Math general

What are you guys up to?

Other urls found in this thread:

publicationsthomashales.wordpress.com/motivic-integration/
cambridge.org/catalogue/catalogue.asp?isbn=0521149762
arxiv.org/abs/1504.02401)
msri.org/summer_schools/419
en.wikipedia.org/wiki/Zeta_function_universality
en.wikipedia.org/wiki/Knaster–Tarski_theorem
change.org/p/robert-l-barchi-stop-sexism-at-rutgers
twitter.com/SFWRedditGifs

Cute fingers.

Thanks!

What are you studying? What are you researching? What are you thinking about?

OP is thinking about starting K-theory to see a connection between rings and topology.

Starting exams soon so I don't have much time to do some of my own stuff but I was reading through a book on Lie groups last night.

Rather interesting for those in undergraduate studies, you can take the exponential of a matrix A in an obvious way, setting:

[math] exp(A) = \sum_{k=0}^\infty \frac{A^k}{k!} [\math]

It's rather useful, especially for solving DEs with matrices.

I'm studying linear algebra and it's kicking my ass. Guess I was a brainlet all along.

Who isn't?

LA is also kicking my ass
>at least I've got stats down

trying to get a handle on clifford algebras and find some applications of lifting modular forms

Reading on motivic integration and kinda getting my ass kicked

something by Hales? might find these useful
publicationsthomashales.wordpress.com/motivic-integration/

>publicationsthomashales.wordpress.com/motivic-integration/
Ah neat ! I'm reading this at the moment cambridge.org/catalogue/catalogue.asp?isbn=0521149762 cause it's the only book they had on the subject at my library (that being said, it's really good) but it can't hurt to have more references at hand

In topology to prove that f:(X,T)->(Y,T') is continuous you can prove that for every open O' in T' f^-1(O') is an open of X.
Now Let's say I want to show that R^n\{0} and (R*+) x S^(n-1) are homeomorphe (where S^(n-1) is the sphere of radius 1).
for n=1
f(x,y)=xy from (R*+) x S^(0) to R\{0} is a bijection.
Now how would I show it's continuous ? Id' take the opens of R without the 0 ( ]a,b[ is a basis of all of the opens of R right ?) and then show it's an open of the topology of products where an open is open of (R*+) x open of S^(0) .
Could you show me how to this with the intervals ]a,b[. I'm lost.

In the first line it should be "is an open of T. " Sorry.
Also how would you do the same thing for the general case. (I've got the bijective function but I'm again blocking on how to manpulate intervals).

Consider an interval [math]I = ]a,b[[/math]. What is [math]f^{-1}(I)[/math] ?
Since [math]I \subset \mathbb R^*[/math], you have either [math] b < 0[/math] or [math]0 < a[/math]. In the first case, [math]f^{-1}(I) = ]-b,-a[\times \{-1\}[/math], which is open, and in the second case, [math]f^{-1}(I) = ]a,b[\times \{1\}[/math], which is also open.

That helps a lot thanks.
Just a question:
I know that the "reciproque" of f is :
f^-1(x)=( |x|, x / |x|) right ?
So I got how you were able to take the absolute value of an interval but the second part when it is -1 or 1 (which I know is S^(0) I don't get.

Me again I think I got it by just instead of thinking about the whole interval just taking one element of it and doing the operation and I get either 1 or -1. The interval just makes it for all of it.
And taking intervalls is the right way because they are a basis of opens for the usual topology of R right ? Because you need to show for ALL opens right ?

>I know that the "reciproque" of f is :
Are you french ?
>And taking intervalls is the right way because they are a basis of opens for the usual topology of R right ?
Oui, si tu prends un ouvert U de R* et (u, v) dans [math]f^{-1}(U)[/math], alors par définition il existe [math]\eta > 0[/math] tel que [math]]uv - \eta, uv + \eta[ \subset U[/math]. Alors [math]f^{-1}(]uv-\eta, uv+\eta[)[/math] est un ouvert de [math]]0,\infty[\times \{\pm 1\}[/math] par l'argument vu plus haut, contient [math](u,v)[/math] et est inclus dans [math]f^{-1}(U)[/math].
Du coup, [math]f^{-1}(U)[/math] est voisinage de tous ses points, donc est ouvert.

Just took my third exam for combinatorics, it was on graph theory.

let's be reality here guys, combinatorics > everything else.

Ok merci magl. J'ai enfin compris !

Should I focus on studying analysis or algebra this vacations? I can't decide which will benefit more and I find both interesting af.

Stats was my absolute worst math class so far

Why not study both then?

What level are you studying?
>2nd year undergrad here

What's a good progression to learn analysis to a beginner level? Baby Rudin->Papa Rudin->Rudin Functional Analysis? I'm nearing the end of Baby Rudin. I've had a course on vector spaces but I've heard that Halmos' Finite Dimensional Vector Spaces can help to prepare one for functional analysis.

What was bad about it for you? Taking it next year.

Halmos is just a pleasant writer in general, very concise and easy to understand. I haven't tried to delve into Rudin though, so I can't comment on the difference between the two.

Is ( f'(x2) / f'(x1) ) * ( f(x2) / f(x1) ) solvable if you don't know/care who f is but know its values at x1 and x2?

Sounds like a plan then.

Ok, I think there's actually a way for category theory to be useful for once.My end goal is to completely mathematically characterize topological phase transitions.

I'm currently looking at topological insulators and phase transitions, and to determining if the system has a topological phase is to look at the quantum particle statistics.
In general this can be done in two ways: the braid group (holonomy) formalism or the operator product expansion (principal bundle) formalism. However they each had their own drawbacks: firstly, it is not a priori clear how the braid group formalism can be used to determine particle statistics if the gauge symmetry is a Lie group other than U(1), while the tensor fusion categorical formalization of the OPE approach can characterize Chern-Simons actions (and therefore the particle statistics) with arbitrary semisimple Lie algebras as gauge symmetry. On the other hand, the categorical approach has only been studied on closed compact manifolds, which means that edge effects cannot be characterized in this way, while (I believe) this can be done from the braid group perspective.
Now a recent paper caught my attention (arxiv.org/abs/1504.02401) that tells of a way to establish an equivalence between the holonomy and the principle bundle formalization of gauge theories. What I'm hoping is that this would serve exactly as the bridge that I'm looking for. If the author establishes this equivalence in a constructive manner I may be able to transfer the structure that I need from the OPE/categorical approach in order to capture non-Abelian statistics into the braid group formalism.

If all of this works out (it probably won't) you can expect a publication and maybe a Nobel.

You are right, it won't work out.

I am currently tackling Hilbert spaces. I have an exam soon and we only got a shitty hand out which is not very helpful in explaining the steps

>intermidiate stats
>allowed 1 note sheet for exams
>got 100% on first 5 exams
>forgot calculator and notes on counter at home for 6th exams
>67%
Is this what brainless feel like when they have their notes?

>Taking any stats at all
>having to use a calculator
You're already a brainlet m8.

>unironically appraising your own work as nobel-worthy
the level of delusion is unreal

the ability to do mental arithmetic is no reflection on the ability to understand and apply concepts to real world problems

You didn't even understand. I'm not talking about your ability to do stupid mental calculations, but the need to use a calculator at uni for fucks sakes.
Are you still in high school ?
I've never had to use a calculator once at uni.

good for you
>I'm in university
>still using a calculator
What's your point? I prefer not to do stuff in my head. Greater chance of error

The point is if you have to calculate stuff for your exams you're likely not to do any real maths.
By that I mean actually using concepts and ideas instead of doing stupid calculations.

In stats (and numerical methods) you're very much applying concepts and calculating...

>have you ever seen a stats paper?

This is why I said
>Taking any stats at all
It shows you're a brainlet.

>autist can't detect obvious joke

im out
>this guy
>must be trollin me

>my courses are the exact same as everyone else's
Some courses emphasize computation where it's only reasonable to use a calculator. Fuck off with your stupid attitude.

What's you school m8.
Doubt it's a good one.

It's in the top 20 for math. So yeah, fuck off now pls.

>top 20.
this is the new meme.
Next year it'll be
>top 200

Lol bunch fuckin dorks arguing over who beter at putting numbers together. Here's a helpful hint faggots...when you can sell a ketchup Popsicle to a dumb bitch in white gloves all you'll need to put your numbers together is commas

Basic question. I do not understand some of the assertions here. How is CAB acute? I also do not understand how this proves that 3 and 4 are acute, given that they are congruent with right angle triangles.

I just started working through a calculus textbook despite having dropped maths in yr 10 and not having any formal mathematical education in 3 years. I'm having a lot of fun and I'm excited for gaining new knowledge.

>Ok, I think there's actually a way for category theory to be useful
>for once
nice try m8e

Lou van den Dries has some good notes on motivic integration if you haven't already looked at them.

>yfw geometers have a proof for the Riemann hypothesis for varieties over finite fields
>yfw number theorists still don't have a proof of the Riemann hypothesis for the zeta function

Any geometry overlord here? Can you give me some tips to git gud at it?

Ah I didn't know about these, very nice, thanks !

stats was and never will be math

What kind of geometry?

Catching up on machine learning papers before getting back to topos theory. I'm going to go through the DNC and GGS papers. After that, I'll go through some of the OpenAI papers, then it's back to Kostecki's Intro to Topos Theory.

What books are you using? I found particularly using the one written by Porteous

How do I get better at math when I have no one to ask questions?

Ask questions here

I'm in calc 1 and a retard so I would just waste time and people would shitpost at me

what about other people on your course or whoever is teaching you?

CAB is acute because it's the constructed situation. It is a fact. Note that the figure does not match that (AB should be sloped to intersect BD). Then, the indirect method is used to prove that the assumption that AB||BD leads to a contradiction, and is thus false. Obviously, under the parallel postulate, CAB is acute xor AB is parallel to BD.
My best guess at the hidden parallel postulate is concluding that FE=GH=BA due to parallel lines.
It can also be shown under the assumption that CAB is also a right angle, which is a contradiction.

square area

Post in SQT or here. No one cares if you are dumb since we are all dumb at some level of mathematics.

It's a good way to start.

Getting your ass kicked by math every now and then is a good thing as it forces you to study the things properly.

Let's hope it works. What would be the physical implications if it did, or would it be to reformalize the stuff?

Nice. Is it going well?

learning clifford algebras in the world of quadratic forms, so the book by Lam (intro to quadratic forms over fields)

i'll take a peek in Porteous though, thanks

thankyou my man

by DEs, you mean the encryption?

I have been working through this shit in my free time this semester. msri.org/summer_schools/419


Currently learning about quotient stacks.

What kind of stat class did you take? Its built up from measure theory, probability theory, analysis, calculus and linear algebra. I dont like it either but it sure as fuck is mathematics.

I love these threads by the way, fellow math nerds.

differential equations

Dunno if I should become a physicist or a pure mathematician, which one brings more flexibility?
I want to finish my bachelor/master and work in whatever I feel like without to much restriction.

What do you like in math? What do you like in physics?

Ask in MSE, seriuosly. Those guys always answer my questions no matter how stupid they are.

>What kind of geometry?
Analytical geometry.

preparing for my second midterm in calc 3

not sure how important this will be to me as a CS major, but i love it

CS or Engineering?
I'm a junior in hs. 4.1
I've taken AP CS at my school
and approx 7 other AP courses.
Taking AP Calculus.

>no question thread in catalog

How do I write the negation of this statement? Do I just negate the red part, or do I have to do something to the blue bit? We were only taught how to negate very simple p, q statements and I honestly have no idea where to start with this.

...

Are you retarded? Switch the universal quantifier to an existential one and the existential one to a universal one

>Are you retarded?

Quite possibly. ty user

In highschool atm. Going to Geneva's university in 2 years in the the physics degree

Exploring possible graph theoretic ways to model Sokoban and other "grid-based" games.

Has anyone tried this approach before? Any papers I could check out?

I feel like I have seen something on Sokoban before. I will check.

Another grid game I know of that is solvable using math is "lights out".

And you also have to negate the if,then statement

Currently doing Linear Models in R with the package Swirl() !!!!!!!!

not having a gf

Going to teach myself a course's worth of statistics. So far managed to get A's on exams by cramming through, but taking time series next semester so I should probably actually learn the prerequisite material instead of bullshitting the grade. Statistics is such an interesting field, but also such a fucking slog to actually get through.

>What would be the physical implications if it did, or would it be to reformalize the stuff?
The point is to completely mathematically characterize particle statistics, which can provide a theoretical origin for topological phases, including all quantum Hall (integer and fractional) phenomena.

The historical record disagrees with you. Mathematicians not exclusively doing statistics, astronomy or accounting is a recent trend. Maybe 50 years old. You've been lied to. Even today, *with* the growing trend of linguistic mathematics, most mathematicians still do statistics or statistics related work.

I'm studying the basics of modular arithmetic. I have a lot of work to do.

Any college faculty on here or am I the only one?

>tfw you get cucked out of teaching discrete math in the spring

wtf
en.wikipedia.org/wiki/Zeta_function_universality

What's up, folks?

...

en.wikipedia.org/wiki/Knaster–Tarski_theorem

Learning theoretical CS with prof, for use in FOL in finite domains

I made it past all the code monkey shit I think I finally made it FeelsGoodMan

>go to a great school for math
>fuck around and get Cs and Bs
>kinda sorta want to get back into math to eventually teach at community college
fugg

If you're a woman just say its sexism and they'll re-appoint you. That's what happened with some Professor at my college. Worked out great.

My college is the "most diverse campus in America," so they've got to prevent sexism like reassigning a teacher.

url related

change.org/p/robert-l-barchi-stop-sexism-at-rutgers