/sci/ - Science & Math

Maths is a meme degree. Why would anyone do that? Civil engineering or computer science is better and has stable job prospects.

>>12321849
Some anon is doing a Lie Theory reading group if any of you are interested.
>>12316665
>>12316665

>>12321864
Because it's interesting to study?
And in my observations, those who study maths tend to be able to transfer well into other fields anyways.

>>12321870
This.
>>12321864
FPWP

>>12321864
have you reduced your aspirations from "achieve dreams" to "live comfortably" due to inadequacy or fear of failure?

Post doings.

Intro ring theory here.

>>12321895
As >>12321866 said someone seems to be hosting a reading group, so I think whenever that starts I'll join in by reading pic related

>>12321866
>>12321899
Largo tends to do summaries of some of the content covered on Saturday, followed by more casual discussions. This was the case for the reading of the previous books.
There will be a meeting in 5 days but presumably you should have to have tried the first exercises in the one in 12 days

>>12321947
i just joined, excited for saturday's discussion of clifford algebra

>>12321971
Has a mathematician ever been more wrong?

>>12321973
Yes. Mochizuki.

>>12321971
>>12321973
https://link.springer.com/article/10.1007/BF03024067
>Did poincaré say “set theory is a disease”?
>He expressed his views with considerable vigour. But nowhere did he argue for a position nearly as sweeping as sometimes attributed to him, hung on the alleged remark that set theory, of whatever kind, was a disease

>>12321992
Either way, he was certainly not alone in the sentiment (I say this as someone who enjoys foundations and some set theory)

This awesome professor agreed to supervise my undergrad thesis, but he's a (complex) differential geometer and I'm really getting filtered in my differential geometry course right now. Have I made a bad choice asking this prof? The topic will probably be in complex algebraic geometry.

>>12322012
Who is this witch?

>>12322012
Grimes is NOT a mathematician

Is linear and integer programming any interesting?

>>12321971
>says one of the most responsible for filling the geometry community with mentally derranged people

>>12322082
sorta, its kind of boring to do

>>12322082
linear is based, but not as based as dependant

>>12322222

>>12321849
Why does everyone call it “maths”? I know that’s the “international” way of saying it, but it sounds retarded. When I study history I don’t say I’m gonna study histories.

>>12322253
It's not a plural though.
You have mathematics, similarly to robotics. None of these are plural and the former is abbreviated as maths.

>>12322253
gotta run some stat(istic)s

Is it possible to total differentiate multiple dependent variables with multiple independent variables? Or I can only differentiate one dependent variable against multiple independent variables?

I have 2 dependents (volume of liquid, and friction of the pipe, both of these will change over time and they are randoms) and 2 independents (time intervals, and pipe sections).

How to differentiate these variables?

>>12322613
Look up multivariable chain rule

>>12322613
Wtf are you even trying to say
Is this some murican thing?

>>12322782
Thank you sir. I will try and work on this.

>>12322791
Sorry I cannot put it into words properly. Must've been because I didn't understand what to make of my data.

For each time interval, t and for each pipe section, p, My sensors will puke out the volume of liquid flowed through a section, v, and the friction of the pipe's section, r. I just want to know how to differentiate all of these at once.

Any charts for applied maths? Recommendations?

I hate my undergrad classes, all they do is distract me from research. If I wanted to do drills all day I'd be in the army

>>12323205
Take grad classes if you're at that point.

>>12321849
>ultrafinitism
not maths

>>12323225
>philosophy of mathematics about what is and what is not mathematics
Not maths. Go back.

>>12323182
Applied math is just math

Ssup faggots

are these differentiables?
w = f(x, y)
z = g(w, x, y)

what about this?
p = a(s, t)
q = b(s, t)

>https://www.gap-system.org/index.html
>GAP is a system for computational discrete algebra, with particular emphasis on Computational Group Theory. GAP provides a programming language, a library of thousands of functions implementing algebraic algorithms written in the GAP language as well as large data libraries of algebraic objects. See also the overview and the description of the mathematical capabilities. GAP is used in research and teaching for studying groups and their representations, rings, vector spaces, algebras, combinatorial structures, and more. The system, including source, is distributed freely. You can study and easily modify or extend it for your special use.
thoughts?

>>12323466
Use it through Sage.

>mfw student tries to correct me or impress me

>>12323652
>uhh professor can we do this without the axiom of choice?

>>12323667
That's literally me lol. I have a recessed chin and I asked this question in a class.

>>12323679
well...stop doing that?

>>12323704
I only did that once. And I can't stop having a recessed chin.

>>12323679
If you want to give a proof something, then you must by definition avoid the axiom of choice. Or really stretch the meaning of the word "proof"

Is it worth a read?

>>12323708
you can at least make is less prominent.

>>12323721
>you can at least make is less prominent.
How?

>>12323720
no, read this instead
https://en.wikipedia.org/wiki/Mathematics_Made_Difficult

>>12323723
google?

>>12323724
Kinda wanna buy that desu

>>12321973
He's right though

Prof sez we can't have an eigenfunction which is identically 0. For context, we are solving Laplace's + lambda times the eigenfunction inside a box in two dimensions, where all the boundary conditions are identically 0.

When he says we can't have an eigenfunction which is identically 0, does he mean so in a paradoxical sense, or does he mean that it's just trivial and therefore inadmissible as a meaningful solution?

>>12324030
The latter.

just got filtered by group actions ama

>>12324147
Are you actually retarded?

>>12324234
Yes.

>>12324147
just look at a couple of examples that are simple enough and look at some examples that don't work. abstract algebra is kind of hard if you're new to mathematical thinking but the other thing you might want to pay attention to (if you really don't get it) is just what kind of "symbolic maneuvers" you can make with a group action on a set. like a group homomorphism is f(mn)=f(m)f(n), and a coset gH=ghH and so on, things like that. You'll find there's something similar for group actions on a set.

can I post some abstract algebra homework without getting laughed at?
this is due tomorrow morning and I'm toast and can't figure out how to write the proof for the last question, just know that I ought to use the right coset equality theorem but IDK where to proceed

>>12325065
Aren't a-e just the conditions needed to satisfy the isomorphism theorem to conclude that (C/A)/(B/A) is isomorphic to C/B?

>>12325085
How should I be using the normal subgroup relations between A, B, and C?
and how do I prove the well-defined-ness? I think i need some coffee

>>12325115
The normal subgroup relation just means that C/A and C/B are defined. f takes in cosets of A and multiplies them by c. Well defined means that for different choices of representative for the coset the function behaves the same. So show that for any x,y in C if A*x=A*y, then f(A*(xc))=f(A*(yc)). You should review how the first isomorphism theorem is proved.

>>12325145
>for any x,y in C if A*x=A*y, then f(A*(xc))=f(A*(yc))
why isn't this
f(A*x) = f(A*y)
? I thought that generic x, y in C are standins for the c in C from the question.

Poisson random measures seem very cool. Does anyone care about these outside of intro probability classes?

>>12325164
Yeah your right I was overthinking it, show f(A*x)=f(A*y) when A*x=A*y.

>>12325180
but the algebra is hard ;______;
I can see B*x = B*y
by the formula
but how to make them equal??

>>12325212
Its pretty easy homie. Since A*x=A*y, there exists a in A so that ax=y, then f(A*y)=f(A*(ax))=f(A*x). The last equality holds since a in A and A is a subgroup then a^(-1) in A, so A*(ax)=A*x.

until today i thought that "graduate" means someone who is a phd student, and i've been thinking american must be a bit retarded if their curriculum goes so slow
turns out the real retard is me

reporting for math sirs pls teach now thank

real mathaticians speak latin huddled around demonic circles

https://en.wikipedia.org/wiki/Talk:Numerology#Dubious

:^) enter if u dare

Hello anyone know if this book's any good? or any recommendations for starting algebra?

https://books.google.com/books?id=3Rg8AAAAcAAJ&printsec=frontcover#v=onepage&q&f=false

sounds boring... would rather read old renaissance books untranslated for free on google kthxbai

doing physics bsc, one course is called calculus but we havent done 1 derivative or integral.
we run around prooving garbage about series, groups, sets and inequalities.

what is this supposed to be? basis for limits of functions?

>>12325751
always wanted to try tutoring math...

but I'm too stupid can't help you.

Just discovered... drums...

>>12325751
Study calculus on your own, it shouldnt be too hard

>>12325955
>>12325754
im not having trouble with the subject, im just confused. isnt CALCULUS about limits/ derivatives and intergrals of functions?

>>12325560
>Slow studies
There is no such thing.

>>12325739
Too hard for beginners, start with Herstein or Dummit and Foote.

>>12326113
Herstein's Topics in Algebra or Abstract Algebra?

>>12322253
Historically, mathematics used to be considered a group of disciplines, like geometry and arithmetics.
Hence the idea that there is a plurality of mathematics.

>>12326113
Is this really true? I remember that my modern algebra professor recommended Artin as intermediate level and D&F as a more advanced undergrad reference

>>12325560
>until today i thought that "graduate" means someone who is a phd student
It does mean this. Grad level = PhD level

>>12323405
whats your point

>>12323405
all are differentiables except p = a(s, t)

>>12321870
So what are the job prospects for pursuing a math degree? What do you plan on doing?

>>12325560
It literally does mean this, and yes some mericans do start a PhD without knowing measure theory, functional analysis, diffgeo etc
Literally they just finished muh 'calculus' and maybe babys first analysis/algebra and ODE courses...

Hi, how do I show that if X follows a multivariate normal distribution in R^n then (X'X)/n converges to a definite positive matrix?

What should the cardinality of [math]\cos(0)[/math] be?

For simplicity let's stick to the standard meme foundations of mathematicians.
Do we want [math]|\cos(0)|={\aleph}_0[/math] or [math]|\cos(0)|={\aleph}_1[/math] or generally something bigger than that?

>>12327295
cos(0) = 1 = {O}
cardinality of cos(0) is 1

>>12327295
The cardinality is easily seen to he the continuum if youre dealing with equivalence classes of cauchy sequences and aleph null if you look instead at dedekind cuts.

>>12327314
I was obviously just shitting on set theory, but what do you think should it be?

I'm wondering if in this day and age, there's anything we can suck out of Dedekind cuts on Q that would still be of interest to use in some proof. (And they are not really helpful for applications I think.)

>>12322082

Both are interesting (at least to me). They are inordinately useful though, which is probably why they receive as much attention as they do.

>>12322082
>>12327336
I think their history is very tightly linked with Soviet national planning

>>12327360
That is true, for many of the basic methods in Operations Research their origins are tied either to centralized planning or with military operations. Famously max-flow and min-cut problems had their origins in how to most efficiently bomb a rail network.

>>12321971
>Frog hates Kraut maths
Colour me surprised. Not.

That said, I hope we will eventually move past the Reals.
There is too much fuckery in them, that probably is not "real".

>>12325977
It's about calculating things if I'm not mistaken, what are you trying to calculate?

>>12326662
Do you mean q isnt differentiable too?

What exactly is being asked for in part (c)? Is he asking for a confidence interval sort of idea, or the relative efficiency of such an estimator?

>>12321849
Who is this guy?

>>12327715
>not knowing Wildberger

>see a problem in the book
>solve the problem
>later learn that the problem is flawed and actually the statement is not true
fuck

>>12327982
>trusting books

>see a theorem in a book
>use it to solve a problem
>publish the solution to the problem
>later learn that the theorem is flawed and actually the statement is not true
fuck

>>12328024
If you haven't independently verified your own critical infrastructure you're gonna have problems.

>>12321877
yes, but also I am stupid.

Knowing sympy, mathematica, etc. exist, is being good at calculations important?

Should I be a beast at computing derivatives and integrals?

Is there some insight to be gained from being good at calculation?

>>12327771
What did burgerman do?

If[math]f:\mathbb{R}^m \rightarrow \mathbb{R}^n[/math] is continuous and surjective (with the usual metric) then there exists [math]r>0[/math] for which [math]f(B(0,r))[/math] has a nonempty interior.

Any help with this one? We're supposed to use Baire category theorem.

>>12328361
You can't really use BCT if you're not working with complete metric spaces.

>>12328185
basically I've found that it's useful to be decent at finding primitives because then you know pretty quickly whether a problem is nontrivial.

>>12326113
I think I'll try it, I'm wouldn't say I'm a beginner. finishing undergrad but missed out the algebra subject. Appreciate the advice though

>>12328361
This is such a simple question im honestly surprised you would even ask it on mg. Next time I suggest working on it a bit more yourself before posting it here.
Anyway, here goes.
Let A_n be the closure of the image of n-ball around 0. The union of A_n's is the whole space so by BCT one of them has a nonempty interior, say A_m. Then take some r slightly smaller than r and youre good.

>>12328472
>Then take some r slightly smaller than r and youre good.
Messed up here. Meant take r to be m+1.

How do I into Calculus
Ive got a month left to the semester and dont understand shit, and all I can get is a C, is it still worth it?

>>12328236
2D algebraic geometry, lots of history related stuff, and then.. you know..

>>12328472
Thanks for the help, but I'm having problems understanding why BCT implies one of them having a nonempty interior.

>>12328562
Sorry, I found the right version of the theorem and that cleared it up.

>>12328506
Find the optimal way to kys

>we ask the interested reader to fill in the details

I need to prove the following isomorphism for a problem I am working on. Apparently, [math] I\frac{R}{J} \cong (I+J)/J[/math] as an isomorphism of modules where [math]I,J [/math] are ideals of the ring R. So I have the map [math] \phi(i(r+J) = ir+J[/math]. Something about this map feels wrong tho. I've proved that it is bijective and a module homomorphism. However, it seems like I straight up get set equality instead. Something feels really cheesy about this and I'm curious if I did something wrong.

>>12328506
Calc 1 is a lot of building on limits to get to the good stuff. If you're doing fine with the applications then I'd say keep trying.
Calc 2, if you have to take it, is a lot of difficult applications.
Calc 3 is that good shit.

>>12326851
Besides >muh teaching,
you can get into anything remotely quantitative with a math degree, especially if your uni isn't meme-tier and forced you to sit through some programming classes. With just a BS, you have access to quant jobs in finance, or meme "analytics" jobs, or even steal straight programming jobs from CS grads if you took extra programming courses on the side. If you're willing to get accreditation and go through exams, you can even try your hand at actuarial science.

If you're more interested in research or pretty much anything that requires an MS or PhD, math is pretty much the gateway to any field. For example, it's rare to find researchers who got a BS biology move out of the wet lab, because they're more or less digitally and mathematically illiterate. However, if you have a math degree and apply for a bio grad program, you can research more interesting fields such as biostatistics or bioinformatics, instead of being a lowly pipette bitch. Besides natural science, other fields you could get into with a math degree plus grad school include operations research and data science (aka applied statistics).

Basically, by not being a complete mathlet, you pretty much get a leg up in starting your career.

Have to finish my undergraduate degree by taking a two-semester sequence. I want to work for a hedge fund eventually, should I take Numerical Analysis I and II, or Complex and Real Analysis (both are intro courses)?
Num sounds easier and simpler (Intro Real Analysis is considered the hardest undergraduate course in my entire uni), and at the end of the day I want my fucking degree with a strong GPA and I don't think I'd ever use real/complex analysis at work.

But, real/complex analysis sounds a lot more fun and would make me a better mathematician.

Anybody want to tell me what to do?

>>12330003
well i mean obviously numerical analysis is far more relevant to quant work but gonna be honest, you should really take all of those classes or your degree is pretty sad.

>>12330128
my uni only *requires* 12 credits of 4000-level math, which is what includes stuff like numerical analysis, intro real/complex analysis, number theory, etc.

hey /mg/, how do you call the cardinal [math]\sup \{2^{\aleph_0}, 2^{2^{\aleph_0}},2^{2^{2^{\aleph_0}}} \dots \}[/math]? (i.e. the cardinal obtained by iterating the powerset operation countably many times, starting at [math]\aleph_0[/math]). if not a direct characterization, can you suggest any lower/upper bounds on its size, in terms of [math]\aleph[/math] numbers?

>>12330003
Well, obviously, if you complete an undergraduate degree in maths without knowing basic real and complex analysis you're a complete embarassment and your degree isn't worth the toilet paper it's printed on.

>>12330181
You just get [math]\beth_{\omega}[/math]. A more interesting construction is to take [math]\kappa_0=\aleph_0[/math], then set [math]\kappa_{n+1}=\aleph_{\kappa_n}[/math], let [math]\kappa=\sup \kappa_n[/math]. This is a weakly inaccessible cardinal of countable cofinality and an aleph fixed point. You could also do this with the beth function.

>>12330206
Woops, wrote the implication wrong. Every weakly inaccessible cardinal is an aleph fixed point.

>>12330003
> Intro Real Analysis is considered the hardest undergraduate course in my entire uni
Jesus fucking christ the absolute state of american mathematical education

>>12321849
im doing a report on game theory. is pareto optimal in the context of the prisoners dilemma where both prisoners co-operate (not betray), and both get shorter sentences. but the Nash equilibrium is both betray as they have an incentive to betray to get a reduced sentence?

>>12330340
If you go to the right schools there are undergraduate classes like "intro to combinatorics" that are taught at a higher level than first-year grad classes.

>>12330003
how is "intro to real analysis" not a first semester mandatory course?
can u quickly say what are the contents of the course?

>>12330382
Fair enough and I've had some really good experience with meth majors from the top 5 or so universities.
On the other hand we have several people here who have an american undergrad degree from a mid-tier uni and don't know what a manifold is or haven't heard any measure theory, lack in foundations like functional analysis and stuff like that.
Those are things that even at the worst uni in germany undergrads will know

>>12330478
I'm not saying all American universities are great, but part of it is also cultural. There are tons of SE Asian kids who drill how to define an abelian category or how to state a recent trendy theorem in topology, but they don't have any real understanding of those things and can't produce more similar material or solve problems they haven't seen solved before. In the US the focus is on understanding and creative, intelligent responses to material over just consuming as much content as possible.

>>12330562

>>12330565
Seething.

>>12330562
No offense but isn't 'caluclus' or whatever a computation based course? How is that creative and understanding based? This is not the standard a math student should be held to, writing essays on social justice and mindlessly drilling integrals in muh calculus course with the engineers.
I'm not criticizing students here (which are most of the time indeed are more intelligent than europeans, at least in my experience, and will relatively quickly learn the basics they get deprived off in mid-tier US universities).
But someone who doesn't know what a lebesgue integral or a manifold is really should not be awarded a math degree.

>>12330168
How the hell are those 4000 level? At my uni its stuff like algebraic topology, Partial differential equations 2, functional analysis, number theory 2 (elliptic curves and Dirichlet L-functions)
>>12330003
If your intro to reals is really an intro, i.e. epsilon-delta, convergence, etc, then you should really take it, otherwise not sure. For your endgame, I'd go with real 1 and num. anal. 1. Then go back next year to take num. anal. 2 and complex for the knowledge

>>12330639
I was referring more to upper-level classes for math majors, although the first-year calculus classes are often segregated into difficulty tiers and the math majors will use something like Rudin and see more rigorous arguments. As to whether a math graduate should know what a Lebesgue integral or a manifold is, I would say that many who would go onto grad school do, but knowing what either of those things are, even just vaguely, isn't as important as developing the kind of mathematical reasoning and intuition that are stressed in the first algebra/analysis/topology courses.

>>12330403
first semester mandatory course??
Do you imagine people are graduating high school writing complex proofs and understanding discrete math concepts?
When do you think people are learning linear algebra, ODEs, multivariable calculus, etc.

>>12330803
>algebraic topology, Partial differential equations 2, functional analysis, number theory 2 (elliptic curves and Dirichlet L-functions)
>4000 level
How the hell are these 4000 level classes? These are all 1000-2000 level at my university. Shit like noncommutative ring theory, several complex variables, stochastic differential equations, hodge theory, teichmuller and inter universal teichmuller theory are 4000 level at my uni.

I'm studying algebra for the first time in a decade. Does anyone know any good resources? I'm planning on going to Uni, either Maths or CS, but I don't want to be one of those nontraditional students who needs remedial math. Remedial English is w.e, but I want to become an expert in maths.

>>12330917
Unironically, you're better off using a common core high school textbook. There's always a shit ton of exercises and examples.

>Algebra 1:
https://www.amazon.com/HIGH-SCHOOL-ALGEBRA-PRENTICE-STUDENT/dp/0133500403/ref=sr_1_1?dchild=1&keywords=algebra+1+prentice+hall&qid=1605121754&sr=8-1

>Algebra 2:
https://www.amazon.com/HIGH-SCHOOL-MATH-ALGEBRA-STUDENT/dp/0133500438/ref=sr_1_1?dchild=1&keywords=algebra+2+prentice+hall&qid=1605121736&sr=8-1

>>12330917
In addition to
>>12330936
If you're comfortable with Algebra 1 this would make also for a good algebra 2 textbook
https://www.amazon.com/College-Algebra-James-Stewart/dp/1111990166/ref=sr_1_3?dchild=1&keywords=college+algebra+stewart&qid=1605121804&s=books&sr=1-3#reader_1111990166

Despite the hivemind circlejerk about Stewart being a shithead, his books are actually pretty good and you can relyl on there being tons of exercises for you to practice with

>>12330936
>>12330945
I'm using "Beginning Algebra Eighth Edition" by Gustafson and Frisk currently. I'm currently on Chapter 5 (Factoring). It's still very basic stuff obviously, but I've been pleased to have only As so far, albeit self-scored. I'm rather disappointed with myself that I gave up maths for so long. It is what it is when you're a jaded and depressed 18-2x year old though.

I have a question. suppose [math]f(x)[/math] is Riemann integrable on [math][a,b][/math] and that antiderivative of [math]f(x)[/math] exists on [math][a,b][/math]. does it follow that [math]x \mapsto \int_a^x f(t)\, dt[/math] is antiderivative of [math]f[/math]?

>>12330987
yes

>>12330880
linear algebra = 1st semester
limits, series, integrals, integration, other 1-real-variable topics = first two semesters
multivariable calc, inverse function theorem, implied function theorem, stokes etc = 3rd and 4th semester
odes = 3rd year

>>12330997
So we're agreed real analysis is 3rd or 4th year?

>>12330994
can you prove it?

>>12331014
yes

>>12331023
do it or give idea pls

>>12321895
faggot
>>12321971
so based

>>12331028
Take the derivative of your integral and use Leibniz's Rule

>>12331039
I don't know if it's differentiable, that's the point

>>12331028
try writing out the definitions of each of your terms

>>12331044
Apply the limit definition of the derivative to the proposed antiderivative and see if it exists!

What is it about numbers larger than 5? Whenever I see them used for any (purely) mathematical purpose, I feel confused and disgusted.

The same generally goes for transcendental numbers and functions. I've grown to accept them somewhat, but I'm still disgusted by the widespread usage of logarithms.

>>12330562
Can u back this up with data?

>>12331057
>>12331061
how do I deduce that the upper bound function is differentiable from the fact that f has antiderivative? it's not trivial.

>>12331092
You can't, the initial problem must include a statement that x is within [a, b].

>>12331107
of course x in [a,b]. what now?

>>12331113
Are you asking us to prove the fundamental theorem of calculus?

>>12331135
no. fundamental theorem of calculus assumes continuity of f.

>>12331067
I think that would be interesting to see, but it's only from my personal experiences and what I hear in the math community. For what it's worth, Asians also bring this up to me. It does make sense that cultures which are more collectivist and poorer will focus more on rote memorization. Creativity is very individualistic and prone to failure. There's a reason everyone in India wants to be an engineer and not a scientist.

What are the steps involved in factoring 16(x - y)^2 -9?
Am I retarded? My autodidact ability doesn't normally fail me like this.

>>12331142
Riemann integrability implies gauge integrability, even if the function is discontinuous in the interval. The gauge integral coincides with the antiderivative.

>>12331250
It's a difference of squares

>>12331250
You talk like a fag and your shit’s all retarded.

>>12331280
Why are you doing anon’s homework for him?

>>12330889
>noncommutative ring theory, several complex variables, stochastic differential equations, hodge theory, teichmuller and inter universal teichmuller theory are 4000 level at my uni.
holy shit lmao. I think those are all prerequisites to even be admitted to my uni. I suppose they might offer these as sub 1000 level remedial courses.

>>12331446
haha, my 6th grade Morse theory teacher said if you don't know Hodge theory by the time you are 15 you will never make as even a baker.

>>12331362
Yes, that is what this lesson is on. Thank you.
>>12331433
My shit may be retarded, but you're anonymously posting. This means that without evidence of credentials, we have no evidence that you aren't just as retarded as I am. Unless of course, you tell me what exactly I am missing here.

>>12331509
I'm not that poster but I can tell by your writing that your kinda dumb and trying to hard too sound clever or erudite.

>>12331509
>Yes, that is what this lesson is on. Thank you.
Don't you wonder how I recognised this? You yourself don't seem to have identified the squares in the picture because if you had then you would know how to factor it by the simple difference of squares formula.

>>12331509
>anonymously posting
>without evidence ... we have no evidence
Nice english, ESL-chan. Plenty of evidence right here.

Well, that was every bit as easy as I thought it would be.

I'm one of those ADHD idiots who dropped out. My English on the GED was terrible (about 74th percentile) but my math was 98th percentile.

I'm strongly considering the possibility of returning to high school before entering college. The opportunity cost may be higher though.

>>12331580

>>12321971
anything set related past union and intersection is cancer and should be thrust into the depths of the ocean where that shit belongs

ignore the retard yapping about how you must take topology etc. to "earn" your maths degree
the minimum is simpy analysis, linear algebra, maybe some stats and lastly some number theory/discrete maths

>>12331584
Nice work anon.

>>12326864
>without knowing measure theory, functional analysis, diffgeo etc
useless things in based applied mathematics

>>12327295
you have no idea how much i hate faggots like you

>>12331613
I don't agree with this in earnest but there are tons of mathematicians who know fuckall about any of those subjects.

>>12331604
You are quite literally getting an inferior maths education if you learn only those things. I'm not trying to shame people or make them feel bad for their university or whatever, but you are massively handicapped trying to go into a PhD with only those things. I'm not from some elite university deep in Russia either, I didn't learn Morse theory in primary school. I did however learn "basic" things like algebraic geometry, algebraic topology, measure theory, diff geo, etc in my undergrad.

>>12330003
most uni professors are shit at explaining and probably the reason why the class is so hard is bc of the shit teachers that teach it. id suggest going with num1 and 2, ending ur degree with a high gpa and reading books on your own about real/complex analysis if youre interested.
DO NOT LEARN USELESS SHIT

>>12331632
>"basic"
>algebraic geometry, algebraic topology, measure theory, diff geo, etc in my undergrad
you have to be trolling my mans, or you're the biggest autist i've ever seen

>>12331632
https://math.mit.edu/academics/undergrad/roadmaps.php
where the fuck do you study where you suppose the bare minimum for people is to do all those "basic" things in undergrad?

>>12331667
I'm not trolling, any student at my university aiming to do a PhD has seen all of these things (plus usually functional analysis but I skipped this). I took two courses on algebraic topology (three if you count K-theory), three courses on algebraic geometry (classical, computational, modern), a course on measure theory, and a course on diff geo. I also took a bunch of computing courses and I know students who took all pure maths and saw a lot more than me.

>>12331685
ANU. I'm talking specifically about anyone aiming to do a pure maths PhD (probably 10-15 people a year). It's not mandated on the syllabus but the almost all of these people will have done these courses. Of course other people do applied maths degrees which don't cover all these things.

Bros I got filtered by basic topology. Accumulation points, Lindelof thm, open-closed sets, I don't understand the solutions to exercises at all. It's an advanced calc course and I'm really not comfortable with the professor. What do?

>>12331698
so ANU is Acharya Nagarjuna University ?

and you havent taken functional analysis but 2 courses in algebraic topology and 3 in algebraic geometry kek, that's just ridiculous.

>>12331724
Australian National University.

I've also never solved a differential equation in my life. We get a lot of freedom beyond the basic requirements (linear algebra, real/metric analysis, measure theory, groups, rings, galois theory).

>>12331755
Forgot to add: we don't have any courses in graph theory which I would say is our biggest weakness.

>>12331761
Discrete mathematics?

>>12331704
Change majors

>>12331704
google "introductory topology book pdf"
Sutherland is my recommendation
read relevant parts
it can't be that hard

I am a number theory PhD student in the UK, you can ask me any questions you might have about algebra/number theory or PhDs in general

>>12331931
which numba is the best?

>>12331931
Would you recommend an American apply to unis in the UK for graduate school? Are you funded during the summer? If not, what do you do during the summer?

>>12331949
1

>>12331952
I'm funded for 3 and a half years and I'm paid 4 times a year. I self study or do seminars and study groups over the summer. I don't see why an American shouldn't apply here. I'd say you should apply to a Master's though before doing a PhD. I don't know what kind of school you're going to but unless it's really good it probably won't prepare you for a PhD where you're supposed to start doing research very quickly.

>>12331963
What's the cardinality of 1?

>>12331984
1.

>>12331963
Why 1? 2 is far superior. You have the square root of 2, twice the quantity, primality, powers of 2... What can 1 even do that 2 can't? 1 doesn't even behave like most numbers do.

>>12332003
>1 doesn't even behave like most numbers do
>that's a bad thing
I shiggy

What's the deepest theorem you know?

>>12332003
1 generates the integers, 2 doesn't. Algebraic objects have a canonical "1" but not a 2.

>>12332015
also the complex roots of 1: they give us things like cyclotomic fields, Tate modules, Iwasawa theory.

>>12332015
If there is at most one morphism between two objects, you have a fairly degenerate structure. Two is already better than one in that respect.

>>12332015
>he doesn't work exclusively with rngs
Oh am I laffin

>>12332019
What's the square root of -2?

>>12332021
You can't have 2 without 1 :^)

>>12332011
Theorem is relative, but let's say that accessible pointed directed graphs are in one-one correspondence with sets.

x={x}

(not compatible with regularity, but that's somewhat of a meme anyway)

>>12332003
>1 doesn't behave like most numbers do

>implying that 2 isn't the most pathological prime by far

>>12321864
Mate I'm a graduate student in maths (applied mathematics to be precise) and I literally never heard of a jobless mathematician
And it's not like here in Croatia job market is all that well (although a lot of us do go somewhere else in the EU to work)
Also when you're studying math these days you're also doing a lot of programming at least that's what we do

>>12332049
>he's doing applied maths

In my undergrad I had to do one class that was half python. Literally 2% of my degree and no c*ding after that.

>>12331487
>>12331446
>>12330889
>>12330803

What the fuck are you guys talking about? Is your curriculum really that stupid? Hodge theory was a prerequisite for Kindergarten, it was one of the many things learned in Pre-K that were required to enter the school system.

>>12332058
>doing Hodge theory over the complex numbers at all

That shit was assumed when they sung us p-adic Hodge-Tate theory nursery rhymes.

>>12332011
Probably the main theorems of class field theory

>>12332057
We Slavs are traditionalists so we had 3 classes of C and 1 class of C++ in undergraduate
Now in graduate we're doing a mix of everything, mostly C again and MATLAB

>>12332041
Consider the rng [math] 2 \mathbb{Z} [/math]

>>12332066
>That shit was assumed when they sung us p-adic Hodge-Tate theory nursery rhymes.
???? Why are you guys talking as if this was stuff you "learned". This is just basic knowledge you should understand naturally as a part of your growth cycle. You don't "learn" IQ, you experience your inherited IQ. You don't "learn" Hodge-Tate theory. This is a subject that is either in your genetics or not. I was doing problems in Hodge-Tate theory and began to solve the Riemann hypothesis as I was learning to walk. I didnt do this using books, it was already engrained in by brain from birth. I keep my personal solution of RH to myself as a reward for my inherited knowledge

>>12332093
>traditionalists
>c*ding in a maths degree
How the fuck can you say that

>>12332104
For undergraduate (which is just called mathematics, 3 years) it's because we have different graduates after (programming mathematics, financial mathematics, statistics, applied mathematics and theoretical mathematics, all 2 years)
So besides theoretical (and that's debatable) all the others require knowledge of programming
As someone said: today, a mathematician is as good as his programming

>>12332118
that just tells me that Croatian academia is shit and I'm not surprised. No pure mathematician needs to know any coding.

>>12332142
Again I'm guessing theoretical maths graduate has a lot less programming than any other if any
Also Croatian mathematicians get jobs all the time in the rest of eu and America, we have great results for such a small and relatively poor country
Also all the best colleges are state ones (free) and that allows me to be a NEET

>>12332156
>Also all the best colleges are state ones (free) and that allows me to be a NEET
but... thats a contradiction?

>>12332177
Technically yeah
But I don't work anything on the side to pay the bills and I also extended my undergraduate to 4 years because where's the rush

>>12331975
Do you have a gf? Have you ascended above the desire for women? What do you plan to do after grad school?

>>12332209
galois fields are the only gfs yule need now

>>12332209
I have a qt gf. I wanna stay in academia after my PhD.

help pls

>>12332395
I'M FUCKING GIGA RETARDED

>>12332395
Seems like your axes are fucked. And is that the number 13? Maybe it was a typo? What's the .01 for?

>>12332422
I typed x, y instead of x1, y1. See >>12332398 for further information.

>>12332422
Oh and the 0.1 is the step size on t. Yes 13 is correct.

>>12332432
Ah. I did notice that but I don't know what kinda shit these ultra high level languages do for you. I hope that's GNU Octave and not some proprietary garbage language though.

>>12332466

WHY THE FUCK IS PI EQUAL TO SOME RANDOM DUMB IRRATIONAL NUMBER AND NOT JUST 3 OR 4? REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

>>12332476
That's the million dollar question.

>>12332476
it is equal to 1 in base pi

>>12332496
You mean 10, silly

>>12332481
Who will pay me a million freedomshekels if I answer it?
>>12332496
Okay then in base pi, why is one irrational?

>>12332103
incredibly based

>>12331704
point set topology is quite intuitive. spend more time with it.

>>12331250
The square root of 16(x-y)^2 is 4(x-y).
The square root of 9 is 3.
The factorization of A^2-B^2 is (A+B)(A-B)
Proof: (A+B)(A-B)=A^2+AB-AB-B^2 and the +AB and -AB cancel each other leaving A^2-B^2
so your factorization is (4(x-y)-3)(4(x-y)+3)

>>12331509
The (x-y)^2 is only multiplied by 4^2, not by 3^2, so when you set 4^2(x-y)^2-3^2 equal to (x-y)(x-y)(4+3)(4-3) in the second line of the third paragraph is where you went wrong

Came across something which is basically a binomial expansion but all the coefficients are 1. Is there a name for this. It basically looks like,
a^n+a^n-1b+...+ab^n-1+b^n

>>12332662
Yeah, it's called a geometric series. Each term is just the last one times b/a.

>>12332689
Thanks I'm retarded; as a gift, next time you open your fridge you'll see an extra Pepsi DO NOT DRINK IT. The Pepsi isn't the gift, you have to pour exactly half of it out into your garbage disposal, then wait five days and you will receive one wish for your help today

Anyone have experience with automated reasoning? Currently looking into theorem provers and proof assistants but there doesn't seem to be many resources out there.

>>12332736
I've used agda a bit and I think it's really neat, though more proof verification than generation.

>>12332736
I've used Lean a little but also mostly on the verification side.
This guy has a blog doing basic maths in it: https://xenaproject.wordpress.com/
There's also a pretty good documentation manual that you can google for.

>>12332709
Don't tell me what to do with my pepsi NIGGER

>>12326353
Topics in Algebra

why the FUCK doesn't overleaf have basic maths vocabulary

>>12332736
Coq and Idris are proof assistants (and dependently typed programming languages)

Let M and N be normal subgroups of G, and suppose MN = G. Suppose also that H and K are normal subgroups of M and N respectively, such that M/H and N/K are simple. Is [math](M\cap N)/(H\cap K)[/math] simple?

pill me on based sets and based maps

>>12332736
Some introductory Coq-biased references:
- https://homotopytypetheory.org/book/
- https://math-comp.github.io/mcb/
- https://softwarefoundations.cis.upenn.edu/lf-current/Preface.html

>>12333029
this reminds me:
can someone post the retarded question related to groups that appeared a few /mg/'s before?

>>12333259
Was this one of:
>If H is a subset of a group G is it a subgroup?
>If H_1 and H_2 are subgroups of G is H_1 a subgroup of H_2?

>>12333259

>>12333269
>>12333282
makes me kek every time
i hope the poor anon didn't feel too bad when we laughed at him...

Im studying a course and my professor isn't really good. I want to study from the internet but I dont know what to search.
When I google the name of the course I get an absolutely different subject, so I ask you guys:

What do you call a math subject that deals with proving certain things about given inequalities and groups/sets?
For example, given two groups with boundaries groupA->a, groupB->b, say you do groupA+groupB then their boundary is a+b, now I prove it by stating there's an positive epsilon etc etc.

Optimization, what's it good for?

>>12333397
I think you are looking for real analysis ESL-kun.

>>12333397
do you mean stuff like "if every element of A is larger than every element of B, then inf A ≥ sup B"? this is just basic analysis and it's easy, you're just not used to it. any real analysis textbook probably deals with this in exercises to the first chapter.

Quick question here, is this eqivalent to proving the curl of [math]\Bar{F}[/math] is zero? I'm guessing the approach then is through Stokes' Theorem

I'm trying to prove pic related, but I'm having some trouble.
I know if I can prove that f is irrotational (zero curl) and that the region is simply connected then the statement follows.

I'm struggling to prove that F has zero curl. Would stokes' theorem prove this?

>>12333660
Further, why do we need the fact that the Laplacian is zero?

>>12332982
You can add words to the dictionary but you have to ask customer service to remove one. I guess «homomrphism» is in my spelling dictionary forever now.

>>12331064>>12331064
>What is it about numbers larger than 5? Whenever I see them used for any (purely) mathematical purpose, I feel confused and disgusted.

any number larger than 2 is a meme

>>12333414
Optimizing things

whats the bump limit again>?

>>12333971
310.

>>12333259
>>12333269
>>12333282
>>12333380
Is this a samefag? The question is just making sure you understand the definition of a subset and arn't thrown by the introduction of the concept of a group. Questions like these are par the course in almost every textbook.

>>12334053
Here he is, everyone point and laugh.

What would it mean if a counterexample to P=NP was found with complexity equal to a degree-470,000 polynomial?

You know what makes me laugh about threads like these? How unaware you guys are. I'm all for people getting math degrees, because without your social inept dorks. I wouldn't be in a manager position. You guys are pretty smart, but horrific when it comes to getting people together and being social with each other. You doofus dorks tend to isolate yourself and work by yourself for hours on end. You guys think you're making a lot of money but in reality it's nothing compared to what I make and stock options that are offered to me by the company. You guys could come together if your life depended on it. Zero skills when it comes to team meetings, discussing different ideas, being social among each other, and actually working together. I can describe my job as a baby sitter. It's funny too when math dorks try to hit on girls, it's easy picking for me, because I actually know how to have a conversation with actual human beings.

>>12334440
>You guys think you're making a lot of money
I doubt anybody thinks that

>It's funny too when math dorks try to hit on girls
Nobody here does that

Anyway, sounds like you're a bit bitter. If you're a manager and want to get the most out of people, having a base negative attitude towards them will block you. Hope that helps.

>>12334451
it does, but I'm not a manager this is just my life

>>12334451
>Online attitude transfer to reality
This is exactly what I mean. You nerds have zero understand on how humans interact with each other. You guys are basically cyborgs and I get a kick. lol

>>12331704
I'd recommend taking a look at some other explanations of the material. Whenever you're in a position when you can't understand your materials after spending hours on it, it may be more efficient to look at other explanations rather than slamming your head on the table until it sticks.

>advanced calc
if you're doing stuff on metric spaces, try an easy analysis book like Abbott. Then go back to Rudin or tao or whatever you're using

>>12334440
>Zero skills when it comes to team meetings, discussing different ideas, being social among each other, and actually working together.
Yeah, you've never met a mathematician.

I'm probably not failing my calculus 3 class but at what cost? I feel like I didn't learn shit, I'm so pathetic frens...

>>12334503
>Yeah, you've never met a mathematician.
Yeah, you're correct. Because they shut down the second they enter my presents. I don't met them, they work under me.

>>12331704
>Spending 10k+ on education and not having the balls to ask for a proper education.

I just scored a perfect 100 on my test in Calc 2.
AMA, I may be able to dispense some of my wisdom onto you

>>12334440
Come on now

>>12334559
What is [math]\int{\sqrt{tanx}} \ dx[/math]?

>>12334629
>>>integral-calculator.com

>>12334629
Now, you have put me in an interesting dilemma. If you worked on that problem yourself until you solved it by yourself, it would most definitely be a valuable learning experience. If I gave you the answer, I would deprive you of valuable wisdom that you cannot get in any other way. However, I cannot prove that I can solve it myself without giving you the answer. So really, the only way I can get out of this without looking like a dumbass and without doing irreversible damage to your mathematics career is to insult you and shame you out of this thread. I'm sorry, but you leave me no other choice.

What kind of fucking baby question is that? Maybe you should ask for help on Reddit. Cuck.

I'm incredibly sorry that you had to make me do that.

>>12334648

>>12334648
>I cannot prove that I can solve it myself without giving you the answer
Assuming that you actually want to do this, rather than simply ignoring the post, you could simply adopt the standard schizo method of posting the encrypted solution and withholding the key until the problem has been solved.

>>12334671
He can't solve that.

>>12334629
Approximately [math]x^\frac{3}{2}/\frac{3}{2}[/math]

>>12334690
Learn LaTeX.

>>12334690
Using ^ normally just gets the next character, i.e. [math]2^10[/math] (right click on it and select Show Math as Tex Commands to see what I mean), hence you need to get put braces, as in [math]2^{10}[/math].

>>12334648
>Now, you have put me in an interesting dilemma. If you worked on that problem yourself until you solved it by yourself, it would most definitely be a valuable learning experience. If I gave you the answer, I would deprive you of valuable wisdom that you cannot get in any other way. However, I cannot prove that I can solve it myself without giving you the answer. So really, the only way I can get out of this without looking like a dumbass and without doing irreversible damage to your mathematics career is to insult you and shame you out of this thread. I'm sorry, but you leave me no other choice.

What kind of fucking baby question is that? Maybe you should ask for help on Reddit. Cuck.

I'm incredibly sorry that you had to make me do that.

>>12334792
Hooo sugooi ne, domo arigatou

All right, I'm on a dilemma here, next semester Geometry I and Analysis I will be at the same hour, which one do you guys think I should get? I was supposed to do Geometry I a long time ago, but I kept postponing it.

>>12334829
what the fuck is "geometry 1" supposed to be?
on that basis, i think you should get analysis 1

>>12334833
It's Proof-Based Euclidean Geometry. Geometry II is Non-Euclidean Geometry.

>>12334855
Like real euclidean geometry? Like can we draw ______ with just a ruler and a compass? If yes, it's completely useless, take literally anything else. Analysis is v important

>>12334870
I know it's useless and boring, but it's mandatory in my shitty uni, I was supposed to have done it a long time ago and now I'll have to do it with the freshmen, God it'll be embarrassing, all my friends already did that shit except for me.

>>12334882
Oh god that's fucked up, I'm so sorry for you

>>12334882
>>12334901
>disliking euclidean geometry
That's gonna be an immense yikes from me, reconsider having such garbage opinions.

It is true that the space of all bounded real sequences is a Banach space with the sup norm. What is an example of a Cauchy sequence in the space of all real sequences that is not convergent under the sup norm?

>>12334882
>>12334855
>>12334829
euclidean geometry is absolutely useless from the perspective of any other field of math, but at least it's aesthetic
can u elaborate what are the contents of "analysis 1"?

>>12334935
the problem with "all real sequences with sup norm" is that the norm of unbounded sequence would be +infinity and we don't want that

>>12334955
>bounded real sequences
>unbounded sequence

>>12334855
is this highschool or university?

APPROACHING BUMP LIMIT

>>12334941
It's Real Analysis, I think it covers all of Tao's first volume and a little of the second one.

INCOMING BUMP LIMIT

>>12334958
Uni

>>12334967
>>12334962
This isnt /ptg/ on /pol/ fucktards. Thats not how this works

>>12334967
Calm down lad, you've already made the new thread.

>>12334829
Analysis for sure. Much better course

>>12334684
Yes he can. You just have to believe in him

>>12334971
yikes

>>12334973
i didnt make the new bread. but very well

>>12334984
Here it is, someone made it anon was right
>>12334965
>>12334965
>>12334965
>>12334965
>>12334965

>>12334798
Kill yourself.

>>12334870
how can one be so soulless?

>>12335117
Bro I don't care if we can "construct" a thing, I just wanna know if it exists algebraically. Can we trisect an angle? Yes

>>12335139
1