/mg/ - Math general

Deep down we all love poor Haskell edition
Previous thread: Comfy rain sounds for proper mathematical study
mynoise.net/NoiseMachines/rainNoiseGenerator.php

What have you been working on lately? What have you been reading? Any interesting articles/textbooks/areas you might want to recommend? Want to circlejerk about foundational mathematics while posting smug anime girls? Then come and show us!

For stupid questions, go to . Challenge questions and discussion about open problems are more than welcome, but don't just spam IMO and Putnam problems.
Physics discussions will be tolerated if they pertain to mathematics (i.e. mathematical physics, mathematical rigor in Physics, etc...), otherwise go to Bickering about reddit spacing will be reported, and discussions about "applied mathematics" not existing will be redirected to a thread discussing that very issue.

Verbitsky's guide on how to be a proper Mathematician:
pastebin.com/DAGdbVxv

Pleb guide to be a simple mathematician:
- Pick any uni you like (Cambridge, Princeton, etc...)
- Look at the courses you're interested in, and the prof that imparts it
- Look if the uni page or the prof's personal page has notes
- If not, look at the recommended bibliography and download it from libgen.io
- For further information, check Veeky Forums's wiki, MIT OCW
- If this isn't enough, THEN you ask for recommended books or articles (which may be downloaded from sci-hub.io)
With time, I'll create a pastebin with the books people usually recommend for you plebs, but for the moment, what you have above should be more than enough.

Suggestions of any kind are more than welcome.

Other urls found in this thread:

katmat.math.uni-bremen.de/acc/
cut-the-knot.org/proofs/Furstenberg.shtml
arxiv.org/abs/1506.05805
arxiv.org/pdf/1303.1202.pdf
twitter.com/NSFWRedditVideo

>Physics discussions will be tolerated

>Deep down we all love poor Haskell edition
(strike 1: programming cancer)
>Physics discussions will be tolerated if they pertain to mathematics
(strike 2: attempting to justify the pollution of mathematics)
>Bickering about reddit spacing will be reported
(strike 3: encouraging lax posting etiquette)
>discussions about "applied mathematics" not existing will be redirected to a thread discussing that very issue
(strike 4: bringing up fictive domains such as the purported "applied" area of mathematics as a shiv to split up the community)
Basically, this whole OP is an exercise in transparent entry-ism. You will not succeed Devil! Mathematics is pure and will always remain pure!

Death to all who seek to corrupt mathematics!

Someone ban this brainlet already.

You have 1 minute to come up with a (incomplete) solution to Riemann hypothesis

OP is obviously a freshman or high schooler stroking his own ego about how great he is for liking pure mathematics

Lmao, how [math] not [/math] to do categorify a result: the post >Who can help me out?
First of all the 'categorification" of something is not merely an attempt at rephrasing it in the language of "objects and arrows". It is an attempt to distill the key features of a result, allowing for its (ideally, absolute) generalisation. Attempting a sort of literalist "translation" of terms, like "a divides b" as "there is an arrow from a to b" is not only incorrect, it's not even in the right general direction of what you'd have to do. The fundamental theorem of arithmetic already has been generalised, beyond algebraic number rings. Think ring ideals, not elements. (Look up Dedekind domains.)

Haskell?

>Physishits will be tolerated

>Can't you prove Euclid's theorem with topology? You don't even need to appeal to infinities lmao
>implying that a topology on [math] \mathbb{Z} [/math] constructed precisely so that every non-empty open set is necessarily infinite has nothing to do with infinities
Stupid posts like this one perfectly illustrate why physishits should be kept the hell away from mathematics.

inb4
>I/she was only pretending to be retarded

daily remainder that category is a meme and Haskell is fat added to untyped lambda calculus .

Also, if you really insist, let C a category having an initial element e, D the category whose objects are triples (a,x,t) where a is in C,t:is in Hom_C(a,a) and x is a map from e to a; and whose arows are defined in the following manner: an element of Hom_D((a,x,t),(a',x',t')) is an arrow f: a->a' such that t' o f = f o t.

The object which is the "set of integers" is simply an initial object of D if it exists.

But then how the fuck is this even pratical.

I forgot of course
>an element of Hom_D((a,x,t),(a',x',t')) is an arrow f: a->a' such that t' o f = f o t.
I must add "f o x=x'" obviously

Never forget the power of meme magick! Besides, cat theory has many practical uses meow meow, for example homological algebra.

It's easy to tell why you'd consider category theory a "meme".

>The fundamental theorem of arithmetic already has been generalised, beyond algebraic number rings.
Why is this relevant? Things can be generalized in more than one way

>Why is this relevant?
Because it's an example of how to proceed.
>Things can be generalized in more than one way
Sure, but if you read that post, you'll notice that the guy didn't actually generalise anything. He's only trying to reconstruct the same result with different semantics.

>cat theory
>meow meow
[math] \mathscr{Q}\mathscr{T}^{\mathscr{est}} [/math] [math] \mathscr{mathematics!} [/math]
[math] \mathfrak{The}\ \mathfrak{Joy}\ \mathfrak{of}\ \mathfrak{Cats:} [/math] katmat.math.uni-bremen.de/acc/

>Anime avatar fagging
you're not any better.

Meow meow [math]^o\omega^o[/math] nice link!

>talking out of her ass
cut-the-knot.org/proofs/Furstenberg.shtml

>((((her))))
Underlying this scheme is a nice result coming from applying the theory of dynamical systems to number theory (typically Diophantine approximation) and goes under the name of Fürstenberg orbit closure theorem, which came be used to prove statements of this type.

Good trips but terrible post.
>category theory isn't practical
arxiv.org/abs/1506.05805
arxiv.org/pdf/1303.1202.pdf
Read up boy.

Fucking garbage. Kill your retarded selves.

Real thread: Real thread:

see