/mg/ math general: Jim Simons Edition

What are you studying today, /mg/?

en.wikipedia.org/wiki/James_Harris_Simons

Previous thread

Is there a way to represent the following function:

>f(x) equals the number of 1s in the word x.
as a function like "f(x) = y"?

So if I were programming, I would do:
>Create a counter variable to count the occurrences of 1
>Create a loop to step through each character in x
>+1 the counter variable for each time x[index] = 1
>Return the value of the counter variable

Is there a way to represent functions like this like f(x) = y? I'm interested in learning to write functions this way, what are some resources I should look into?

[math] f(x)= \sum_{1\in x} [/math]

Alright, sigma notation. And what field of mathematics deals with this sort of thing? Like what books should I read

Threadly reminder to work with physicists.

Recently I've been doing a bunch of problems of the form "Here is a sequence of natural numbers, find a formula for this sequence using the floor function" and I started to wonder, has there ever been a deep study on what general class of sequences can be written using elementary operations (addition, multiplication, division and natural roots of integers) and floor functions?

An interesting example a sequence that can be written with floor functions is [math] 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,... [/math] (the sequence that repeats the nth number n times) as [math] \lfloor \sqrt{2n} + \frac{1}{2} \rfloor [/math] so obviously the class of sequences that have this property is diverse and interesting, but what are the limits? Are there any papers on this?

Algebraic Topolgy

>studying
>not just watching Rick and Morty
I'm too smart for this brainlet board

redpill me on the Curry-Howard correspondence

there's so much i want to do why am i limited to 24 hours in a day

Guys anyone has a good text on inequalities?
I'm struggling with any inequalities that are not linear.

Also yeah I'm a fucking retard, I know.

Guys anyone has a good text on inequalities?

>Guys anyone has a good text on inequalities?
I'm not a "guy".

will you go out on a date with me?

>will you go out on a date with me?
Maybe. Are you handsome?

I'm a solid 7/10.
I think.
I'm bad at math though.

Still Kalman filter stuff. More for GPS systems and such.

Something else: Is anybody here knowledgable in C# and up for a short programming challange?
I need a very simple realization of a classical one-tape Turing machine. Will have two classes and a bunch of for loops.
If someone's up for that, I'd +tip ya 30$ or so, it'll only be 300 lines of code max (write me an email www.axiomsofchoice.org).

sorry, I only help qts

I know a few, I can hook you up

I also just started a series on (the very most) basic math of finance with a dancer, this is also something I study right now, I suppose. Wrote a trading bot, but he wasn't very effective.

Today I did a proof on comparison of the Riemann and Lebesgue integral...basically any Riemann int'able function is also lebesgue int'able
Then I went to class and graded a bunch of papers for the trigonometry class I teach. Riveting shit.

You can continue by completing the hierarchy, here some more

>Riemann integral
>Lebesgue integral
>Burkill integral
>Bochner integral
>Daniell integral
>Darboux integral
>Henstock–Kurzweil integral
>Haar integral
>Hellinger integral
>Khinchin integral
>Kolmogorov integral
>Lebesgue–Stieltjes integral
>Pettis integral
>Pfeffer integral
>Riemann–Stieltjes integral
>Regulated integral
>Itô integral
>Stratonovich integral
>Skorokhod integral

And here some trig function stuff to check

[math] \forall \, f.[/math]
[math] \int_{-a}^a f(x^2) \dfrac{1}{1 + e^{ x^2\sin(x) } } \,dx = \int_0^a f(x^2) \,dx [/math]

:^)

You can continue by completing the hierarchy, here some more

>Riemann integral
>Lebesgue integral
>Burkill integral
>Bochner integral
>Daniell integral
>Darboux integral
>Henstock–Kurzweil integral
>Haar integral
>Hellinger integral
>Khinchin integral
>Kolmogorov integral
>Lebesgue–Stieltjes integral
>Pettis integral
>Pfeffer integral
>Riemann–Stieltjes integral
>Regulated integral
>Itô integral
>Stratonovich integral
>Skorokhod integral

And here some trig function stuff to check

For all positive values [math]a[/math] and all functions [math]f[/math], you have the simplification

[math] \int_{-a}^a f(x^2) \dfrac{1}{1 + e^{ x^2\sin(x) } } \,dx = \int_0^a f(x^2) \,dx [/math]

:^)

>I'm bad at math though.
BEGONE THOT

I'm working on it though.
And studying engineering.

Would anyone be willing to help? I don't know how to answer this.

Let f : W → X, g: X → Y , and h: Y → Z be func-
tions. Must h ◦ (g ◦ f ) = (h ◦ g) ◦ f

(h ◦ (g ◦ f ))(w)=h((g ◦ f)(w))=h(g(f(w)))=(h ◦ g)(f(w))=((h ◦ g) ◦ f)(w) for every w in W.

>engineering
my boner is gone

why?

>engineering
Lmao might as well just get neutered.

Come on, I'm thinking on switching to CS. I like math, just bad at it.

>no Tai's integral

this: Also:
. Equations and Inequalities by Kucera et al.
. Problems and Theorems in Analysis by Polya and Szego

Everyone here either was or still is bad at math. Just practice more. Every day all day.

What book deals with sigma notation? Huh? Just check the wikipedia article

Here's Veeky Forums's famous tranny fucktard again. Do kill yourself you pathetic attention seeking cuntfuck.

>Here's Veeky Forums's famous tranny fucktard again.
Not everyone who isn't a "guy" is a tranny.

>Do kill yourself you pathetic attention seeking cuntfuck.
You're the only one here looking for attention.

I am not that guy but THIS. This is exactly what I needed! I have 3-month breaks from uni starting December and I was wondering what I should study in that time. I do not want to spoil topology or algebra for myself so I was afraid to study those topics but this is perfect!

Do you have any commentary on the difficulty of this book in terms of mathematical maturity?

>the BHK interpretation of intuitionistic logic
ftfy

>I'm not a "guy".
Leave this board then since it's strictly for humans.

>>the BHK interpretation of intuitionistic logic
Uh, can you please repeat that in English next time Mr. Scientist?

Suit yourself.

Analysis / Group theory exam in 2 weeks lads
what should I expect

python


literary analysis


ligand shyt

>what should I expect
Probably some analysis / group theory

intuitionistic conjunction is product type is product in a category

taking product with A in a category has an adjoint (-)^A which acts like "currying" of the ambient category is cartesian closed (the existence of all such adjoints is the statement of being cartesian closed). The adjunction induces a version of modus ponens, which shows that this type can be seen as intuitionistic implication. Since this is essentially currying, applying (-)^A to any object B returns B^A, which can be thought of the "internal hom". Things of type B^A can be thought of as being of "function type".

We then finally say something like
intuitionistic conjunction product type products in a category
intuitionistic implication function type exponentiation

they are related by:

modus ponens function application evaluation counit

i'm cute and good at math but i do a lot of drugs and am currently emotionally unavailable

test, think im banned?
Anyway, I admire Jim Simons too OP.

Are you the same
>girl
I thought I was talkjng to?
let's be internet bf and gf

Studying algebra for the first time. Just got done with quotient groups.

I am new on the subjects and I was looking to purchase some books.

Anybody here had any experience with these? If so, do you recommend them? (I am an absolute beginner).

Thanks

That topology book is good.

What's a good book for calculus? Stewart's level is alright for a dummy like me but it has way too much fluff... I know Rudin and other people get recommended here but are they actually any good or are they just memes?

Basically, if you have a function of type X then you can interpret X as a logical statement and your function as a proof of X. Then the typechecker that compiles your program is essentially verifying that your proof is correct (that it actually produces type X).

So, in a programming language with a sophisticated enough type system you can encode logical statements as types, functions/programs as proofs, and the typechecker can verify correctness. Curry Howard was the first correspondence discovered but now the idea has been generalized to all sorts of logics and stuff. It has also created a special class of programming languages called "theorem provers" that are especially geared towards encoding mathematical statements inside the type system.

In general you have a correspondence that looks like:
Type Theory Logic Category Theory Type Theory
also, type theory can be used to describe or implement the type systems for programming languages. Abusing this allows one to give a language all sorts of interesting semantics based on the associated logic (eg. temporal logic may be useful for concurrent programming languages or something).

Sorry that I could not reply to the user who sent the probabilities questions last thread. Thank you though.

The first questions seems easy. There are n! ways that the letters can be labelled, and (n-1)! ways that there can be one or more correct ones. Therefore, the probability that there is atleast one is 1/n, which approaches 0 as n grows.

However, I have no idea how to do the second one. Am I supposed to start with proof thorugh induction, or can I have a hint?

PS are smilies tolerated here?

>PS are smilies tolerated here?
No, we will personally hunt you down, and hunt down everyone you hold dear and torture them before your eyes. Why even ask? Just keep spamming smilies so those superautistic faggots will get a brainstroke and die. We will fight cancer with cancer.

Spivak

What are you talking about, user?

Stop making the thread about yourself you disgusting thirsty tranny/or ugly whale.

Why are you even responding to his garbage?

>implying cs isn't even worse

lads how the fuck do I prove limits at infinity of sequences? I can do epsilon delta proofs for functions. pls help

im going to the gym lads, if I dont get help by the time I go back then OP gets it

Answer: find some reflective surface and take a look.

It's not "his" garbage, it's her garbage.

>lads how the fuck do I prove limits at infinity of sequences?
By using the definition of a limit.

user, if he was born with a dick he will always be a he.
I am sorry.

>user, if he was born with a dick he will always be a he.
I'm not a "he".

Firstly there are some unwritten rules on this website (but please post them in an unrelated thread, to not pollute the purity math).

Secondly having a neo-vagina does not make you a "she".

>Firstly there are some unwritten rules on this website (but please post them in an unrelated thread, to not pollute the purity math).
Irrelevant, anyway I've been here long enough to know any rules.

>Secondly having a neo-vagina does not make you a "she".
Who said anything about a "neo-vagina"?

>Irrelevant, anyway I've been here long enough to know any rules.
Then follow them and post them already.

>Who said anything about a "neo-vagina"?
I.

>Then follow them and post them already.
Posting unwritten rules would make them written rules.

>I.
And so what is its relevance?

>Posting unwritten rules would make them written rules.
I was not talking about the rules, I was talking about you finally following the rules and post "them" (not the rules).

>And so what is its relevance?
You should know.

Anyone here from mathematical physics? Can you give me some insight into the field? I interested in what you guys do/research, and what is the main difference between a mathematical physicicist and a typical physicist.

What's the best textbook for Classical Mechanics given that I have a solid understanding of pretty much all undergrad math subjects?

>What's the best textbook for Classical Mechanics given that I have a solid understanding of pretty much all undergrad math subjects?

Thanks! I'll check it out?

I don't know why I put that question mark there.

Fields in mathematical physics include geometric quantization, toplogical quantum field theory, quantum algebra, tt* geometry, integrability, etc. Basically it's the study of mathematical underpinnings of physical theories and the new fields of mathematics that are borne from them. It does not care about the real world, but rather where it can abstractly lead starting from it. That's why you get theories (like string theory) from mathematical physics that use sophisticated mathematical machinery while having very little physical relevance.
Theoretical physics studies actual real systems with mathematical models. They're less concerned about formalism and more about investigate the right models and cold hard calculations.

What category theory have you done on windows today /mg/?

I was tinkering around the category of all axioms when I found a huge contradiction and realized that category theory is a lie. A dirty trick played to us by very powerful people or beings that really do not want our math to get more advanced. They want us to stop discovering things. Maybe we are getting too close to something important. So close that they needed to personally interfere and make sure that for the next years all we would do is draw arrows on windows like autists while accomplishing nothing of value.

What was the contradiction? I thought the category of all axioms was well defined

>What was the contradiction?
You know what it is. He, I bet you are one of them. Go shove those arrows up your ass retard. You will never stop mathematics. Everyone knows set theory is the highest level of abstraction. Anything beyond is pointless drivel meant to distract us from the real shit. What are you huh? Are you aliens? The descendants of some ancient civilization? WHO IS BEHIND CATEGORY THEORY?

can anyone help me with a pumping lemma problem? I'm trying to prove that a language is irregular through contradiction.

I know the outline but am getting stuck on the first step. The language is:

L = { w ∈ {a, b, c}* | number of 'a' chars in w = number of 'b' chars in w + number of 'c' chars in w}

1) Assume L is regular
2) Let P be pumping length for L
3) w =

This is the part I get stuck at, choosing a string w. I'm trying to think of ways to write the language in terms of P.

Maybe something like w = a^(num b chars + num c chars) b^(num b chars) c^(num c chars)

I think you can represent the language by
a^(j+k) b^(j) c^(k) , but Im having trouble writing that using the pumping length, maybe

a^(n+j) b^(n) c^(j)
where n >= p and j >= p

?

Sorry, but a dog you wanted to eat suddenly attacking you and mutilating your penis doesn't make you into a "she".

Those are the brainlet definitions of a monad and adjunctions.

Thanks. What about Rudin, or Apostol?

Rudin is a meme.

Is it possible for a mathematical physicist to discover a theory for quantum gravity? Thanks for the info

I don't understand...

proofs boii

the topology book is very short, although it's quite good. Maybe you should look into a cheap (like international?) edition of Munkres if you want to go further

Some other user got the right answer, idk if you saw. As for the second one, a hint is:

the problem can be reformulated as: for every integer [math]M[/math], we can find positive integers [math]n,k[/math] such that [math]10^k\cdot M\leq 2^n < 10^k(M+1)[/math]

Then you can take logarithms of both sides, create appropriate real line intervals, and wind them up in a circle of circumference 1.

Please help...

So is the dog-eater the tranny poster as well? His posts just got deleted. Not like I'm surprised.

What have you tried?

>His posts just got deleted.
It's "her" posts.

No, I think I mean "his" posts. Being a roleplaying subhuman doesn't make you a "she".

>No, I think I mean "his" posts.
I'm a "her", so it should be "her" posts.

>Being a roleplaying subhuman doesn't make you a "she".
No one is "roleplaying".

Mutilating your penis does not make you female.