/sci/ - Science & Math

>>10119075
maths

>>10119075
maths

>>10119075
maths

>>10119075
MATHS

math

yes, i also enjoy 9gags

MathematicS <---------
It's maths

Which unsolved math problem do you want to see solved in your lifetime? For me, it’s the formulation of self-avoiding walk function.

>>10119112
whichever i want to solve for my phd research, specifically solved by me

>>10119110
>he doesn't write mathematica in latin

>>10119119
matha

>>10119125
You learn quick.

>>10119119
>mathematica
>not mathematika

>>10119119
Reminder that if you do this you have to pronounce the 'th' as a lightly aspirated 't', not as /þ/.

>>10119110
One usually abbreviates the end of a word rather than the middle of it. If you take out the middle it's usually a contraction.
>math
>math's

>>10119112
The Collatz conjecture.
https://en.wikipedia.org/wiki/Collatz_conjecture

It seems so true, but no one can figure out how to prove it

>>10119322
>Yeah bro I study 'matics, it's good shit

Would any of you people be interested in a minicourse about one of the following?
1) analysis (= measure theory and integration for the babies)
2) algebra (slow paced commutative algebra or field theory or model theory with applications to them)
3) geometry (classical algebraic geometry with few examples or complex geometry)
Seeing the CA thread ending I realized that many might not be willing to leave 4chan to open a book, maybe writing the theory here and leaving a small amount of exercises would be profitable to the laziest ones (and I'm going to rewrite those notes anyway).

>>10119110
You don't shorten fabulous to fabs you shorten it to fab.

5 weeks into my PhD and I just... don't get it.... it's way way harder than anything I've ever done. I got nearly 100% on all my masters modules. Why is this so difficult for me? What should I do?

>>10119477
We need more detail. Did you stay at the same school between masters and Ph.d? What are you researching? What is the exact topic?

>>10119484
Switched schools, researching number theory, exact topic is modular forms.

>>10119471
My analysis is weak as fuck so I'd be up for that

>>10119486
>Switched schools,
That is normal then. Just toughen up and keep at it. 1 month is not enough to start worrying. Usually they give you up to a year to find yourself.

>>10119486
>modular forms
Nice

>>10119477
Prepare to have your ass raped for the next six years.

In general do you guys read through all the examples in a text? I'm going through Dummit and Foote and there are loads of them. I want to skip them to save time, but at the same time I have this ominous feeling of guilt when I do.

>>10119680
If you're reading literally everything in Dummit and Foote you're going to be there a long time

>https://en.wikipedia.org/wiki/Dominated_convergence_theorem
so fucking based

>>10119471
I would follow along if you did model theory or complex geometry
The other things I already know to a level I'm happy with

>>10119112
I think a solution of the inverse galois problem would be pretty cool, especially if the answer is that there is some freaky counterexample
Also it's not exactly a "problem", but I am interested to see if geometric complexity theory ends up actually being good for anything serious or if turns out to just be a meme

and obviously specific things I work on but I'm not too hot on doxxing myself down to a pool of <5 people by posting them

>>10119112
I want to see a solution to Martin's Conjecture, in particular a negative solution, so that Turing equivalence is a universal countable Borel equivalence relation. There is a stronger conjecture that would imply this. If E,F are Borel equivalence relation and E is a universal countable equivalence relation and F is finer than E, then F is universal. Since arithmetic equivalence is universal countable this would immediately imply that Turing equivalence is universal countable.

>>10119112
I want to see Wildberger be taken seriously.

>>10119488
>>10120022
So I will give a run of real analysis and model theory in a few days.

>>10119680
Examples are probably the worst thing you could skip. They don't take that much time to read and they're honestly more instructive than the theoretical text most of the time. If you need to move faster, work out all the examples by hand without reading the book and then cut out time spent on exercises instead. Dummit and Foote is well-written enough that almost every important case has an example, so you're not missing much critical stuff this way.

>>10119680
Examples and theorems are how you pass exams anon. Pick one easy and one difficult exercise, and then you’re done. If you can’t apply general concepts no amount of rote learning will save you.

>>10119112
Whatever you crazy fuckers are working on. I'd love to say that I met the guy who solved X on a mongolian tennis polo shirt weaving forum.

>>10119486
what is the relevance of modular forms? Im also doing NT but more alg-geometry stuff and my adviser doesnt do modular forms at all, but it seems everyone else in my department does and im too scared to ask

>>10119471
I'd be more interested in field theory or classical AG/CG, but of course, everyone's different.

>>10120177
The only problem that I have with examples is that most of them don't tell you what theyre going to prove, they just take you "on a journey" and conclude the result at the end, but most of the time there's no way to understand what they're concluding unless you read all of it.

Hence it's hard to work out the examples before the author gives you the solution.

>>10119075
I'd love to see that book anyways

>>10119471
I'm doing all of this this winter break. I'm in 3 classes right now with lots of exams, so I gotta wait

>>10120319
Fuck I meant >>10120157

I'm a brainlet. Anyone got a good resource talking about uncorrelated random variables with non independent distributions?

>>10120329
yeah just study my girlfriend

>>10120345
I was studying her when you were at class if you get what I mean

>>10120355
i don't actually could you please elaborate?

>>10120329
>>/an/hero

>>10120329

>>10120444
>farming: local fields
kek

>>10120444
none of those look like dedicated probability books?

>>10120444
Hey I have one of the books right beside me

>>10120589
y_0 buy bollobas?

Undergrad whose graduating soon, I'm filled with immense angst over the choice of going to grad school and aiming for a PhD or not, send help.

>>10120555
https://www.youtube.com/watch?v=HNbMRAsJ9cw

>>10120605
Choosing to do a PhD isn't necessarily an easy decision but I think it's a pretty simple one. You're signing up for 4-6 years at a job where everything about it sucks except for the fact that you get to do math all day.
If you're one of the people for whom that's a good trade, then go for it, you'll do well. Otherwise run for the hills.

>>10120617
BASED.

>>10120186
>guy

>>10119112
Cobordism/tangle hypothesis and Witten conjecture. Just for fun I'll throw in the 5/2 Quantum Hall state.

>>10119680
>>10119680
>read through whole chapter, skipping examples and basically just let the book tell me the conclusions
>then return to the start and take a thorough dig
>then to problems

>>10120605
same except trying to decide between masters and then PhD, or straight to PhD

>>10119471
2 or 3

>>10120744
Ugh why isn't that picture Maribel and Renko.

>>10120057
Would F = equality be a counterexample to the strong claim?

>>10120625
Yeah I don't know if I love math that much. But at the same time leaving math feels like losing a part of myself.

>>10121883
No. Equality is not a universal countable Borel equivalence relation. By Harrington-Kechris-Louveau theorem = is strictly less than complex, in terms of Borel reducibility, than the finite difference equivalence relation. The finite difference relation is amendable and a universal countable Borel equivalence relation cannot be.

>>10120744
>Cobordism/tangle hypothesis and Witten conjecture.
I thought Lurie and Kontsevich respectively solved those problems a while back?
>>10119112
I want to see the full Langlands program finished, the geometric variant as well.

>>10121883
>>10122094
I'm retarded, I misread the question. You still require all classes be countably infinite.

How does it feel to work on problems that takes weeks (or even months) to solve? When one starts to get exposed to these kinds of problems?

>>10122309
Pretty sure it depends on the field.
Most mathematicians look through previous similar results and attempts and try to build up to a proper proof by solving partial cases. Working on a single problem for that long is hard, so you do it by bits.
Number theorists probably go study something completely unrelated in hopes of finding a coincidence.

>>10122309
fun as long as you have initial ideas to explore
after that, less and less productive and pleasant

>>10122309
It's actually not as bad as people have told me it is. I spent months on a problem that I broke up into more manageable pieces. Sure, it didn't feel great not being able to move past a particular step, but over time you make progress and it's pretty vindicating to see it all complete. The real fun comes from exploring the problem and looking it at from different angles, the boring part is typing it up and putting it in a publishable form.

>>10121884
>But at the same time leaving math feels like losing a part of myself.
That's how they get you

I'm starting my master's in applied math at the moment, and I'm having a hard time deciding whether to go into the financial, or the more physical(diffeq, some physics, etc) branch.
Any advice? Any experience with what sort of work either lands itself to?
If I'm being honest, I don't have a very good idea what sort of employment applied mathematicians can expect.

>>10122705
What is one to do?

>>10120444
>farming: sheaf theory into local fields
>autism: cat theory
my sides. this diagram is so good

What are good intros to graphs and trees? I'm good with abstract algebra basics.

>>10122904
>graphs
See:
>>10120589

>>10120036
What's some conjecture that has been actually refuted thanks to a freaky counterexample?

>>10122912
Euler conjecture.

>>10122906
I don't trust the meme chart. And what about trees? There was a creative writing excercise on /lit/ that asked you to describe a tree first without using the word 'tree' or synonyms, and then progressively removing all tree-related words—I want to publish a paper about it.

>>10122904
trees by serre

>>10122922
Springer's "Graduate Texts in Mathematics" is a meme here because it's actually good.
>trees
First worry about graphs.

>>10119112
Constructive formulation of univalence axiom.

>>10122927
can't be done

>>10122914
Woa that's some freaky integers all right. I also find it amusing when in pure-math theorems integers greater than 5 appear. Like that Riemann-surfaces one saying that if some ramification index is greater than 2, then it is greater or equal that 2+(1/42). I also recall a 1328 in a theorem about elliptic curves.

>>10122926
Ok.

>First worry about graphs.
Hai! MariKon-sama-sensei!

>>10122924
Thank you as well.

>>10122930
cubical type theory

>>10121884
Same here. I guess I'll just study mathses in my free free time (meaning free time I'm not already using for something else).

>>10122937
>he doesn't comment on the fact they just told a computer to test random integers until it finds a counterexample and the fucking thing actually did
Beautiful stuff.

>>10122926
>is a meme here because it's actually good

>>10122957
Beauty is difficult. The plain ground precedes the colours.

>>10120063
I'm unable to see why he spits so much on set theory and then he says functions are not real things because he thinks they're vaguely defined as "rules" that "associate" "things" to other "things".

>>10122912
Hilbert 3rd problem. I was surprised when I read this for the first time, and still am.

>>10122960
That pic is what I see in the darkness when I experience sleep paralysis

>>10123027
Sleep paralysis used to me traumatic but then one night it started feeling comfy and it started to arouse me. I no longer fight it.

/wsr/ cant do math
I posted the pic in /wsr/ and now im drowning is anxiety that I'm gonna get a zero for this project.

why can't /wsr/ and I do differential equations?

>>10123027
>>10123031
>>>/x/

>>10123065
what exactly are you not getting?

>>10123070
What? Sleep paralysis is not supernatual.

>>10123071
I have initial values and need to solve for r
and I just don't see what method to use for solving it.

>>10123071
>>>/wsr/587050
heres the thread if you want the entire problem

>If [math]H\subseteq G[/math] and [math]K\subseteq G[/math] are subgroups with [math]HK=KH[/math] show that [math]HK=\left< H\cup K \right> [/math].
What the heck is does this notation: [math]\left<H\cup K\right>[/math] mean here? I know for an element, [math]\left<g\right> = \{ g^{k} : k\in\mathbb{Z} \} [/math] but what does it mean for sets?

>>10123101
Anything that can be written as combination of elements of the set

>>10123101
The group generated by the elements in that set

>>10123065
https://en.wikipedia.org/wiki/Separation_of_variables

>>10123143
>https://en.wikipedia.org/wiki/Separation_of_variables
already tried that, curious to see how you would manage that. maybe you know something I don't

>>10123163
see example 2 and 3 https://www.math24.net/linear-differential-equations-first-order/

you have a nonhomogeneous ode, the wiki page covers it but with no example. check this link instead

Brainlet here, help. Solve 32.
Isn't there a problem because x could be 0? So the number could be either a positive (if x is any other number not 0) or negative (if x is zero)

>>10123215
Consider this rule

>>10123215
|-x^2-1| = |-1||x^2+1| = |x^2+1| = x^2+1 (since x^2+1 is always positive), assuming x is real

>>10123224
Can someone confirm this?
I'm doubting if
>|-x^2-1| = |-1||x^2+1

>>10123230
it's just |(-1)(x^2+1)| and the rule |ab|=|a||b|

>>10122912
https://en.wikipedia.org/wiki/Conway_base_13_function

>>10119471
Algebra for me. Even though I already took this class. Would maybe like to see some AG/CG

>>10123239
Seems about right. Thanks my man

>>10123106
how do I prove this by the way

>>10123065
first one is a bernoulli differential equation
the second one is obvious

>>10123255
One of the inclusions is obvious, the other you can prove by iteratively invoking the subgroup properties on a generic element

>>10120147
do complex analysis/geometry at some point. i would be interested in joining. i like the idea

>>10123101
>>10123101
the forward inclusion [math]HK\subset \langle H\cup K\rangle[/math] is obvious, since any element of the former is a product hk which is clearly inside the latter group.

The backward inclusion is proved as such: let [math]g\in\langle H\cup K\rangle[/math]. Then [math]g[/math] can be written as a finite product of elements in [math]H[/math] and [math]K[/math], all jumbled up. Something like [math]g=h_1k_1h_2h_3k_1h_4k_2[/math]. You get the point. Then by assumption, [math]HK=KH[/math], so any pair of elements in the form [math]kh[/math] can be written as [math]h'k'[/math] for some other random elements. Using this successively, since there are only finitely many steps, you will arrive to an element in form [math]g=hk[/math]. So [math]g\in HK[/math]

>>10123173
it's not linear, so that doesnt work
>>10123143
you can't separate it
>>10123065
you cant solve it using regular methods. are you sure you're not meant tot solve it numerically?

>>10122129
Ah I see. Figured that couldn't be an actual counterexample, way too trivial, so thought I misunderstood the conjecture. Glad to see another logicbro here

>>10123277
Thanks for fucking over my front page formatting on mobile, cunt

>>10123381
niger

>>10120186
This already happened
>https://science.slashdot.org/story/18/11/06/1114219/mystery-math-whiz-and-novelist-advance-permutation-problem

>>10123391
Why the blackphobia?

>>10119075
I really wish I could learn to love math like you guys.. as an undergrad who finds math very boring how can I find to enjoy math more and what doors does having a strong math foundation open?

>>10123498
stop the niggering the nigger general with your pointless niggery

>>10123290
>you can't separate it
that's where you're wrong kiddo, just watch
spent about 20 minutes doing this before i realized you most certainly could fucking do that

>>10123065
[math]\displaystyle \frac{dv}{dt}=g-\frac{r}{m}v^2\\ \int\frac {1}{g-\frac{r}{m}v^2} \frac{dv}{dt} dt = t+c[/math]
case where [math]g-\frac{r}{m}v^2=0, v=\pm\sqrt{\frac{mg}{r}}[/math] is a solution, this ends up being an asymptote
since r is assumed to be positive (the negative sign implies this), we should use hyperbolic trig sub instead of trig sub, although it would work either way, it would just require care to be taken when dealing with each square root
[math]v=\sqrt{\frac{mg}{r}}\tanh{(u)},\ dv=\sqrt{\frac{mg}{r}}sech^2(u)du,\ t+c=\frac{1}{g}\int \frac{sech^2(u)}{1-\tanh{^2(u)}}du = \frac{1}{g}\sqrt{\frac{mg}{r}}u=\sqrt{\frac{m}{rg}}u=\sqrt{\frac{m}{rg}}arctanh{(v\sqrt{\frac{r}{mg}})}[/math]
[math]v=\sqrt{\frac{mg}{r}}\tanh{((t+c)\sqrt{\frac{rg}{m}})}+v_0[/math]
c is really just t0, the time offset

>>10123381
>>10123391
>>10123498
>>10123538
>>>/pol/
>>>/b/

>>10119112
-Caclulation of percolation values
-Jacobian conjecture
-F1 proof of Riemann Hypothesis
-Calculation of mass ratios of elementary particles from first principles
-Explanation of why the sporadic groups are what they are, short proof of CFSG

>>10122912
Weierstrass function

>>10122945
So, isn't it already done?

>>10124129
maybe, idk what >>10122927 meant by constructive formulation
afaik (i'm nowhere near HoTT for quite some time), there used to be some issues with creating a fully constructive model of CuTT so in this sense, constructive UA might still be an open problem

I hate inequalities

Free course on Galois theory, starting today (although all episodes have already been filmed)

https://www.coursera.org/learn/galois

>>10122912
People have suspected the four dimensional (smooth) poincare conjecture is false, so whatever counter example that is, it's gonna be one bad mama jama, same with all fake spheres. Another suspicion is that the Navier-Stokes millennium problem is actually false, this is because the higher dimensional analogue of this conjecture is actually false, a related problem with the Euler equations, under the name the Onsager's conjecture, is false, and Tao constructed a counterexample for a closely related set of equations, the so-called averaged Navier-Stokes equations. Special mention goes to Cantor's leaky tent
https://en.wikipedia.org/wiki/Knaster%E2%80%93Kuratowski_fan
A topological space that is connected, totally path-disconnected, and if you remove a single point it becomes a totally disconnected space.

>>10124124
>-F1 proof of Riemann Hypothesis
>-Calculation of mass ratios of elementary particles from first principles
Didn't know Connes and Atiyah posted here
>-Explanation of why the sporadic groups are what they are, short proof of CFSG
Let's be honest, if such a thing exists it's very far off.

>>10124264
>Onsager's conjecture, is false
I made a gaff, the conjecture isn't false, it was recently proved true, but part of the conjecture requires constructing really nasty solutions that make the Euler equations spit out nonsense, the kind of thing you would want to disprove the Navier-Stokes problem.

>>10119477
it happened to me too anon. i was depressed the first 4 months of my phd, posting on /sci/ asking for help and if i should just an hero. it gets better, anon. keep trying hard everyday even though it feels like nothing changes and you're not making any progress. ask your advisor questions and tell them honestly when you don't get it. hopefully it will improve, it will seem like it will never improve but it does eventually somehow. plz stay strong

>>10124124
>-Explanation of why the sporadic groups are what they are
this would be nice because they make less and less sense the more you think about them

>>10119471
Complex Geometry would be coolest. The book by Huybrechts would be awesome to work through

Love coming here in my wagecuck break hours and pretend I'm not dumb :)

>>10119112
Navier-Stokes existence and smoothness, and the Riemann zeta hypothesis. Both have concrete implications that are worth determining.

>>10119112
ergodic hypothesis

>>10123241
Neat

>>10124267

>Didn't know Connes and Atiyah posted here
:^)

>Let's be honest, if such a thing exists it's very far off.

From what I read incidence geometries / buildings have given some insight into the sporadic groups. But as for a short proof, yeah maybe.

>>10124413
...and moonshine as well

>>10124267
People who post here:
Hilbert's literal ghost.
Atiyah.
God.
The King of Norway when he wants to know who deserves the Abel.
Me.
Witten.
Langann.
The entire string theory community.
Bogdanovs.
Yukari Yakumo.
Nitori Kawashiro.
Ted Kaczinsky.
Slavoj Zizek.
Perelman (rare).

>>10124553
>forgetting the mochizuki shill Fesenko

>>10124553
Zizek was banned after he kept spamming his attempt at formalizing ideology in terms of ZFC and responding to any criticism by saying that it was absurd and modernist to expect him to prove his own theorems

Is there some book or resource for quick revision of undergrad math? I need to remember all that I learned five years ago in the span of a couple of months.

>>10124616
Lang's basic mathematics.

Is there an easier way to integrate this ? We did not learn any reduction formula trick at uni so maybe there is an easier way ?
Also i start to feel that university is a fucking meme (EU), the teachers are fucking bad and I don't like studying at uni, I have much more motivation working alone with a book. What should I do ? Start learning at home and just go to exams ? It's pretty much impossible to miss many hours at my uni so I might switch to a special university for that ?

>>10124719
reduction formulas are just black magic tricks to solve general case formulas

just do x=tan(u) dx=sec^2(u)du and you get integral of cos^2(u) du, which you should know how to solve

>>10124719
subsitute x = tan(u)

>>10124719
[math]\int da/a^2=\int 2dx/a^2 =1/2 \int dx/a^2=\int da/b =\int 2dx/b=1/2\int dx/b =
2ln(b)=2ln[(x^2+1)^2[/math]

>>10124739
okay this is epic

>>10124731
>>10124732
>>10124739
Thank you anons !

Sorry if this is kind of off-topic.
I'm interested in particle cosmology and related fields (mainly QFT and ST). I know those subjects don't really belong to math, but apparently they require a very deep understanding of mathematics.
Would it be better to major in math and take some physics classes, or is general physical knowledge more important at the undergrad level?

>>10124764
why do you frenchies space out your punctuation like that
it looks just as bad as if i did this .

Are you supposed to breeze through undergrad coursework if you're aiming for a PhD?
I'm not a bad student at all, but I find some courses difficult, and I often have trouble understanding some concepts and have to take time to visualise them and so on. Am I going to get raped in grad school?

>>10124792
>Are you supposed to breeze through undergrad coursework if you're aiming for a PhD?
not necessarily, unless you are aiming to go to Princeton
>Am I going to get raped in grad school?
Probably. Most people get steamrolled by the workload for the first few months. Then you adjust.

As long as you can get As out of your upper-level courses by putting in whatever amount of work is necessary you can pass a grad class.

>>10124799
I'd like to go to a good university, but I'm in Europe, so it won't be Princeton.
>As long as you can get As
There are a couple subjects I'm just mediocre at, like number theory, but overall when I work hard I get good grades. I thought that simply being good without being very talented wasn't enough for graduate studies.

>>10124809

brainlet here

how can you have different proficiencies at areas of math? I thought you were just either good at everything or bad at everything

>>10124818
I don't know what to tell you. I'm good at real and complex analysis and abstract algebra, but number theory eludes me, as do some other things.
Different areas of math require different kinds of reasoning, probably.

>>10124771
>Would it be better to major in math and take some physics classes, or is general physical knowledge more important at the undergrad level?
I would double major math and physics or at least do a minor in physics. If you do want to do more theoretical stuff you will have to learn more math but it's not uncommon or you to learn the relevant material in grad school. There's a math methods grad course at my uni that goes into some more advanced mathematics relevant to physics. You won't gain a deep understanding of the mathematical fields themselves but you will understand how they're used. Above that it is very important that you have a solid understanding of physics (hence why you should get a degree in physics) since even if you are good at math that doesn't necessarily imply that you'll be able to understand the physical implications of what you're doing. Standard math for a physics student is Calc 1-3, linear algebra, ODE, PDE, complex analysis, probability, some group theory. Going off from that in grad school or maybe an undergraduate class you'll learn more about differential geometer, general/differential topology, and some functional analysis. This isn't enough to get you to the forefront mathematically though, it will take you quite far though. Again, it's more important to get a solid foundation in physics and mathematics instead of rushing into advanced material without a good understand of what you're doing. I would ask the grad students at your school or maybe some professors what the best classes at that school would be best to take to achieve your goals.
>>10124792
One thing I found useful in undergrad was to work as a TA for calculus. A lot of the times it seems that thing that really fucks over grad students is the act that their workload increases dramatically very quickly and they don't have time to adjust. If you have some experience with TA work prior, and maybe have taken a grad course or two, you'll be in good shape.

>the set of finite Cauchy-sequences has different cardinality from the set of limits of Cauchy-sequences in spite of the fact a limit only depends on the finite elements of the sequences
This is why people are finitists.

guys eurofag here wanting to do applied maths in usa, since i want to work in private sector consulting but not regarding banks/economics but rather industrial/biomedicinal stuff (which is scarce in europe)

what good american masters (applied maths) should i look at¿?

>>10124825
A double major would be good, but if I can't do that, wouldn't a physics major + math minor be better than the opposite?
I'm definitely going to ask students and faculty what they recommend.

>>10124818
You'll find that the types of problems, ways of thinking, and proof techniques can vary wildly from field to field. Hell, they can vary wildly in a single field. Part of this is because each field has different goals. If you want to understand how a surface will distort under some process then of course you'll use different methods that those used to count the number of colored nodes of a graph. Some people are good at using some tools and some aren't.
>>10124809
>I thought that simply being good without being very talented wasn't enough for graduate studies.
Terry Tao almost failed his qualifiers and his thesis was good, but nothing amazing imo. Stephan Smale was almost kicked out of his graduate program until he studied as hard as he could to pass. Not everyone comes into grad school at their mathematical peak, far from it. The point is to hunker down and study your ass off. Trust me bro, if Piper can get a PhD, then so can you.

>>10124839
>wouldn't a physics major + math minor be better than the opposite?
I fucked up, I meant to say physics major + math minor. If you want, I can try finding some sources on math methods to help you out.

>>10124771
If you specifically want to do physics, study physics. Mathematics is a tool used by physicists, more often than not in ways that are far removed from what mathematicians would do.
It's like the old analogy that you don't need intensive study of combustion engines to drive a car.

>>10124825
I'm not too worried about the workload itself because I can adapt fairly well, I'm worried about the difficulty.
>>10124840
Thanks for the motivation. Does that mean there's no definite indicator at the undergrad level of how well you'll fare in grad school?

>>10124843
I want to do physics, and I'm already dead-set on the branch I'd like to focus on. I asked that question because all renowned particle physicists seem to do more than just dabble in pure math.

>>10124842
>I can try finding some sources on math methods to help you out
I'd appreciate that. I have a few books but more resources are always welcome

Anyone familiar with TeX? I need to generate pictures out of a document, and I want them trimmed with a border of some fixed length (say 1in). I tried to use the standalone document class with preview option(and border=1in), but it deletes all the spaces before and after environments sucj as itemize, which is ugly. Do you know how to do what I want to? Even using external (linux) tools is fine, but I would very much like to avoid having to trim them cutting a picture out of the screen.

>>10124846
>Does that mean there's no definite indicator at the undergrad level of how well you'll fare in grad school?
Unfortunately, basically yes.
The coursework/quals part of graduate school does not require or select for a lot of talent. It's gruntwork, only difficult because of the quantity of things you have to learn and the rate you have to learn them at.
The actual point of grad school is to get you doing research and there's really no good indicator at all of whether you will suck at that or not until you do it. Talent for research is a very different talent than the ability to learn fast. It's correlated, but not very heavily.

>see a complicated formula that requires the use of some obscure lemma
>have to spend some time understanding it, then look up what I have to use to solve it
>prof glances at it
>he immediately figures it out and nonchalantly pulls the lemma out of his ass even though it's not even relevant to the class he's currently teaching

>>10124846
>I'm worried about the difficulty.
Try taking or sitting in on a grad course before you enter grad school to gauge the difficulty. Honestly at times I found grad courses easier than undergrad, if that makes sense. When I took a few special topics courses there were no problem set, no grades, you just came to learn. For the lower level grad courses, I would try and find out what book you are going to use a few months ahead of time and get a head start so you don't get overwhelmed. I usually use the summer and winter breaks to prep for the coming semester. As long as you diligently study, I don't think you'll have many problems. Also understand that it's not uncommon or students to help each other in grad school, sometimes it's encouraged, so don't be afraid to rely on others some times to help you understand some material or get some advice.
>Does that mean there's no definite indicator at the undergrad level of how well you'll fare in grad school?
For the most part, no. Sure, if you have a good work ethic, are fairly talented, and had a good education you're likely to succeed, but that'd basically true for most things in life. But as for a definite checklist of what is both necessary and sufficient for doing well in grad school, such a thing doesn't really exist. People grow immensely in grad school, and at the end of the day it boils down to how much you're willing to work for it. If you're willing to work for it you should be able to get past your prelims. After that it's research time and frankly, that's a whole different ball game. Doing well in coursework =/= doing well in research. All the problems you solve in your grad classes are ones that have already been solved and are hand chosen so that they can be solvable in a reasonable amount of time without any groundbreaking insights or requiring 200 pages of work. When doing research, however, there is no indication that the problem you are trying to tackle is even solvable at all.

M A T H G U Y
A
T
H
G
U
Y

>>10124888
it's Nuny, a/k/a Nunu Bunkenshterner

>>10124888
What formula?

did anyone ITT started learning at their 20s? feels like everyone who's good at something began learning really early and always had a good work ethic

Reminder that the "complex numbers" are really just a subalgebra of the 2x2 matrix algebra over the reals and that "complex analysis" is just matrix calculus

>>10124926
Oh I have a terrible work ethic trust me, I don't know how I'm still in school I do literally no work on the average day

>>10124926
I already had some exposure to college math but I recently just started a math degree even though it's been five years since I graduated high school.
Does this weigh into graduate admissions?

I'm doing Analysis I, and I find that I face a problem (as I did in previous calculus modules) where I solve problems solely by examples, and that I lack mathematical intuition so I struggle with any question that requires the slightest bit of thinking. How do I overcome this?

>>10124963
I'm pretty sure it's literally impossible for a person to have no natutral problem solving skill in every single field of maths.
So try taking a geometry textbook and going through some of the problems, and if that doesn't work try algebra, and if that doesn't work try number theory, and if that doesn't work try fucking physics, then finally build a capacity to solve problems there until you can come back to Analysis.

>>10124963
I have the same problem with arithmetic. I think it just comes down to practice.
I'm good at analysis and I suspect it's because I did a metric shitton of exercises and eventually the process just burned itself into my mind, and now I manipulate the relevant mathematical tools easily and intuitively due to being so acquainted with them.

>>10124975
I think this will work. I think a large part of it was having an awful foundation in mathematics.

>>10124979
I have heard that practice is the best way to become a good mathematician, but I want to be able to solve problems by figuring them out from theorems, not by just 'getting used to it'. Maybe it's a matter of me being impatient and lacking the discipline to take my time and think properly. But how would I go about that?

>>10124996
>an awful foundation in mathematics
You don't need to know everything by heart. I don't, and whenever I need something I just do exercises so that I eventually memorize it (and the method). Might not be great advice since I often notice there are theorems and definitions that I forget and it's my main issue during exams.
> I want to be able to solve problems by figuring them out from theorems
You mean having a good enough understanding that, when faced with a problem, you immediately know how to solve it? I'm pretty sure that comes with practice.

>>10125005
I suppose you're right. There is a reason why everybody says that practice makes a good mathematician, and I don't do it enough, clearly.
Anyhow, many thanks to you and the other anon for your guidance!

>>10119075
Am I fucked? I’m so bad at math it isn’t even funny. I’ve taken both semesters of college organic (now taking biochem with no trouble) but I’ve failed PreCalc 3 times and it’s looking like a fourth. Im not a complete brainlet I just can’t into math.

>>10125033
>Im not a complete brainlet
>I've failed PreCalc 3 times and it's looking like a fourth.
Anon...

>>10125033
I used to be garbage at math (talking about consistently getting less than 30% on high school tests) due to a perceived lack of interest + lack of work ethic + immaturity. Now I'm a math major and I'm doing quite well.
Depending on what you're struggling with, and the amount of work you put in, the answer will be different, but if you failed calculus thrice it obviously means you don't understand the fundamental principles on which it relies.
I used to have a mediocre understanding of calc and I found that doing some newtonian mechanics helped me understand what exactly it represented.
What's a derivative, how do you express it with a limit, what's a limit in the first place, why can you derive a function to study its behavior, etc. Make sure you completely, fully understand those things. Don't learn them buy heart, just take the time to picture what those concepts represent and how they interact with each other.
The next step is doing a lot of exercises to apply your theoretical understanding of the subject.
But really, what fucked me over so many times in math was that I thought I understood a subject, when in fact, my understanding was vague at best. You might be in the same situation.

>>10125045
>I am now reminded that Zyzz is dead
Thanks anon

I thought I liked doing proofs and pure math but this real analysis class is kicking my ass. Most the questions in the book need me to construct a weird ass function or epsilon for triangle inequality, and I'm wondering if I'm just not smart enough to think of solutions to proofs. Should I just give up pure math?

>>10125102
wait I realized someone asked the exact same fucking question. guess i better start grinding

Complex analysis is kicking my ass, how do I salvage this?

>>10124771
wtf is ST

How do any other undergrads deal with their nonmath courses?
I just don't care about them, and I know that's a childish way to think since I need a good gpa and have a few papers I haven't even started, but fuck if it's not math I might as well be watching paint dry.
>inb4 autist

>>10125201
>complex analysis is hard
I don't even remember that stuff anymore, mind hitting me up with a problem?

>>10125239
string theory

>>10125245
stop being a boring stem autist and become a well rounded scholar

>>10124931
>Reminder that the "complex numbers" are really just a subalgebra of the 2x2 matrix algebra over the reals and that "complex analysis" is just matrix calculus

Sort of. They are geometric transformations.

>>10125033
get a tutor asap

>>10125102
nah, that's just analysis. algebra proofs are much less retarded.

>>10125033
>ive taken two semesters of orgo
>i failed precalc 3 times
>i am not a brainlet
How did they let you even take chem, much less orgo without precalc finished? What do you struggle with in precalc? You are aware you definitely are a brainlet, yes?

>>10125033
wtf is your precalc? Mine, as far as I remember, was just basic trigonometry, some random algebraic shit like partial fractions, and basic integration / differentiation.

exam on friday. mostly introductory group theory. how best to study? there's so much material

>>10125400
Relax you have like three theorems you need to know, first isomorphism, lagrange, correspondence. That or be more specific with what you've covered.

>>10124828
>a limit only depends on the finite elements of the sequences
What?

>>10125245
>nonmath courses
Don't take any

>>10119112
The elliptic curve discrete logarithm problem, obviously.

Requesting more pictures of anime girls with math books

>>10125245
>How do any other undergrads deal with their nonmath courses?
Why would you take nonmath courses?

>>10125503
Because liberal arts

>>10125503
Because you're not a robot

>>10125527
>Because liberal arts
Why would you take them?

>>10125538
the greatest mathematicians that ever lived did not purely focus on math 100% of the time.

>>10125562
You're taking liberal arts courses because you want to be like yuler?

>>10125568
what do you mean by "liberal arts". don't tell me you just got off /pol/ and think all humanities classes are SJW garbage.

>>10125568
If you can't appreciate things other than math you're a brainlet, I'm sorry. Universities have strayed far from this path in recent years I will admit, and there are, particularly in America, financial reasons to dislike classes outside of your major, but fundamentally a university education should allow you to grow as a person and educate yourself in all of the major human pursuits.

>>10125575
I wasn't the one who used the term "liberal arts", that was the anon here >>10125527
I don't browse /pol/ and would probably be described as an SJW by most of the people who do.

>>10125585
>If you can't appreciate things other than math you're a brainlet
Nice strawman. The suggestion that you can only appreciate something if you take it over a maths course at university is obviously ridiculous.
>fundamentally a university education should allow you to grow as a person and educate yourself in all of the major human pursuits
Keyword here being allow, not force.
Besides, the original anon doesn't seem to be appreciating their non-maths course, hence the question.

>>10125596
That anon is a brainlet or a hollow person

>>10125596

>fresh outta STEM at leet uni
>halfway illiterate

Kinda sad don't you think.

>>10124343
agreed. Mike Atiyah claims he has found a solution for Riemann though.

Is [math]\left< x,y \right> = H[/math] just short hand notation for saying that [math]H[/math] is generated by both of those elements separately or does it mean something else?

>>10125633
>Is [math]\left< x,y \right> = H[/math] just short hand notation for saying that [math]H[/math] is generated by both of those elements separately or does it mean something else?
https://en.wikipedia.org/wiki/Presentation_of_a_group

>>10125562
I imagine it was a lot easier to be a polymath in the olden days when there was less to learn in order to be at the forefront of a field.

I respect the intent though. I'm currently reading classics and trying to familiarize myself with the western canon. I'm also not even a math major but I study mathematics and physics to expand my knowledge.

>>10125635
is it just [math]\{x^{k}y^{k^{\prime}} :k,k^{\prime}\in\mathbb{Z}\} [/math] ?

>>10125608
Sure, if you decide to define brainlet in an open enough way so that you can call anything you disagree with brainletism.

>>10125622
I don't know about you anon but where I'm from you're expected to learn how to read in primary school.

>>10125649
No it's all words in x and y.

>>10125666
And their inverses I should say

>>10125664
Same where I'm from. You learn to read the Cat in the Hat, never pick up a fiction book again, and by the time you're done with your STEM program you're still at 3rd grade reading proficiency.

>>10125666
The devil is right.

>>10125649
You would be correct though if they commuted.

>>10125735
>His point only makes sense with hyperbole
This is embarrassing anon. No one is entering a maths degree at a 3rd grade reading proficiency. Personally I think maths courses actually teach reading comprehension and expository writing to substantial extent.
Even if that weren't the case it's not like you need to take LIT101 to read books. I'm reading picrelated at the moment for example. Miraculously I've never studied French at university and somehow read that at beyond 3rd grade standard too.

>>10125772
>Uses hyperbole to make his point

Is different from.

>His point only makes sense with hyperbole

As far as STEM goes math majors are the most intellectually inclined of course. I've met some shockingly poorly educated STEM students though; usually engis or pre-med students. They would benefit from being forced to read something imo.

>>10123239
that "rule" is a consequence of the definition brainlet

>>10125807
>>Uses hyperbole to make his point
>Is different from.
>>His point only makes sense with hyperbole
Yeah and I wrote the latter for a reason.

>They would benefit from being forced to read something imo.
I agree with this in theory. The ones who would benefit are the ones who are going to avoid engaging though (and have been doing so for all their schooling before university).

>>10124772
It's only done with multi-element marks, and for ease-of-reading.

>>10119112
P=NP

>>10125983
this but only if it's true

Man I love reading almost as much when its not a math textbook. Just finished "something happened", what is /mg/ reading?

>>10125485
you mean a lower bound for it? :)

>>10125633
It's generated by both of them. It's not a presentation.

>>10126279
C&P

>>10125772
>reading Beauvoir
Do you have literally nothing to do?

>>10126279
Bulgakov's Master i Margarita.

>>10119471
Could you paste it anywhere besides 4chan? Such that I can read it in some months again? Would be nice thx

>>10126400
My intent is to write it in latex (which is the real goal for me), and leave it in a git repo; moreover I want to crop it into small pieces of png format, so that you can follow on 4chan (if anyone wants, if not I will give up on that).
Contrary to what I said earlier I will start just with model theory, easy stuff like the most basic result to see what is the advantage of adding logic to algebra (for example it is enough to prove Nullstellensats over field with enough transcendence, which is easy as explained in [Eisenbud], or other basic results).
I said also real analysis but this is a bit of a pain right now because I'm not familiar with pgf, and there are a low of drawings to be made.

>>10125311
>>10125311
General topology up to Tietze extension and some metrization theorems, topological manifold theory and some measure theory was covered in precalc 1, precalc 2 follows from algebra 2, so we cover Galois theory and representation theory, and precalc 3 goes over algebraic topology and k theory.

Basically, one of the top profs here decided that there's no point wasting time over basic integrals and derivatives, so calc 1 starts with Riemannian manifolds so we need more precalc classes

>>10125400
Remember that you don't need to learn all the lemmas by heart. Just the theorems (which are few) and some computational propositions

>>10126447
kek

In picrelated, Down is apparently strictly dominated by Level. How come this is the case? Up has better payoffs than Down if Player 2 plays Left, but otherwise Down has better payoffs if Player 2 plays Right. How exactly does this work? Game theory is a bitch and I'm not sure I fully understand

>>10124553
>yukari yakumo
that's just a self insert toymaker faggot who wishes he was a little girl

>>10126447
Bullshit.

In picrelated, Down is strictly dominated by Level for Player 1. In the answers, Down is taken out after this but why is it the case? Player 1 has better payoffs for Down compared to Up if Player 2 chooses Right. How come Down is eliminated right off the bat?

hhelp me /mg/... whenever i read these books on intro proofs or pure logic, my mind starts falling asleep. it is only when i survive up to the actual questions do i come back awake again. it is frustrating trying to read all of this. should i change my strat?

>>10126563
seriously though, does anyone have the same experience? im also going to start trying to unironically sleep at 9pm and see if that helps

>>10126563
>>10126565
I experience that too. I always need a mug of coffee before I start or else I'll fall asleep in the first 20 minutes and wake up 2 hours later drooling on my desk. I really need to get better sleep, only 6 hours isn't enough.

>>10126502
>compared to up
If player two chooses Right, Player 1 is better off choosing Level, so why would he use Down just because it's better than Up?

Can adderall make me able to sit down and study for at least 3 hours straight without me wanting to masturbate, listen to music or eat?

How does a PhD program teach you to write papers in such a relatively short amount of time?
I mean, looking at something like the Green-Tao theorem's proof makes undergrad work seem utterly trivial in comparison.

>go to a school with a mediocre math department
>talking to professor
>mentions he got his PhD at MIT
>even he couldn't get a good professorship
>the job market is even worse now
I'm never going to make it

Okay is it wrong to write something like 3 ∈ 4 strictly speaking? Because as far as I know naturals are defined such that xth natural is N_x = {N_(x-1), N_(x-2), ... , {}}.

>>10126752
You're mistaking the Reals and Naturals.
>https://en.wikipedia.org/wiki/Peano_axioms
And it's not wrong, it just doesn't make sense.

>>10126752
Yes because no one actually cares about the details of how naturals are defined using set theory - look up category theory.

>>10126752
Yes you can, which is in part why things like type theory were developed to try to avoid these nonsensical situations.

>>10126760
What are you talking about? That's the standard construction for the naturals.

I just discovered my love for math and I'm taking a dummie test for the real thing, and I think a significant amount of the answers are wrong.

Is it the Dunning-Kruger kicking in or is this a common problem?

>>10126766
>That's the standard construction for the naturals.
No it isn't.
https://en.wikipedia.org/wiki/Natural_number#Formal_definitions
>>10126772
Common.

>>10126773
>Common.
well, at least the wrong answers in the multi-option test are the closest to the real answer, compared to the other results.

>>10126773
You just linked a page that literally lists anon's construction as the standard

>>10126563
>>10126565
>>10126599
Same here for most of the books. I literally cured insomnia by reading few pages before bed.

>>10126599
I highly recommend sleeping 9-10 hours a day, it's life changing.

>>10126784
No, it lists it as the second result.

Brahs...

>>10126849
Are you illiterate? The first subsection is about the peano axioms, which aren't used as a foundation and can be derived from ZFC. The second section lists some set theoretic constructions, the first of which is anons, and clearly states
>With this definition, a natural number n is a particular set with n elements, and n ≤ m if and only if n is a subset of m. The standard definition, now called definition of von Neumann ordinals, is: "each ordinal is the well-ordered set of all smaller ordinals."

>>10126868
>he can't count

>>10126447
based prof

>>10127054
grug need help

I think I'll just give up and becoming a machine learning meme code monkey. I don't have the drive to make it as a grad student, let alone a researcher, I can't dedicate my life to it like some people seem to be able to. I've never felt really passionate about anything, I thought maybe math could be my thing but it looks like I was wrong again. Fuck me.

>>10127141
You need a hobby.

>>10127055
because they are cyclic and have the same size

Although it would be better if they at least put the numbers in the right order.

Anybody know any cool stuff about mediants? They're related to the Riemann hypothesis, but the relation is a bit obscure to me...

>>10127222
That's the problem, I can't treat anything as more than a hobby. I'd be content with math if it was just something I read for interest a few times a week instead of a fucking job.

>>10119075
When is all his work going to get translated to English?
I aint doing maths in French

>>10125772
I'm also reading Against the Day
How do you like it so far?

>>10127289
after everyone in his generation +1 dies.

>>10127292
I really like it, it's my favourite pincone novel and this is actually a reread. All the traverse family parts are super comfy. Merle and Deuce are cool too. It's such a cool time politically that isn't really talked about anymore (because the dynamiters lost basically). It's very funny at points too.

Heh mathfags
I got a F on my calc1gayexam. That's fine though, I threw the test on the ground. Closed my eyes and held my hands up high and screeched. I imagine my hands using interdimensional energy (you fags should be able to calculate this), to vibrate the molecules in my professors hear until his brain exploded, there might have been some collateral on nearby classmates. I promptly left the classroom, knowing I was still superior and wasn't about to let gaythematics lower my spirit.

>failed high school algebra 1
>havent done any math since
Is there hope for me

>>10127531
No way to know until you try. It's going to be obnoxious learning elementary algebra all over again though.

>>10127629
I was going to do math but they wanted me to take algebraic geometry, which all brainlets do in highschool. Pretty sure I did them in 7th/8th grade being ahead and all. I went into Mech. Eng. though so you have to take calc up to diff. eq.

>>10127686
>algebraic geometry
A-anon...

underage
https://www.youtube.com/watch?v=zJTU6mMeIXs

>>10127839
I'm pretty sure it's one of those courses that they want to college to teach you, because their way is the "right" way, and it's literally 2 years of highschool condensed into one college quarter

>>10127921
The anon you're replying to is joking that "algebraic geometry", in addition to being what you're thinking of with equations and shapes and graphs and stuff, is also a field of higher mathematics were some the most complicated and brainmelting research is currently being done.

>>10127940
wtf my highschool didn't do anything like that, the highest they went was AP calculus

>>10127949
FUCKING B& MODS UNDERAGE
>>10127940
GO JOIN HIM YANKEE SPOONFEEDING THE FOREIGNER

>>10127974
bruh Im in college right now doing precalc so I can do calc for mech engineering, and precalc is literally brainlet tier, idk how ppl are struggling here, I dont even study outside of class

I was interested in math because I wanted to make a bitcoin crypto, but after going over with the adviser anyone with half a brain could realize that math won't make you $$$ and engineering/cs is better

>>10127985
>doing it for money
unironic npc

>>10124264
i feel like cantor exists just to ruin everyone's fun
then again, i love analysis and set theory both precisely because they are so fucking pathological so i guess i can't complain

>>10128034
Other guy does research in highly pathological framework:ignore pathologies
I do research in marginally pathological framework: this is wrong, read a book.

Quantum field theory says the energy density of the vacuum is infinite. <---true story

>>10128317
grug need help

>>10127940
that's analytic geometry, not algebraic. AG starts at hilbert's nullstellensatz, not at writing y=x^2 in "algebra symbols"

>>10128319
every divisor gives a unique and different subgroup, yes

What is the definitive course on Diff Geometry+Topology? What you do after babytier DoCarmo? I know of Nakamura and Frankel but they aren't very theoretical.

I'm searching for something rigorous but also thorough since my foundations are not so great. And with lots of exercises.

I miss the old days where we used to kill geometers for formulating doing geometry

how do I get more comfortable working in different number bases.

>>10128965
work with them more

>>10128965
learn how to count, then add, etc.
There's probably flashcard programs out there

>prof assigns problem for the class to discuss online over the week
>post complete solution the day it was assigned
>entire collaborative exercise BTFO by my autism

>>10130106
The rest of the class would still have to be able to interpret the solution at the individual level though? So it's still useful

>>10127531
I can teach you. I need to up my tutoring skills anyway and via internet would be easy. Besides it will teach me too.