/mg/ maths general: Mochi edition

so can do calculus on them

Ah. It has a fourier series expansion for non-integer x though.

>dea of the unit circle and right triangles and how they're related

nothing mystical about it
1) a^2+b^2=c^2
2) create a situation where c=1 at all times

since sin = a/c and cos = b/c,
now that c=1, you get sin and cos
straight from a and b

youtube.com/watch?v=spUNpyF58BY

>almost all periodic functions are sinusoidal
define "periodic function," and what the hell does "almost all" mean? i'm not sure i buy this. if you're saying that certain functions can be decomposed as linear combinations of sinusoidal functions, then sure

>create a situation where c=1 at all times
Can you explain this a bit more?
Apologies, it says that "almost all" periodic functions can be _described_ using sine and cosine, I misread that misinterpreted it as "almost all" periodic functions _are_ sinusoidal.

>fourier series
>has more than four terms

what do think the "unit" in 'unit circle' means?

lightyears

're ya go, you just reinvented relativity

greatest common denominator with one argument fixed.
[math]\gcd(a, b) = \gcd(a+b, b)[/math]

Infinite polynomials

Is this the "engineering general"? Why does it say "talk maths" then? My browser seems to be malfunctioning.

>9516444
it's you that's malfunctioning, weebshitoid degenerate subhumANO

You don't mean that.

Does anyone know a source for the proofs of at least some of the cases that [math]\mathbb{Z}[\sqrt{D}], D < 0[/math] is a PID?
Wikipedia gives the complete list of negative integers it works for, but I can't find proofs for any of them other than the Gaussian integers.

Picked up a book on constructivist analysis, gonna be MAXIMUM comfy learning this

Do graduate classes (in math) usually have exams?

One of mine straight up doesn't, and in the other the professor hasn't really made up his mind.

>Does anyone know a source for the proofs of at least some of the cases that Z[D−−√],D

Can posting this be an evidence of autism? "Homology groups of a Pokeball".
math.stackexchange.com/q/2576957/434968

What's so special about Feller processes? Why do we care about the Feller property and don't just simply deal with Markov processes only?

>Why do we care about the Feller property
We don't care about engineering properties around here.

All analytic periodic functions are sinusoidal, which is why modular forms have a q-expansion with q=e^2ipiz

How does one go about showing that all projective transformations of [math]\mathbb{F}P^{n}[/math] take the form
[eqn] \mathbf{y} \mapsto \frac{ \mathbf{c}+D\mathbf{y} }{ a + \mathbf{b}\cdot \mathbf{y} }[/eqn]
in affine coordinates [math](y_{1},\dots, y_{n})\longleftrightarrow [1 : y_{1} :\dots : y_{n}] [/math]

>Brownian motion and the Poisson process are examples of Feller processes. More generally, every Lévy process is a Feller process.
>Bessel processes are Feller processes.
>Solutions to stochastic differential equations with Lipschitz continuous coefficients are Feller processes.
>Every Feller process satisfies the strong Markov property.

not sure if this is the right place but what are the best books on measure theoretic probability theory for someone who has only a bit of familiarity with functional analysis and the idea of measure?

The Holy Bible.

Bishop?

Is it possible for brainlet to love math and hate physics?
They like to say that physics in close relationship with math and I must love(or hate) both.

For a brainlet, yes.

Physcuckery is really terrible.

Better to take pride in ignorance then.

Check out Probability and Measure by Billingsley, the book introduces measure theory so you dont need to know it

>We tried to hire a mathematician who actually had expertise in this and failed. Which is actually sort of sad, because if we actually did we're pretty sure they could solve this entire field of engineering we're in, greatly reducing the need for peons like us.

Probably. What field are you in?

What differential geometry books take a geometrically meaningful approach (think curves as opposed to derivations), but don't make you go into coordinate hell?

Also, all you need to do is give him (yes, him) a few months to learn it. Learning domain-specific applications is easy for a mathematician.

any differential geometry for physicists book

nah I want something mathematically rigorous.

>What field are you in?
I'm curious as well, I can't really imagine any kind of practical (in the sense of money-making business) application of category theory besides maybe in computer science.

Any good books (or other resources) to learn calculus and linear algebra, Discrete math, Proof techniques ?

>Calculus
Spivak
>Linear Algebra
Hoffman & Kunze
>Discrete math
don't
>Proof techniques
Daniel Velleman's How to Prove It and Solow's how to do read and do proofs

Hammock's Book of Proof is also good if you got the time

>don't
why ? I need it.
I can't afford a good school that will teach me.

I forgot to say thanks.
Sorry

what do you need it for, anyway?

Not that guy, but my impression is that discrete math is generally a hodgepodge of a bunch of important topics that should be studied individually.

Why are math textbooks always full of type errors? Particularly differential geometry books. Sick of this shit.

>what do you need it for, anyway?
Genetically engineer cat girls.
[spoiler]Computer Science.[/spoiler]

Course Content:
>Mathematical vocabulary
>Basic techniques from discrete mathematics
>Integers and number theory
>Graph theory
>Generating functions
>Recurrence relations
>some stuff with primes
looks like you're right.

this but if you're not interested just grab Schaum's discrete math

start with the greeks

euclid: unrigorous, you can prove all triangles are isosceles with his axioms
apollonius: who the fuck cares about them conics
archimedes: anything this brainlet came up with is doable with integration

archimedes INVENTED integration nigga

that was yakub, though

> Draws impossible picture
> "Euclid isn't rigorous"

Maths books for three lives.

mathblog.com/mathematics-books/

doCarmo's Riemannian Geometry

Try Barrett O'Neill's "Semi-Riemannian Geometry With Applications to Relativity".

>physics in close relationship with math Retardedly wrong. The physics threads are over at .

that's specifically what I had in mind when I said "coordinate hell"

How do cloud storage algorithms work?

What's preventing someone from constantly uploading junk data and filling up the provider's storage space?

Just use derivations. They are more universal anyway.

Actually revolting.

Explain what a derivation is intuitively

A linear map satisfying the Leibniz rule. The real intuition behind the algebraic definition of the tangent space comes more from the cotangent space. Pretty much the following...

"If [math]{\mathcal{O}_{X,p}}[/math] is the local ring of a variety/scheme/manifold at a point p and [math] \mathfrak{m}_p [/math]its maximal ideal, then the cotangent space of [math]X[/math] at p is [math]{\mathfrak{m}_p}/{\mathfrak{m}_p}^2[/math]. We also have [math]\operatorname{Hom} \left( {{\mathfrak{m}_p}/{\mathfrak{m}_p}^2,k} \right) \cong \operatorname{Der} \left( {{\mathcal{O}_{X,p}},k} \right)[/math] where k is the residue field at p.

Consider the local ring [math]R = C_{{\mathbb{R}^n},0}^\infty [/math]. Then [math]R/{\mathfrak{m}^2}[/math] splits canonically as [math]\mathbb{R} \oplus \mathfrak{m}/{\mathfrak{m}^2}[/math]. So consider [math]f \in R[/math] and look at the Taylor expansion [math]f\left( {{x_1},...,{x_n}} \right) = f\left( 0 \right) + {\sum {\left. {\frac{{\partial f}}{{\partial {x_i}}}} \right|} _0}{x_i} + r\left( {{x_1},...,{x_n}} \right)[/math].

See [math]f\left( 0 \right)[/math] lies in [math]\mathbb{R}[/math], the remainder [math]r\left( {{x_1},...,{x_n}} \right)[/math] lies in [math]{\mathfrak{m}^2}[/math], and we are left with the differential [math]\operatorname{d} f = {\sum {\left. {\frac{{\partial f}}{{\partial {x_i}}}} \right|} _0}{dx_i}[/math] in our cotangent space (where the differential map is viewed as the natural projection [math] \operatorname{d} :R \to \mathfrak{m}/{\mathfrak{m}^2} [/math] under this splitting)."

They won the Nobel Prize for discovering dark energy in 2011 and I solved the anomaly in 2009. Did anyone find an error yet? Fuck no.

>Modified Spacetime Geometry Addresses Dark Energy, Penrose's Entropy Dilemma, Baryon Asymmetry, Inflation and Matter Anisotropy
>vixra.org/abs/1302.0022
>old timey guy's illegible cursive is fine and we like him but fuck your MS Word bullshit

>MS Word
>using software that isn't Free As In Freedom

All that paper does is state nonsense. It doesn't even attempt to prove it.

I see lots of symbols here but no intuition. Manifolds are supposed to embody geometry and there is no geometry in what you're talking about.

>geometry
Please define this.

Tangent vectors are supposed to represent some type of infinitesimal displacement. What I explained shows this algebraic stuff clearly captures that notion.

That's to be expected. It is a physics paper after all.

When did you realized you will never learn all the maths?

I can't understand a concept unless I have a visual to hang it on. Can I ever become a decent mathematician?

Depends on what you mean by "visual".

You would do well in geometry but algebra might be difficult.

>mr mochi ball edition

'tis the season
youtube.com/watch?v=LqPj5cA-1gw

I'm trying to teach myself stats and I'm a dipshit and I'm wondering about working with different random variables and their PDFs
Say I have a random variable X with a distribution f(x). I also have another random variable N = tan(X). Generally speaking, if I want to know the distribution of N, it would simply be f(n) = tan(f(x)), right?

Work with the cumulative functiom and apply chain rule

>geometry
What's that?

Has anyone here reached a state of quasi-enlightenment where nothing even angers you anymore?

My secret is, I'm always angry.

Are you sure you're not just depressed?

Is this what you mean:

X is a rv with CDF fx(x) and N = tan(X)
fn(x) = P(N < x)
fn(x) = P(tan(X) < x)
fn(x) = P(X< atan(x))
fn(x) = fx(atan(x))

and then to find the pdf I take the derivative d/dx(fn(x)) = p(x) / (x^2+1)?

>confusing apathy with enlightenment

I'm not weak enough for that anymore.

I'm pretty sure "apathy" means something different, user. And I said "quasi-enlightenment", not the ascended version of it.

stats.stackexchange.com/questions/239588/derivation-of-change-of-variables-of-a-probability-density-function

Combine rigid motions with inversions.
>local ring variety/scheme/manifold
In particular your example is most concretely realized as a sheave of germs on a Riemannian manifold. Sheaves on paracompact manifolds are the essence of Cousin's theorem for the existence of global sections.
>but no intuition
What do you mean? It's plenty intuitive.

9520157
>concretely
Nobody gives a fuck about this here, proceed to .

Yes, applied math is like a professional sport for brainlets.