/mg/ = /math/ general: ebil Gowers bogeyman edition

I still think his advice to start with an interesting mathematical curiosity and fill in prerequisites from there is pretty good t b h.

Who is he? What prerequisites? Advice?

What's /mg/'s opinion of hyperbollic geometry? I decided to do my undergrad "thesis" on it after reading Geometry of Surfaces by Stilwell. The distinct models are pretty cool, and being able to recreate so many different geometries in [math]\mathbb{H}^{3}[/math] is breddy nice.
Would you recommend number theory to someone who's very interested in geometry? For the moment I don't think very much of it because it look a bit meh to me, but if there's interesting geometric interplay I may get something out of it, I don't know.

Qiaochu Yuan, graduate student at UC Berkeley. I'm referring to his SE answer here: math.stackexchange.com/questions/181387/motivation-and-methods-for-self-study/181410#181410

He's pretty much a meme though. Probably browses this site.

Mathfags, tell me: if you know the values of a+b, c, and the hypotenuse, is it possible to find the value of b? This is not homework, don't worry

>Would you recommend number theory to someone who's very interested in geometry?
In my experience number theorists seem more up to the idea of diving into geometry than the other way around, they just have very distinct aesthetics. Maybe it's easier to find interesting number theoretic problems in geometry than geometric problems from number theory. Anyway pic related is easy reading (not easy math, but mostly conjectures and theorems without proofs), sort of a blueprint for a lot of work done in arithmetic geometry from the last 30 years (+ probably the next 100 years)

I don't think so. I think you can keep a+b, c and the hypotenuse the same but change a and b.

I.e. if you change that picture to a+ (something small) and b - (same something small) you get the same triangle

>What's /mg/'s opinion of hyperbolic geometry?
It's fucking nice, m8. I was introduced via Wildberger's series on Universal Hyperbolic Geometry.

I'm gonna go with 'maybe' because i don't have time to play with these variables more.

If you like hyperbolic geometry and number theory than dynamical systems/ergodic theory is probably the route you wanna take.
From what I've seen a hell of a lot of solid state physics (at least at the level of studying crystals and metals) basically boils down to group theory so looking at cft as a tool to describing condensed matter systems becoming group theory when looking at basic crystalline structures may not far fetched I suppose.
No, consider the following, let a+b=12, c=5, and the hypotenuse be 13, then two possible solutions for (a,b) are (2.10) or (5,7), in fact there are infinite positive real numbers (a,b) s.t a+b=12, basically being on the line (a, 12-a) for 0

Why is he a meme exactly?

>Why is he a meme exactly?
Because he's only known for posting on stackexchange a lot

>leave math to me

Currently reading Differential Equations, by Shepley L. Ross. Really enjoying it, especially after I switched from digital to physical copy.

Hello /mg/ faggots come visit our cool new fresh Graduate Maths Discord server.

discord.gg/AZxmmXr

Not a [shitpost everwhere] normie server, but also not a nazi where you get banned for saying word "nigger" :DDD
Graduate level channels currently follows arXiv ontology, with many graduate level topics are covered, though we accept further suggestions on channel structure.

Also you can animefag there!
Thanks for considering!

>discord

Man, Gowers even looks like a villain. How do we stop this motherfucker?

Le obligatory suicide anime post face LOL! I must say Atiyah's book on K-theory is really easy to read, I like it.

>preparing for a calculus II final
>Have to study lineal differential equations and bernoulli's little shit
>Khan Academy DE section ends with separation and exact DEs

OH SHIT WHAT DO I DO

>What's your favorite number theorem in number theory, anons?
Do the Sylow theorems count? (I'm not into number theory.)

>Do the Sylow theorems count? (I'm not into number theory.)
No.

>From what I've seen a hell of a lot of solid state physics (at least at the level of studying crystals and metals) basically boils down to group theory so looking at cft as a tool to describing condensed matter systems becoming group theory when looking at basic crystalline structures may not far fetched I suppose.
Actually the equivalence comes from the operator algebra. If the conformal dimensions of all the primary operators are 0 then the fusion relations basically just form a presentation for some group. Crystal symmetries aren't universal while conformal invariance is, so the former really isn't really what's at play here.

I WANT MY MEME LIST

RATE MY MEME LIST

YOU DEPRESSED FAGGOTS BETTER LISTEN TO ME RIGHT NOW IM NOT GOING AWAY

MUH BOOOKKKKSSSSS

You know, Scholze is an awful lecturer. I have to watch this on 2x. He spends too much time repeating what he's already written down, with minimal exposition.

youtube.com/watch?v=TU39h4rDJAs

He also spends too much time looking at the blackboard. Scholze my man, if you're reading this, engage with your audience more. There no point to the lecture if it's just a paper by dictation.

Given this relation, what properties does a function
f have to satisfy so that
[eqn]S=\{(x,f(x)|x\in dom(f)\}[/eqn]
is a maximal chain? Clearly f must be monotonically
increasing, but must f be onto [math]\mathbb R[/math]?

Example: if f is the identity for all reals, then S is a max
chain. Proof: try to add (a,b) with a < b, then choose
c so ac>b.

What assumptions are necessary to generalize this?

>[math]\mathbb{R}[/math]
No such thing.

How long does it take to have your article reviewed?
I submitted a paper to a journal 2 months ago via an online submission form, and received no information yet (except for an automated email)
Was is so bad they didnt even reply?

not even our best Big Ashkenazi Brain can compete holy shit

>reddit images

>we
Speak for yourself, subhuman.

brainlet here, can you write the absolute value function without it being a piecewise function? I don't care how deep down the math rabbit hole you need to go to do it, I'm not pretending to understand the solution, just want to know if it's possible.

sqrt(x^2)

Help me with my algebra excercise: "for every positive integer [math]n[/math] construct a group containing two elements [math]g, h[/math] such that [math]|g|=2,|h|=2, |gh|=n[/math]"
For [math]n \geq 2[/math] it's simple:
Let's take a dihedral group [math]D_{2n}[/math] generated by [math]x^2 =
e, y^n = e, yx = xy^{n-1}[/math]
[math]g = yx, h = x[/math]
[math]g^2 = yx yx = yx^2y^{n-1} = y^n = e \implies |g| = 2[/math]
[math]h^2 = xx = e \implies |h| = 2[/math]
[math]gh = yxx = y, |gh| = n[/math]
But what should I do with the case [math]n = 1[/math]
If I try to make a multiplication table for a group to satisfy this condition:
[math]g^2 = e, h^2 = e, gh = e[/math]
such table would violate cancellation rule. The problem would be solved if [math]g = h[/math] is the same element yet I'm not sure I'm allowed to do this. What should I do?

The cube fitting problem from the previous thread could easily be solved once you find a way to count how many squares fit into a circle, but then I don't know if there's a slick way to simplify the resulting sum in a slicker way. Any thoughts?

How do I answer this? I'm unsure as to what a Cp value is, or how I can use them to determine the answers to the questions.

Please help this poor brainlet

It can take a few months depending on the journal. If none of the editors are interested, even more. I know some guys who had their papers in review for more than 2 years.

Read your notes dummy. How should we know what Cp is? (It's probably Mallows' [math] C_p [/math] statistic though, just a hunch.)

You've provided and proved an answer for n>1. You've provided and proved an answer for n=1. You're done, kiddo.

And even if you weren't sure your answer for n=1 was legit, you've proved that no other answer is possible. So, you've check your answer as well.

that alone is not a trivial problem, hell packing cubes into a cube is not even trivial.
assuming that you can get to the optimal 3d packaging from stacking up optimal 2d packages is also foolish

I'd be just as happy if you could do it for [math]\mathbb Q[/math]

I am glad that people took my bait and started to work on the packing problem. Don't give up user!
Packing problems are awesome.
quantamagazine.org/sphere-packing-solved-in-higher-dimensions-20160330/

Don't be a killjoy. Splitting the problem on rows like that can at least give you a lower bound on the number of cubes you can fit.
By the way, the horizontal cross section is a circle only for paraboloids of revolution.

— — — — — — — —

0. Remedial Mathematics
Khan Academy

— — — —

>1. The Prerequisites of University Mathematics
Pre-Calculus - Carl Stitz & Jeff Zeager
Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley
How to Prove It - D. J. Velleman

— — — —

Pick One Path:

>2a. Introduction to Applied Mathematics (Some Proofs)
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Differential Equations - Shepley Ross

>2b. Introduction to Pure Mathematics (Proof-Based)
Calculus Vol. I & II - T. M. Apostol
Principles of Topology - Fred H. Croom
A Book of Abstract Algebra - C. C. Pinter

>2c. The Mixed Approach
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Differential Equations - Shepley Ross
Principles of Topology - Fred H. Croom
A Book of Abstract Algebra - C. C. Pinter

— — — —

>3. Foundations for Advanced Pure Mathematics
Linear Algebra - K. M. Hoffman & Ray Kunze
Analysis I & II - Terence Tao
Visual Complex Analysis - Tristan Needham
Algebra - Michael Artin

— — — — — — — —
Is this legit? I'm an EE freshmen but I don't want to be a total brainlet ;_;

Visualizing R^2 as a Cartesian plane, the relation (a,b) ~ (c,d) simply requires that (a,b) lie below and to the left of (c,d), with both inequalities being non-strict.

So you shouldn't need any more conditions beyond f:R->R being monotone (with f(a)=a for a

>I'm an EE freshmen but I don't want to be a total brainlet
Impossible.

You won't

Get this crap outta here, no one cares about your meme list. Weren't you supposed to be a chemistry major anyway?

>meme

>Analysis
Analysis needs to be banned.

Why?

t. bitter sophomore

Algebraic * > *.

Because it relies heavily on nonexistent garbage.
>t.

>it relies heavily on nonexistent garbage
The empty set?

>nonexistent garbage
go on

Not just the empty "set".
What were you trying to say here?

I was wondering what *you* were trying to say in your previous post.

I was just saying that analysis needs to be forbidden.

I know it's bait, but I have nothing better to do, so I'll ask why and what you mean by "nonexistent garbage"

The empty "set", or any other "set" for that matter.

The only ontologically problematic concept in set theory is the empty set, which is vacuous. How can nothing exist when obviously something does? It is much easier to accept infinities than nothingness.

What sort of math do you do that doesn't rely on sets ?

>Because it relies heavily on nonexistent garbage.

I kind of agree with this user. There is such thing as constructive mathematics which states that all mathematics is computable(this is about computation theory, arithmetics is irrelevant) implying that we should throw away all the uncomputable mathematics(which is user said "nonexistent garbage"). For example, actual infinity is uncomputable which potential is just fine. Excluded middle shouldn't be taken as an axiom and used in general case(in intuitionistic type theory by Per Martin-Löf it is a theorem). Axiom of choice is garbage as well.
To sum up, mathematics should get rid of all undecidable problems(read about this on wiki) and uncomputable garbage, otherwise it's just FAITH, not science

>The only ontologically problematic concept in set theory is the empty set
Set theory itself is a "problematic concept".
I didn't claim that my math doesn't rely on sets.

>There is such thing as constructive mathematics
Which is consistent with set theory, which means it's garbage as well.

Nice false dichotomy you have there.

So why does relying on sets make analysis more deserving of being banned ?

>There is such thing as constructive mathematics which states that all mathematics is computable
Wrong.

Type theory, especially HoTT is just fine, though.

It relies on them heavily.

>mathematics should get rid of all undecidable problems
I agree. Mathematics should be complete, consistent and decidable.

Inaccessible cardinals exist. Deal with it.

Can you be more specific ?

Analysis relies heavily on "sets". This is already pretty specific.

Of course they do, set theory is inconsistent.

You didn't explain what you mean by "analysis" or "heavily".

By "analysis" I mean "analysis". By "heavily" I mean "heavily".

you literally have nothing to say aside from "SETS ARE ICKY EWWWW"

>mathematics should get rid of all undecidable problems
Which "set theory" already does. You would have known if you weren't such a retard.

And can you characterize how it makes heavier use of set theory than linear algebra ?

I'm pretty sure "set theory is inconsistent" and "SETS ARE ICKY EWWWW" are different statements.

Which set theory? Tarski–Grothendieck set theory? Prove it.

Do you even know what "heavily" means?

>Which set theory?
ZF is definitely inconsistent.
>Tarski–Grothendieck set theory? Prove it.
I'm currently working on that. You'll have to wait.

they're literally the same if you have nothing to say about them. you keep parroting it and I don't even think you know what it means. which of the axioms do you have a fucking problem with?

Stop feeding the troll please.

>ZF is definitely inconsistent.
elaborate.

>which of the axioms do you have a fucking problem with?
It's not currently known precisely which axiom causes ZF to be inconsistent. We are working on it.
There is nothing to elaborate on.

Not him. I don't like the axiom schema of specification. I also can't stand the axiom of choice. And anything you can use to arrive at the empty set.
Whether infinite sets exist or not is something that remains to be ascertained but we know for a fact that something exists, therefore no-thing doesn't.