/mg/ math general -- snake edition

This

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.

>caring about incompleteness
set theory does suck balls though

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?

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

the current one does already, sad to say

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.

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

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

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

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.

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

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.

except computers and people that actually need to calculate stuff

that debasement of meaning tho

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

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

An invariant is a functor generally speaking.

Pauls notes

Rudin.

>Rudin.
Rudin is a meme.

Why? Definitely less meme than

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

Sure!

amazon.com/Div-Grad-Curl-All-That/dp/0393925161

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

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?

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

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

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; 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?

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?

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

>foundations (including logic and set theory)
not math

>not math

commutative diagrams are for gays

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

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

What do you mean?

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.

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

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.

Hartshorne's Geometry: Euclid and Beyond

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

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.

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.

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

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

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.

...

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

>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

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

>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?

>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.

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.

>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?

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

en.wikipedia.org/wiki/Tensor#As_multilinear_maps

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.

Abstract wankery.

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.

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

Context?

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] .

Computer scientists are the future

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

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

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

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

>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.

Wtf are you even trying to say?

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.

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

>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.

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

>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.

>intuitionistic logic.
not science or math

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