/sci/ - Science & Math

*Curb Your Enthusiasm Theme starts*

2nd for 1/∞≈0

for what it's worth, when someone says "let R be a ring" i just pop Z into my head and think about it there, and if that doesn't help I pop in Z_12 or Z x Z.
both very easy to visualize shit on.
my next choice is typically Z[x] or Q[x].

>>10769175
I just visualize the abstract set of objects that satisfy the ring axioms.

>>10769175
>both very easy to visualize shit on.
Rings are non-visual objects.

>>10769175
What do you do for noncommutative ring or ring without identity?

>>10769197
>ring without identity
No such thing.

My morale is low

>>10769209
Okay I'll bite, a rng

>>10769285
I think you can get a subrng for any ring by taking out the units. Haven’t thought this out so there may be degenerate cases.

>>10769415
There are, i.e. z+(1-z), for non-invertible z.

>>10769102
Get in there retards !
>>>/k/41915426

>>10769175
That is what people normally do yeah.

>>10769197
For examples of noncommutative rings, you may take a matrix algebra over some field. I cannot think of many interesting nonunital rings but you may take eg. continuous functions on R^n that converge to 0 at infinity. It is a natural one to consider, but it is hard to say nontrivial things about it, as is the case with most rings of functions.

>>10769450
I'll leave an explicit counterexample for the sake of it.
Consider R^2 with pointwise multiplication.
Every connected subrng is trivially a straight line, but a discrete subrng can be a bunch of points thrown around that aren't inside some line, i.e. the one generated by (1, 2).

Made a video elborating on
https://en.wikipedia.org/wiki/Hereditarily_finite_set

https://youtu.be/-kLNlzbNRQQ

>>10769480
Never mind, the bunch of points aren't necessarily within some maximal subrng.

>>10769191
found the brainlet

>rings are non-visual objects

bet this poster can't even cum to his own imagination, very low IQ

>>10769415
In rngs, ideals form subrngs, however, this more general context doesn't solve the problem that modules solve. That is, kernel objects are not in general rings, but only ideals, and not all subrngs are ideals in rngs, while in the case of groups or modules, they do belong to the same category always. Ie, rings are not abelian categories.

who's in charge of naming things lol

>>10769708
a better pic

>>10769708
Irreducibility was already a concept in topology.
Reduced because you remove the fat in the ring: elements that are already in any prime ideal and determine no algebraic structure.

>>10769714
I know, I just thought it was funny how oxymoronic it looks

>>10769688
>bet this poster can't even cum to his own imagination, very low IQ
I'm not a "his".

>>10769830

forgot mathematicians use "we" and "their"

>>10769879
>forgot mathematicians use "we" and "their"
I'm not a "mathematician". "Mathematics" is not well defined and therefore "mathematician" is also not well defined. I'm an algebraic geometer and I use "I", not "we".

>>10769910
>algebraic geometer
Refer to >>>/lgbt/

>>10769915
>Refer to >>>/lgbt/
>>>/pol/

>>10769191
Most of ring theory that I've been exposed to is largely geometric in nature.

>>10769967
That's because you were studying algebraic geometry, not ring theory.

Now that exam session and lectures are over and I have 2 whole months without uni I feel so empty and dead inside.
What's some fun introductory read on Riemannian geometry, Alexandrov spaces? I'm having this course next semester.

>>10769910
>defined
Refer to >>>/lit/.
>>10769492
>Hereditarily_finite_set
See the above message.

>>10769910
>I'm an algebraic geometer
Algebraic geometers use "we are", not "I'm".

I took Diff EQ and I couldn't truly understand or wrap my head around what a laplace transform or fourier transform are and now I'm in Calc 3 struggling to understand what Curl is and I'm having trouble with double/triple integrals. It might be over for me...

>>10769830
>>10769879
>>10769910
>>10769915
>>10769931
Fuck you. Fuck. This thread is the fucking worst

>>10770576
I don't get it. Why his posts aren't deleted? It wasn't always like this here.

>>10769102
good news anons!
analysis is finally getting fixed!
http://www.tac.mta.ca/tac/volumes/20/10/20-10abs.html

>>10770457
I'm taking vector calculus right now and I've never bothered to understand the physical interpretation of curl, div, flux, etc. Why do you need or want to understand it? Just have an algorithmic picture for solving problems.

>>10770641
lol

>>10770641
>Why do you need or want to understand it?

prime numbers? based

analysis? """Real''"" numbers? weeb shit

What's the best maths font in [math]\LaTeX[/math]? Pic related is fouriernc.

>>10770610
>fixed
What is broken?

any drawing board lads ITT? pic related is my current problem-solver right here

>>10770812
The one and only computer modern or it's derivatives.

>>10770931
Mathematicians use pen and paper, good fucking Lord what's wrong with you?

>>10770935

It carries many advantages:

-friendlier to the enviroment
-can store / retrieve your notes more easily
- writes better than physical paper when you get the hang of it

>>10769102

dat Larry David?

>>10770943
>-friendlier to the enviroment
What??
The polition required to build that is certainly larger than many lifetimes of paper.

>writes better than physical paper when you get the hang of it
I have a very hard time believing that.
What Resolution does it even have? How small can you write?
Paper is very good as it has a pretty high friction.

Am I missing something here? Aren't connected components always open? (clopen, in fact)

>>10770955
According to wikipedia, no.

>>10770962
oh right, apparently only the case if there's finitely many components

what's the coolest radix in your opinion?

>>10771062

(-1+i) also known as "binarions"

>>10770931

> Chinese international student starter pack

>>10770927
>What is broken?
The "theory" of analysis was built on shaky foundations

>>10771137

loved your foundation series mister wildberger

>>10770927
analysis texts aren't 600 pages of trivial commutative diagrams
this needs to be fixed immediately

>>10771164
>commutative diagrams
garbage

>>10771137
Why don't you answer the question?

>>10771207
>Why don't you answer the question?
Read the first four words of my answer.

>>10771213
>Question:"What part of analysis is broken"
>Answer "The "theory" of analysis"
Should we kill all algebraists? Or is that fate too merciful.

>>10771218
>"What part of analysis is broken"
Who are you quoting?

>>10771144

That's DOCTOR wildberger to you, shitheel

>>10771226
Myself.

>"What part [of analysis] is is broken"
Here, I corrected it for you, algebrashit.

>>10771231
>>"What part [of analysis] is is broken"

>>10771233
>"What part [of analysis] is broken"
Now satisfied? Don't you have some finite groups to classify?

>>10771243
>Don't you have some finite groups to classify?
Not everyone who recognizes the shaky foundations beneath analysis is a finite group theorist.

>>10771274
So you are classifying infinite groups, whatever.

>>10771281
>So you are classifying infinite groups, whatever.
Not everyone who recognizes the shaky foundations beneath analysis is an infinite group theorist.

Can you write a usual limit of a function, say, as a categorical projective limit (alternative names are inductive limit, direct limit, or colimit)?

>>10771284
Yeah, you can be a finite group theorist too, we just went over that.

>>10771291
>Yeah, you can be a finite group theorist too, we just went over that.
Here, have a read: https://en.wikipedia.org/wiki/False_dilemma

>>10771286
I was thinking something like giving the open sets of [math]\mathbb R[/math] a directed ordering [math](r,s)\preceq (t,u)[/math] iff [math]r\leq t[/math] and [math]s\leq u[/math]. Ultimately we would just choose the cofinal subset [math](n,\infty)[/math] anyways.

However, I'd need to choose a value within the open set, and the only canonical one would be [math]\inf_{x\in (n,\infty)} f(x)[/math]. So it would just be an overly complicated way to write the [math]\liminf [/math]

>>10771293
What else do you algebrashits do?

>>10770457
First, mathematics is not understand in the way that you belive it is. One can only understand mathematis through the connections that certain ideas have with other ideas. In the case of Curl, curl alone is meaningless. Curl only makes sense in view of the relations that curl has with other mathematical objects. Let's say that a function represents a vector from the domain to the codomain, imagine that there is a field with various arrows and each of these arrows is an application of the function over some coordinates (x, y), imagine that the function is defined in such a way that all the arrows go in a circle around the field, suppose that in a visual representation, the function defines the force of the arrow and therefore each arrow has a length that is proportional to the result of the application of the function over the coordinates x and y, and notice that the force is not the same as the change of an object at point P in x and y but rather the force is something continuous and relative to other functions in the same place, so that if the force is greater and you let it happen for some while then it'll move more than if the force is not as great. Now if you do the cross product between the "delta operator" and the function, my hypothesis of what would happen is the following: so first it's impossible to get anything from the cross product of the function with itself, but this is not the case if the function is moving, and in order to make the function move one way is to use the cross product between the "delta operator" and the function and I believe this gives the effect of the points across the field moving as a result of the function and then you can tell that since it's in the x-y plane that the resulting vector will be perpendicular to the x-y plane and will have some intensity that will be greater if there is more rotation and lesser if there is less rotation.
The first definition of wikipedia is more complex, but notice that C is arbitrary

>>10771324
you annoy me toymaker

>>10770457
I just discovered from more careful reading on wikipedia that the first definition is actually the reuslt of Stoke's theorem, which can be read from here: https://proofwiki.org/wiki/Kelvin-Stokes_Theorem

now for fourier transform perhaps you could use this: https://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/ and maybe this http://www.thefouriertransform.com/
to gain some intuition

But I just want you to take a more taoist orientation to mathematics, it's clear that you won't understand certain things, but don't fret about it, just pay attention to that which you don't understand and remember the questions that you make yourself and that if you want to understand you have to see what are the associated results

>>10771333
toymaker?

>>10771323
Higher algebra, Hopf algebras, ring theory, inverse Galois, etc.
>>10771333
That obviously isn't Yukarifag, retard.

the structure sheaf on a scheme X is written [math]\mathcal O_X[/math], and the ring of integers of a number field K is written [math]\mathcal O_K[/math]. Is there any relationship or is it coincidental?

>>10771544
For an affine scheme defined by a ring R, the structure sheaf of can just be identified with R because the sheaf structure is completely determined by the localisations of R.
A field K is the function field of the affine scheme defined by its ring of integers. So with some abuse of notation, you can call this scheme K as well and identify the ring of integers with the structure sheaf.

>>10771575
Let me rephrase the question. Is there a non-trivial relationship between [math]\mathcal O_X[/math] and [math]\mathcal O_K[/math]?

>>10771348
>Higher algebra, Hopf algebras, ring theory, inverse Galois, etc.
Yawn, classifying groups with a bit of autism added.

>>10771659
That's not true but okay

>>10771784
Tell yourself that algebrashit.

The crisis at the foundation of algebra is much more significant then the one if analysis, as algebraists still can't answer why anyone would care, lmao.

>>10771809
what is the crisis at the foundations of analysis specifically?

>>10771814
No clue and people refuse to tell me.

>>10770933
computer modern too lightweight for printer

>>10770812
i like heuristica
for the moment at least
https://tug.dk/FontCatalogue/

>>10771809
>The crisis at the foundation of algebra
What is this?

>>10771853
>computer modern too lightweight for printer
Why? I have dozens of works printed in CM all of them look great.

>>10771882
"Why would anyone care?"

>>10771889
they're probably not in computer modern if you look carefully
although i concede with a good printer they can look fine
springer print on demand books that use computer modern are particularly bad

>>10771906
>they're probably not in computer modern if you look carefully

sorry, i don't want to sound like i'm doubting your ability to tell fonts
they may well be in computer modern

>le analysis vs algebra xDD
Do not respond to LARPing undergrads

What is the crisis at the foundations of analysis?

>>10771917
>What is the crisis at the foundations of analysis?
deep, underlying issues in the subconcscious of analysis; rooted in the paradoxes and contradictions of infinity and choice

>>10771809
hearty kek

t. algebraist

>>10771906
>>10771911
I mean the LaTeX default, not sure whether it's actually exactly Computer modern or one of its very close derivatives.

And it looks great, even if I print them myself or it's used in some book.

>>10771917
>What is the crisis at the foundations of analysis?
"Why would anyone care?"

>>10771917
it isn't algebra

>>10771924
>contradictions of infinity and choice
axiom of choice and something about infinite sets? not a mathematician help me out here

everyone knows it's actually (based) number theorists against the world, algebra vs analysis is infighting

>>10772018
You mean "number theorists are the illuminati engineering wars between fields to reap theorems it can exploit", right?

This algebra vs analysis infighting is for fucking high schoolers and not serious mathematicians. You can favor one over the other, but don't put down the other field just because you don't like it as much. Fucking retards

>>10772035
>You mean "number theorists are the illuminati engineering wars between fields to reap theorems it can exploit", right?
You mean "algebraic topologists are the illuminati engineering wars between fields to reap theorems it can exploit", right?

>>10772158
Obviously not. Algebraic topology actually gives back to other fields when it uses their techniques, number theory simply sucks them dry.

>>10771951
>not a mathematician
No need to mention this, we can tell just by you engaging in discussions about "foundations" instead of actually doing math.

>>10772209
>we
Speak for yourself.

>>10772018
>(based) number theorists
Based on what?

>>10772232
We do speak for ourselves.

>>10771924
fuck off wildberger

>>10771917
https://plato.stanford.edu/entries/mathematics-inconsistent/

Set theory is inconsistent and topos can fix it, but no research in analysis care about autism categories.

grothendieck start as analysis and change to algebraic geometry, he want other foundation for topology.

>>10772209
>>10772301
So what is the issue that people have with the foundations of analysis? You seem to think its trivial or nonexistent but what are they even getting at?

>>10772344
nevermind, thanks

>>10772350
>foundations
Refer to >>>/lit/.

>>10772344
>Set theory
See >>10772470

>>10770610
what in the fuck?
go fuck yourself!
you know what, i actually hate that i recognize some of the things in this book

>>10771293
>read
I think you may have meant to post this on >>>/lit/.

>put a better foundation under topology
>suddenly analysis is fine
analysis is just topology with extra steps

topology is just category theory with extra steps

category theory is just set theory with extra steps

category theory is just homotopy theory with extra steps

>>10772582
>go fuck yourself!
Use >>>/b/.

>>10772679
>set theory
Use >>>/lit/.

homotopy theory is just model categories with extra steps

>>10772689
Ontologically speaking, model categories aren't "truly" homotopy theory, they're "just" a "model".

>>10772699
>Ontologically speaking
>truly
Refer to >>>/lit/.
>>10772597
>foundation
Refer to >>>/diy/ and/or >>>/lit/.

>>10772699
discussion of ontology belongs on >>>/lit/
i fucking hate that i'm doing this now

>>10772710
>is
See >>10772710

>>10772715
>responding to my post twice
this kind of self reference is clearly philosophical masturbation and belongs on >>>/lit/

>>10772710
>i fucking hate that i'm doing this now
So does everyone else, please stop

>>10772734
>So does everyone else
see >>10772232

>>10772745
>self-reference
Refer to >>>/lit/.

>>>/lit/13395988
Here

>>10772750
>homotopy
I don't think >>>/lit/ is ready for this yet.

>>10772754
>think
We don't discuss cognition here. Use >>>/lit/.

>>10770610
>analysis is finally getting fixed!

>>10772582
>you know what, i actually hate
Cool. Use >>>/blogspot/.

>>10772791
thanks for liking my post!
>>10772788
analysis is perfect as is

>>10770714
>/mg/ - Physics General

>>10770610
Just looked this guy up, seems like he was accused of doing some weird shit to his daughter
>>10769102
So, anyone else feel really autistic when talking to other grad students at conferences? At first it felt like they should be pretty easy to talk to, but I was wrong. I hated how everyone already knew each other and how difficult it was to slide my way into the conversation, only to realize that we were close enough to know the rudiments of each other's research but far enough not to really understand the details so much of the conversation was very surface level and just sort of petered out as quickly as it started. I fucking hate conferences.

>>10770771
>dealing with any numbers at all
What is this, a physics general?

>>10773234
What kind of conference, anon? Any particular specialization?

>>10773234
>only to realize that we were close enough to know the rudiments of each other's research but far enough not to really understand the details so much of the conversation was very surface level and just sort of petered out as quickly as it started.
Yup, same. I don’t think it actually ever goes away either.

>>10771581
Well if R is the ring of integers of K and X = spec(R), then [math]\mathcal O_K = \mathcal O_X(X)[/math]
I don’t think there is anything deep to this, it is just a notational coincidence. Structure sheaves of schemes are noted O_X because that already was the notation for sheaves of holomorphic functions on complex manifolds (see eg. FAC).

>>10773311
> non-trivial

>>10773334
Well, he/she says that he/she believes there is no such relationship.

>>10771286
https://math.stackexchange.com/questions/60590/category-theoretic-limit-related-to-topological-limit/62800#62800

>my uni lists ergodic theory as an applied class
Is this a bad sign?

>>10773257
One of them was the very nonspecialized JMM which was a pain because there were WAY too many people. Some other minor conferences here and there in harmonic analysis.
>>10773304
I just curse my own autism at these kinds of things.

>>10769102
what are some good introductions to topology for someone who hasn't read above hs math

>>10773718
unironically a good book about real analysis

>>10773718
george simmons topology and modern analysis

Is this a good book?

>>10773718
Not sure about someone who hasn't taken HS math, but Munkres is pretty accessible to anyone who has only taken a class on proofs.

>>10773718
Why would you want to do that?
I doubt there are many books about topology targeted at your demographic, as pretty much any math student first takes classes in analysis, Linear algebra and such and that knowledge, at least the basics, are assumed at the beginning of any topology text book.

>>10773798
I don't know, I haven't read it

>>10773811
Nonesense, topology one of the few advanced maths that doesn't require prior knowledge of calculus or linear algebra.

>>10773838
True, but one should have a decent amount of mathematical maturity before approaching it.

>>10772710
Certain ontological questions are relevant to mathematics, and not in the philosophical way.

Any ideas on how to solve problems like this one?

Given polynomials A(x) and B(x), can we write the coefficients of A(x)^2 + B(x)^2 in terms of the coefficients of A(x)x + B(x)?

>>10773838
>>10773811
I understand that & hence was my reason for asking

if I dislike proofs am I like likely to enjoy topology?

t. Physics student looking to take postgrad courses in branes, manifolds & GR

>>10773904
less likely*

>>10773904
>>10773907
ignore I said that

>>10773718
Try topology without tears

>>10773904
> if I dislike proofs am I like likely to enjoy topology?
If u dislike proofs you will dislike all (serious) math. Including but not limited to "postgrad courses in branes, manifolds & GR (aka differential geometry)".
Seriously if you hate proofs why would you EVER go a theoretic route?

>>10773915
I'm willing to change my opinion for the sake of pursuing the material they're related to

>>10773904
>physics student
try >>>/lgbt/

>>10773887
lol
>>10773904
not going to make it

>>10773957
>>10773964
not by arguing w/ you I won't

>>10773978
I sympathize with your cause but if you think you can into advanced maths without reading and doing proofs or serious study you’re in for a bad time anon

>>10773993
dont show the lgbt physicist any sympathy. he can go fuck himself

>>10773904
You will not enjoy topology if you dislike proofs. Why do you dislike them anyway?

>>10773999
because he is busy obsessing over phallic shaped objects

>>10773993
I'm more than willing to learn the basics well before & up to that point

>>10773999
>ignore I said that

I'd only looked at real analysis before remembering how instrumental it is in studying anything beyond that

>>10773995
that would require two of me

>>10773718
I find this one very easy to understand even with most basic knowledge of analysis and "hs math".
http://www.pdmi.ras.ru/~olegviro/topoman/eng-book-nopfs.pdf

>>10773911
>>10773731
>>10773761
>>10773802
>>10774042
thanks

would any genuine answer begin w/ "start by learning proofs" & are there any other branches I should familiarise myself w/ first?

How do I go about evaluating a limit like [eqn]\lim_{x\rightarrow 2}\frac{\sqrt{6 - x} - 2}{\sqrt{3 - x} - 1}[/eqn]? I tried rationalizing the denominator but I still get an indeterminate form.

>>10774067
real analysis

>>10774067
>any other branches I should familiarise myself w/ first?
Some analysis for sure at least the basics. Or you're going to have a bad time trying to catch up when it will be required.

>>10774070
L’hopital’s rule

>>10774081
I mean yeah, you're not wrong, but that doesn't get introduced until like 4 chapters from where I'm at.

I already took calc btw I'm just refreshing in prep for Analysis 1.

>>10774071
>>10774074
that's fine
I'm looking at this being a hobby while taking undergraduate courses in physics & philosophy

>>10774067
Yes it will. See
>>10773731
>>10774071
A good (course/book) on real analysis already contains some amount of "topology" (in particular: topology of metric spaces and topological notions of convergence and continuity, connectedness/compactness and similar things)

>>10774094
>physics & philosophy
Is this a thing?

>>10774104
if only

>>10774070
expand both numerator and denominator with [math]\sqrt{3-x}+1[/math], and then with [math]\sqrt{6-x}+2[/math]. you get a polynomial fraction times [math]\frac{\sqrt{3-x}+1}{\sqrt{6-x}+2}[/math]. try to continue from there (hint: it works).

>>10774104
does metaphysics count?

>>10774067
Real analysis isn't necessary for topology. In fact, I learned topology before I learned real analysis, though it may serve to motivate topology. Just learn calculus and how to read and do proofs and you'll be good to go.

>>10769102
https://discord.gg/sJpcEqV

>>10774104
Its part of the "I want to explore what reality really is" starterpack. Of course when those people discover there's actually mathematical proofs involved in modern theoretical physics it quickly gets boring for them...

>>10774169
Pretty much.

>>10774169
what do reading & writing proofs have to do w/ being sarcastic

>>10774164
It isn't, but as you said it serves to motivate topology plus will be covering most commonly used things in metric topology.
Also recall that he wants to do
>postgrad courses in branes, manifolds & GR
which will require more weaponry of analysis than typically tought in a calculus course anyway.
Also "how to read and do proofs" courses or literature are a complete meme, you are much better of just reading analysis proofs and trying to replicate them/doing your own.

>>10774180
I would go dl those books and get started instead of impotently replying to people on 4chan

please ignore what I said about not liking proofs

>>10774193
I've been reading through one of them while relentlessly spamming f5

>>10774067
Set theory (which is included in intro to proofs)

>>10774071
>>10774074
>>10774097
>>10774164
>analysis/calculus
Not strictly necessary

>>10773887
CAN ONE WRITE X^2+Y^2 IN TERMS OF X^2+Y?

>>10774320

>>10774265
>Set theory
already looking at taking this as one of my 3rd year philosophy options

When I mentioned disliking proofs I meant for things like Pythagoras' theorem or calculus; forgot to weigh in my reevaluation with regards to it being integral to any aspect of higher mathematics prior to making the claim.


I'd recently come across a research publication by one of the professors at my university, a Phys&Phil graduate, concerning spacetime functionalism & I'm looking to familiarise myself with the mathematical grounding for each of the relevant branches of mathematics it's based upon.

So reading proofs for 3 years isn't an issue. Similarly; if I know which areas I want to end up in I was hoping to build competency in the prerequisite fields & potentially bypass areas of pure maths that you'd find on an undergraduate degree that aren't directly relevant to where I want to end up.

>why yes, I do solve every problem I come across by turning it into a PDE and solving it
>of course, my main area of interest is combinatorics, but I also dabble in higher algebra quite a bit

woke up too sad to do math :( I wanna keep reading, what to do folks?

>>10774542
turn an algebra problem into pdes then

>>10774547
>woke up too sad to do math :( I wanna keep reading, what to do folks?
go for a walk to clear your head

>>10773798
>Is this a good book?
Why don't you read it and find out?

>>10774547
Watch anime and talk to your cat. Helps me everytime.

>>10774517
For topology one needs only basic set theory, nothing deep. Familiarize yourself with the notation, countability, de Morgan's laws, and you'll be good to go. These things can be found in the first chapter of Munkres' Topology, so you should take a look at that. Amazon has a pretty cheap pajeet edition that you should buy.

>>10774070
multiply by the conjugate of the denominator or numerator (depends on problem)

Probably taking calc 2 this semester (still waiting for AP exam results), thought calc 1 was easy, what am I in for?

>>10775662
fuck off

Hi /mg/. I got my undergrad in math in 2016. I havent done any math since then and have forgotten a lot of it. I want to do some challenging math for fun. Anybody have any recommendations?

should i quit my phd program lads? i'm seeing how peers that didn't go into grad school have made a serious amount of money and i have less than 1k in the bank because of mediocre grad school stipend
i'm 2 years in and only starting proper research in earnest now..
how do i tell if i can land an industry job without first finishing the phd? the opportunity cost of getting a phd is through the roof and i've already spent 2 years...i feel i'm wasting away but i don't know what options are out there

>>10775702
Who is the retard telling kids you need a fucking PhD to land an industry job?

>>10775702
>opportunity cost
You'd think someone throwing around such buzzwords would already know the answer to this retarded question, or at least have enough sense to ask this on >>>/biz/ or >>>/adv/ instead of /mg/.

>>10775662
easier than calc 1
>>10775669
you fuck off

>>10775713
Stfu underrage faggot before you get banned and I fuck your mother

>>10775753
When you're so retarded that you think you found a samefag when you didn't

>>10775756
Sorry anon

Do I need to work through Atiyah-McDonald before this or can I just start here if I know basic Abstract Algebra?

>>10774517
Why are you spacing your posts in such a retarded manner?

>>10775945
to get this response

>>10775902
You can start right here

>>10775902
What >>10775947 said, but there's nothing wrong with also looking into Atiyah-McDonald.

>>10775707
the intent was originally academia and research in a very pure area but I made friends with our analysis TA and learned how miserable the life of a postdoc and even young professor is.
plus the rush of finding the solution is coming slower and slower as the problems become more and more unsolved, so the fun factor is decelerating

also the guy suggesting biz or adv, boards which have much fewer people who have experienced the same thing or even know what a math phd is like, is a faggot who can suck my farts

>>10776197
>the intent was originally academia and research in a very pure area
oh, so you're just a brainlet who doesn't want to admit it on a mongolian 2d-art appreciation forum.

>>10769102
I fear formal logic. I can't get around formal proofs. Should I quit Maths?

>>10776197
>analysis TA
Can't you at least specify the analysis?

>>10774145
Tried that. Still getting the same thing.

>>10776296
Oh wait nevermind I figured it out. I am a fucking ingenious.

>>10776256
>formal logic
>formal proofs
Refer to >>>/lit/.

>>10776256
It's okay. To this day I still don't understand how to prove, say, x^2 - 6x + 15 is divisible by M using induction.

Can you define an alternative addition / multiplication on the integers such that the resulting structure still has interesting algebraic properties? Quotients don't count, I mean on the whole set Z not residue classes of it.

>>10776493

The 2-adic integers with the operations of bitwise And and bitwise Xor ?

Any countably infinite ring, and a bijection R->Z?

>>10770931
I use my drawing board to draw, not to do math.

So does this mean algorithms to compute Grobner bases are a guaranteed way to test if a system of nonlinear equations has a solution?

>>10777003

>>10777003
>algorithms
>test if a system of nonlinear equations has a solution
Refer to >>>/g/ and/or >>>/sci/eng/.

>>10777003
>algorithms
Refer to >>>/lgbt/

>>10776264
>made friends with out analysis TA
See >>>/hm/

>>10776865

if it's good enough for art then why not some funny greek letters and numbers?

>>10777018
>>10777023

>>10777047
A drawing board is a drawing object, not a mathematical one.

>>10777069

boomer cope

>>10777096
>boomer
Refer to >>>/r9k/ and/or >>>/b/.
>cope
Refer to >>>/r/eddit/.

>>10777047
Because the goals of mathematical writing and art are entirely different?

Anybody got anything for me?
>>10775683

Hungerford or Lang?

>>10777116

Donald Knuth art of computer programming books have a lot of excercises that will keep anyone occupied.

>>10777116
Pick up a textbook on a subject that interests you.

>>10777108

>goal

both are to record something

>>10777137
Epic bait

>>10777137
>both are to record something
Yes. And a child with crayon also wants to record something...would you want to write mathematics with crayons?

Finishing a PhD in structural engineering. Wish I studied maths at uni. where I come from there was a stigma regarding studying mathematics (viewed as a useless subject compared to engineering).

Even at the end of my PhD I can't comprehend many interesting papers in detail that involve tensor calculus. Too much of a brainlet to understand that (although I should because my PhD is purely computational).

Hope one day I will be able to understand tensors manifolds and mathematical language in general. Will get there even if I am a brainlet if I try hard enough.

>>10777156
If you already know vector calculus, it's just a matter of picking up an adequate general topology book and following it up with a text on manifolds (i.e. Lee).

>>10777156
I'm basically in the same boat sans a PhD. Every time I try to get into that stuff I just end up losing interest. There's seemingly so much to remember with constant identities and shit getting thrown at your face that I feel like it's a subject meant for computers, but I never get far with I try to write programs for it.

I really want to learn stuff like continuum mechanics and GR but the tensor aspects have always been a huge hurdle.

what the hell is modular and Maass forms and what is it's connection to RH? pls respond

>>10777194
Don't insist on memorizing it all at once, nobody ever moves forward doing that.

>>10777123
bump

>>10777248
Yeah but then you go along the text and they start using identities from a few pages back and you have no idea where anything came from and no intuition for where its going and then your eyes glaze over and you give up.

>>10777253
>he doesn't keep going after his eyes glaze over
You failed right in the basics, man. You don't need to follow every proof, just gain a grasp of the main theorems, take a look at the motivation (end results and applications), and reread the text after a week.
Has consistently worked for me.

>>10777194
>computers
>write programs for it
Use >>>/g/.
>continuum mechanics and GR
Use >>>/toy/.

>>10777132
>Donald Knuth art of computer programming books
what makes you think that he was asking for a "art of computer programming" book? refer to >>>/g/ for that kind of shit.

>>10777156
>engineering
See >>>/hm/

>>10777132
>computer programming
Use >>>/g/.

>>10775902
anon, first answer me this question. Why are you reading this book?

>>10777258
Im going to try this today. Wish me luck.

>>10770457
>I couldn't truly understand or wrap my head around

You are not stupid, you have bad teachers.
Most math teachers just want to present the material and move on.

These are NOT hard things to understand IF you find a good explanation.

Look on the web or on YouTube for a decent explanation.

The rest of us are not super-geniuses, we just understood what they were teaching in the way they taught it.

>>10777281
>>10777312
>>10777327
you niggers and your fucking unfunny meme posts are ruining /mg/

>>10777480
I want to learn algebraic geometry? I am also interested in Hodge theory and complex geometry. I'm studying on my own btw I'm not in grad school (at least not yet..)

>>10777503
they are right about engineering

>>10777563
I predicted that, which is why i asked

Although one of the key points in the book is to introduce all the theorems in Hartshorne, there are far better and faster books that show essentially the same. Atiyah Macdonald pretty much covers the majority of the important ones. However, I would also recommend Bosch's AG + CM book since it also leads quite well into AG, and covers roughly the same

Which of these are maths and which ones aren't maths?

>>10777719
>are
>aren't
Refer to >>>/lit/.

>>10775902
Read a book on algebraic geometry first or at the same time.

>>10777123
Both would be good to have.

>>10777719
General mathematics and history and overview aren't maths.
Mathematical physics, information theory and quantum algebra are arguably not maths, but that's finicky.

>>10777123
>Hungerford or Lang?
Lang is a meme.

What are some good sites where I can talk to mathsematicians other than mathoverflow and r/math?

>>10777762
>What are some good sites
Use >>>/wsr/.

>spectral theory
>you don't hunt specters
bravo hilbert

>mixing transformation
>read the definition
>instantaneously pictured mixing dough in my head
That was probably the fastest I've ever understood a definition.

I saw Shinichi Mochizuki at a grocery store in Los Angeles yesterday. I told him how cool it was to meet him in person, but I didn’t want to be a douche and bother him and ask him for photos or anything.

He said, “Oh, like you’re doing now?”

I was taken aback, and all I could say was “Huh?” but he kept cutting me off and going “huh? huh? huh?” and closing his hand shut in front of my face. I walked away and continued with my shopping, and I heard him chuckle as I walked off. When I came to pay for my stuff up front I saw him trying to walk out the doors with like fifteen Milky Ways in his hands without paying.

The girl at the counter was very nice about it and professional, and was like “Sir, you need to pay for those first.” At first he kept pretending to be tired and not hear her, but eventually turned back around and brought them to the counter.

When she took one of the bars and started scanning it multiple times, he stopped her and told her to scan them each individually “to prevent any electrical infetterence,” and then turned around and winked at me. I don’t even think that’s a word. After she scanned each bar and put them in a bag and started to say the price, he kept interrupting her by yawning really loudly.

>>10769688
>>>/pol/

>have been struggling to study or even to open the book for almost 2 weeks now
When the fuck does this end ?
I was having so much fun learning from Spivak, Stewart etc.etc and then it just stopped, im at the point where I cant open a textbook without getting dizzy or spacing out. What the fuck ?

>>10777870
Ok, no more bitching. 4hrs minimum today; 2-3hrs reading and 1hr of solid questions
IM GONNA BREAK THIS FUCKING WALL

>>10777872
Meditate a little

>>10771659
Imagine thinking the algebra of Feynman graphs "yawn" heh.
>>10773234
You should consider socializing with them outside of a formal academic setting. Usually what I do is that I talk to people during breakfast, show genuine interest their research then invite them out later that night to have dinner/a drink with.

>>10777288
>>10777327

The dirty weeb trashboy choir strikes again

>>10777942
>choir
Refer to >>>/mu/.

Was /mg/ clamped?

>>10777987
damn, why is it always summer when memes become super shit
the cant build muscle one wasnt even this bad

>>10778008
everything this board has created in the last 3 years has been downstream from reddit, you are one of the worst board cultures on this site rivaled only by /lit/

>>10778018
calm down internet historian
go have more prune juice gramps

>>10778018
What's your reasoning? Sci and lit are two of the only worthwhile boards that even somewhat move, cuz out and some of the other niches are quite slow

Just because it's maybe 75% trash doesn't mean the 25% doesn't keep us around

>>10778018
>board cultures
cringe

>>10778032
what are you going to do about?

>>10778031
>Sci and lit are two of the only worthwhile boards
You have to be mentally ill to believe this.

>>10778018
>cultures
That's a bit too generous for this shithole.

>>10777905
I think that's solid advice, the last conference I was at had a lot of downtime during lunch so I think over the table would be a good place to start. I think I just need to talk less and let them say more about themselves. Plus talking about other people's talks is usually valuable, at least I may learn something new or get some further clarifications. I never really appreciated that aspect until recently. Like, the stuff people present is the most clarified point of their research, but usually their thinking is five steps ahead and you can scope out a lot more of where the field is heading. If you just read papers you'll always be somewhat behind.
>>10777870
>>10777872
Look man, I had a similar problem when studying for my quals, kept running around in circles thinking that I had to memorize every theorem and results under the sun. Things turned into a chore and I started loathing it until I realized my method of studying was essentially sucking all the fun out math. How I got myself back into it was by treating it less as a novel read line by line and more like a guidebook. There's this quote I quite like "you should know everything in this book without reading it". Basically, instead of doing things dryly, try proving as many of the theorems of the book as possible on your own, utilizing and absorbing the techniques and theorems naturally rather than trying to artificially stuff them into your brain. It's a lot of fun and will actually help you retain the knowledge and sharpen your own skills. Of course this takes a bit longer in the short run, but I think it's actually more efficient in the long run since you'll spend far less time getting stuck on things you already should have learned.
>>10778018
>last 3 years
While there are FAR worse boards than /lit/ or /sci/, this board has gone down hill in the last few years

>>10778078
>try proving as many thoerems instead of reading the book as a text book
yeah, thats exactly how i read it. I was having fun precisely because of that but now i encountered a block... a plateau where I cant find it as interesting as before

>>10778084
What part are you on? Why the blockage?

>>10778088
its hard to explain but its not really related to what im studying, but studying in general.
I tried switching to studying German but then I was having a bunch of troubles reading and concentrating,
im only on Calc2 so its just standard math and nothing too hard but since im mostly self taught (bad high school math background so my Calc1 semester was me salvaging past knowledge in AP Calc while learning new stuff) I end up second guessing my knowledge allot (more then I should).
It feels like im going dizzy while reading stuff, like my eyesight has gone too shit or something, its a very physical reaction to trying to concentate and study

PS: i take ADHD medicine from time to time but either taking it or abstaining from it doesnt make a difference

>>10778111
>It feels like im going dizzy while reading stuff, like my eyesight has gone too shit or something, its a very physical reaction to trying to concentate and study
Oh shit anon, well I'm not qualified to give advice on this. I don't know man, maybe you just need to burn off some energy with exercise or try meditation or something.

>>10778119
meditation has next to no well replicated physiological benefits, it is as good as taking a nap or walking which is to say not that useful or likely to change what are almost certainly genetically determined behavior patterns. What’s happening is that he is not interested in the material.

>>10778122
precisely what ive been fearing,
when i was reading before I was memorising all the proofs with no effort and could visualise almost everything as an object in relation to existing theories and concepts.
But now when i try to open a book about anything be it: discrete/continues math, philosophy or even language its just a blur and not interesting in the slightest
I thought i needed to take a break but its been about 1.5weeks since this happened and nothing seems to change, I also have some exams coming up which is making me feel abit useless and anxious

>>10778122
>>10778142
That's actually kind of strange, going from motivated and interested to just being totally unenthused. Have all the previously interesting things in your studies just lost their luster? Like, if you thought something was cool before, why, and why do you suddenly feel that that is not interesting anymore?

>>10778150
Yes, not so long ago I started my CS degree and I started distancing myself from programming as much as possible as I became more interested in the mathematical side of CS theory (even thought I've been programming for 5 years now), but after a term of full on mathematical studies (since I finished all programming for uni very early) including easy discrete stuff like sets and probability along side interesting stuff in calc1&2 I've begun to give no fuck about that either...
It's as if my interest in ANYTHING was really only there while I wasn't on holidays, since I was actively learning Korean dialect and German vocabulary at the same time
Looking back it was a cluster fuck interns of scheduling - since I hate timing my studies ( ie. Study for 3hrs this then that for 4) - instead I just studied all the time and anytime I found something interesting I would lose sleep just to do it (I even spent 4 consecutive days without sleep writing a hobbyist program and setting up an Arch Linux install on my laptop)

Now I wake up , smoke, masturbate, watch YouTube/4chan and feel sorry for myself
I can't wait for new semester to start so I feel like I'm a dog being chased or something, this relaxed state is killing me. I'm sure if will all change in August. Sorry for Blog post

>>10771659
Why do analysts and algebraists always fire shots at each other? The topologists are off being way more autistic than either of you.

>>10772169
Ayyyyy, so true.

>>10778182
>It's as if my interest in ANYTHING was really only there while I wasn't on holidays
Okay, NOW I get it, I've actually got a friend like you. Basically, you need structure in your life, usually one dictated by an outside force, that gives you some sense of purpose in doing these things. But without any structure, you just wander and dawdle. I had a somewhat similar problem until I set a strict summer regimen for myself so I could make more progress on my research/thesis ahead of time. Maybe you should get a part time job, like grading or TAing, or maybe do one of those summer programs. If you're still in undergrad there are REUs which are pretty fun, if you're a grad student there are usually summer workshops or schools or positions you can take. Because doing this
>Now I wake up , smoke, masturbate, watch YouTube/4chan and feel sorry for myself
is actually super fucking unhealthy, I've also been there anon, I'd have twelve /gif/ and /hr/ threads at once, I'd beat it till it started to hurt, facebook stalk some girl I used to go to school with that I had a crush on, and spend my time browsing until the sun came up, and I'll always hate myself knowing I'll never get that time back. Try having some sort of obligation that gets you up and productive in the day and that may help you keep motivated throughout the day.

>>10773904
If you dislike proofs, topology will seem too abstract unless you already know enough GR/QFT to understand why it's relevant.

>>10778216
I'll try, I'm undergrad also I live by myself in an apartment (money isn't an issue since I'm kinda a trustfund-kid) and no family or friends in the same country to be an outside force compelling me to do shit. I'll see if my I can do some techdesk work for uni or I might just pick up gym again to get me in a regime

Thanks anon, ur a real human bean.

>>10778182
have you ever considered that CS is gay and you’re a faggot for wanting to do anything in that field?

>>10778249
Did you read my post ? I have fully realised how much of a faggot I was thinking IT/CS was cool in HS (I am physically repulsed by tech culture and people in programming classes make me want to kill myself because they talk about gaming and know/care nothing for how CS theory relates to other topics or even CS theory itself), but the only path I could have gone was CS (I flunked a science in year 12 which means I didn't have enough ATAR/grade average to get into a good degree from high school), I'm actively trying to transfer to another degree or just do a double degree in math/CS since I have a decent GPA and have taken math courses

>>10778182
>Now I wake up , smoke, masturbate, watch YouTube/4chan and feel sorry for myself
I’m exactly like that, and I wasted a semester of PhD funding like that (I’m not american so I only have 3 years of funding).
I had a death in my close family last year right before I finished my masters and I’ve been pretty much lost all interest in whatever I was doing.
I was able to hack my masters thesis together but I have been spending most of my days looking over papers and not remembering a thing ever since or just napping at home.
You need to make a change because the more time you spend in these limbo, the harder it will be to return to normal. I can feel like I’m all dulled out now and I used to be among the top students in my program (one of the best in my country)
I have started therapy, sport and am trying to reduce masturbation but it will take a while until I get back to normal.

>>10773904
Why do you dislike proofs?

>>10777905
>Imagine thinking the algebra
I don't think about algebra at all.

>>10778277
I'm sorry for your loss guy.
I like to think this will all go away once I start my actual term because as the term got closer to finishing I was getting more and more lazy (I was the best student in the unit interms of progress - as pointed out by my course coordinator and tutor - even then at the end of my semester I was literally making arcane excuses and writing assignments which justified and even made be look better for not writing better code - I managed to write an essay regarding my shitty project which I couldn't be fucked rewriting and so I said it was intentionally left with errors to contrast my previous work which shows my deep understanding of the unit and ideas covered, this ended up getting me a 98% mark on my whole unit), I was making up as many excuses why not to do the work because when I tried doing relevant work I was experiencing very much physical and negative reactions like dizziness and poor concentration which prevented me from making progress

Like I said before, I'm gonna go today and join a gym to see if that fixes something and in the morning try find assistant work at uni

>>10777123
For what ? Calculus or Precalc for college ?
Either way as someone who had to do precalc while doing calc1 (i know its fucked timeline) i found Israel's Algebra to be the fastest way to get as much necessary stuff to get going (even thought my college algebra is shit i still would recommend it).

Calculus you could go with Spivak, Stewart, Lang etc. just look over the style of writting and see which one does it best for you !
I personally really enjoy Spivak's Calculus book since it felt like he was explaining concepts to me like a real person, the book felt like it had all the necessary information to get going and never felt lifeless like Stewart - but Stewart has actual pages upon pages of reference questions to do so you might aswell use that book as well for questions and theory.

>>10776254
i'm starting to wonder if it's worth it, even if i can get a decent postdoc and positions after. there are a huge number of 22 year olds with better pay than the average math prof., who haven't had to sell their souls or hobbies or free time.

i didn't expect the rewards from doing math to decelerate past the point of sustaining a career on passion alone, and with that slowly leaving i'm seeing there's nothing else of worth here
also it was the qual. course real analysis TA, really nice guy but the lonely 40k/year life at age 30 shows on his face

>>10778322
That's fine anon, not all of us were blessed with at least a double-digit IQ.

>>10778205
Topology isn't autistic at all.
>>10778523
Israel as in Israel Gelfand?

>>10778784
>Gelfand
Yeah, I mean he is fine too

I'm learning math on my own and I'm trying to understand the concept behind the calculations. Sometimes it completely baffles me tho. Why is my answer (in red) wrong? Correct one is in green.

>>10779105
>Why is my answer (in red) wrong?
(-x)^2 =/= -(x)^2
Your bracketing is wrong, try your formula for n=2.

>>10778727
Please attach a cute 2hou to your posts so I can look at them and smile.

>>10778182
computer science has no place on /mg/
try >>>/hm/

>>10779572
I take calc2 though retard , did you even read the post and briefly mentioned why CS is garbage

>>10779578
Dont respond to the spammer(s). Hopefully they'll get bored and leave.