/mg/ -- ergodic edition

i don't think it's legal, but try library genesis

E-books are easy, I want a physical copy.

Nigger, If you want the cheapest legally books just compare prices in different stores/online, maybe ask if they have second hand books idk. Do you expect there is some secret society that gives you discounts in old soviet texts?

Well, why so rude, it is completely possible that there is a website with some low-quality second-hand books I dont know about.

You don't know about amazon? Don't be a cuck just pirate them.

How do I get a job with maths knowledge

Amazon is for good quality second-hand books.

The same way you get it without maths knowledge.

So how can I get into chaos theory? I know probability, stochastic process and time series.

You are supposed to write /mg/ - Math General in the title for the newfags.

csc.ucdavis.edu/~chaos/courses/ncaso/Lectures/

Go to a university where you are offered a library which includes almost all books about mathematics a lot offline and many more online.

If you want physical copies (and are willing to go into grey areas) print them on your parents printer.

>lubos not connected to bognadoffs

It certainly wouldn't hurt to learn more measure theory. You won't know to use a tool unless you know things about it.

>Should I learn more measure theory.
Well probably, but bear in mind that measure theory is the most disgusting mathematical field.

>legally

what's disgusting about it?

solve this without a calculator.

no

Can someone clarify how ergodic theory is related to chaos theory? Apparently it is supposed to have given birth to the latter, but I can't put the pieces together.

I don't know, too pedantic. It was a torture studying it. Not that it was hard. I was just like "I don't fucking care about that, you fucking autistic writer", but I had to so that I could pass the class.

Anybody has a GOAT youtube lecture series on Homology/cohomology that is more on the axiomatic side and at the same time doesn't assume much, but goes quite deep, and has material on fibre/vector bundles?

I'm looking for a treatment similar to Eilenberg/steenrod Foundations of AT.

The tree's height over the shadow's length is the tangent of 23.3°.

Taylor series maybe?
Some kind of approximation?
Still don't need a calculator if you're not a brainlet

not that user, but that's just your opinion

This, I felt like the first person to enter since decades when I went into the cellar of my universities library where the truly old books are kept. Almost broke my heart seeing all these tomes of knowledge rotting away because students are forced to buy the newest overpriced special edition of a low effort course book, and seem to not find time or are afraid to seek inspiration from books written a few generations back in the past.

Well, obviously.

pls respond

No fuck you.

At last I truly see.

>and seem to not find time or are afraid to seek inspiration from books written a few generations back in the past.
To be fair, almost all math books (and science too, somewhat) age pretty rapidly. Stuff from the 60s is sometimes still relevant but earlier than that it becomes iffy whether it's very outdated or not. "a few generations back" and you're basically guaranteed to be using ancient notation/language to study stuff nobody cares about anymore.
It's not like philosophy where a 200 year old musty piece of shit is still valuable to scholars.

I doubt such a thing exists, but I'm also interested.

Seems like to advanced a subject to have video lectures from a standard course on, but to basic to have lectures from somewhere like msri on.

I really enjoy Tao's Analysis

>Tao's Analysis
memebook

Tao is a meme.

"lecture notes on X" google search

what the fuck is post anabelian froeboid geometrics

Unless you actually have anything to say this time, kindly fuck off

>fuck
There's no need for vulgarities.

Is "Motive: Unknown" for Grothendieck a joke?

basically PAFG spawned off from a connection the twins saw between General Relativity, Witten's work in string theory and Grothendieck's work in anabelian geometry. They realised if they applied a new metric called the froeboid to the algebraic fundamental group G of an algebraic variety V, a pattern emerged which was fundamentally similar to patterns found in both string theory and later works in general relativity, thus connecting the two. Objects are already capable of traveling through space, but this provided an answer as to how we can travel through time by connecting two points in time much like a wormhole connects two points in space, and it also gave us the answer as to why we experience time in only one direction and how we can build a device to travel in both (which they already built). Further work in this field by the brothers showed us that just like space can have multiple dimensions, so can time. So rather than just being able to go "forwards" or "backwards" through time, we might also be able to go "up" or "down". Space and time are essentially two identical constructs (of which there are more, though these are inaccessible to us, these different constructs are called existence yielding matrices or EYMs) just like horizontal and vertical are identical constructs, it's just from our reference point as beings which primarily exist in space and only secondarily in time, they seem very different. It's possible that other beings live primarily in time, primarily in both, or even primarily in all possible dimensions of all possible EYMs in existence. Ready for the next bombshell? Just like an infinite number of dimensions exist in each of the infinitely man EYMs, an infinite amount of EYMs exist in each of whatever the next structure is (we still understand little about it), and so on for every single structure on top of that.
not intended

Check out "Invitation to Ergodic Theory by Silva", it introduces the needed measure theory seeing as you haven't seen it before. If you want to do measure theory in detail before trying ergodic theory, the book by Stein and Shakarchi is a good introduction. I think knowing differential equations or probability before going in can help motivate somethings, but it's not strictly necessary.
Let me tell you why you're wrong.
>Measure theory lets us answer one of the most obvious mathematical questions you can ask "what is the area, volume, length" of this thing. If you have any intuition about these quantities, you can use that in measure theory.
>The first thing you establish in measure theory how you can define the volume of an arbitrary subset of R^n. Thanks to Banach-Tarski, you can't do this completely, which is why you need sigma-algebras. It's mind blowing that you can't define the volume of every set.
>Measure theory fixes the integral. If I have a function f, and I change the value of f on a set of length zero, that shouldn't change the value of the integral. The Riemann integral fails to do this, the Riemann integral of the characteristic function on the rationals should be zero, but it's undefined. The Lebesgue integral fixes these problems.
>In elementary real analysis, you learn you need some uniformity condition to do anything useful. In measure theory, you prove that you can get the conditions you want up to a set of measure zero, which is usually good enough.
>Along these lines, you get really good limit theorems. If you want to learn to appreciate these theorems, go read the first chapter of Theory of Functions by Titchmarsh.
Basically, measure theory is the best thing that's happened to analysis since calculus, and even if you don't want to go deep in to pure measure theory, it's still super useful and cool.

>tfw reading about the German Tank Problem

>undergrad real """""""""analysis"""""""""""""""
>literally have to use an arbitrary "trick" each proof to get it to work
whata load of shite

>>literally have to use an arbitrary "trick" each proof to get it to work
>he/she doesn't understand the big picture so calls everything a trick
yikes...

false

Lumo is actually the mastermind behind the Bogs.

The problem with that approach/opinion is that the problems mostly occur in the cases you dismiss as shit you don't care about. Heck the whole subject is more or less shit you don't care about. But it turns out studying the subtleties actually gives us something (why did we need measure theory in the first place?). To me it's the nice kind of math, the one where you think you understand something and then after 2 hours realize that some detail you thought were completely irrelevant fucks up your shit. (Maharams theorem is very nice for instance).

I havent found anything yet, but I've found an extremely interesting and fast introduction to bundles from literally defining predicate logic and axiomatic set theory with a brilliant lecturer (although aimed at physicists, it's still pretty rigorous and good) youtube.com/watch?v=V49i_LM8B0E

Here's the lecture notes + whole series titles

mathswithphysics blogspot co uk/2016/07/lectures-on-geometric-anatomy-of html
(add a dot between spaces)

When did you realise that math is just an evolved feature as hunger of fear of height?

Just learn real stuff on your own.

Anons, I failed you. I went over my attempt at a disproof of the RH with a colleague over the weekend and it's useless. The correct part of the proof is a pointless tautology...

It was so embarrassing I am thinking of quitting my post-doc. Actually, I think I'm going to quit math altogether and get into something else, more fitting for brainlets.

Good

Don't worry user, no one believed in you in the first place.

who are you again?

Is that the guy posting gay anime and category theory? I never liked him.

...

What should I look for in a university if I'm considering doing a master's there (just in Europe)? Do I just look at the courses, or should I also worry about the proffessors? Also, how do I know if the proffessors there are any good? And how much does it matter that I get to do a master's thesis with a "high-tier" prof?

RH is known to be independent. Nice try though.

>RH is known to be independent.
But that doesn't mean anything

Your post doesn't mean anything.

>Your post doesn't mean anything.
My post means that "RH is known to be independent" is meaningless.

This is wrong.

>This is wrong.
All I'm saying is don't throw around buzzwords like "independent" if you don't understand how to use them.

Please refrain from posting such nonsense.

>Please refrain from posting such nonsense.
Please refrain from posting such meaninglessness as "RH is known to be independent".

What a stupid post.

>What a stupid post.
Are you referring to ?

you could always just explain what it's supposde to mean

No.

Are you okay?

yes, but if you think it means something why not explain what it means?

>RH is known to be independent. Nice try though.
Independent of what?

Is there any book that reviews all of general mathematics from high school to undergrad? I badly need one. Yesterday I was trying to do a geometry problem and the core idea was applying the relationship between an equilateral triangle and the circle it is inscribed in. I realized I did not remember that relationship. It made me realize how much trivial math I have been casually forgetting. I realized that the only taylor series I have perfectly memorized is the one for the exponential and the logarithm. I should know all of them. I am afraid I need to badly review all of that unless I want to risk becoming a mathlet after coming this far.

I am looking for a book that just quickly reviews topics from probability, geometry, calculus, maybe number theory but I know all my number theory 100% so I don't care, linear algebra, and other undergrad topics I should know, and is then just filled with challenging problems.

I'm about to have months of free time and by problem-solving, I am sure I will again involuntarily memorize all the neat facts I've forgotten. But I would like to have one book with all the knowledge so I can focus on that instead of needing an entire library.

Any ideas?

Do you need to talk to someone?
Independent of any axiomatic system in which modus ponens holds.

>Independent of any axiomatic system in which modus ponens holds.
Why is it independent?

>"why"?
Maybe you should try an engineering thread?

>Maybe you should try an engineering thread?
But leaving out reasoning is what engineers do

Asking "why" a result holds is something only engineers and their ilk do.

>unless I want to risk becoming a mathlet
You even wanting to study such trivial topics already means you are a mathlet.

>i need a book that covers all of the topics covered in 8 years, half of those entirely dedicated to math

I just want to stay fresh, man. I don't want to forget those small facts. They are like a part of my childhood, I want to die knowing the taylor series for sine from memory. The more I get into higher math the more I forget the good old days and I wish I could turn back time to the good old days.

Elementary geometry, probability and calculus are actually not that much if you really think about it. The book I am thinking off would just list all the important theorems and then have like 20 problem sets per section.

And it can just be one single calculus section. I don't need a section for every single integration trick. I am thinking of a pure review book. One that already assumes you understand everything and just throws problems at you.

>higher math
What would be some examples of "higher math"?

My focus is in algebraic number theory.

>not analytic

>number theory
So basically garbage. Go ahead then.

Are there any topics where the analytic and algebraic theories meet?

modular forms

>I want to die knowing the taylor series for sine from memory
you should be able to derive its form if you have at all any idea what taylor series are like and claim to understand them - maybe you wouldn't be able to show convergence but still.

You should be able to derive most trigonometric identities from the pythagorean and sum of angle identities, which you can also derive from the complex exponential. You don't need a book if you know how it works.

Calculus is literally just tricks. The rest is analysis. The only theorems in calculus are those in analysis (or topology). Any further computation techniques that isn't just using clever substitutions or integration by parts uses either complicated real analysis or complex analysis. You don't need a book to remind you how l'hopital, IBP and substitution rules work.

Any elementary (unrigorous) probability are usually just counting arguments, permutations and combinations. You don't need a book for that.

Elementary geometry is maybe a bit more involved, but any book will do, maybe Coxeter

If you so claim that you do algebraic number theory, all the information I'm telling you is completely obvious, so I highly doubt you have more than a casual interest in it