/sci/ - Science & Math

>>9497500
sage

>>9497538
sry your shitty physics generals never catch fire
anti-sage, btw

>>9497500
Advice on learning category theory if you're a brainlet? I'm working through spivak and having trouble.

>>9497561
75% learning advice, 10% homework, 10% anime, 5% math. I'm a math major. Sage

there is literally nothing wrong with mathematical logic

0.999999999999..... = 1

>next generation of mathematicians hate logic and set theory

We're doomed

>>9497872
any takers?

>>9497710
Keep working on Spivak for now.

>>9497919
This

>>9497919
>>9497960
nobody's cared about your shit field after Hilbert's program was BTFO by Gödel and certainly not after CH was proven independent of ZFC lol.

>>9497966
>caring about incompleteness
set theory does suck balls though

>>9497991
but it's true, logic and set theory were one of the hottest fields of the day due to Hilbert's program and it was based Gödel who put a stop to that madness.

Any good crash course for multivariable calc? I need to briefly know about line integrals, Stoke's theorem, gradients and so on
I plan to study it the right way but I need it's methods to understand Fluid Mechanics (multivariable calc is a corequisite).

Mother took me out of second grade because teacher wouldn't let me go to my mom's car yet because of bus. All my knowledge of Mathematics comes from Khan academy. Pretty much only know arithmetic and algebra. I'd like to go to college for Mathematics, but honestly where do I start learning by myself? any book recommendations?

>>9498001
If you think he put a stop to it you don't understand what he was saying

>>9497919
the current one does already, sad to say

>>9497919
It's just a change in working language. The math community always had its trends just like anything else. Set theory is passe right now, and people would rather study topos theory than logic because it's a more hip way of doing the same shit.

>>9497729
Anime will always be an indispensable element in this thread. Deal with it.

>>9498028
Read wikipedia page. It's just calculus in 3d. Derivatives are now triangles. Stoke's and the divergence theorem can simplify calculations by changing the integration domain. It's all you need to know. I would just jump into fluid mechanics. If you read the book and understand the vector calculus there, you're good. Otherwise, go back to wikipedia page

>>9498253
He put a stop to Hilbert's program. Objective fact of history. Kys.

>>9497919
People have stopped caring about a century ago

I'm thinking about doing youtube videos where I pose problems to encourage users to talk through them. Kind of a like a moderated Putnam.
Any takers? Topics? Or, even better, problems?
I'd like to ramp it up in terms of difficulty, i.e. not start on the hard end but rather on the simple end and get harder with time.

>>9498403
> I would just jump into fluid mechanics
You seem lost. This is the math general.

>>9498384
Topos theory isn't exactly a "cool" subject either. Talk about elementary topoi with an algebraic geometer and watch them crap all over the idea.

Are there any groups known to be non-canonically isomorphic to their automorphism group other than [math]D_4[/math] and [math]D_\infty[/math]? That is, isomorphic through a map other than the map sending g to conjugation by g.

Fuck constructivist autism.
The excluded middle and axiom of choice never hurt no one.

>>9498464
except computers and people that actually need to calculate stuff

>>9498464
that debasement of meaning tho

>>9497500
Where to look for at least somewhat formal definition of invariant.

>>9497919

the "mathematicians" on this board who hate logic and set theory are really (((engineers))) larping

>>9498487
An invariant is a functor generally speaking.

>>9498028
Pauls notes

>>9498028
Rudin.

>>9498550
>Rudin.
Rudin is a meme.

>>9498557
Why? Definitely less meme than >>9498545

mentioned it in the other thread, but would you all be interested in metal gombocs that aren't super expensive? I have access to a 4-axis cnc machine. might have to make them a bit big though for the proper tolerances

>>9498581
Sure!

>>9498028
https://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161

>>9498627
great book, my dad gave me the old copy he used while at MIT when I went off to college.

>>9497500

How do you study? I have my finals coming up so tips would be much appreciated.

Ever shed a tear at the sight of a truly marvelous proof?

>>9498583
gonna ask a math prof if he could help with modeling one and figuring out the GD&T needed; I'm not a math major; just a mech e that thinks gombocs are cool

>>9498679
Something like that. What's really beautiful is the idea or insight that leads to the proof.

>>9498076
You're fucked anyway, might as well go all out with the good old Kolmogorov program. It was meant for people half your age, but whatever, start with his Methods, Meaning etc. then move on to his Elements series, while also reading some baby-tier linear algebra book (Axler if you feel like retard, Shilov if you're confident, Hoffman&Kunze if you're delusional about your capabilities). Also get Shafarevich for intro algebra (or Algèbre by Gourdon if you're still delusional about your competence).

would a "gomboc"-gomboc be desirable, or would it be neat to just generate a solution from the proof; http://www.gomboc.eu/93.pdf; and then make whatever pops out? It is also somewhat doable to make whatever number of stable or unstable equilibrium points as you want.

also, it turns out that slablike bodies can never be monostatic. who'd a thunk?

>>9498883
furthermore, it might be complete ass to try and generate an algebraic solution from the set-based proof. Not to mention the perturbation issue.

I'm just a lowly mech e in over my head I guess...

What's a good N value to pick to ensure [math]a_{n} = \frac{(n+1)(n+2)}{2^{n-1}}[/math] is Cauchy?

>>9497919
This. Tbh I'd rather see more talk about foundations (including logic and set theory) rather than some shit like this >>9499002

>>9499384
>foundations (including logic and set theory)
not math

>>9499388
>not math

commutative diagrams are for gays

>>9499406
this. heterosexuals prefer diagrams which commute up to an n-isomorphism.

>>9498757
why do people keep calling Mathematics: its Methods etc. Kolmogorov's even though he only wrote the chapter on probability theory?

>>9498429
What do you mean?

>>9498497
Shut up LaForge

Does anyone know of a recent (around post-WW2 as a rough starting point) textbooks on Synthetic Geometry? I wanna see how its done without selling my soul to Al-Jabr.

>>9499456
For the same reason they keep calling theoretical physics bible Landau's. They had huge influence on how the subjects were taught.

>mfw I agreed to give a talk at the algebra seminar in two weeks
send help

>>9499479
Barely anyone studies categorical logic in its own right, category theory is mainly seen as a tool by people in "mainstream" areas like alg top and alg geom, though it is slowly changing.

>>9499633
Hartshorne's Geometry: Euclid and Beyond

What is the best (and preferably shortest) way to learn differential forms?

>>9499896
Best is debatable, but I don't know of any short way. You have to do the whole set up for differentiable manifolds, or else take the physicist approach and just pretend like you understand them.

>>9499903
I should have be more specific. I already know some differential geometry and differential topology, it's just that I've been neglecting differential forms because I'm lazy in regards to big formulas.

>>9499912
You shouldn't need any big formulas. Check out this section, it's not that hard: https://en.wikipedia.org/wiki/Differential_form#Intrinsic_definitions

>>9497500
>stop with the l*gic talk
ok so you DON'T want to talk about math?

>>9497710
Chapter 0 by Paulo Aluffi gives a good intro
then go read a category theory text of your choice

I took Logic and Algebra last semester. Did my deductive reasoning improve?

Just started studying "Simulation Methods".
The subject seems really damn interesting.

>>9500010

>>9498464
If P -> Q is true, then Q must be true if you accept the LEM.
>inb4 it makes sense tho uuuhhh

>>9500014
>hurr guys look at me i don't understand logic!
Q will be "true" so long as P is "true"
if you see any problem with that then you should have your head examined because something in its middle has been excluded

>>9498487
invariant means it doesn't change (usually under transformations)
for example, we say that the Euler Characteristic is invariant under homotopy, meaning if the characteristic of the domain is N, then the characteristic of the image under a homotopy is also N

>>9497500
>get duped into doing a math phd
>think I'll get to talk about varieties and decidability problems with my fellow universal algebros
>turns out everyone at my university is a muh cohomology topologyfag who thinks pure algebra is dull and boring
>even my algebra professor thinks categories are a meme only good for proving things in rep theory

Should I just switch to computer science?

Is covariant and contravariant proper mathematical concepts?

>>9500077
>universal algebra
>categories

If you're gonna study that stuff you'll want to find an advisor who's into it. CS can be pretty category-heavy but again look for the right advisor.

>>9500105
A functor as usually defined is covariant: F(fg) = F(f)F(g).

A contravariant functor has F(fg) = F(g)F(f). But a contravariant functor C -> D is the same as a covariant functor C^op -> D or C -> D^op. Same thing, different viewpoint.

>>9500114
>same thing different viewpoint
Exactly. I don't know much about functions, but how on earth they tell me some particular objects (vectors, tensors) are "contravariant" if it seems it just a convention?

>>9498566
You're the retard asking for a crash course of literally the easiest class. You clearly have no clue that rudin is useless here, so how can you feel entitled that Paul's notes are shit? Yes, they in fact are, but they are tailored to brainlets like you

>>9500123
https://en.wikipedia.org/wiki/Tensor#As_multilinear_maps

>>9498497
Bullshit. 70% of my grad student peers and 100% of my professors hate set theory.

Can someone explain homological algebra to me? Shit looks scary but interesting.

>>9500177
Abstract wankery.

>>9500164
To be fair, current research in set theory (ZFC) is pretty uninteresting. Anything beyond forcing and some of its applications (solovay models and how to use it to prove independency results in other areas) is too specific for anyone outside the field to care.

>>9497919
>set """"""""theory""""""""""
>"""""""""""""""""""logic""""""""""""""""""""""""
oh dear. my condolences.

>>9500013
Context?

>>9500193
Say you want to compute an integral of the form [math] \int_{0}^{1} g(y) dy [/math] , then
[math] \int_{0}^{1} g(y) dy = \int_{0}^{1} g(y) \cdot 1 dy = E(g(Y)) [/math] where Y is a random variable following the uniform distribution U[0,1] .
If Y1, Y2 , ... is a sequence of independent random variable from U[0,1] , then g(Y1), g(Y2), ... is a sequence of independent and identically distributed random variables.
By the Law of Large numbers we have that the average [math] \frac{1}{n} \sum\limits_{i=1}^{n} g(Yi) [/math] converges to E(g(Y)) with probability 1.
But, E(g(Y)) is equal to the integral we want to compute.
Therefore, if you somehow get a big ass sample from U[0,1] (say of size N) you can approximate the integral by using [math] \frac{1}{N} \sum\limits_{i=1}^{N} g(Yi) [/math] .

And if you have an integral of the form [math] \int_{a}^{b} f(x) dx [/math] , you can always transform it into [math] (b-a) \int_{0}^{1} f(a+(b-a)y) dy = (b-a) \int_{0}^{1} g(y) dy [/math] .

>>9497919
Computer scientists are the future

Not the ones doing shitty software engineering degrees disguised as "computer science", but people who actually study computer science

>>9500077
>decidability problems
>universal algebra
>/mg/ math general

>>9500246
This. Wanna join me to compute some python integrals later?

>>9500022
Suppose P -> Q is true. By the law of excluded middle, P must be true or -P must be true. If P is true then by modus ponens Q is true. If P is false then because anything follows from a false premise Q is true. In both cases, Q is true. Therefore, if P -> Q is true, Q must be true, no matter what truth value P has.
>still defending jew-LEM

>>9500283
>Therefore, if P -> Q is true, Q must be true, no matter what truth value P has.
This statement is trivially seen to be intuitionistically valid.

>>9500330
Wtf are you even trying to say?

>>9500358
What exactly in my post is confusing you?

If x = y, does it necessarily follow that y = x? I'm trying to find a counterexample but I'm stuck.

>>9500387
>If x = y, does it necessarily follow that y = x?
Yes.

>>9500365
>If a proof of P can be transformed into a proof of Q, then I have a proof of Q duurh duurh
This is what you said. It doesn't make sense intuitionistically.

>>9500387
Suppose there exists x,y such that x=y but y=/=x. Then, since x=y, it means that y=/=y, a clear contradiction because something must be equal to itself

>>9500398
>r*ddit frog
I'm not surprised that you are not able to grasp such basic concepts.
[math](\varphi \Rightarrow \psi) \vdash \psi[/math] is trivially seen to hold intuitionistically (and thus classically) since it holds in every Serre-Kripke model of intuitionistic logic.

>>9500461
>intuitionistic logic.
not science or math

How do I get into Logic, Lambda Calculus and Game Theory without pursuing a Math degree?

>>9500467
It's a subfield of topology.

>>9500493
Do you mean subcategory?

>>9500497
Every field is a category.

>>9497919
>>next generation of mathematicians hate logic and set theory
>We're doomed
Logic is a dead field, there's simply no good reason to bother with it anymore

>>9500482
>How do I get into Logic, Lambda Calculus and Game Theory without pursuing a Math degree?
What do you mean? You wouldn't get into those while pursuing a math degree either.

>>9500508
There aren't any good books about those subjects?

>>9500513
There probably are, but people studying math wouldn't know about them.

>>9500513
>There aren't any good books about those subjects?
Probably not.

>>9500513
Take a look at the engineering section of your uni library.

>>9500504
Intrinsic value.
>>9500246
>>9500262
>tfw cs major
>better at proofs than the math majors
>the math majors just seem to be good at memorizing formulas and quick mental math in their heads

>>9500550
>Intrinsic value.
And what "value" would that be?

>>9500461
>"If it rains it is cloudy" is true (P->Q)
>duuurh so it is cloudy always holds (Q) duurh
This is how you sound. Prove your statement or GTFO.

>>9500246
Logic is essential to CS you mong

>>9500246
>>9501056
>CS
>>>/toy/
CS trash is not welcome here.

>>9501056
>Logic
>>>/lit/

>>9500262
>>9500283
>>9500256
>>9500330
>>9500365
>>9500387
>>9500467
>>9501064
>>9501067

>trolling this badly

>>9501074
>>trolling this badly
Who are you quoting?

is this the 2.0 gpa study group?

>>9501084
Sorry, the CS threads are located at >>>/toy/

>>9501089
>t. engineering major larper

>>9501098
This thread is strictly for discussing mathematics. Proceed to the engineering threads over at >>>/toy/

>>9501103
>t. applied physics major larper

>>9501110
This thread is strictly for discussing mathematics. Proceed to the physics threads over at >>>/toy/

>>9501110
>applied physics
As opposed to what?

>>9501119
see >>9501114

>>9501119
theoretical physics you high school babby

>>9501127
see >>9501114

>be """mathematician""
>can't even define a set
this is why no one takes you seriously

>>9501144
>define a set
Sorry, the philosophy threads are located at >>>/lit/
This is a place where people discuss mathematics.

>>9501165
glad to see we're on the same page. I'd never be caught dead with a joke of a person that calls themselves a ""set"" th*or*st

define "mathematics"

>>9497710
Do what I did switch to Stewart and never look back. Spivak is garbage and even states it's not a calc book

sorry to be a bother but does anyone have that math textbook flowchart? I saw it once but forgot to save it.

What are some important properties of real functions of one variable? Say
>Monotony
>Periodicity
>Parity
>Injectivity/Surjectivity/Bijectivity
>Continuity
>Differenciability

Is there anything I'm missing? I want them all

>>9501682
Integrability, uniform continuity and linearity/affinity.

>>9501682
odd/even (is that what you mean by parity?)
C^n (n times continuously differentiable)
measurability
open
closed
connected
concave up/down
convexity, strict convexity

>>9501084
yes

>>9497919
hott all the way brother

>>9502087
>type """"theory""""
>>>>>>>>math
>>>/g/hetto

>>9501693
>uniform
>not α-Hölder

>>9500283
p -> q = ~p -> q

>>9500283
>>9500398
>Therefore, if P -> Q is true, Q must be true, no matter what truth value P has.
Assume this is true. Then 0 = 1 -> 0 = 1, therefore 0 = 1 holds. Is this the true power of "CS" students?

>>9500387
Depends on the rules of the set that the elements x and y belong to

>>9497710
>>9499990
>heard Category Theory can be used to formalize all Math
>decide to learn
>get a book on the matter, intro says the are no prerequisites
>the very first definition of category talks about "class" and "objects".
>where the fuck was all that defined

>>9500387
>>9502309
Also depends on the properties of X and y as objects, eg scalar/vector objects etc

>>9500283
the statement [math]false \Rightarrow true [/math] is true but so is the statement [math]false \Rightarrow false [/math]

>>9502310
>formalize all Math
This is not well-defined. Where have you ""heard"" this? In your CS department?
>get a book on the matter
On the matter of category theory or on the matter of ""formalizing all Math""?
>where the fuck was all that defined
Classes are an undefined, primitive notion in any sane system. Objects are part of a definition of a category. I know it's hard to actually read while being a CSfag, but you should at least try.

>>9502249
I'm not a subhuman analcyst, so I am not familiar with such properties.

>>9502328
I bet you can't even code a hello world in Phyton, fag.
>On the matter of category theory
Yes.
>Classes are an undefined, primitive notion in any sane system
In which systems are they primitive notions? What are their properties?
>Objects are part of a definition of a category
So are objects a primitive notion too or what?

>>9502403
Objects are elements of a class. That a class is primitive does not imply that objects are.

>>9502388
brinalet

>>9502411
Again, in / for which systems are they primitive notions? What are their properties?

>>9502403
>I bet you can't even code a hello world in Phyton, fag.
>>>/g/hetto
Such trash is not welcome here. This thread is strictly for discussing mathematics.
>Yes.
Then why would you expect it to contain things not directly related to category theory? What kind of retardation is this?
>In which systems are they primitive notions?
Certain formulations of NBG and MK s*t theory. Although these are for plebeians such as yourself. The proper way to go would be assuming the existence of Grothendieck universes and defining a class to be a subset of a Grothendieck universe.
>So are objects a primitive notion too or what?
I'm so sorry that just reading the book you have is too complicated for your puny "CS" "brain".

>>9502411
>Objects are elements of a class.
Elements of classes are called sets. Objects of a category need not be sets.

>>9502420
Do you need to swear?
>things not directly related to category theory
It appears in the very definition of category, anon. Of course it is directly realted.
>The proper way to go would be assuming the existence of Grothendieck universes and defining a class to be a subset of a Grothendieck universe
What books would you recommend to learn about that?

>>9502422
>Do you need to swear?
Yes. Discussion of CS garbage is not welcome here.
>It appears in the very definition of category, anon.
That doesn't mean the study of these objects is directly related to category theory. See Mac Lane's "Categories for the Working Mathematician" for another definition.
>What books would you recommend to learn about that?
See https://arxiv.org/abs/0810.1279 after you are done with the basics.

>>9502420
Every set is a class, too. Therefore a small category also has a class of objects. Every category has a class of objects.

>>9502314
>the statement false⇒true is true but so is the statement false⇒false
This is a meaningless notion.

>>9502403
>I bet you can't even code a hello world in Phyton, fag.
Why the homophobia?

>>9502435
>See Mac Lane's "Categories for the Working Mathematician" for another definition.
His "definition" is hardly rigorous.

>>9502504
>fag is homophobia
?
Plus this is 4chan mate, reddit's down the hall

>>9502509
>?
> Plus this is 4chan mate, reddit's down the hall
"Fag" is a homophobic slur.

>>9502506
It's about as rigorous as axiomatizing "sets" directly, so rigorous enough for usage in mathematics.
For anything else proceed to >>>/lit/. The philosophy threads are located there.

>>9502515
>as rigorous
>rigorous enough
These are meaningless notions. Rigor is binary, while "as rigorous" and "rigorous enough" imply some sort of spectrum.

>>9502518
>Rigor is binary
>some sort of spectrum
Proceed to >>>/lit/.

>>9502511
What is context for 100
>that shirt is gay
vs
>that guy sucking cock is gay
and
>my professor is a fag for giving us that exam
Vs
>my professor is a fag that jerked off two dicks during a lecture
Either way why do you even care?

>>9502518
>binary
This is a meaningless notion.

>>9502524
Don't respond to the spammer.

>>9502527
My bad, I just love (you)'s

>>9502524
>What is context for 100
Irrelevant, https://en.wikipedia.org/wiki/Category:Homophobic_slurs

>Either way why do you even care?
Because there's nothing mathematical about homophobia, take it somewhere else.

>>9497966
Can someone explain in brainlet terms what Gödels theorem showed?

>>9502543
>Gödels theorem
not science or math

>>9502506
Indeed.

>>9502555
more like Categories for the Applied Mathematician

Mac Lane was a hack, his book would be better off burned and the PDFs/djvu files deleted

>>9502310
ETCS is a categorical set theory that can be used to formalize everything that doesn't need large categories.

Category theory itself can be founded either with ZFC + universes, NBG, or HoTT which is a true categorical foundations.

What is objectively the best research area in 2018

>>9502555
What's a "metacategory"?

>>9502571
>What is objectively the best research area in 2018
Non-mathematical physics

>>9502581
Here you go
>>9502560
Agreed.

>>9502592
>Here you go
What is a "metagraph"?

>>9502600
That's a good question! Refer to pic related for the answer.

>>9502583
see >>9501114

>>9500404
>because something must be equal to itself
found the brainlet

>>9500387
In a lot of programming language equality is not transitive. Of course this only means they failed to correctly implement equality, but if you define the set of PHP as your universe then you can do all sorts of retarded math

>>9502555
What exactly is """unrigorous""" here?
>>9502560
CStard detected. Proceed to >>>/toy/
>>9502651
>programming language
Fuck off to >>>/toy/.

>>9502655
>CStard detected.
Only a CStard would learn category theory from such an unrigorous book.

>>9502658
>Only a CStard would learn category theory from such an unrigorous book.
Only a CStard would learn category theory at all. Category theory is wholly irrelevant to most of mathematics, actually.

>>9502661
>this is what CStards who couldn't understand Category Theory actually believe

>>9502658
What exactly is """""""unrigorous""""""" about this book?

>>9502655
haha epic anon, you sure showed those CS nerds!

>>9502670
>>9502667
>>9502664
>>9502661
>>9502658
>>9502655
>CStard / CSnerd / etc
Do you need to swear?

>>9502655
No need to be angry. Swallow the Tsurunen pill and embrace his calmness. His infinite wisdom will guide you through this phase in life, a phase called puberty.

>>9502664
>>this is what CStards who couldn't understand Category Theory actually believe
Who are you quoting?

>>9502678
My thoughts

I see the Mac Lane shills from /g/ have crawled out of the woodwork...

Alright I give in.

Nabbed this problem from /sci/ a while ago, but never fully solved it. What’s the easiest method?

My approach was to, in Cartesian coordinates, set the origin at the center of the smaller circle, such that the vertical axis goes through the center of both circles. Then integrate for the area of the region in Q1, and double it. I never solved it because determining the bounds by hand was a super arguous task that I suspect would be easier to deal with with a different coordinate transform.

Anyone know of a more efficient method?

>>9502670
>>9502676
>>9502682
Deport yourself to the >>>/g/hetto. CStards are not welcome around here.

>>9502682
>I see the Mac Lane shills from /g/ have crawled out of the woodwork...
Does Mac Lane have shills promoting his book here too? I know I've seen both Barry Simon shills and Lang shills already on /sci/

>>9502694
Oh but I am not a CS subhuman.

>>9502694
>CStards are not welcome around here.
Agreed, "Mac Lane" should be an auto-ban.

>>9502694
nigga i bet you havent even published a paper

>>9502673
CSchad

>>9502704
>nigga i bet you havent even published a paper
I'm not a "nigga".

>>9502697
>>9502698
>>9502704
see >>9502694

>>9502708
Why should I go to where I don't belong?

>>9502710
What makes you think you don't belong there?

Why are you people using MacLane? Reihl is far more relevant for the modern student/researcher.

>>9502721
>Reihl
>>>/lgbt/

>>9502713
We could start from the fact that I'm a mathematician and not a CS fag.

>>9502721
>Why are you people using MacLane?
You should ask /g/.

>>9502721
>Reihl is far more relevant for the modern student/researcher.
>female author
dropped

>>9502726
What makes you think so?

>>9497710
I find spivak to be way to roundabout and introduces too many idiosyncratic notions that won't translate to "real" math.

Borceux is fucking great though. Puts in all those details most people leave out.

>>9502420
>elements of classes are called sets
Says who? "Class" as used in ct usually just means a thing with elements (that could be larger than a set).

>>9502721
DAMN. I just read the definition of category in Reihl's book, and I am understanding it better than all this bullshit:

>>9502555
>>9502592
>>9502607

>>9502763
>I am understanding it better
Yeah, it's known to be better for the more simpleminded ones of us.

>>9502726
Upon which evidence are you basing this conclusion?

>>9502729
>>9502767
I know myself.

>>9502764
I adscribe it to the fact the author's is a woman. Women more often tha not need to have the presented mathematical concepts to be simple and already "digested" in order for their brains to cope.

They know better than any man what brainlets need to grasp anything.

jfc, this thread is shit

undergrads should not be allowed to post here

category theory feels very unmathematical

>>9502809
>feels
Proceed to >>>/lit/.

>>9502812
category theory is very unmathematical

>>9502816
proofs_rooster.jpg

>>9502816
>category theory is very unmathematical
Being mathematics or not is binary, while "very unmathematical" implies some sort of spectrum.

>>9502816
why?

>>9497500
I'm confused. So if algebra and logic are CS now, what do you guys consider to be "real math?"

>>9501660

>>9502900
>So if algebra and logic are CS now, what do you guys consider to be "real math?"
All math is "real", you'll have to be more specific.

>>9502900
>algebra
Nobody claimed that algebra is "CS".
>Logic
It's not "CS", but it's not math either.

>>9502900
>"real math?"
This is a meaningless notion, since there is no viable definition of maths.

>>9497500
Any good intro to physics books that are aimed at math students that dont know shit about physics?

>>9502988
Physics threads are located at >>>/toy/

>>9500283
>If P is false then because anything follows from a false premise Q is true.

>>9500513
Philosophy of Logics by Susan Haack

>>9503006
>Philosophy of Logics
Please use >>>/lit/ to discuss such topics.

>>9502956
>It's not "CS", but it's not math either.
why is that?

>>9502684
You can reduce to a simple integral, anon. Is that too difficult or something

>>9500482
I used these
logic: Kleen, Ebbinghaus and Enderton
lambda calculus: Type Theory and Functional Programming - Thompson

t. someone with an actual math degree

>>9503275
Arbitrary integrals need not be well defined.

>>9503441
In this very case it is well defined

>>9503444
Please provide a proof of its existence.

>>9503454
The semi-circle is a continuous function. Continuous functions are Riemann integrable.
Q.E.D.

I thought it was a meme

>tfw reading Lockhart's "A Mathematician's Lament"
How can one man be so right? God, I'm so depressed.

>>9503617
dumb frogposter

>>9503642
rather a frog than a category theorist.

Anyone knows of a good introduction book to differential geometry ?

>>9503667
Category Theory rocks, tho

>>9503673
"no"

>>9503688
Only brainlets and CStards who can't understand it think otherwise. Are you one of them? If so, consider commiting sudoku.

>>9503695
Would rather study fungus growth under a foreskin then categories.

>>9503706
Spoken like a true brainlet

>>9503707
t. brainlet

>>9503713
>t. brainlet
Do you need to swear?

>>9503720
do YOU need to swear?

>>9503732
Where did I swear?

>>9503746
Where did I?

>>9503754
Right here: >>9503713

>>9503757
>>9503707
>"Spoken like a true brainlet"
Hmmm, ah yes. Leave it to a category theorist to be a living contradiction.

>>9503763
That was no swear. That was an accurate description of you and your post.

>>9503706
>study fungus growth under a foreskin then categories.
sounds like quite the afternoon.

>>9503768
Likewise.

>>9503771
Wrong

What does the exponential map actually amount to? How do I compute a vector's image under it?

>>9503774
kk sweetie

>>9497500
WILL AN EVER WIDENING ANGLE EVENTUALLY ENCOMPASS 360 DEGREES AND BEYOND ASSUMING IT ACCUMULATES A WHOLE UNIT VALUE OF AT LEAST 0.00001 DEGREES EVERY SECOND?!?

>>9503804
define "degrees"

>>9503853
define "define"

>>9503914
it's an axiom

>>9503924
define "axiom"

>>9503935
An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Greek axíōma (ἀξίωμα) 'that which is thought worthy or fit' or 'that which commends itself as evident.'

>>9503946
in what way is "define" true or a starting point for further reasoning?

This thread has taught me that Category theory is super gay

>>9503959
Your question is logically incoherent.

so ring spectra can be partially ordered by inclusion, but is every poset the spectrum of some ring?

>>9503983
definitely a spectrum, probably of autism.

>>9503983
I don't think ring spectra means what you think it means.

>>9503983
Ring spectra aside from the spectrum of the trivial ring haven't been shown to exist.

>>9503977
i didn't pose a question

>>9504027
A logically incoherent question is still a question.

>>9501682
>nobody mentioned analyticity yet
also, square integrability

>>9503983
No. Spec(R) is a lattice and not every poset is a lattice.

>>9503983
No: https://www.sciencedirect.com/science/article/pii/0021869373900914#
"every totally ordered set of primes has a least upper bound"
That's not true for every poset.

>>9503642
>complains about frogposting on a site where frogposting is common
Maybe reddit is better for you

>>9503617
>reddit filename
>reddit fr*gs
Your kind isn't welcome around here. Fuck off to >>>/r/eddit/
>>9504522
see the above message.

>>9503671
I'm taking differential geometry right now and we're using the book by Pressley. It's alright so far, haven't read enough to really judge.

>>9504577
>reddit frogs

>Socratic method

>>9500388
a square is a rectangle in all cases but a rectangle is not a square except in specific cases

>>9504625
You're confusing subsets with equality. The set of squares is a subset of the set of all rectangles. That's kind of like saying "if x<y then y<x".

>>9503671
Do Carmo differential geometry of curves and surfaces is the classic

What's a good Measure Theory book?
Preferably non-dry one for self study that doesn't make me want to kms.

>>9504981
https://www.amazon.com/Integral-Measure-Derivative-Approach-Mathematics/dp/0486635198

>>9504987
Thanks! I'll check it out.

>>9504987
Wait a minute, is this the actual Shilov?

I am writing my bachelor's thesis (well just getting started) on Linear Logic and symmetric closed monoidal categories anyone have some recommendation for literature that treats the connection between them?

Have you guys ever noticed how it's usually the dumbest guys in class/the weakest professors in the department that are groggy all the time and quick to call other out on their mistakes?

>>9501056
this, CS people are more likely to study formal logic than a math guy who might just do PDEs or something

so what is mathematics then? if it's all cs

>>9505009
* The book "Topoi" by Goldblatt is simple and very logic oriented (but odd in terms of the order of things)-
* That "Rosetta Stone" article by Beaz mentiones those judgement rules, but doesn't go in-depth at all.
But maybe the references in those two.
* There is "toposes theories triples" by Baar, which might be relevant.
Maybe there's hints in the study guide for logic in "Teach Yourself Logic" by Smith.
* There's abook "Non-classical logic" by Priest which I had in my hands at one point and which may cover that logic (although hardly the category part)
* There's also "Categorical Logic and Type Theory" by Jacobs, which is hard and it's been a while and I don't know how much linear logic is in it.

>>9503958
In what way are our eyes true or a starting point for further reasoning?

>>9505106
>mfw Jaden Smith made fucking sense.

This thread is fucking gay and this world has to be engulfed in the flames of everlasting nuclear war.

>>9505106
No...

>>9505106

>>9505106
>>9497500

https://www.youtube.com/watch?v=JCeOf2q6_TA

I hope you are happy OP.
This is what you have wrought.
THIS IS WHAT YOU HAVE DONE.
WHY HAVE DID YOU DO THIS!?
REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE


https://www.youtube.com/watch?v=Jm2D7ohWos0

>>9505106
"I have no mouth, and I must scream."

Somewhere, there is a God.
Here...there most certainly is not.

>>9505106
._.

https://www.youtube.com/watch?v=CpFdP5yATw0

>>9505100
see >>>/toy/ for avatarfag-physishit threads.