Math General

The previous one () is about to reach the bumplimit, so let's start a new one.

>what are you researching?
>what are you studying?
>any good problems?
>book recommendations?
>cool theorems?

Other urls found in this thread:

freebookcentre.net/SpecialCat/Free-Mathematics-Books-Download.html
Veeky
arxiv.org/pdf/0906.5137.pdf
twitter.com/NSFWRedditGif

first fro ct

freebookcentre.net/SpecialCat/Free-Mathematics-Books-Download.html

This is the best collection of free online texts I've seen. Has texts on pretty much every subject of mathematics except logic and a few specific sub fields.

general advice for an undergrad math major?

about mathematics itself or academics/careers?

>what are you studying?
Renormalization techniques for TQFT.
One of the defining features of a TQFT is the functoriality [math]\tau(M) = k \tau(M_1)\circ f_{\#} \circ \tau(M_2)[/math] where [math]k\in K[/math] is an invertible element of the ground ring, and [math]M[/math] is a [math]\mathscr{B}[/math]-space glued together from two cobordisms [math]M_{1,2}[/math] along the [math]\mathscr{A}[/math]-homeomorphism [math]f: \partial_+ M_1 \rightarrow \partial_- M_2[/math]. A TQFT is said to be anomaly-free if [math]k = \operatorname{id}_K[/math].
Apparently the existence of a [math]G[/math]-valued 2-cocycle [math]g \in \mathscr{P} \otimes G[/math], where [math]\mathscr{P} = \{P = (M,N,f) \mid M, N \in \mathscr{B}, f: \partial_+M \rightarrow \partial_- N\}[/math] is the collection of gluing patterns [math]P[/math] between [math]\mathscr{B}[/math]-spaces, on the cobordism theory [math](\mathscr{B},\mathscr{A})[/math]is sufficient to guarantee that the TQFT [math](\mathscr{T},\tau)[/math] based on it (possibly with anomalies) can be made anomaly-free.
This is a generalization of the usual process of renormalization in QFT where the quantum anomalies are gauged away by gauge-fixing in gauge-space (say that three times fast). The [math]k[/math] can be thought of as an obstruction to the quantum Ward identities.

99.7% sure the majority of uses of renormalization are not cases where you can sharp ans sweet get rid of particularly well specified QFT anomalies

Your overly verbose posts are genuinely cringe-inducing. Especially since what you keep yammering on about is (non-deep) category theory and elementary topology thinly veiled in pretentious physics lingo.

And those would correspond to cases where you can't find the 2-cocycle.
Remember that TQFTs only contains topological data. Normal QFTs also contains dynamical data that needs to be taken into account when renormalizing. This is part of the reason why non-renormalizability is rampant in QFTs with non-Abelian interactions or non-conformal geometry.

some resources for computer science math for beginner?

SICP

Samurai > Wizard

Well, Veeky Forums?

Veeky Forums-science.wikia.com/wiki/Computer_Science_and_Engineering#Mathematics_Primer

especially recommend concrete mathematics

Do you're own homework

no your do you're own homework

Im studding derivatives but im stuck on how the highlighted part becomes possible.

its literally just the last equality rearranged to put the cosines and sines on the same side

>you are now manually thinking

What a useless subject.

>you suddenly feel itchy
(but in an abstract kind of way)

...

I see now, also could you please explain why 2x is infront of sin2y. i dont know where it came from

the 2 comes from when u use the chain rule on cos(2y)

the x is in front of cos(2y) already

Thanks mate its all clear now.

Say that to me irl not online see what happens I'll hook you in your gabber

Name one possible use.

Are you asking how a topological quantum field theory can be used when a large chunk of the previous thread had been people talking about using it for topological superconductors?

Why didn't you protect his smile Veeky Forums?

>what are you studying?
Trying to teach myself some measure theory.
>any good problems?
Here's an easy problem with a cute solution: you have a jar with 20 blue balls and 10 red balls. You remove balls one at a time until only one color is left in the jar. What is the probability that only red balls are left in the jar at the end of this procedure?
>cool theorems?
This was a problem in the measure theory book I've been working through that was satisfying to prove: A sigma algebra cannot be countable.

A sigma algebra of [math]\mathbb{R}[/math], perhaps? Given any finite set, all the sigma algebras would be countable.

Countable as in countably infinite. The cardinality cannot be [math]\aleph_0[/math].

hope im not entering an undergrad thread
>researching
electrochemical materials for Li and Mg batteries
>studying
organometallics and solid state chemistry as well as electrochemical engineering
>any good problems?
yeah, how do I avoid high order lithium polysulfides forming in a Lithium sulfur battery? How do I make a solid state Lithium battery with a conductivity high enough to match liquid electrolytes? how do I get a magnesium battery to work reliably?
>book recommendations
Hartwig organometallics, Handbook of batteries by Linden
>cool theorems
no

Doesn't sound like math to me.

>retard can't even read the subject of the thread

Well isn't that immediate? A sigma algebra is a subset of [math]\mathcal{P}(X)[/math] which is uncountable for countable [math]X[/math].

What if you have a countable subset of [math]\mathcal{P}(x)[/math]? Why can't that set be a sigma algebra?

Closure under arbitrary union

A sigma algebra is closed under countable, not arbitrary union.

>engineers literally cannot read
bravo brainlets

Oh I was thinking of a topology

Both

Not to mention the fact that you can have countable topologies (see the cofinite topology on IN)

:DDDDDD

>niggers making new generals before the other one even hits bump limit, let alone dies
why

How about {{},X}

300k startin for a 30 iq

That is a sigma algebra, when I said countable, I mean countably infinite.

any canadians?

sup

ubc here

Yes.
Wtf same what are you studying? I may have TA'd you before rofl

i'm a grad student

>he's a gorillaposter
Math?

>Math?
of course

[too close for comfort]

Ok good, I'm in physics.

i definitely have no idea who you are then, i only know one person who went from physics to math

is the physics dept good here?

I have to give a presentation on that paper : arxiv.org/pdf/0906.5137.pdf

If anyone has an elementary proof that two quaternion algebras on a local field that have the same subfields are isomorphic I'd gladly take it.

I know there are only two (up to isomorphism) quaternion algebras on such fields, one that is split and one that is division.

I thought every quadratic extension would embed in the split one but I read somewhere that it was the case for the division one, and I'm a bit lost.

>is the physics dept good here?
It's pretty good, there are a few world-renowned condensed matter theorists that I work with here and the high energy team is also pretty strong I've heard. It's very competitive for physics here, I imagine that being the same for math as well?

idk how competitive it is (i got in lol) but there's some great algebraists/topologists/geometers/number theorists here at least, i don't know much about the applied people

you going to the 'Supermassive Black Holes' talk on wednesday?

That's cool. It'd be nice to talk to them about some of my categorical ideas but I don't have the time to do substantial research (and I don't want to waste their time). Also I'm heading off to McMaster for my PhD since it's much more chill there.
No I don't like astrology.

am i just high rn or is the centered display symmetric in ij?

i wanna skip from linear algebra to topology. what do

1/(30 choose 10) ?

>i wanna skip from linear algebra to topology. what do

Stop being a brainlet, they're unrelated and you can learn them both at the same time, and they're both important topics.

let S be a non-finite sigma algebra. suppose we have an enumeration of all sets in S in disjunctive normal form. we can use closure under complements to do something cantor diagonalization-esque.

treat the classes as a day job and learn whatever the hell you want to

look up prerequisite knowledge as you need it

Do you work with Ian Affleck?

I-I'd rather not say

I am a mathematical physicist, I am not a leaf though, I just have seen your posts in these threads and I remember skimming some of his work.

Well grad student and more on the math side.

That's cool. Yeah my posts here aren't at all representative of the work I do with Ian, he's very smart the more physical sense.

God damn error bounds of Composite Simpsons Rule. Our coursework gives [math]f(t) = \frac{W(t)Q(t)}{M(t)}, W(t) = 3000\left(1+\frac{t}{T}\right), Q(t) = \frac{500000}{256}\text{exp}\left(-\frac{t}{12T} - \left(\frac{t}{T}\right)^3 \right), M(t) = 500000 - \int^t_0Q(x)dx[\math] and wants us to find the maximum value of [math]f^{(4)}(t)[/math]

oh yeah. He also wants it done by hand.

Fuck this class

god damn it I got all the formatting right and fuck up on the /math

question mark is the drowned god.

Nope. This has more of an ah-ha solution than a brutal calculation.
I'm not really sure what you mean by disjunctive normal form, and google isn't too helpful.

Same UBC here too, I'm BIE (Econ) first year

Taking topology research. Basically baby's first research class. Not bad. Doing motion planning based off of Father's work

>Farber's
Fixed

How much math do I need to know if I want to understand the anime categorist's posts?

I'm done with calculus and diff eq and will be taking abstract algebra and real analysis next semester

category theory can be a standalone activity

I'm a physicist, not a category theorist. My goal is to find a way to use and abuse category theory like a dogtoy as a tool for physics.
You can find some resource recs in the prevoous thread. You can follow the chain starting from here .

I got into Waterloo for graduate pure math.

WTF Real analysis
WHY CANT I FUCKIN STUDY FOR A TEST 5 DAYS PRIOR AND ACE IT? WHY THE FUCK DO I HAVE TO PAY ATTENTION TO LECTURE AND DO HW AND NOT MASTER THE Material 5 days prior? MATH IS A SHIT MAJOR SHITTTT

ay yo UoA here

real analysis is about as bad as undergrad gets tho

No, it can't.

yes it can

What do you need to know?

Not a shitpost:

Alright guys, I'm sure you've heard this a million times, but I need some help with the Monty Hall Problem. Before you skip the rest of this, I understand the basic idea that switching gives you 2/3 chance of winning. The issue I have is that people keep telling me that it only works if the host already knows which door is the right one, and then intentionally chooses to reveal an incorrect door. Why would this be true? The problem already ensures that Monty did end up revealing the door with the goat. At what point does the logic of "He reveals a goat. At this point if you switch you will get the prize you didn't initially choose. You had a 1/3 chance of choosing the car so switching gives you a 1/3 chance of getting the goat." rely on him knowing what he's going to reveal?

To put it another way, imagine you were running the Monty Hall problem yourself, with no host. You randomly pick a door. You reveal a second door. If it is a goat, proceed as the standard problem. If it is the car, your universe is invalid. In what way does this situation mathematically differ from the original problem (if at all)?

For him to always reveal a goat he needs to know where the goats are. If he didn't then he would guess himself and sometimes he would reveal the car's location instead.

You have the chance of the random selection opening the door with the car or prize behind it. What the fuck is the point then if you know exactly which door to pick, given you literally and physically see the car behind one of the opened doors. Or are you then limited to choose between two remaining doors you know for a fact both contain goats. That would be absurd and the example would have no practical application.

this is interesting, what's the solution ?

Let me try to explain better:

You have two goats and a car. You put them behind doors and then they are randomly shuffled so you have no knowledge of any of them. You select a door but don't open it yet. You then select a second door and open that one.

By random chance it happens that the second door contains a goat. This always happens. It is preestablished in the rules of the scenario. If you did happen to reveal a car, throw out the whole scenario and start over. The question only takes place in universes where you happened to reveal a goat. You are now faced with the choice to switch or not.

How would you do this?

1/3

If in this universe he always reveals the goat by chance, then it is the exact same as the other universe where he reveal the goat knowingly. What is in his mind does not affect the outcome of the game if it results in him taking the exact same actions as it would if something else was in his mind.

Thanks. That's what I assumed, since the original problem states that he did in fact reveal a goat.

Since the ray starts at the origin, it will not perfectly repeat since if it did, it would repeat infinitely in both directions, and every line passing through the origin will escape immediately in at least one direction. The only other case is convergence, but that is impossible with convex surfaces.

You sure?
>there is a unique trapped ray from any starting point, but it is not trapped in backward time unless it is on the shortest path between the bodies. One can find it by minimizing distance of a zig-zag path alternately touching the two bodies a finite number of times, then passing to a limit.