9358239
Okay, I see. But then you are defining yourself by what you are not. Could you define yourself by what you are?

Perhaps, a better way of phrasing my question is this: Biologically speaking, what are you?

>>9358242
>Could you define yourself by what you are?
No I can not.

>Biologically speaking, what are you?
Sentient and sapient

>>9358247
>Sentient and sapient
No no no, I need something more specific. Let me ask you again.

When you were born, did you come equipped with the pink fleshy hole that is typically used to put penises inside, that is not the butthole?

>>9358250
>When you were born
I'm not sure what you mean by this?

>entertaining this mentally ill attention whore
/mg/ has fallen

Threadly reminder to work with physicists.

>>9358262
I was trying to remove the ambiguity of you having a pink fleshy hole that is typically used to put penises inside that is not the butthole (I will call it [math] \mathbb{PFHTITUTPPITINTB} [/math] from now on) that you obtained from surgery.

So I mean is that were you born without a Y chromosome?
Are you an XX chromosome?
Biologically, do you not have a penis and were not born with one?
Are you a non-male human that is not a trap or maybe trans? Are you a non-(male or trap or trans) human?
Do you have the same gender as your mom?

Those are all the same question so I expect only one answer.

tranny btfo, probably off to chug pills and cry.

ayo i made an /mg/ discord.

join it for bants and math.

https://discord.gg/qnyBW3Q

>>9358302
>>>/v/

>>9357573
It's been a while, but how's everybody's research going?

>>9358345
Currently under review

>Binary valued logics
>not many valued logics
>mfw this thread isn't fuzzy
>mfw this thread isn't modal
>no quantified predicates
>no quantifiers at all

Stop shitting up muh logic.

(∀x)□((◇x=u) ⊃ Fx)

where Fx is a unary relation that asserts that x is a faggot.

>>9358355
Cool, what's it about?

>>9358367
Why would you use homophobic unary relations ?

>>9358367
>not using an inconsistent logic

>>9358010
Intuitionistically you think of OR as a union of open sets in a topological space, AND as intersection. But then you interpret negation as the interior of the complement so in general it's not the whole space.

>>9358270
No.

>>9358367
All of many valued logics, fuzzy logics, modal logics and so on, can be constructed as models within binary value logic. In fact, that is how they are approached.

>>9358212
>thanks for proving the uselessness of pure math faggotry.
Are you okay?

real analysis and algebra quals this week

wish me luck boys

>>9358385
I don't tell you how to be a loser, don't tell me what relations to use.

>>9358414
That's stupid please don't post in my general again.

>>9358496
Congrats on missing the point.

》doing logic instead of math
what's the point?

>>9358543
>That's stupid
Why is that?

>>9358538
Good luck, and remember, always leave a room for epsilon and representation theory makes algebra a hell of a lot easier.

Was the 20th century the greatest century for mathematics? Will it ever be surpassed?

>>9358697
>Will it ever be surpassed?
Yes. I'm surpassing it as we speak.

>>9358697
Assuming a feminist school of relative logic is formed, yes. It will be surpassed by this group equipped with the superior female logic. The pioneers have already started. Just remember Piper Harris or whatever its name is.

So this year I finished my Calc sequence (1,2,3 and Diff Eq) and my Linear Algebra sequence (1,2) and now I found a neat way to combine the theory seen in Linear Algebra with the concepts of Calculus called Differential forms. I'm reading a book on it and I already know what k-forms are and what differential k-forms are and the wedge product and how the derivative on these differential forms look like the divergence, curl and gradient, etc.

My question is, what will I gain from this? I already know all of Calc 3 which means I can solve problems that involve it. But obviously, I learned Calc 3 in the naive "Let's generalize the concepts from Calc 1" way, not with differential forms. Will knowing differential forms enhance my problem-solving skills? Will this new perspective enlighten me to solve harder problems?

>>9358695
how? i really don't get representation theory. Like whats the point even? Nah but srsly please elaborate, maybe i'll even learn something.

>>9359305
Give you a way to study groups using linear algebra. Linear algebra is always easier.

>>9358466
But since finite disjoint sum is the same as finite product of topological spaces then AND and OR would be the same, which they aren't

I'm asked to proof or give a counter example if false.
For a non empty set X
[math]TO\preceq \land S\subseteq X \land S\neq\varnothing\;\implies\;\exists!x:S.\forall y:S.x\preceq y [/math]
or in words( if there is a totally ordered relation on X and S is a non empty subset of X, then there exists a unique x lower bound in S)

Is [math]S=-\infty..0[/math] with [math]X=\mathbb{R}[/math] a valid counterexample?

>>9358978
That girl is very cute. I wish we could hold hands.

>>9359575
She's not real bud, no matter how much math you show her she's not real.

>>9359504
>finite disjoint sum is the same as finite product
it isn't though?

How do you formally prove a negation in intuitionistic logic anyway?

>>9359598
Yes it is, they're isomorphic

>>9359647
To prove not P, assume P and derive a contradiction

>>9359265
It can, people use differential forms to define De Rham Cohomology, doing that allows you to understand properties of the solutions of some important differential equations, the most readily available example is maxwell's equations. This video goes more in depth
https://www.youtube.com/watch?v=6qMGz5hCx94&index=3&list=PL7aXC0jU4Qk7K778c5nmgQImd6VKKFMYu

>>9357573
Do you rewrite lecture notes?

>>9359265
It's hard to go into more sophisticated theory (de rham cohomology, etc) without the appropriate analysis and algebra background, much less use them for engineering problems

>>9359718
used to but it takes too much time

>>9359504
#1 it's not disjoint sum, it's the actual sum inside of a single space

#2
>finite disjoint sum is the same as finite product of topological spaces

no it's not. You're thinking of vector spaces.

>>9359533
yes

>>9359930
>actual sum

sorry, meant to say union here

>>9359732
When did you stop doing it?

>>9359930
I was actually thinking about groups. Since direct product is a product and direct sum is a coproduct and direct sum of finitely many groups is the same as product of finitely many groups and I thought that if the product of topological spaces is a product and disjoint sum is a coproduct then it would be similar as with groups and finite product would be isomorphic to finite disjoint sum

Ok what the fug do I need /sci/. I was asking for a PhD position in algebraic geometry and he responds back with this - what is a strong background at a top uni?

>>9360307
I would assume Chapter 2&3 Hartshorne (or equivalent) minimum.

>>9359583
and neither is feminist logic or any of this stupid shit you spergs are arguing about, are you cute irl? r u a chestlet or a titcow?

>>9360335
assuming I complement it with Eisenbud's comm algebra, what other background do i need to start Hartshorne and how long will I take?

>>9360356
Classical Algebraic Geometry would be good for motivation, but desu aside from a few select exercises you don't actually need it.

>>9359647
The same way you do in classical logic.

>>9359583
>She's not real bud
She is though.

>>9360066
>if the product of topological spaces is a product and disjoint sum is a coproduct then it would be similar as with groups and finite product would be isomorphic to finite disjoint sum
This has no chance of being true without a zero object, something like the trivial group which has a unique homomorphism to and from every other group.

p-adic geometry by Peter Scholze
https://arxiv.org/abs/1712.03708

>We discuss recent developments in p-adic geometry, ranging from foundational results such as the degeneration of the Hodge-to-de Rham spectral sequence for "compact p-adic manifolds" over new period maps on moduli spaces of abelian varieties to applications to the local and global Langlands conjectures, and the construction of "universal" p-adic cohomology theories. We finish with some speculations on how a theory that combines all primes p, including the archimedean prime, might look like.

>>9360704
>geometry

you got trolled anon

I'm in calc II right now and want to self study calc III (multivariable calc, parametric equations, polar coordinates, vectors and vector calculus, partial differentiation, multiple integration, Green’s theorem, divergence theorem of Gauss, Stokes’ theorem etc.) which textbook covers these topics? I know Stewart does but I don't like it. Anything better? Does Spivak? All advice is appreciated.

>>9360749
Marsden and Tromba.

Why is the derivative called "derivative"?

>/mg/ at page 9

>>9361908
Just let this physishit ridden hellhole die already.

>>9360356
not much, but do try to read volume 1 of Shafarevich's book concurrently

>>9357573
During the Jedi training scenes on achto about 30 minutes in:
Luke: "so I see you've made some new friends Rey"
It shows Rey with a couple porgs and a goofy smile.
Rey: I felt them call to me through the force
Luke: it's true. The porgs are pure beings of the force, that's why I came to this place. The porgs tender meat holds the key to a power only Jedi masters can harness.

He grabs a porg from Rey and bites it's neck, blood sprays into his mouth and he gets a wild look in his eyes.

Luke: yes, the power! I can feel the force growing inside me, and inside my pants the force is growing!

The bulge is massive and throbbing. Rey wastes no time derobing, showing Luke the wetness dripping down her legs and mixing on the floor of the hut with porg blood.

Rey: now show me the power of a Jedi master, as we partake in the ancient ritual of the porg blood orgy!

Luke: hey r2, help me out with this sluts loose poon, will ya?
R2d2: beep boop (a flap opens up and a pulsating dildo emerges from r2.

A familiar voice emerges from the force, it's han "great job kid now let's blow this thing and go home"

Luke: aaaaaaahhhhh the pleasure! I'm blasting your inner wet walls with my jaws juice!

Rey: thank you, my master. The ritual is complete. Now I am the Almighty Mary sue! All white males must commit suicide in my honor!

Luke: as you wish, my vaginal god

Luke ignites his green saber and slices off his dick and balls and then stabs himself in the chest.

Should maths research be subject to ethical clearance?

What's the quick rundown on the Millennium Prize Problems?

Riemann Hypothesis is obviously true
Birch Swinnerton Dyer is obviously true
P is obviously not equal to NP
Navier Stokes is ?
Hodge Conjecture is ?
Yang Mills is ?

>>9362923
>Navier Stokes is ?
Tao is going for false

>Hodge Conjecture is ?
likely false

>>9362983
>>Hodge Conjecture is ?
>likely false

Why?

>>9359687
>>9360630
Then how do you show this:
[eqn]\frac{\Gamma,\, \varphi \vdash \psi \qquad \Gamma,\, \varphi \vdash \neg\psi}{\Gamma \vdash \neg\varphi}[/eqn]
From these?
[eqn]\frac{\Gamma,\, \varphi \vdash \Delta}{\Gamma \vdash \neg\varphi,\, \Delta} \qquad \frac{\Gamma \vdash \varphi,\, \Delta}{\Gamma,\, \neg\varphi \vdash \Delta}[/eqn]

>>9363020
Not those anons, but in intuitionist logic you aren't allowed to use sequents with more than one formula on the RHS. So you'd have to use the top rules for negation, or use natural deduction.

>>9363038
But to use the LJ system, you have to restrict the LK system and not invent a whole different system. Otherwise, this becomes allowed in an "intuitionistic" system:
[eqn]\frac{\Gamma \vdash \neg\forall x,\, \neg P\left(x\right)}{\Gamma \vdash \exists x,\, P\left(x\right)}[/eqn]

>>9362989
Is has been proved to be false several times for stronger requirements already several times in the past

>>9363020
There are a million frameworks. Principle of explosion is often adopted and then you're there. I don't see where the later two judgements come from.

If you like, you can just few intuitionistic logics as systems with semantics richer than the Boolean classical logic. Notably, inutionistic logic enabled the Heyting-Kolmogorov reading and is interesting for programming.

And in any case, any classical theorem has an inutitionistic pendant, so that they are classically equivalent. For for example, you can't intuitionistically proof, A∨¬A, but you can prove, ¬(¬A∧¬¬A). And if you take the latter in a classical context, then it reduces to the former. In that sense, LEM is a trick to get simpler proves, but you don't "really" prove more. In fact, you restrict your theories (assuming you want them to be consistent), as you might want to add more axioms that contract LEM.

>>9362923
Yang Mills possibly undecidable

>>9363048
>But to use the LJ system, you have to restrict the LK system and not invent a whole different system. Otherwise, this becomes allowed in an "intuitionistic" system:

I don't follow - how is this allowed at all? What intuitionistic rule are you using? And what is your point?

>>9363020
There are a million frameworks. Principle of explosion is often adopted and then you're there. I don't see where the later two judgements come from.

If you like, you can just few intuitionistic logics as systems with semantics richer than the Boolean classical logic. Notably, inutionistic logic enabled the Heyting-Kolmogorov reading and is interesting for programming.

And in any case, any classical theorem has an inutitionistic pendant, so that they are classically equivalent. For for example, you can't intuitionistically prove, A∨¬A, but you can prove, ¬(¬A∧¬¬A). And if you take the latter in a classical context, then it reduces to the former. In that sense, LEM is a trick to get simpler proofs, but you don't "really" prove more. In fact, you restrict your theories (assuming you want them to be consistent), as you might want to add more axioms that contract LEM.

>>9363056
more like

>Yang Mills we have no fucking idea

contradict LEM

>>9363061
>And what is your point?
To get LJ (intuitionistic Gentzen), you need to start from LK (classical Gentzen) and put the restriction on it, not create another system with your own rules with only one conclusion. This means that before using the contradiction rule, you'd have to first prove it using LK. Except that with LK all you can do is this:
[eqn]\frac{\Gamma,\,\varphi \vdash}{\Gamma \vdash \neg\varphi}[/eqn]
which gets you stuck right away.

>>9363094
>you need to start from LK (classical Gentzen) and put the restriction on it, not create another system with your own rules with only one conclusion

No, you don't.

>>9363237
Then I guess existence proofs by contradiction are fine.

>>9363056
>Yang Mills possibly undecidable
I know there's an undecidability result for the spectral problem of general 2D lattice Hamiltonians but it is not at all clear if this has anything to do with the corresponding problem in Yang-Mills.

>>9363262
Physishit avatarfags should head to >>>/x/

>>9363530
He posted a reaction image. That's not what avatarfagging is you obnoxious faggot.

>>9363066
see >>9363530

>>9363531
>constantly using images of the same character is not avatarfagging
Are you retarded?

>>9363531
>faggot
Why the homophobia?

>>9363561
see >>9363530

>>9363561
>homophobia
Why the homophobiaphobia?

I have such a respect for "real" mathematicians.
I clawed my way to a BS in the topic, but haven't been working in it and it's just gotten rustier.

That beautiful feeling of solving a problem, I've only known it at the undergrad level, guided to it by mentors and classmates.
I was never great at math to start with. And now I have no reason to delve into it, so I'm just face to face with my disgusting pig nature of disregarding things unless they come to me in the form of whip or carrot.

>>9363905
Forgot my youtube
https://www.youtube.com/watch?v=6mWF1kmCo3U

>page 11 into textbook “application: the fundamental theorem of algebra”

>>9363920
>application

>>9363920
>>9363968
>hurr durr muh ivory tower autism who cares about knowledge actually being useful

>>9363920
>>9363968
imagine posturing this way while accepting the real numbers in daily practice (application)

>>9364222
What are these "real numbers"?

>>9357573
Are 101-201 what are considered Calc 1-3 on here?

>inb4 brainlet can't read

I just want to make sure.

>>9364284
>math for social science
more like numerical literacy for retards.

>>9364284
>>>9357573(OP)
>Are 101-201 what are considered Calc 1-3 on here?

looks like it

>>9364284
>Intro to PDE's before elementary linear algebra

What the fuck anon

>>9364284
Day by day, I am constantly feeling happier I'm not a yankee doodle boy when I see stuff like this.

>>9364299
I took a PDEs class and barely remember any linear algebra, it just was a lot of methods of characteristics, millions of inequalities and integrals

>>9360419
So very wrong. Do not attempt to read Hartshorne without having a good grasp on classical AG.

>>9364405
Why not?

>>9364424
A lot of it will just feel so incredibly pointless and unmotivated that it's likely the reader will reach a point of having exactly zero intuition beyond pushing symbols around.

>>9364468
I see, so your opinion can be safely ignored. Thanks anyway.

>>9364468
>>9364477
FIGHT FIGHT FIGHT FIGHT FIGHT FIGHT FIGHT

Does Curry-Howard/BHK/whatever-it's-called have anything to say about the semantics of Peirce's law [math]call/cc : ((A \to B) \to A) \to A[/math]?

My current understanding of [math]call/cc(f)[/math], using what meager knowledge of programming I have, is to imagine a program in the process of producing a value of type B, with type A as an intermediate representation, and [math]dots : A\to B[/math] as representing the remainder of the procedure. [math]f[/math] is a function that is "allowed to peek ahead" and inspect [math]dots[/math] in order to do its thing and return a value of type A. So [math]call/cc[/math] -- i.e. the map [math]f \mapsto f(dots)[/math] -- is what "actually" invokes [math]f[/math].

The problem is that I know this interpretation is wrong, because it places the blame for the intuitionistic violation on the definition of [math]f[/math], instead of the operator [math]call/cc[/math]. So what would the correct interpretation look like, then?

>>9364424
Hartshorne is a meme

>>9363076
all functions are continuous
t. brouwer

>>9364405
>>9364468

I said classical algebraic geometry would be good for motivation. But ultimately you don't actually need it when working through the heart of the book (ch. 2&3) outside of a few exercises.

>>9364735
No it isn't. Working through the exercises is the most straightforward way to get a solid ground in algebraic geometry.

>>9362443
>>9364405
>>9364767

how about Eisenbud's Geometry of Schemes? It says on the preface that is just between Hartshorne's chapter 1 and chapter 2

Currently I have Eisenbud's Comm algebra and Hartshorne, and just borrowed from the library Shafarevich vol 1

>>9364904
Eisenbud's Geometry of Schemes is a great. It spends a lot of time actually building geometric intuition for all the standard constructions for schemes. Would help to have around when doing ch.2 of Hartshorne.

However it does not discuss anything on cohomology.

>>9364299
This is just a list of courses in the order of course number. I also cropped out a bunch of other courses. It is in no means a structure of any program.

So, can you answer my question please?

What are some good books for learning classical geometric constructions and projective geometry?

Does this pattern for calculating determinants generalize to higher dimensions? I.e. can I take the cross product of its rows in greater than R^3?

Does this pattern for calculating determinants generalize to higher dimensions? I.e. can I take the cross product of its rows in greater than R^3?

Which European unis would be good for someone interested in PhD stuff and algebraic topology?

>>9365152
>Does this pattern for calculating determinants generalize to higher dimensions? I.e. can I take the cross product of its rows in greater than R^3?
The cross product is only for dimension three, but you might want https://en.wikipedia.org/wiki/Laplace_expansion

>>9365212
Is there such a thing as an in-place laplace expansion that doesn't involve making lots of copies of the submatrices? I need a high performance way of calculating the determinants of small matrices for some code I'm writing. I'm trying to calculate the enclosed space of a bunch of n-simplexes.

>>9365152
no - look up false sarrus rule on math overflow - basically, it fails for all matrices over 3x3 unless their rank is small enough

>>9357573
when do i know that a limit gives a horizontal, vertical or oblique asymptote?

pic unrelated.

>>9365232
Mutability is really a property of your implementation language, but there's a non-recursive determinant formula using the 'Levi-Civita symbol' (it should be on Wikipedia), which should be easy enough for a low-level language to apply.

>>9357573
>tfw to smart to take the axiom of choice

>>9365232
>>9365579
>>>/g/

>>9358010
>>9358466
The more "intuitive" interpretation is that a proposition is proved after you've constructed the object that the proposition is about. In order to prove $p \vee q$ it isn't enough to e.g. assume there is no example for $p$ and then construct one for $q$: you need, directly, to construct an example of p, or construct an example of q.

>>9359715
How intalegant do i need to be to understand this stuff? Im kinda intrigued by the interaction between space time and electricity but never was good in math or physics. Is there something else i should watch understand b4 completely watching this`?

>>9366814
Why is that more intuitive?
Like what is >the object that the proposition is about
?
You need some kind of notion of "space"/type/set to make sense of it. Then the object is an element of the space.

>>9365385
Vertical: if you have a division by 0 at some point in your function
Horizontal: if the function tends to a specific number as x tends to infinity (in particular, f(x) does not tend to infinity)
Oblique: If the function tends to a linear polynomial, ie: for large x, f(x) ~ x-a

>>9366864
Why do laymen feel entitled to understanding advanced physics in particular?

>never was good in math or physics
Gee, maybe you should start there?

Over the year through my probability courses we finished "Mathematical Statisitics and Data Analysis" by Rice. I liked the rigor and derivations, and how they built everything, but I want to learn more advanced probability theory, stuff to do with martingales, copula, time series and whatever, what is a good book for this?

if x=2arctan(t) how do i find out that cos(x)=(1-t^2)/(1+t^2) and sin(x) = 2t/(1+t^2)

>>9364511
You write
>cc/call : ((a->b) -> a) -> a
>dots : a->b
and then both
>cc/call(f)
and
>f(dots)

so it's not clear what type your f has. Is it of type "(a->b) -> a" or "a->b"?

In any case, the theorem ((a->b) -> a) -> a is certainly not intuitionistically provable, just as there is no function of that type within a functional language like Haskell itself.

But when you program, there's the notion of execution and this is where "continuation" pops up. And then some languages can internalize this.

Think of how "runtime" is not explicit in algebra. The functions
(a,b) \mapsto (a+b)*(a+b)
and
(a,b) \mapsto a*a+2*a*b+b*b
applied to (5,6) will execute differently (e.g. in the first case, two additions and then only one multiplication is involved), so you have different runtimes. But "runtime" isn't part of the language and so it's invisible.

>>9357573
Help pls
Does [math](X^TX+\lambda I_n)^{-1}X^T[/math] equal to [math]X^T(XX^T+\lambda I_m)^{-1}[/math], where [math]X \in \mathbb{R}^{m, n}[/math]

>>9369498
>Does (XTX+λIn)−1XT equal to XT(XXT+λIm)−1, where X∈Rm,n
Why would it?

>>9369505
This identity is used in my lecture notes without justification.

>>9369498
Yes, it's quite obvious.

>>9369509
Method of Least Squares using weightings (moving averages?).
Nice.

>>9369498
>>9369509
some heuristics:

(x, (M X) y) = (x (M X)^T, y) = (x X^T M^T, y)

so we need to argue that M^T = M.

>(X^T * X)^T = X^T (X^T)^T = X^T X
so c·X^T * X is symmetric, as well as powers of it

1/(1-S)=1+S+S^2+... is then symmetric too

done

>>9369695
You could just calculate that
[eqn]X^T (XX^T+\lambda I_m)= (X^TX+\lambda I_n) X^T [/eqn]

What's the coziest maths for self-study?
I vote combinatorics

>>9370879
>combinatorics
>maths
What did he mean by this?

>>9370936
This
https://www.amazon.com/Combinatorial-Problems-Exercises-Chelsea-Publishing/dp/0821842625

>>9371022
So just say combinatorics next time, no need to mention unrelated things like math.

>>9364284
What is Higher Geometry?

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

Granting the strict logical consistency of post-Cantorian, axiomatized infinite set theory, Craig concludes that the existence of an actually infinite number of things is metaphysically impossible due to the consequential absurdities that arise.[33] Craig illustrates this point using the example of Hilbert's paradox of the Grand Hotel. In Hilbert's hypothetical fully occupied hotel with infinitely many rooms, one can add an additional guest in room #1 by moving the guest in room #1 to room #2, the guest in room #2 into room #3, the guest in room #3 into room #4 and continue the shifting of rooms out to infinity. Craig points out that it is absurd to add an additional guest to a fully occupied hotel and the absurd result that the hotel has the same number of guests, infinity, both before after adding the additional guest.[34] Stating that the mathematical conventions stipulated to ensure the logical consistency of this type of transfinite arithmetic have no ontological force, Craig concludes that finitism is most plausibly true, which means that the series of past events in the universe must be finite, so it must have had a beginning.[35]

Craig says that just as it is impossible, despite the proponents of "super-tasks," to count to infinity, so it is metaphysically impossible to count down from infinity.[36] Craig says that an inversion of the story of Tristram Shandy is a counter-intuitive absurdity that could result from the formation of an actual infinite. Craig claims that if the universe were eternal, an infinite number of events would have occurred before the present moment, which he says is impossible.[37]

>>9357573
>praise coq
indeed.

>>9365090
Coxeter - Geometry Revisited

Where are can I find problems for Real Analysis with really detailed solutions? I've tried Kaczor and Nowak but many things there make me feel really stupid for not even understanding the solution.

>tfw thinking of taking the easy way out and take my masters in insurance mathematics

>>9372295
abbott with solution manual

>>9370879
analysis

>>9372738
Actuarial science is a meme, especially at the master's level.
No company actually gives a shit about your academic credentials outside of the exams.

>>9372823
Might be a meme but it is needed here since you can't be a licensed actuary without it and I will always have the option to study for a phd in insurance math if I want to stay in academia
>tfw Sweden is so small that only one university has the masters programme in insurance math
Lets hope that it creates artificial scarcity

>>9372839
Ah, I assumed you were American. I know England has very different credentialing structure so yurop probably does too.
Over here one of the nicest things about the actuarial field over here is that all you need to get your foot in the door is a couple of brainlet tests under your belt.

>>9372846
Ah, here it is a bachelor in mathematical statistics, I dunno if it exists in other countries (I saw in the wikipage about Per Martin-Löf, they clarified what it meant and mentioned that it is a swedish tradition) but it is basically a bachelor in math with focus on mathematical statistics, probability theory and some stats, then you need the masters in insurance math.
I'm just scared that if I get a masters in mathematical statistics or a masters in math I won't get a job, which is a bit silly since like 98% of everyone that has a masters in mathematical statistics get a job in 6 months

>>9358034
Depends on how many states P has

>>9372295
schaum's outlines - it's literally a problem book

>>9365152
Determinants are stupid (mostly)

http://www.axler.net/DwD.html

>>9373285
>Determinants are stupid (mostly)
t. freshman

>>9373293
lel, a first linear algebra course can be described pretty succinctly and elegantly in a few pages without determinants, it's actually pretty interesting the way Axler presents it

also this is a meme paper from 1995 that everybody here should have already read

>>9372295
Another book that's good is titu's problems in real . It's made for people taking the putnam and a good way to learn how to solve tougher analysis problems with complete solutions.
http://facultymembers.sbu.ac.ir/shahrokhi/ProBookMathAnal2.pdf
Happy problem solving anon.

>>9358010
How can people be this retarded?

>>9372295
>>9373434
A few more that I forgot to mention
http://kryakin.org/am2/_Olmsted.pdf
https://books.google.com/books?id=_YhqCQAAQBAJ&pg=PR14&source=gbs_selected_pages&cad=3#v=onepage&q&f=false
https://books.google.com/books?id=ZRnrCAAAQBAJ&pg=PR5&source=gbs_selected_pages&cad=3#v=onepage&q&f=false

>>9372295
>Where are can I find problems for Real Analysis with really detailed solutions?
Write them yourself.

What's the latest actually important math publication?

>>9374034
Numerical infinities and infinitesimals: Methodology, applications, and repercussions on two Hilbert problems
http://wwwinfo.deis.unical.it/yaro/EMSS_Sergeyev.pdf

>>9369830
since X doesn't even have to be square, why is it clear that this would work?

or do you mean going into coordinate representations to show the matrices commute

>>9374215
browsed through it, but what does he really show?

I can point you to 100 papers of people coming up with their own systems and developing it a bit.

>>9374242
He BTFO'd Cantor

>>9371792
Thanks but I was looking for something more axiomatic, like Euclid.

>>9374285
Hartshorne - Geometry: Euclid and Beyond

>>9358193
>what matters is beliefs

god I hate liberals so much

>>9374346
What?

Is Functional Analysis the class where brainlets get separated from non-brainlets?

>>9374365
yes, in the sense that the non-brainlets took algebraic courses instead

>>9374486
this

>>9374486
based algebra gang killing em

>>9374486
>>9374549
>>9374622
>taking useless courses over useful ones
spotted the brainlets

>>9374635
Spotted the subhuman engineer.

>>9374645
>engineers learn functional analysis

>>9374678
The lowliest of their kind doesn't, the rest do since it's an engineering topic.

>>9374635
kys analet

>>9374236
[math] X^T (XX^T+\lambda I_m)= (X^TX+\lambda I_n) X^T \Leftrightarrow (X^TX+\lambda I_n) ^{-1} X^T = X^T (XX^T+\lambda I_m)^{-1}[/math], right? The things we invert are square, so should be no problemo

Do black holes orbit around anything?

How quickIy do they move?

>>9374984
define black hole
define orbit
define anything
define quickly
define move

>>9374984
>>9375032
>>>/x/

>>9375032
I'm not sure what you mean, but you can look up those words on wikipedia/wiktionary if you'd like

>>9375056
>>9375064
please give the precise mathematical definitions
sheesh I think they taught in intro to proofs class that this is important

>>9375083
>please give the precise mathematical definitions
>sheesh I think they taught in intro to proofs class that this is important
Can you elaborate? I'm not sure what you're still confused by, did you not read the wikipedia/wiktionary pages?

>>9375099
words like "black hole" and "orbit" are not standard math terms so you need to specify so I know what the fuck you're asking

>>9375105
>words like "black hole" and "orbit" are not standard math terms
Yes they are.

>>9375105
>doesn't know the word orbit
pls leave freshman

>>9375105
>"black hole"
Terminal object in the category of holes.
>"orbit"
For a group [math]G[/math] acting on a set [math]X[/math], the orbit of a point [math]x \in X[/math] is the set [math]G_x = \{g \cdot x : g \in G\}[/math].

>>9375105
if you don't even know the words being discussed just stay in your lane, you can chime in and try to answer a question when someone posts a question more fitting to your level of knowledge

>>9375105
>you need to specify so I know what the fuck you're asking
Consult any textbook on the matter. There are a lot of those even for undergraduates.

>>9375105
>words like "black hole" and "orbit" are not standard math terms so you need to specify so I know what the fuck you're asking
the absolute state of /mg/

>>9374984
This probably isn't the right thread to ask this.

>>9375158
>This probably isn't the right thread to ask this.
Why not?

>>9375105
Black holes are solutions to Einstein's equations with apparent singularities.

>>9375165
this is math general not physics general

>>9375166
[math] physics \subset maths=(pure maths\cup applied maths) \subset computer science[/math] (as categories)

>>9375165
Geometric Analysis faggot

>>9375177
>faggot
Why the homophobia?

>>9375176
No.

>>9375161
It's not a math question?

>>9375185
What's not mathematical about black holes and orbits?

>>9375105
I'm not sure what's more amusing: this post, or the replies.

>>9375194
There's a difference between having a mathematical model of something and that something being inherently mathematical. For instance, migration patterns of birds would also make for a poor question. You'd be more likely to receive satisfactory answers asking a group whose interests lie in physics.

>>9375180
homophobia is natural

>>9375201
>There's a difference between having a mathematical model of something and that something being inherently mathematical.
What's not inherently mathematical about a black hole in spacetime?

>>9375176
>appliedmaths
No such thing.

>>9375205
Mathematics is a human invention. Physicists use it to describe stuff. It's a somewhat pedantic thing at the end of the day, but mathematics is distinct from physics.

>>9375212
>Mathematics is a human invention. Physicists use it to describe stuff. It's a somewhat pedantic thing at the end of the day, but mathematics is distinct from physics.
I'm not sure what this has to do with black holes in spacetime. There's no 'mathematical ambiguity' or whatever it is that's misleading you

>>9368121
Sure you can do that in haskell:

f :: (( a -> b) -> a) -> a
f q = q ( \f -> undefined )

It gives magical errors though as you run it:

*Main> f (\q -> q 2)
*** Exception: Prelude.undefined
CallStack (from HasCallStack):
error, called at libraries/base/GHC/Err.hs:79:14 in base:GHC.Err
undefined, called at Bla.hs:2:17 in main:Main

>>9375205
They're just things that exist in our physical universe.

>>9375127
>Terminal object in the category of holes.

>>9375220
it's just complaining that \f returns undefined and so f (\q -> q 2) evaluates to undefined

>>9375220
>>9375236
>>>/g/

>>9375226
>They're just things that exist in our physical universe.
black holes are like atoms, they're useful for making models and coming up with theoretical ideas but they don't actually exist in practice

>>9375226
>They're just things that exist in our physical universe.
I'm not sure why you'd work with physical manifestations instead of mathematical formulation given the context

>>9375201
>There's a difference between having a mathematical model of something and that something being inherently mathematical.
But black holes are inherently mathematical, they just happen to also appear in nature.

>>9374486
>>9374549
>>9374622
>Not realizing that at the advanced level functional analysis involves C*-algebras and is intimately connected with the representation theory of infinite compact and discrete groups, as well as the representation theory of lie groups.

>>9375292
>at the advanced level
see >>9374365

>>9375292
It's still analysis, analcyst.

>>9375316
>>9375296
>Hating on based representation theory
It makes algebra even more beautiful

>>9375406
>beautiful
>>>/lgbt/

Mathematician in Kyoto cracks formidable brainteaser
http://www.asahi.com/ajw/articles/AJ201712160034.html

Latest on abc
http://www.math.columbia.edu/~woit/wordpress/?p=9871
>reports today (see here and here) that indicate that Mochizui’s IUT papers, which are supposed to contain a proof of the abc conjecture, have been accepted by the journal Publications of the RIMS.

Latest news on Mochizuki's proof
https://plus.google.com/+johncbaez999/posts/DWtbKSG9BWD
>Today, long term supporters of M's case began their Echternachian-retreat after finding out that Mochizuki himself is the editor in charge of that respectable journal.

>>9375420
>Implying half the fucking posters here aren't female (male) and are attracted to other females (males)

>>9375636
In other news Scholze has published a survey article that will presented at the rio ICM, so it's very clear he's either getting the Field's medal

>>9375226
>black holes exist in our physical universe
No.

>>9375282
>also appear in nature.
No.

>>9375808
>he's either getting the Field's medal
please finish the sentence

>>9375636
Mochizuki is a fraud who's only interested in prestige in his home country. Typical east-asian ant-man behaviour.

>>9376229
Either getting the Field's medal now or the next ICM, I'm pretty sure it's gonna be this time around though.

>>9376336
Who're you guessing will be the other 3 mathematicians to get it?

>>9376583
Simon Brendle, Maryna Viazovska, and Ciprian Manolescu , though it's very possible that Geordie Williamson will take one of the positions as well

in the finite 8 element field [math]\mathbb Z_2[e^{2i\pi/7}][/math], to what element does [math]1+e^{2i \pi/7}[/math] correspond to?

>>9377761
>in the finite 8 element field Z2[e2iπ/7], to what element does 1+e2iπ/7 correspond to?
What do you mean?

>>9377774
https://math.stackexchange.com/questions/2572483/compute-the-addition-table-of-the-finite-field-mathbbf-8

>>9377779
I still don't know what you mean. 1+e^(2i pi/7) is an element of Z_2[e^(2i pi/7)], what would it 'correspond to' other than itself?

>>9377804
There are only 8 elements in the field. Namely, [math]0,1,\zeta,\zeta^2,...,\zeta^6[/math]. Since it is a field, it is in particular closed. So [math]1+\zeta[/math] has to correspond to one of [math]\zeta^2,...,\zeta^6[/math]. My question is, which is it?

>>9377779
>to what element does 1+e2iπ/71+e2iπ/7 correspond to?
To an element that's not in the Field, since no power of it gives 1 or 0.
You know what this implies...

>>9377817
[math](1+\zeta)^7=0[/math]
Also i dont know what it implies

>>9377817
>To an element that's not in the Field, since no power of it gives 1 or 0.
Why would no power giving 0 or 1 make it not a field element?

>>9377824
>82
>>9377817
oh shit [math](1+\zeta)^7=(1+\zeta^3)(1+\zeta^4)=0[/math] so it's not even an integral domain? What went wrong here

>>9377833
>oh shit (1+ζ)7=(1+ζ3)(1+ζ4)=0 so it's not even an integral domain?
Why is that equality true?

>>9377852
>Why is that equality true?
the first equality*

>>9377852

Oh crap [math] (1+\zeta)^n=1+\zeta^n[/math] only works for even exponents

>>9377810
>There are only 8 elements in the field. Namely, 0,1,ζ,ζ2,...,ζ6.
Maybe use the representations
0, 1, z, z^2, 1+z, 1+z^2, z+z^2, 1+z+z^2 instead

>>9377864
damnn just got that since [math](1+\zeta)^7=1[/math] since it must be a power of zeta, then [math](1+\zeta)(1+\zeta^6)=1\implies \zeta^6=1+\zeta^5\implies \zeta^5(1+\zeta)=1\implies \zeta+1=\zeta^2[/math]

>>9377896
Why is (1+ζ)(1+ζ6)=1?

>>9377864
>Oh crap (1+ζ)n=1+ζn only works for even exponents
Why?

>>9377934
>>9377920
stop busting my balls

>>9377369
>Maryna Viazovska
Definitely, because she possesses a vagina.
>Simon Brendle
Why though?
>Ciprian Manolescu
Same question.

>>9378718
>>Simon Brendle
>Why though?
He did a lot of highly influential work in differential geometry, plus since he's 36 this may be his last chance. A lot of the other front runners for the fields medal are younger (like figalli) so it makes sense to pass them up this time around
>>Ciprian Manolescu
>Same question.
Disproof of the Triangulation Conjecture and contributions to Floer Homology. Plus he's also 38, so the argument from before applies.

>>9378922
Both are white males though (ok, one is arguably a gypsy). Surely we can find some young lasses and give them the medal, right?

>>9374288
thanks, looks good so far

>>9378999
Trips wasted by a sexist pig. Great.

>>9378999
Fuck off.

>>9378999
>manolescu
>gypsy
Do you have any reason to believe he is a gypsy other than his name? Confusing Romanian people with Romani people is a gradeschooler's mistake. We can then divide the case into three options:
>you didn't know romanian and romani people were two different peoples
Then you are an idiot.
>you knew they are two different peoples but you still call romanians gypsies because why not
Then you are an idiot, and you are also disrespectful towards men like Vlad III and Ceaucescu.
>he really is a gypsy
Then your idiocy is undetermined, but you are obsessive and focus on people too much. Stop worshipping cogs of the academic machine. That he was a gypsy is highly unlikely, though, since gypsies tend to be violent and selling stuff (possibly stolen stuff) instead of academically inclined.

What's a reasonable estimate on the number of Boltzmann brains floating around the universe?

>>9379542
Chill out gypsy, it's just banter. If Manolescu gets a Fields medal in per capita terms the gypsies' results will be equal to Germany's if Scholze and Brendle also get it. http://stats.areppim.com/stats/stats_fieldsxcapita.htm

just a thought.

>>9379322
>>9379380
Ooh, the PC police is here I see.

>>9379829
I may be on the mathematical level of a gypsy, but I am not one. I have once tripped a gypsy and then kicked him a few times when he walked at me when I was drunk and walking home, but he didn't even bleed. Therefore, I have no gypsy blood in or on me.

>>9379844
Kicked him when he was lying on the ground. > bit nasty perhaps, but people with darker skin deserve to taste the boot a few times in their lives.

>>9379699
420

>>9379847
Wait no, that was a nigger. Forget.

>>9379852
I didn't know there are niggers in Finland.

>>9379877
Maybe like 25k darkies in total or something. I don't know the actual number, but not more than 50k for sure. Oh and yet another reason why you shouldn't call Romanians gypsies is mr Diaconescu.

>>9379890
>In mathematical logic, Diaconescu's theorem, or the Goodman–Myhill theorem, states that the full axiom of choice is sufficient to derive the law of the excluded middle, or restricted forms of it, in constructive set theory.
No, fucking, way. I swear to god if someone proves the converse I'm going to kill myself.
>tfw can't reject axiom of choice without rejecting LEM

>>9379918
>tfw can't reject axiom of choice without rejecting LEM
AC -> LEM => not-LEM -> not-AC, not not-AC -> not-LEM. ZF with no AC can still be used with bivalent logic. You had the implication reversed. Now is not the time for suicide. That comes later.

>>9379947
>AC -> LEM => not-LEM -> not-AC, not not-AC -> not-LEM.
Yes, that's why I'm scared of somone proving the converse giving not-AC -> not-LEM.
LEM is every mathematician's best friend but AC is some spooky shit.

>>9379983
Ah, I was a bit dumb. Have a nice day/evening whatever it is.

>>9379991
You too. (evening (je suis français))

I'm trying to do some multivariate (dim=100+) optimization. Can I cheat when using newton's method and use finite differences for the second derivative so I don't have to calculate dim^2 second derivatives? Would there be any problems with doing that?

>>9378999
There actually is a woman who has a very slight chance getting the fields medal, she's 37
https://en.wikipedia.org/wiki/Sophie_Morel
She has one some bigger awards and given an ICM talk

>tfw forgot all of linear algebra

>>9360758
Any other recommendations? Should i just go with stewart?

>>9379542
>disrespectful towards """ men""" like Ceaucescu
Good.

What is the best path towards proving the negation of AC?