/mg/ math general -- bernoulli numbers edition

talk maths fagets

Other urls found in this thread:

arxiv.org/pdf/1801.05337.pdf
math.stackexchange.com/questions/2574902/prerequisites-for-gunnar-carlssons-topology-and-data
en.m.wikipedia.org/wiki/Long_s
en.wikipedia.org/wiki/Function_(mathematics)#Binary_operations
en.wikipedia.org/wiki/Infix_notation
discord.gg/hTSFbn
Veeky
en.wikipedia.org/wiki/Ramsey_theory
twitter.com/NSFWRedditVideo

...

Why is an integral sign used as a symbol for a sumation? Also the notation is not well defined.

>Why is an integral sign used as a symbol for a sumation?
Can you give an example? I haven't seen it used that way.

The fucking OP...

>The fucking OP...
Do you need to swear?

go ask bernoulli

What could that giant "S" possibly stand for?

>Why is a large S used as the symbol for summation
The absolute state of American education.

I dislike that every textbook hides the relation between sums and the power rule.
Whereas in this picture it is obvious

Is it possible to survive half a year of Galois theory with acceptable grades if you struggle a lot even with Linear algebra proofs?

Why would you want to ?

I'll have to pass that course if I decide to continue studying maths.

>Galois theory
This is a maths thread.

Well you don't really need to know a lot to understand Galois theory but it's going to be a rough ride if you struggle with linear algebra

yeah that's what I'm talking about
They more or less allow us to choose what courses we want to take from the 5th semester, but I'm not sure if I can make it through 3 more, let alone pass the upcoming exams

Maybe if you change your study habits. How did you study for linear algebra?

during the semester? Not much so I can't really say. It sounds like I'm a failure, and maybe I am, but I'm just not used to working.
Currently studying, Two weeks before the test. Although not very efficient.
Basically doing all the homework we were given over again, even though I haven't really done the last few sheets, so just doing homework. Before that I took some time to write down all the relevant theorems and definitions. Wanted to do the previous exams next.

galois theory relies on linear algebra

it's not just that specific subject / course, I was just wondering in general - about how, and if I'm even able to continue with maths.

> fagets
Why the homophobia?

Cuz they are dumb fucks who cant do math and deserve to die

[math]\mathbb{F}_1[/math] for everyone
Oliver Lorscheid
arxiv.org/pdf/1801.05337.pdf

>This text serves as an introduction to [math]\mathbb{F}_1[/math]-geometry for the general mathematician. We explain the initial motivations for [math]\mathbb{F}_1[/math]-geometry in detail, provide an overview of the different approaches to [math]\mathbb{F}_1[/math] and describe the main achievements of the field.

linear algebra is fundamental. you're supposed to struggle with it, if it's taught right. it means you're learning. so carry on, and work hard

>look mom I did it again hahahahahaha

Let A_1, ..., A_m be subsets of {1, ..., n} such that for all i, j, A_i is not a subset of A_j.

Show that
[math]\sum_{i=1}^m \frac{1}{\binom{n}{|A_i|}} \leq 1[/math]

Any idea ?
I think I could prove it combinatorially when the sets all have the same size, but that would be ugly and incomplete. There should be a clever solution.

Do you guys know about inverse problems?

Every approach to this subject feels wrong.

How do I prove that, if x and y are real numbers, then |xy| ≤ |x||y|?

>How do I prove that, if x and y are real numbers, then |xy| ≤ |x||y|?
Use the fact that |xy|=|x||y|.

how do I prove that without doing "for x>0, |x| = x and for y

you don't, that's exactly how you have to do it

that's a definition

Define the positive and negative parts of x to be x+ = (x+|x|)/2 and x- = (|x|-x)/2, so that x = x+ - x- and |x| = x+ + x-. Show case-by-case that either x+ = |x| and x- = 0 or x- = |x| and x+ = 0. Then expand out xy = (x+ - x-)(y+ - y-) = x+y+ - x-y+ - x+y- + x-y-. Out of these four different combinations, only one can be nonzero, and will then equal |x||y|.

Has anyone here read Gunnar Carlsson's paper on Topological Data Analysis? I am looking to figure out the prerequisites from algebraic topology.

math.stackexchange.com/questions/2574902/prerequisites-for-gunnar-carlssons-topology-and-data

Hey guys, brainlet here checking in. Soft question: how important is this crap? I'm taking my intro proofwriting class and although I'm not really struggling with it or anything, basic symbolic logic manipulation just seems trivial in comparison to the real math proofs I see. I know you have to crawl before you walk, but I need to know, is this babby-tier symbolic logic stuff a meme?

It's not a "giant S" but a large ſ.
en.m.wikipedia.org/wiki/Long_s

Yes and no.
Very low likelihood you will ever see symbolic logic notation again unless you seek out a logic textbook.
But manipulating propositions in that manner will occur in literally every theoretical course you take so it's important to internalize the results themselves.

Boolean algebra is kind of useless, the real deal will be when you get to natural deduction / sequent calculus. Then you'll define what a proof actually is.

How can i model rough jagged manfiolds evolving into frsgmented pieces and recombining in a rigorous way? I need a tool to describe this for properly modeling turbulent systems.

I still find it amazing that the odd bernoulli numbers turn out to be zero.
Also, who the fuck decided B_1 might be convenient as +1/2?

>Yes and no.
What did he mean by this?

>I'm taking my intro proofwriting class
Which school for brainlets do you go to?

It is a contradiction. It means zů can introduce a negation and cancel the assumption leading to yes and no. Zů will learn this stuff on zįr introductory course on logic, assuming zů hasn't already done it in hs.

>zů

Yes, and?

Why does zįr have zůcchini on xhr face?

I don't discuss such matters with """""people""""" for pronouns are too hard to use. And you are one of them. Literally vomit inducing. (Vomit = food^*)

For whom*, your retardation of mental sort is contagious.

Remark: poo = food_*

>It is a contradiction.
Which he proved with no assumptions.

What you want to do only works for [math]n[/math]-manifolds with [math]n\geq5[/math].

>>>/tumblr/

[math]
\frac{1}{\binom{n}{|A_i|}} = \frac{|A_i|!(n-|A_i|)!}{n!}
[/math]
So, you want to show that [math] \sum\limits_{i=1}^{m} |A_i|!(n-|A_i|)!\leq n! [/math] (1) .
By noticing that [math] |A_i^{c}|=n-|A_i| [/math], (1) becomes [math] \sum\limits_{i=1}^{m} |A_i|!|A_i^c|!\leq n! [/math]

Maybe you can get it from there, dunno.

You are going to be using these stuff literally in every proof. Sometimes they are going to be trivial, so you won't be needing to think about them symbolically, but you'll eventually find yourself checking logical stuff symbolically so that you are sure you don't fuck up.
For example:
A function is not continuous at [math] x_0 [/math] means:
[math]
\neg (\forall \varepsilon >0 : \exists \delta >0 : \forall x : (|x-x_0|0 : \exists x : \neg\{ \neg [ |x-x_0|0 : \exists x : \neg\{ |x-x_0| \geq \delta \lor |f(x)-f(x_0)|0 : \forall \delta >0 : \exists x : ( |x-x_0| < \delta \land |f(x)-f(x_0)| \geq \varepsilon )
[/math]

You can definitely derive the last thing without symbolic manipulation, but you might fuck up.
From it you can for example derive that there exists a sequence [math] x_n \to x_0 [/math] , but [math] \neg ( f(x_n) \to f(x_0) ) [/math] .
So for if for all sequences [math] x_n [/math] you have that [math] x_n \to x \implies f(x_n) \to x [/math] , then f must be continuous at x_0.

> [math] x_n \to x \implies f(x_n) \to x [/math]
meant x_n \to x_0 \implies f(x_n) \to f(x_0)

How do i into odes/pdes? Ive heard arnolds book is good for odes. I know baby rudin analysis

>but you might fuck up
Only if you are a brainlet.

Evans PDE. The appendix will direct you to any material you need to learn.

if + is a function, what kind of notation rule allows one to represent an addition as
>x + y
when it should be
>+(x, y)
context: i am playing with peano's axioms.

that's exactly the notation rule
a + b is defined as +(a,b)

fugg. either high-school sucked or i didn't pay attention back then. thanks.
en.wikipedia.org/wiki/Function_(mathematics)#Binary_operations
en.wikipedia.org/wiki/Infix_notation

I had a user there. Sadly I don't remember the log in stuff.

Looking for a book on graph theory. Anyone have recommendations?

Bondy & Murty.

Much appreciated, /mg/ is one of the most reliable places for good math recommendations.

I'm not a "place".

I complemented you. Why respond like this user?

anybody want to collaborate on Number Theory stuff? I like trying to solve open problems and just dicking around with primes and various tests and stuff like that. Any undergrad math majors or the like want to join a Discord and work on stuff together? Looking for 1-3 people

I am down for that. I do number theory every day. Quick disclaimer though, I only know elementary number theory and the first 5 chapters of Apostol's analytic number theory. I can also solve IMO/Putnam tier problems some of the time. Going from the putnam scale, I can solve #1's 100% of the time, #2-4 70% of the time, #5-6 10% of the time.

sure

Yes, almost there.

n! is the total number of permutations of [math]\{1, \ldots, n\}[/math].
[math]|A_i|! |A_i^c|![/math] is the number of such permutations that start with elements of [math]A_i[/math] and then elements of [math]A_i^c[/math] (when I say "starts", I view a permutation as an ordered list [math]\sigma(1), \ldots, \sigma(n)[/math])

Then if these sets of permutations are disjoint, we're done.
Suppose we have a permutation that both begins by all the elements of A_i and by all the elements of A_j, taking the least of those prefixes then one of them is included in the other, which is a contradiction.

ok, sounds like you have a bit more experience than me but that's good. My knowledge comes mostly from wikipedia but I've tried solving some Putnam problems and it's fun. I mess around with Mathematica and Matlab mostly. Join quick and I'll delete this once we have everybody

discord.gg/hTSFbn

I actually have Apostol Analytic Number theory open right now on my computer.

I need to get home. Can't download the discord app on my phone.

kk I'll wait

Did you check the wikia?
Veeky Forums-science.wikia.com/wiki/Mathematics#Introduction_to_Graph_Theory

thank you for the link. i also like to ask what people here have read as well.

your mom's

is ramsey theory considered mememath?

en.wikipedia.org/wiki/Ramsey_theory

techniques and introduction to writing proof is offered at many universities, including top 10 schools like UC Berkeley. If you do not have such a class, you are probably a brainlet at a shitty school.

sorry f@m.

>you will never be Kolmogorov

>techniques and introduction to writing proof is offered at many universities, including top 10 schools like UC Berkeley. If you do not have such a class, you are probably a brainlet at a shitty school.
When people ask me if I went to a school for brainlets with an intro to proofs class, I tell them, "No, I went to math classes."

Absolutely not. The fact that you would think you need to link the wikipedia like you just discovered some obscure topic is embarrassing and I suggest you delete your post to save face.

asking in a very broadly way, is there any mathematical model, or sub-field that can be used to talk about self-reference? - be it from systems or just an abstract way - I've read something about Operads and first-order logic,etc.

>need to link the wikipedia like you just discovered some obscure topic

You might like the links between differential equations and recurrence relations, and generating functions

What's the mathematical definition of an "economy"?

I made a discord for discussing number theory. Anyone interested or knowledgeable in the subject is welcome to join.
discord.gg/hTSFbn

Mathematical means it's well defined, so define it shithead

>Mathematical means it's well defined, so define it shithead
What do you mean?

Ask your question more specifically

>Ask your question more specifically
What do you mean by "Mathematical means it's well defined, so define it shithead"?

>I'm not a "place".
Then what are you?

Give me one good reason to care about HoTT.

What's the simplest non-trivial result worth knowing about it?

You want to play stupid games, or you want an answer to your well-defined question?

>You want to play stupid games, or you want an answer to your well-defined question?
The latter, obviously.

Oops, well looks like you forgot to include your well-defined question

>Oops, well looks like you forgot to include your well-defined question
What do you mean?

Not szïr, but Fritz von Bothmer said he is not a meaningless point in the universe. This is the antroposophical basis for pointless topology, and similarly this pointless approach makes it reasonable to assume people are not places, but instead a concentration of aether twirls on some area. This is why one should start their day by practicing yoga with electrodes attached all over the body in order to find the optimal aether flow through one's corporeal manifestation. This was taught to me by mr. Kauko Nieminen.

maybe your brain is wrong.