/mg/ math general -- gömböc edition

If you require positive and minimal _together_ then yes, there is only one answer.
Probably you at least know that you get 3 with remainder 6, meaning 7 goes into 27 3 times with 6 left over.
Symbolically this is 27 = 3(7)+6.
But you can make the remainder smaller if you allow negative numbers by writing 27 = 4(7)-1.
Usually this isn't how we divide things (the definition is accurate) but I don't know what your book is trying to say.

Ah I see thank you all. This isn't that bad then but the wording and different way of doing division threw me off.

link the previous thread

i dont fuckin care about the previous thread

In differential geometry, a choice of local coordinates is a choice of chart in the manifold's atlas.

A chart is some open subset together with a diffeomorphism to R^n.

exist as abstract objects

Also, that's not what formalism is. Formalism should go under the "meaningless question" part since it doesn't even acknowledge meaning.

why are so many math professors uncharismatic

Anyone knows where I can find Joseph Kitchen - Calculus of One Variable? Google search, libgen and scribd doesn't work, and I can't buy it. Looks like the book don't even exist on the internet.

In the kitchen.

math.stackexchange.com/questions/731087/joseph-kitchens-calculus-reference

It doesn't exist in PDF form you have to find a rare physical copy or just alternatives.

Getting profs to like you is about adding to the class(think before speak, speak only when necessary), for maths just enjoy the class and murk the curve while everyone else whines and drops, the maths prof will like you

How do I get set up doing research with a professor or getting research experience as a math undergrad ?
I'm not really an exemplary student really. The only thing that sets me apart is that I never complain or give up. Interns of actual achievements and intellect I'm pretty middle of the road.
There's only one math professor I'm on speaking terms with . I'm now in a class that's basically his research PHD topic with me and maybe 5 other people(it's not popular at all among math undergrads here) and of those people I'd argue I have some of the higher level of enthusiasm for the subject .

The thing is I'm so much of a dumbass that I don't see what I offer. At least in other sciences you can do lab monkey work and some other stuff for the professor and just get to observe and listen but I don't see what I can do as a dumb math undergrad.

I was reading a book and pic related appeared, asserting [math]f(\emptyset) = \emptyset[/math], which I could not prove; actually, it's pretty easy find a counterexample: any constant function works. If, say, [math]f(A) = Y[/math] for any [math]A \in \mathcal{P}(X)[/math], then [math]f[/math] is a completely additive constant function, but [math]f( \emptyset ) = Y \neq \emptyset[/math]. Is there a missing hypothesis?

How much stuff do you know? Assuming this is a pure math field, you won't be able to crunch any numbers or do any monkey stuff on a computer.

Honestly, because math is solitary, it's hard to do anything as an undergrad. Honestly, maybe just ask him? He might give you a "toy" problem to work on and you can try proving it and then writing a paper about it to cut your teeth on doing research

To be recognized, you need to do a couple things

Destroy your classes
Ask well informed questions during lecture (because you read ahead and already know what is to come, but maybe there is something you didn't understand that the professor can clarify)

And maybe this is vague, but respect mathematics, in front of your professors. Don't ask stupid questions, do the reading, don't complain, don't give up, don't cheat, and don't trivialize anything.

Understand that a research professor in math has devoted his life to that craft. Don't diminish math and thereby him by complaining or acting bored, or any stupid bullshit your peers do. Be interested and be an adult

Do all that and you'll stand out

Your counterexample doesn't work, it is mapping the empty set to something. Not mapping elements of the emptyset to something. Think about it.

>it is mapping the empty set to something.
The empty set is an element of the domain

I don't know a whole lot to be honest. Just finished with the absolute basics of a math degree and getting into more specialized subjects . I have done foundations of math courses and have experience in proof writing and formal logic.
Presumably by the end of the course I'll have dipped my toe into the basics of the field the professors PHD topic is in.

>math is solitary
Yeah. I'll clarify that he is a pure math professor and this is math so there isn't any monkey work for me to do. He's open to giving puzzles and thinking exercises to students but I don't think either he or grad schools would consider that "math research"

Finding research experience for a math undergrad who wants grad school is hard. Would I be better off contacting another field and being their monkey for a bit? I'm not horrible at bio, chem, and physics... maybe try to squeeze some pure math out of something in one of those disciplines that is less solitary ?

I'm an undergrad doing research with a professor right now (pure math). A lot of what I'm doing is implementing stuff in sagemath and computing lots of examples of the algorithms and methods my professor and his coauthors have developed. There is quite a bit of monkey work involved, but it still requires some understanding of the theory. I feel in over my head a lot of the time but I am also surprised at the things that I can understand and do. I am probably going to get my name on a publication as an undergrad.

I'm good but not the greatest student. I also have a reputation as a hard worker. I like to hang out with my professors. My advice would be to just express your interest in these topics you like. Look up your professor's research/papers and ask them questions about it. Also you can let them know what your career goals are and ask for advice on that (getting into grad school, etc). Also treat your profs like people. Show respect but be personable too.

I have an Oxford interview next week concerning a PhD position. Any fellow anons have any tips?

Mmmh try MAHNZ ZAVIZI ZAVIZI MAHNZ

You're correct, the book seems to have a mistake.

Which is why it can map ot to the empty set. Reread the definition of the function

No

>Which is why it can map ot to the empty set.
Who said it couldn't?

The union of the power set of the empty set is equal to the union of the power sets of all sets of the empty set, or the empty set. Your counterexample doesnt make sense

>The union of the power set of the empty set
This is a meaningless notion.

The counterexample was any constant function from P(X) to P(Y) whose image is not the empty set. For example if X=Y={1}, then you can take the constant function f: P(X) -> P(Y) defined by f(empty)=f(X)=Y, which is completely additive (see below) but does not satisfy f(empty)=empty.

f(empty union X) =
f(X) =
Y =
Y union Y =
f(empty) union f(X)

Defined in that way for any power set that contained the empty set, or all of them, it would be false. That would be meaningless. I think we are talking past each other. Also meaninglessness comes about a lot with the empty set

>Defined in that way for any power set that contained the empty set, or all of them, it would be false.
What are you trying to say here? Every power set contains the empty set.

I'm a bit stupid but what is the union of (abb)* and (bab)* ?

Yeah, I am saying that 0f = 0 would be false. I wasnt trying to imply that power sets didnt include empty sets

...

he probably considers unions indexed over the emptyset

>Yeah, I am saying that 0f = 0 would be false
Why would it be false?

I'm trying to prove linear algebra proposition this but I've reached a deadlock.
Let [math]T : V \mapsto V[/math] be an endomorphism such that [math]T \circ T = 0[/math], prove that [math]T + \itemrm{Id}_V [/math] has an inverse

So this is my attempt. Assume there exist an inverse of such function [math]S : T \mapsto T[/math], using the definition of inverse,
[math] S \circ (T + \itemrm{Id}_V) = \itemrm{Id}_V = (T + \itemrm{Id}_V) \circ S [/math] because T is an endomorphism, but
[math] (S \circ T) + (S \circ \itemrm{Id}_V) = (T \circ S) + (\itemrm{Id}_V \circ S) \\ (S \circ T) + S = (T \circ S) + S \\ (S \circ T) = (T \circ S) [/math]
Here I found myself stuck, I don't know if this reasoning is good, how do I finish?

It was textrm, wasn't it? Damn

hmm yeah, that should work.

>Assume there exist an inverse of such function S:T↦T, using the definition of inverse,
>S∘(T+\itemrmIdV)=\itemrmIdV=(T+\itemrmIdV)∘S because T is an endomorphism, but
>(S∘T)+(S∘\itemrmIdV)=(T∘S)+(\itemrmIdV∘S)(S∘T)+S=(T∘S)+S(S∘T)=(T∘S)
This is all garbage, why do you write that S is from T to T? Why are you assuming S exists when that's what you're trying to prove? Why didn't you use the fact that T^2=0?

Don't assume the existence of what you are trying to prove exists. Instead try to apply [math]a^2 - b^2[/math] in a suitable way to get you want.

S is V to V, made a typo. I though by doing so I could reach some kind of identity statement of something like that.

What do you mean?

Vector spaces over a field give you an abelian category, so the morphisms (which are linear maps) satisfy [math]g\circ (f_1 + f_2) = g\circ f_1 + g\circ f_2[/math], and vice versa, whenever the composites are defined. Now, let [math]T\circ T = T^2[/math] and see where this fact takes you.

I think I got it, thanks.
Still new pls no hate

You are my arch enemy now BITCH.

Wow, I'm glad I don't have you as a student.

Probability Theory is the queen of math

I am the queen of math.

>women in stem

I want to kill myself, i forgot the [math]'[/math] in the equation (it was only a point on the paper) so i was trying so hard to verify if it was a group, I even tested it with a python program.

Wait, that tiny little dot next to "ye" is supposed to be a prime? Can't say that I blame you.
At least name a branch of mathematics that isn't just measure theory but with the names changed.

Yeah, it's supposed to be a prime...

>probability theory is just measure theory
Ok and field X in mathematics is just set theory in different clothes

>I even tested it with a python program

>tfw those cute azunyan tea cups are ruined with some stupid logo inside them
I just wanted a cute cat cup.

Is category theory part of Abstract algebra?

I was mad at testing different value to test if it worked. But i admit it, i'm from /g/ (I'm still in pure maths though, not in CS).

>Abstract algebra
What is "abstract algebra"? Are you implying there is "non-abstract" algebra?

>I'm still in pure maths
That's even worse. We don't need CS monkeys such as yourself shitting the field up.

2deep4me im just an undergrad

I just want to do if it's part of my update course since I can't find any details

Possibly. If you want to include higher category theory, then it is closer to topology.

You'll have to do it either way if you are interested in algebra or anything which makes substantial use of it, which is basically the entirety of mathematics.

>or anything which makes substantial use of it, which is basically the entirety of mathematics.
Not really.

>be /g/tard
>can't read
Yeah that's about right.

Fuck, there is another fucking thing in this paper, is written that this group is not an abelian group. Fuck, i'm done.

i find that math students are a lot more chill than the rest of STEM despite having equal or even higher autism levels, why is this?

I got my complex number exam back (highschool final) and I got zero marks for my final proof. Should I send it back for resubmition or did I do it wrong (1/2)

2/2

Nevermind just saw the mistake lmfao

Any help with proving (without truth tablee) that if p=>q holds, then (p^r)=>(q^r) is a tautology?

I know about the (p^q)=>p property but I don't know if it helps

I'm not gonna start fighting with Latex, so my natural deduction will look a bit wrong, but pretend it looks like what it should.
[math][p\land r]_1\\ \ \ \ \ p\ \ \ \ p\rightarrow q \ \ \ [p\land r]_1\\ \ \ \ \ \ \ \ \ \ q\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ r\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ q\land r\\ \ \ \ \ \ \ (p\land r)\rightarrow(q\land r)[/math]
And you eliminate the assumption 1 in the end when you introduce the implication.

If TT=0, then:

(T + id)(id - T)= TT + T - T + id = 0 + 0 + id

Was is that hard lol

Why do geometers hate algebra so much?

>muh visualization

Platonist master race

You answered your own question. If you do geometry, you can easily spot some kind of algebraic structure in play, like for example hyperbolic stuff and the Möbius groups, but the other direction is when you need to develop a geometric interpretation. Without developing the interpretation, you can't visualize your algebra that easily.

Reminder that:
>algebra = hell
>geometry = purgatory
>topology = heaven

Am I the only person in the world who loves algebra, but thinks geometry is just meh?

What is "geometry" though?

No. I don't like geometry that much. Algebra and topology make a holy duo, adding geometry there would make it an unholy trinity.

I wish I knew.

geometry is a type of topology

similar to how alzheimers is a type of dementia

Geometry has never caught my attention really. At best I can see in beauty in applications like Dirichlet's hyperbola method.

>What is "geometry" though?
I agree with this. I think I have learned quite well that "algebra" is and same goes for other fields like number theory that still have dedicated courses at universities. But what *really* is geometry? Isn't geometry just visual math?

I mean, I guess you could say geometry is the study of shapes (and I mean shapes in the most abstract sense possible) but then that would imply geometry = analysis + algebra - fun which means geometry isn't even a core field itself, but an application of analysis and algebra. But many people will call geometry its own thing. And the ancients thought geometry preceded analysis and algebra. So what's the deal with geometry?

>geometry = analysis + algebra - fun
Analysis and fun can be seen to be special types of algebra.

Do you agree with the statment " pure (measure theory, group theory, number theory) is completely bland an unispiring except you apply it to other fields"?

No way.
geometry = analysis + algebra - fun
geometry = algebra + algebra - algebra
geometry = algebra

But jokes aside
>analysis
>special type of algebra
There is no fucking way you are serious. Please explain.

Not at all. I am pretty sure that once you are hooked on any of those fields you will probably get harder from any new developments about the inherent structures of the subject than about any applications outside the core field.

they're happier
>don't have to sell their future to industry like engineering and CS students
>aren't annoyingly ambitious and constantly stressed premed students, who account for large portions of biology and chemistry majors
>aren't physi-shits who struggle with inferiority complexes

>geometry = algebra
This is assuming "geometry" exists.
>There is no fucking way you are serious.
It's pretty obvious. Analysis is a special type of topology, which is a special type of algebra.

What else is there to pure group theory? Lie groups aren't "pure".

>Analysis is a special type of topology, which is a special type of algebra.

I disagree fundamentally with this. Topology is typically applied to solve problems of interest in analysis but as a whole topology is unequipped for answering the questions of analysis. The analysis is not a subset of topology, it is quite distinct from it.

representation theory is a subcategory of group theory

>What else is there to pure group theory?

Well, there is quite a lot. Not everything about the classifications of groups is settled. And I also disagree with your following point.

What is pure is the study of the structures for their own sake. But let's say that you gain interest in lie groups specifically because of their wide applications elsewhere. This makes lie groups a hot topic of research and I would still consider it pure to study lie groups. Especially if you study lie groups for their own sake, not seeking to really establish anything outside of "this is a property that this class of object has".

Hey /mg/, I'm gonna be starting as a math major this year. What graphing calculator should I get?