Number Theory

[Anonymous No.15410532]

In this thread, we discuss number theory and the best textbooks on the subject. Obviously I have to start with pic rel.

PS: Death to the general, math will not be confined to just sit in the corner.

[Anonymous No.15410562]

>>15410532
The most boring branch of mathematics.

[Anonymous No.15410590]

>>15410562
It is pretty awful, especially when unmotivated. If anyone can recommend books that are actually exciting (but not for retards), do post them.

[Anonymous No.15410641]

>>15410590
Probably any cryptography book would be interesting. And I suppose algebraic number theory would be a lot less boring.

[Anonymous No.15411374]

blocks your path

[Cult of Passion No.15411482]

>>15410590
>recommend books
Norman Wildberger has a number of videos on Number Theory, but they arent labled with that, he just does a lot of work in it. Its very simlar to playing with the definitions of Algebra/Arithmetic etc, also his "Dedekind cut" theory is *very* Number Theory. Once you know how broad the term cam be you will see and hear it many more places, specifically in every single class on Mathematics.

I consider Number Theory to be foundational to any legit Mathematician, Im shocked how few wield it.

[Anonymous No.15411963]

Pic rel has been recommended to me a lot, I think the only background is a course in Algebra.

[Anonymous No.15412032]

>>15411482
Took a quick look at OyveyStein's book. Looks like a comfy read, but at a very elementary level. A more recent book, and a slightly more advanced level is pic related. Seemed to move a bit too slow for my tastes, so I only read the first chapter.

I guess the best thing to do is to read the advanced books, and whatever perquisites they have, and then jump into crypto for fun stuff. As far as I can tell, none of the modern books cover the scope of Hardy's book, as so many authors choose a small subset of their favourite topics and still call it number theory.

[Anonymous No.15412035]

Maths is for faggots, by Henry Schittstain.

[Anonymous No.15412043]

>>15411482
>how few wield it.
The reason so few wield it is because the people who specialize in Number Theory ("the queen of mathematics") do so precisely because it has so few applications - to them, it feels like all the rest of math is the development of tools to be used in Number Theory

[Anonymous No.15412055]

>>15412043
The only thing number theory has been useful to me for involves the trivial stuff with prime decompositions, and for solving puzzles like Project Euler, and maybe 2-3 puzzles in Advent of Code.

[Anonymous No.15412065]

i will literally pay anyone 1 million credits (tentive) if they can solve my pattern (HYPERLINKED) of mathematics.

[Cult of Passion No.15412731]

>>15412043
>do so precisely because it has so few applications
It reorganized, literally, all of Mathematics for me, double so for Pure Math, and even Physics a bunch, as the "base systems" of reality are no so cut-and-dry as "single individual units of infinite scalability". It became a little too abstract for Applied but it was there if needed should a squire attempt to become King Arthur.
>it feels like all the rest of math is the development of tools to be used in Number Theory
Sure...in the sense that "What tools is Math missing, lets look at what we have and ask ourselves what is it we need."

Its for inventors, not "applied", as the application is theoretical until adopted. So "elementary" is just another way of saying rudimentary or axiomatic.
(Thats why Norman and I fiddle with basic "elementary" stuff like "Arithmetic".)

[Anonymous No.15413312]

>>15410532
>"An introduction to the theory of numbers, G.H Hardy, E.M. Wright, revised by D.R. Heath-Brown, J.H. Silverman. Originally published 1938. Sixth edition 2008 with a foreword by Andrew Wiles" is AFAIK a highly praised book. - What seems odd to me is that there are no exercises in the book. This must be the first mathematics book I have ever seen that has no exercises in it. Exercises, with or without hints can't be missed IMO.

>Question. Was this common for books written in that time, i.e. mathematics books without exercises? If not, it must have been noticed by the critics. What did they say about it? Or (shame ) have I perhaps missed an accompanying exercise book?

-- some faggot on math.stackexchange

[Anonymous No.15413358]

>>15410532
Elementary Number Theory - Vanden Eynden
A Pathway Into Number Theory - R. P. burn

[Anonymous No.15413361]

>>>/sci/mg/

[Anonymous No.15413397]

>>15412731
>Norman Wildberger
Since you're a fan of his, maybe you can answer my question. How does he justify rejecting one kind of relation, yet accepting the exact same basis of the relation for everything else? I've a second question that requires some explanation to understand. Simply choosing without justification "that which can be calculated" isn't a justification, it's an excuse. This also results in a paradox such that non-finite representable points between distances "aren't real", and yet traversing along some length requires traversing such points.

I have his book and this is nowhere solved, nor on his blog, nor in what little time I'm going to waste on his videos. He still uses lengths, and still uses points, and therefore has no grounds to justify rejecting irrationals as they must exist somewhere on any given line. The third problem is that defining numbers as he does by field doesn't resolve this contradiction, as if he truly stuck to it his "lines" must consist of infinitely many discontinuities. This violates identity by contradiction. Where does he address any of this?

[Cult of Passion No.15413439]

>>15413397
>How does he justify rejecting one kind of relation, yet accepting the exact same basis of the relation for everything else?
"Its very simlar to playing with the definitions of Algebra/Arithmetic etc"

It will appear chaotic but its not, math gets weird at the most scutinized levels of Number Theory, becomes almost something very different, different perspective. It will look like a stuttering signal until you can see the other perspective hes using.

>non-finite representable
I disagree with him here, Im an Infinitist, minimal/maximal perspective. If one can learn enough...it can become three, min, max, mid, always is the same locations.

>has no grounds to justify rejecting irrationals
He also uses "Dedekind cut", if I remember, replaces the Zero location with sqrt2. Ive also found this in math but I have several+, not just the one, making a very multidimensional base system.

>This violates identity by contradiction. Where does he address any of this?
Lol....this is Theoretical Mathematics, rewriting definitions is the norm, solving puzzles is one thing, making them is another.

[Anonymous No.15413440]

>>15413439
I get the sense your answer is what my answer is, namely that there isn't one and he's a hypocrite. The problem is your idea of what he's doing isn't accurate as you write here,
>Lol....this is Theoretical Mathematics, rewriting definitions is the norm, solving puzzles is one thing, making them is another.
The man is not going "Let's assume they're not real", the man is trying to argue and popularize an asinine notion that they're not real because he seems to genuinely believe it. Hence why the contradictions his rejection creates is a very big problem. By rejecting infinity he creates infinite discontinuities and fundamentally cannot use lines or do anything in geometry, so any geometry based on his rejection is not valid.

It'd be one thing if it was some cute mental exercise but it's quite another considering his apparent activism.

[Anonymous No.15413445]

>>15413361
A general would only foster very narrow discussion. Why not have this thread? Do you want to make more space for "why do black women have black pussy flap" threads?

[Cult of Passion No.15413446]

>>15413440
>The man is not going
Sorry, but I took most of Wilderberger's ideas and went one to two dimensions deeper, invented on my own, so we compared notes after the test. I smoked him, hard.

He is an acolyte of Chaos Math, I write Chaos Math.

Youre not a real Mathematician, youre a high functioning autist, your inability to operate on new rule sets proves this.

Begone, your judgment means less than nothing.

[Anonymous No.15413452]

>>15413446
>Youre not a real Mathematician, youre a high functioning autist, your inability to operate on new rule sets proves this.
My ability to operate on new rule sets and find paradoxes in them proves otherwise.
>Sorry, but I took most of Wilderberger's ideas and went one to two dimensions deeper
Garbage in means garbage out. It can be fun, but in this context garbage in isn't even as reliable as a stopped clock as it becomes infinitely unreliable. By your own analogy I guess I'm infinitely many dimensions deeper than you are, then?
>Begone, your judgment means less than nothing.
It is only by framing judgments and conclusions with coherent structure and sound premise that anything can be meaningful. You're 0 for 3 and we're not even talking about number theory except indirectly. Numerology is not number theory and your reaction suggests you're in the realm of numerology instead.

[Cult of Passion No.15413459]

>>15413452
>My ability to operate on new rule sets and find paradoxes
Ahem.
>and find paradoxes
So....you could not operate? I know, I told you first.
I'm the doctor, you're the patient, Mmk?
t.Number Theory & Psychology, PhD

>Garbage in means garbage out
Indeed, I'd say.

Our works are Post-PhD research level, this is end of the line, the gate of invention of ALL OF MATHEMATICS.

Youre an idiot.

These are facts, court in adjourned.

[Anonymous No.15413467]

>>15413459
>So....you could not operate? I know, I told you first.
I can in fact hold more than one idea in my head at the same time. You're implying you can't, or that doing so is somehow proof of some inability somehow. If the latter is your implication you're no different from any other person who claims not thinking is a virtue.
>Our works are Post-PhD research level, this is end of the line, the gate of invention of ALL OF MATHEMATICS.
The "gate of invention" isn't nonsense. Nonsense only begets nonsense. Staring at noise and claiming patterns that don't exist isn't being inventive. You're a numerologist, not a theoretician, if you do that.

[Cult of Passion No.15413479]

>>15413467
>Staring at noise and claiming patterns that don't exist isn't being inventive.
YOU WILL NEVER KNOW BASE REALITY.

Your critique of Wildberger missing all of his actual defects, lack or originality, over messy/needlessly repeated, works, means you have an amature's at best Mathematical understanding, 2nd year perhaps, enough to follow the words but understanding a perspective of Number Theory takes many Many hours to understand. You latched onto DEFINITIONS.


I have used the word DEFINITIONS a lot but youre not understading what DEFINITIONS means. Go back and look for the word DEFINITION.

Its like youre drunk and angery but have no clue who to be angery at. I get it...I think about fist fighting every person I see. Real eye up cops and security, trigger their nerves a bit. Heh...

COURT IS OVER, GO HOME, DUMBASS.

[Anonymous No.15413495]

>>15413479
>YOU WILL NEVER KNOW BASE REALITY.
Chaos theory exists. And?
>You latched onto DEFINITIONS.
You have me backward. For anything to make sense it must have some identity however defined, and some identity must have some property that is mutually exclusive with some other identity. Constructing some system of concepts is not "latching onto definitions", as in that case you would be unable to entertain or develop constructions. Nor does evaluating the coherence of something constructed by the degrees to which it breaks constitute "latching" onto anything, unless I pinned you rightly and your ultimate justification is "stop thinking".

So are you going to discuss number theory, or keep throwing poo? If your position comes down to "stop making sense of things" you're engaged in numerology and >>>/x/ is that way.

[Cult of Passion No.15413522]

>>15413495
Student, YOU DO NOT HAVE THE PREQUISITS.

YOU CANNOT ATTEND.

YOU CANNOT FOOL ME, YOU ARE NOT A REAL MATHEMATICIAN. Im not even ready your psuedo-intellectual drivel, get a PhD or shut the fuck up about shit you know nothing about. Its offensive to those that do know, hence the capitalization.

BEGONE, STUDENT.

[Cult of Passion No.15413524]

>>15413522
Damn, wrong pic.
These are the interesting ones.

Oh, amd remember that my Mathematical Thesus was in Number Theory, so...yeah, maybe remember that next time you see me. I schooled Norman...who the fuck are you?!

[Anonymous No.15413614]

>>15413524
>Oh, amd remember that my Mathematical Thesus was in Number Theory
Link? It might be fun.
>so...yeah, maybe remember that next time you see me. I schooled Norman...who the fuck are you?!
Wouldn't you like to know.
>>15413522
>get a PhD or shut the fuck up about shit you know nothing about.
I don't need one to keep publishing and I don't care about having an academic institutional position. Why would I? Anyway link your thesis or whatever it'll be fun to read I bet

[Cult of Passion No.15413621]

>>15413614
You failed the first question, you are not a Mathematician, youre a charlatan wanting to feel knowledgable but you are not.

You will never be called Doctor.

[Anonymous No.15413639]

>>15413621
>You failed the first question
lol

anyway i asked about your thesis but if you don't post it due to your name being on it that's fine. Was just curious.

[Cult of Passion No.15413692]

>>15413639
>due to your name being on it
No, because I dont speak about it to liars and charlatans. Its clearly beyond you conprehension level because Im outlining it in these posts and YOU ARE FAILING IN EVERY RESPONSE

YOU ARE NOT A MATHEMATICIAN.

Stop talking like youre "on top", "one to judge" or "is competent". YOU ARE NOT.

[Anonymous No.15413720]

>>15413692
You still are thinking of what I said backward >>15413495
Since you won't discuss number theory continuing to throw empty shit would be totally off topic.

[Cult of Passion No.15413760]

>>15413720
"Imma pretend to be knowledgeable while missing the outline of the Thesis because Im not really knowledgeable...I lied, and I keep lying, with every post I add another lie; Pretending to be a Judge of the topic instead of what I really am; Lost in Chaos Math."

Sheeeit....fuck off, faggot, youre a bowl of shit and nobody believe your bullshit except people that fake like you.

I lecture, nobody "grades" my work, peasant.

[Anonymous No.15415086]

bump

[Cult of Passion No.15415257]

>>15412032
>Looks like a comfy read, but at a very elementary level
What you call "elementary" is Elemetary, meaning axiomatic, irreducable, not what most modern Number Theorist do; convoluted pattern puzzles.

Inventing something like Wildberger's (https://youtu.be/CScJqApRPZg)) is easier than (re)Inventing Arithmatic or Algebra using a native multidimensional Geometry. This is also why Wildberger lectures so much on ancient Mathematicians, as he and I are walking the thought process to (re)invent it with the original inventors, sometimes inventing something new. This is how one can "make" new equations and maybe find an application in the process.

Do not take me for a fool, padawan. Yes, you need "mid training" but after than I can take you deeper down the rabbit hole of Numbers than you will even want to go.

[Anonymous No.15416632]

>>15415257
>Wildberger
Is he your cult leader?

[Anonymous No.15418530]

>>15410562
Continued fractions are kinda cool though, and they're really only talked about in number theory.

[Anonymous No.15419637]

>>15413312
Jim Watson the DNA guy invented the ‘modern textbook’ that we’re all used to seeing in classrooms in our time.

Before him textbooks were written more like any other book.

[Cult of Passion No.15419651]

>>15416632
He's an amature to me.

What do you think that makes me see in you if your giants are my ants? This isnt "shit talking" you fucking retard.

This is cognitive assessments, nothing more.

[Anonymous No.15419942]

>>15413440
>By rejecting infinity he creates infinite discontinuities and fundamentally cannot use lines or do anything in geometry
Euclid managed to get a lot done before developing Eudoxus's theory of proportion in Book 5.

[Anonymous No.15419951]

>>15418530
This along with the related Euclidean algorithm really should be part of the standard high school curriculum. In a sense they're a fundamental tool for using the rational numbers. If you have quantity A which is a rational multiple of quantity B, then you need the Euclidean algorithm to figure out what that ratio is in a reasonable amount of time. Of course in most situations we work with approximate real numbers rather than exact rational numbers, so I can see why it might not be emphasized.

[Anonymous No.15419962]

>>15419637
Redpill me on this.

[Anonymous No.15420702]

>>15419951
In HS, we had a hard enough time getting idiots to comprehend the quadratic theorem, and this was in a class of white students. To teach something more advanced would require building much better curriculum to prepare students sooner

[Anonymous No.15421030]

>>15420702
This is just arithmetic though.

[Cult of Passion No.15421337]

>>15421030
>This is just
A shape. Nothing more. Nonsense. Meaningless. Arbitrary repetition.