/sci/ - Science & Math

>>11568171
>Why do all the mochitards create /mg/??

>>11568195
>>Why do all the mochitards create /mg/??
Who are you quoting?

>>11568201
>>>Why do all the mochitards create /mg/??
>Who are you quoting?
>The voice in my head

>>11568195
>he thinks it's not the same no-life mochitard making it over and over

Please give me a good book on probability with plenty of exercises.

>>11568171
wow that is a nice book does scholze and mochizuki have hot sex at some point?

>>11568333
they suck each other off all the time

i couldnt find a stupid questions thread. can someone help me with computing the divisor of y/x on the projective curve y^2z - x^3 - xz^2 = 0. I can do it but I can't justify the steps using valuations and local rings and such. please thanks <3

What are the best books for bulking up on undergrad knowledge if I am going to apply to a masters this fall? Pure math of course. I'm thinking books with a lot of problem sets? Recs?

>>11568344
>I can do it but I can't justify the steps using valuations and local rings and such.
Show your work.

>>11568365
>What are the best books for bulking up on undergrad knowledge if I am going to apply to a masters this fall? Pure math of course. I'm thinking books with a lot of problem sets? Recs?

What are your favorite open problems?

>>11568410
The ABC conjecture.

>>11568365
Which Master's programme? Which classes are you taking? What's your area?

>>11568378
Oh not this meme shit again. Give me some real reccomenations. I didn't learn algebraic k theory in 7th grade.

>>11568454
>I didn't learn algebraic k theory in 7th grade.
NGMI

Post Elder God Tier books, I'll start
>Homotopical Topology, Fuchs-Fomenko
>Commutative Algebra, Eisenbud
>Smooth Manifolds, Lee

>>11568365
Baby Rudin for analysis in [math]\mathbb R[/math]
Hoffman-Kunze for linear algebra
Dummit-Foote or Aluffi for abstract algebra (whichever you like the most)
Kai Lai Chung's book for probability and combinatorics (you can probably find a better one, up to you)
Conway for complex analysis
Royden-Fitzpatrick for measure theory and metric spaces

I'm missing one for DEs; there's tons of them and they're all different. Go with whichever one you used in your undergrad course.

>>11568171
What book is that? Also your thumb is ugly as fuck, go fix it

>>11568462
>NGMI
Huh?

>>11568489
He already finished undergrad dude, he needs more advanced books
>Advanced Linear Algebra, Roman
>Algebra I and II, Gorodentsev
>Adult Rudin
>Probability I and II, Shiryaev
>Complex Analysis I and II, Conway

>>11568419
10/10

>>11568503
Never/Not Gonna Make It

>>11568373
Okay, let me try. The zeroes of y/z are [0:0:1], [1:0:-1] and [1:0:1]. The pole is [0:1:0].

To find the order of y/z at [0:0:1], let's dehomogenise by setting z=1, so we just need to find the order of y in the local ring O_(0,0) (F(x, y, 1)). x =0 is the tangent to the curve at (0,0) so we can take y as a uniformising parameter. Hence ord_(0,0) (y) = 1. A similar approach works for the other poitns to, so the effective part of the divisor will read:

D+ = [0:0:1] + [1:0:-1] + [1:0:1].

Now to deal with the pole, dehomogenise by setting y=1 and we now need to find the order of 1/z in the local ring O_(0,0) (F(x, 1, z)). The tangent to the curve here is z=0, so as a uniformiser we can take x. From here I am stuck.

>>11568504
>Reading 1000 pages of measure-theoretic probability to prepare for grad school
?

>>11568447
>Which Master's programme?
Don't know yet. Applying
>Which classes are you taking?
Retaking undergrad first then I guess picking a focus or just taking a mix of courses (if I go Ph.D or just leave with masters)
Here's a sample of possible courses from one place:


Linear Algebra.
Concepts of Analysis I.
Concepts of Analysis II
Ordinary Differential Equations
Number Theory.
Abstract Algebra I.
Abstract Algebra II.
Real Analysis I.
Real Analysis II.
Functions of a Complex Variable I.
Functions of a Complex Variable II.
Differential Geometry and Topology I.
Differential Geometry and Topology II.
Partial Differential Equations I.
Partial Differential Equations II.
Topology.
Modular Functions I.
Modular Functions II.
Combinatorial Mathematics.
Topics in Number Theory II.
Homological Algebra.
Representation Theory I.
Representation Theory II.
Commutative Algebra and Algebraic Geometry I.
Commutative Algebra and Algebraic Geometry II.
Riemannian Geometry.
Knot Theory and Low-Dimensional Topology I.
Knot Theory and Low-Dimensional Topology II.
Advanced Probability Theory.
Functional Analysis I.
Functional Analysis II.
Calculus of Variations.
Harmonic Analysis.
Several Complex Variables I.
Several Complex Variables II.
Harmonic Analysis.
Lie Groups.
Riemann Surfaces.
Riemann Surfaces.
Differential Topology.
Differential Topology.
Geometric Group Theory.
Topics in Algebra.
Seminar in Algebra.
Topics in Analysis.
Topics in Functional Analysis.
Topics in Differential Equations II.
>What's your area?
Don't know since I'm going into a masters first. My interests vary. I like Combinatorics, Algebra and Functional Analysis.

>>11568539
>Retaking undergrad first
Why though? Was your undergrad weak?
>course list
A lot of that stuff is undergrad, why is it in the Master's?
>Combinatorics, Algebra and Functional Analysis
Then focus on those, no sense in re-studying a whole undergrad if you're going to focus on this. It's still too vague, though. Just Algebra is fucking massive already.

>>11568539
These are all undergrad courses.

>>11568539
>combinatorics, algebra, and functional analysis

Based and redpilled. You'd probably enjoy dynamical systems too, since it has some close connections to both combinatorics and functional analysis.

>>11568555
>Why though? Was your undergrad weak?
No? I mean I had all the standard courses. I did not; however, get the chance to take any graduate level courses.

>A lot of that stuff is undergrad, why is it in the Master's?
I think some of it may be mixed it with "Math Ed" majors but also I think some of them are the "graduate" versions of undergrad courses and I thought it's standard to retake those.

>Then focus on those, no sense in re-studying a whole undergrad if you're going to focus on this. It's still too vague, though. Just Algebra is fucking massive already.

Yeah, I really don't know. I've liked every math course I've ever taken and I don't have a particular fancy for one over the other. I'm kind of shitty at combinatorics but I like it. I tend to be better at the more "abstract" things like Algebra/Topology or certain parts of analysis.

>>11568567
>Several Complex Variables is an undergraduate course
Kek

>>11568365
>>11568539
>>11568576
Don't listen to meme answers like >>11568378 >>11568504 or >>11568567
Here's what grad schools expect you to know from undergrad, for pure math programs:
>ODEs and basic PDE (Fourier series)
>Undergrad real analysis (Riemann-Stieltjes, metric spaces)
>Basic complex analysis (Laurent series, residues)
>Basic algebra (group/ring homomorphisms, PID, UFD, elementary results from modules, fields)
>Linear algebra in the context of vector spaces and more abstract results (inner product spaces, Jordan normal form)
>3 semesters of calculus (obviously)
>basic probability (distributions, central limit theorem)
>Basic general topology (maybe not even this)

It would make things easier if you were familiar with
>Classical differential geometry
>Basic algebraic topology
>Stochastic processes
>More advanced PDE results
>Mathematical statistics
>Basic numerical analysis
>Basic optimization theory

Good luck anon, don't sweat it as long as you study, and DO NOT FORGET to make lasting connections with people you think could help you.

Consider a separable Hilbert space with an orthonormal basis [math]\{e_i\}_{i=1}^\infty[/math].

Is [math]x = \sum_{i=1}^\infty e_i[/math] an element of this Hilbert space? If not, what is it? It appears to have infinite norm.

>>11568647
Finite sums, my friend.

>>11568647
It's not in the Hilbert space.
Don't assume that an "orthonormal basis" has anything to do with the concept of a basis from Linear Algebra.

>>11568650
>>11568657
I'm just curious what that object is and if it can be characterized in relation to the Hilbert space.

>>11568650
Actually, I don't think it needs to be finite itself. A finite sum of those guys, though.

>>11568647
>>11568658
It's an eigenvector of the bounded operator [math]X(\cdot) = \sum_{i,j=1}^\infty \langle \cdot, e_i \rangle e_j[/math] on the Hilbert space

Start doing maths again picked up the book University Physics.

Has there been any progress towards a theory of everything?

>>11568685
>Has there been any progress towards a theory of everything?
I U T E I C H

>>11568171
OC I forgot I made like a week or two ago

>>11568685
fuck off Stephen Wolfram

>>11568669
A generalised eigenvector more precisely, right?

>>11568696
nice

>>11568503
>He's not /scifit/
ngmi

>>11568696
More Biledwurger, pls.

>>11568685
>Has there been any progress towards a theory of everything?
Yeah, I just solved it

>>11568647
It's not an element. Don't listen to those guys.
Having an orthonormal basis just means that every element may be uniquely expressed as a (potentially infinite) linear combination of elements of the ONB. It does not mean that every infinite linear combination of elements of the ONB is in the Hilbert space. Indeed, such linear combinations must have finite norm, which corresponds to the sequence of coefficients being in little l^2. You should check this.
You should think of an ONB as giving your Hilbert space an isometric isomorphism to little l^2. Not, as your vector would imply, to something like l^infinity or the set of sequences.
>>11568669
Please don't post things like this. It's embarrassing.

Where can I find a lot of derivative questions with answers? I'm teaching myself calculus. Also, is calc 2 harder rhan calc 3 like some people claim? Thanks

>>11568647
>What is it?
It's not anything unless you're deciding to talk about it, say, as the identity multiplication operator on your space (again under this connection with l^infinity) or as some other notational convenience.

>>11568790
Just invent a function, then derive it or do an analysis of the function or whatever, and then check it at derivative-calculator.net

>>11568790
You can download the PDF of any calculus textbook. There should be plenty of exercises. Alternatively, look up "AP Calculus derivatives practice"
It is up to each individual what they find harder. I found both classes to be pretty intuitive. Some people think a lot better geometrically and have an easier time with Calc 3. Some people think more analytically and like the series and stuff in Calc 2.

>struggling on a problem
>take a break by doing a problem from a class you took a few semesters ago to feel like a math god again
anybody else do this?

>>11568816
>1+1=2
>haha nice

>>11568816
I wish I could. Feels like I'm regressing.

>>11568838
YOU ARE REGRESSING, fucking brainlet, you're getting older by each minute and your brain is dying, you intelligence decreases each day, if you're 30 your IQ has probably decreased by 20 points already compared to when you were 22~24

>>11568854
End my pain.

>>11568802
>>11568805

thanks

>>11568805
Oh, sorry, I meant to ask: what's a great calc textbook for a beginner, in your opinion

>>11568871
You're approaching me? Instead of running away, you're approaching me, ho.

>>11568880
End me.

>>11568889
I can't beat the shit out of you without getting closer.

>>11568831
Yes.

>>11568831
Hum, no. First of, you haven't defined the properties of the binary operation '+', you also haven't defined on which set of numbers we're working on, nor did you construct that set beforehand using another set of axioms.

Your proof is pathetic just like you.

>>11568816
No because I also cannot do them. Fuck me.

>>11568961
>Studies for 10 minutes
>'Hum, I wonder what's happening on /sci/ and /mg/'
>Spends 2 hours on /sci/ and /mg/
>'fuck, I need to go back to study'
>Studies for 10 minutes
>Etc
Does this happens to you guys as well?

>>11568875
wolframalpha.com is also a really nice website, and if you can get a copy of Mathematica (you can probably check /t/ for that) then you're set.
>>11568879
There are many answers to this because there are many textbooks. The best answer in my opinion is that you pick something, stick to it, and only consult other books for doubts and stuff. I'm familiar with Piskunov and Granville and liked them (the latter got me into mathematics, so I have a soft spot for it). Apostol is usually recommended, and so is Spivak. Soviet books are usually really good, and are extremely cheap, so that's also a good option.
Just ask more questions if you have them, and remember that you have /sqt/ for whatever problems you may be having with Calculus.

>>11568969
No because I don't study anymore. I'm too busy wanting to fucking die and getting way too bothered by the insults I receive in /mg/.

>>11568969
yes and i hate it

is Gruntz algorithm still the best for finding limits?

>>11568969
Sometimes. The last day was spent trying to find the invariants of a cohomology ring under the action of a group. I couldn't do it, not even after spending 8 hours on it without /mg/ or other bs.

>>11568879
an /mg/ beginner is different than a regular beginner

to gauge what kind of beginner you are, try the first few problems in chapter 1-2 in Spivak, or all of them if you’re up to it. if these are unreasonably difficult for you, go with some like Stewart’s Calculus: Concepts and Contexts and Velleman’s How to Prove It. Maybe once you learn about limits from Stewart read chapter 5 of Spivak and get a feel for a more rigorous problem sets

just my opinion

>>11568992
what level is an /mg/ beginner?

>>11568969
Good resources only take 10 minutes to read, and a good night's sleep to digest.
The rest of your time is better spent shitposting

>>11568991
It's okay anon, don't worry.
>>11568996
Crazy Soviet curriculum for gifted children.
>>11568999
Not everyone here is Chad, Chad.

>>11568996
Math 55 level

>>11569035
>It's okay anon, don't worry.
I've been trying to do it since Friday. Kill me.

>>11569054
I'm just some random faggot on the internet, but it means much more to me that you can put so much effort into something even if it's difficult and you feel discouraged. If it were easy to you, then whatever, you find it easy. I'd envy you because I have a massive inferiority complex, but I wouldn't care beyond that.
But I wish I were that resilient and had that much resolve, instead all I can do is shitpost on /mg/. That I don't envy, but admire.

>>11568991
>invariants of a cohomology ring under the action of a group
Is it hard? Oh boy, can't wait until I reach that level of math, must be pretty exciting.

>>11569093
>hard
not really
>exciting
no, this is 1930's math

post problem >>11568991

>>11569110
>not really
Not an expert, but I'm pretty sure it depends on the ring, group and invariant, right? I mean, these kinds of problems can get stupidly hard in no time.
>no, this is 1930's math
So it's not exciting because it's old? What kind of retard argument is that?

>>11568972
thanks again
>>11568992
Just downloaded Spivak's Calculus and ch1-2 seem to deal with fundamentals of algebra and properties of numbers, i.e. the binomial theorem etc. I like the way he writes though, I will check out chapter 5. ty.

>>11569093
>Is it hard?
Is there a good definition for objectively hard (assuming we exclude actually impossible) things? Will it be hard for you? Maybe, maybe not. Is it hard for me? Yes. Beating the remains of my self esteem to pulp, wearing me to the point that this kind anon's words >>11569083 almost made me cry. Thanks for the nice post.

>>11569110
>post problem
Let [math]p\ge3[/math] be a prime, let [math] G = \text{SL}(2, p^2)[/math]. Compute [math]H^*(G; \mathbb{F}_{p^2})[/math].

>>11569147
Sorry, the coefficients are in [math]\mathbb{F}_p[/math]. And where the invariants come along: [math]G[/math] has a Sylow [math]p[/math]-subgroup [math]P[/math], the order of which is [math]p^2[/math], so it is abelian. If we denote its normaliser by [math]N[/math], we have [math]H^*(G; \mathbb{F}_p) \cong H^*(N; \mathbb{F}_p)[/math] because of the abelianness. This can be reduced to [math]H^*(P; \mathbb{F}_p)^{N/P} \cong H^*((\mathbb{Z}/p\mathbb{Z} )^2; \mathbb{F}_p)^{N/P}[/math].

>>11568969
by doing that and succumbing to the craving you are doing yourself a great disservice and making that problem even bigger

>>11568410
abc conjecture
The entire Langlands program
Continuum hypothesis (does undecidable count as open?)

>>11568969
Force yourself to study. Every time you hop onto /sci/, you make the problem worse. Even if you slip up, clear your head and start again.

>>11569172
>abc conjecture
open

>>11569172
>does undecidable count as open?
no

>>11569147
I'm glad you found my post helpful, but unfortunately kind words are the only thing I can do for you or anyone else, and I can't even do that with myself. Makes me feel like my intentions are worthless and even illegitimate.

>>11569172
>The entire Langlands program
That's unsolved? Wtf?

How does a Comp Sci brainlet git gud at math?

>>11569198
You don't have to worry about doing math, just throw GPU clusters at whatever problem you're trying to solve.

>>11569195
If this eager anon (or someone else) doesn't solve the problem while I sleep, I will simply swallow my pride and ask my supervisor, so no need to worry about not being able to give anything else than kind words. They give me more comfort at this very hour than the solution to my problem would. What are you struggling with?

>>11569226
>What are you struggling with?
My life in general and my Master's in particular.
>I will simply swallow my pride and ask my supervisor
I don't think one can get very far in mathematics by having a lot of pride. For example, my Master's thesis is on hold indefinitely, and when I explained my situation to my advisor he was very sympathetic.

>>11569226
>>11569250
Stop taking life very seriously, just sit down and enjoy the ride. You're not the only ones struggling, we all are, 1 in 20 people are actually satisfied with their lives, worrying too much won't help at all, now's the time to simply accept and enjoy while you still can.

Ok so I'm doing some really basic math but for some reason I can't seem to figure out how to turn 3(x^-2) divided by -2 into 3/2(x^2). I feel like I'm forgetting a rule somewhere. I don't know what to multiply with.

>>11569277
[math]x^-2=1/x^2[/math]

>>11569277
[math]x^(-2)=1/x^2

>>11569280
>>11569283
Thx

>>11569283
[math]x^(-2)=1/x^2[/math]

>>11569275
>just sit down and enjoy the ride
It's not that simple, which is why so many are demoralised and lost. What does it mean to sit down? Enjoy the ride how? And how much worry is too much?

>>11569283
[math]x^{-2}=1/x^2[/math]

>>11569292
Ever heard that song Hakuna Matata?
>What does it mean to sit down? Enjoy the ride how?
It means no worries for the rest of your days. What do you like to do? Watching anime? Playing videogames? Fucking whores? Just do the things you enjoy while working on the side but don't worry too much, we're not geniuses my man, we didn't realize our dreams that we had when we were young, now we're middle aged man worrying about PhDs and stuff, just forget about that crap, it's ok if your dreams won't come true, because almost no one's dreams comes true as well, all that's left for us is to simply lead a normal life while enjoying the things that gives us pleasure.

>>11569250
It's pretty much impossible to get anything meaningful done if your life is a mess. Having supporting people around, be they made of meat or of bytes, is probably the reason a lot of us really come to these threads. It's good that your supervisor understands, not everyone is as lucky. https://www.youtube.com/watch?v=mteGvLWq97A

>>11569275
That'd be nice. I'd like to actually accept myself with all my imperfections, but I am far from that point. Before that, the ride won't be pleasant.

Good night.

>>11569317
You guys are still craving to your dreams and hopes from when you were young, but it's time to face reality frens, we won't be the next Gauss, we won't win a Fields medal and that's ok, once you guys accept it you'll be able to see how wonderful the Hakuna Matata philosophy is.

>>11569314
I know you're right, but somehow I just can't fucking cope with my inadequacies. If I'm not the best, I feel like I don't deserve anything but scorn. I don't why this is, but it drives me insane. Either way I'm not sure how to feel about such a care free lifestyle, I'm not sure it's the best for me. Somehow it seems wrong.
>>11569317
Good night.
>>11569327
I'd rather have an ambition I achieve, however small. It's just that they all seem so out of reach.

Ok so if I turn 3(x^-2) into 3*1/x^2
I can multiply it with -x^2 to get -3. I also multiply the /-2 with -x^2 which gives me -3/2^2. Seems like it works.

>>11568879
I love Calculus Made Easy by Silvanus Thompson. It's so witty and fun, and it's a classic old book. The standard that most people use in classes is Stewart. We'll all recommend you Spivak and Apostol here, they're excellent books but might be scary for a beginner.

What are the prereqs for understanding differential geometry?

>>11568969
>have interesting problem
>work on it continuously with no interruptions happily
>have to mindlessly compute some horrible pullback of some fucking 3-form and then wedge it with some other garbage
>fuck around on /mg/ and add a line to the tex file every 20-30 minutes
fucking geometry courses

>>11569409
Vector Calculus
Abstract Algebra

>>11568996
>what level is an /mg/ beginner?
Freshman on this >>11568378

>>11569314
I hate how you wrote this and you're a dumb fucking pothead, but you're objectively correct and the other guy probably needs to find something to give him some perspective.

>>11569409
Not necessarily abstract algebra but you absolutely need to be strong on multivariable calculus and linear algebra.

>>11569413
>Abstract Algebra
Not really, linear algebra is enough for a lot of stuff. You also missed topology which is really important.
>>11569409
In Lee's "Introduction to Smooth Manifolds" there's really big appendices with all the background required. Go through them, and if there's something you don't understand, just look it up in any standard textbook (he might even have recommendations in there, don't remember right now).

>>11569436
>topology
Not really, it's important for modern Differential Geometry, not classic Differential Geometry.

>>11569317
>>11569330
If you're not willing to do what the other guy said and go along for the ride (believe me, it's not that hard, I remember thinking exactly like you and I've just kind of forced myself out of it) you could always train yourself to revel in the inadequacy and love the sinking feeling of not being the best. I've got a bit of that too. It's like being an adrenaline junkie.

>>11569436
Lee's is modern Differential Geometry, also you're recommending Smooth Manifolds without his Topological Manifolds book which is basically a prerequisite, you've no idea what your talking about, leave.

>>11569426
>but you're objectively correct and the other guy probably needs to find something to give him some perspective.
I'm the guy he replied to and I agree that there's definitely something I'm missing and a kernel of truth in what he's said. But it happens to me a lot of the time that I understand something at a purely rational level (e.g. my friends like being with me and want to help me) but that never "reaches" me at a more visceral, emotional one, so I live in this massive fucking contradiction that sometimes gives me really big cognitive dissonance that I don't know how to handle. And talking about this stuff with them only made the problems worse, and all my psychiatrist has given me are meds that don't work (they don't even have side effects, they just do fuck all) and problems with my insurance.

>>11569436
>topology
it's likely they mean "differential geometry of curves and surfaces" as opposed to a course on differentiable manifolds and riemannian geometry. Lee is mostly a differential topology book, though there are some geometric parts of it.

>>11569444
Yeah, I assumed he was talking about manifolds, not curves and surfaces. He didn't specify, so I just assumed the former, since the latter doesn't require much in comparison.
>>11569447
>Lee's is modern Differential Geometry
Yes, I know.
>also you're recommending Smooth Manifolds without his Topological Manifolds book which is basically a prerequisite
I wouldn't call that book a prerrequisite per se, since all you need is in the Topology appendix of the former book. It is better to be familiar with it, of course, but that's different.
>you've no idea what your talking about
I'm a bit familiar with both books.
>leave
Make me.

>>11569426
>dumb fucking pothead
Go fuck yourself my man, peace

>>11569461
That was a test. If you laughed it off and came back at me with banter, I'd believe that you'd mastered the sort of fluid stoicism you endorse. But instead you told me to "fuck off."
This confirms my suspicion that you're typically a neurotic and you're just high right now.
Either way, it's perfectly possible to live life as though it's an exciting trip, to not take anything too seriously and to treat crises as though they're adventures.
Alright, I'm mostly just fucking around. I'm sure you're a good guy.

>>11569479
I'm not pissed at all man, I was laughing when I made that post. Of course I'm far from this 'fluid stoicism', but I feel I'm getting closer and closer to transcendence. Currently reading the Ashtavakra Gita, may y'all be blessed with illumination at one point of your lives.

>>11568171
im interested in a cs and math double major. Does anyone have advice for me?

>>11569485
I have 2 advices that might help. First start a cs major then go to a math major. Second, start a math major then go to a cs major. Whichever you chose you'll end up with a double major.

>>11569488
So you are saying that I should first complete one major, then after completely finishing the first major, start the second major? Opposed to starting the second major 2, 3, or 4 year; or even starting the second major first year.

>>11569485
Just in case you’re one of those people who want to go to grad school for math but wants a backup plan in the form of a cs degree, don’t double major, just major in math and go hardcore. Trying to get a backup plan will just hinder you.
Otherwise, double majoring is fine.

>>11569479
>>11569484
Wtf am I reading?

>>11569484
>I was actually super chill when I responded with "go fuck yourself"
yeah nobody's buying your shit buddy

>>11569506
Are you guys memeing back and forth?
This is so cringey that it’s making me reevaluate some of my own tendencies on the Internet due to how eerily similar it is.

>>11569502
You're reading what you wanna read and I'm telling you that what you should read is what is actually written, not what you wish was written. You've been through a lot in your life, I know how you feel, believe me, most of us know that feeling of failure, but now's time to move on, man, start looking at reality instead of chaining yourself inside impossible dreams.

>>11569513
how does your large intestine smell?

>>11569516
I.. dont know?

ok bros im gonna start studying again and go back to the uni

>>11569500
I just really torn between CS/CE and math. The universities I'm looking at don't differentiate between applied math and pure math. Being an actuary sounds cool. So does software engineering.

I just don't want to graduate with a degree in mathematics, and be forced to work as a high school math teacher. That would be miserable.
im canadian btw

>>11569525
>Being an actuary sounds cool
Actuarial work is soul-destroying unless you're a bugman who didn't have a soul to begin with. Also in Canada it's not that easy to get into anymore, because Waterloo (and somewhat Toronto, but mostly Waterloo) shit out so many overqualified chinks every year that the entry-level market is extremely oversaturated.

>>11569513
Dude I’m not even the guy you’ve been talking to, chill.
Get off of here while you can and do something productive, chores, a hobby, etc.
None of this real and you’re just wasting your time.
Heed me and leave for your better.

Should I study math if I'm Asian? We are stereotyped as math nerds but almost all theorems/discoveries were made by white people. I mean there's Tao but he's an exceptional case.

>>11569522
Good luck, you're gonna make it, we all will

>>11569534
Did I say you were that guy? It was obvious you weren't, I'm telling you this because I know you're one of us as well, you were once a dreamer and now you're still trapped inside those dreams of your youth, you gotta free yourself friend, you won't find any happiness by ignoring reality and living inside self-deception.

>>11569543
Gotta be more specific
Japanese or Chinese, go for it
anything else, nah

>>11569525
Nothing wrong w/ teaching highschool, plus you can be a volleyball coach there as well. Win win!

>>11569566
Skirt over spats is Ancient Eldritch horror tier. HHHHNNNNGGGGGGG I WANT TOMBOY GF REEEEEEEEEEEEEEEEEE

>>11569484
Oh good, I almost didn't make the post because I was considering the possibility that you were in on the joke.
I think you're closer than you think.
The best part is all the other troglodytes in this thread silently seething that they can't enjoy the ride like we can.

>>11569534
I am the guy he was talking to, you fucking piece of shit. And he's right.
This post >>11569502 is just a look into your horrifically disorganized mind. Spend some time with a homological algebra book and a nice cup of tea, then take a quiet 11 pm walk around your block. Spend some time on yourself tonight.

>>11569657
>tfw no tomboy gf

>>11569748
>The best part is all the other troglodytes in this thread silently seething that they can't enjoy the ride like we can.
I may be a troglodyte, but I'm not seething. I'm just deppressed.

What is the best calculus textbook for an eager high school student.
Preferably one that is on libgen.

>>11569525
I highly recommend you don't study math. If you're not prepared to do at least some mathematical teaching, even if it is to highschoolers, don't do the degree, unless you are at the top .0001% in the field. Or, at least double major in CS or something else.

h-how accurate is this guy's advice bros >>11569977

t. sophomore undergraduate that finished gen eds and has only been taking math classes since

>>11568171
Why is zero not in the set of natural numbers? Name one good reason zero is excluded. Seems natural to me

>>11569327
>we won't be the next Gauss, we won't win a Fields medal and that's ok
Perhaps you won't but how do you know I won't? I still think I can and will.

>>11570023
You're more likely to end up the next Mochizuki

Reminder to the slower of us to not feel too bad about it:
>It's true, I'm not good at solving problems. I would never be good in the olympiad, for example, <.?..> I'm certainly not a speedy worker. That's one beautiful thing about mathematics: it doesn't matter how long it takes if you end up with the result.
-John Tate

>>11570041
right, says the dude who went to harvard and got a PhD from princeton. He is just being humble

>>11569990
If your plan is to leave academics and get a real job, then it's not very accurate. There are plenty of things you can do with a math degree that aren't teaching little shitheads.
If your goal is to be a research mathematician, then you have to teach. Basically all PhDs require their students to teach classes, and other than a tiny handful of brain bull research institutes (like the IAS) all academic jobs require teaching too.

>tfw starting homological algebra in algebra sequence but hate category theory
How do I get into category theory? Because for the life of me I can't use these tool effectively.

>>11570078
Thing is, to my knowledge a bachelors in math has nothing in terms of job opportunities compared to a masters degree, which would then require you to do some amount of teaching to complete it.

>>11569327
I don't want to be the next Gauss, I want to be OK with being myself.

>>11570135
Learn the bare minimum you need to get started with homological algebra, and then expand on that. You learn direct and inverse limits, you generalise those to colimits and limits; you learn the tensor-hom adjunction, you learn about adjunctions in general; you prove stuff related to module categories, you find out what an abelian category is like in general; you learn a diagram lemma, you prove it holds for all abelian categories. This is how I started getting into it.

>>11568333
Scholze is well known as a nice gayboy. There are pictures of him with long hair, a cute face and wearing a pink shirt for god's sake.

>>11568217
based

>>11569147
CS has well developed notions of "objective hardness", but it's more about resources required to compute something than human feels.

Keep pushing (within reason) anon. I believe in you.

>>11570188
I'd say Scholze is more like the type of person we used to call "fruittari", that is, dressing up like a guy someone would probably call gay but actually being (at least mostly) straight. His hair isn't the mess those guys used to have, and that would be sort of like the anime boy hair from the artistically plastic and boring 00's shows, but pink shirts and stuff. Those were their thing back in the days. Maybe Scholze is 13 years late, or maybe he is trying to revive the scene.

>>11570218
Now that you mentioned it, one could also say that physics and chemistry could have objectively hard stuff if the movement of the particles is restricted to the bare minimum. Thanks for the support. I'll try to fight myself out of the mess caused by the stupid linear group. Even if I failed now, I would have been recapping a lot of stuff I may have overlooked before. I may feel useless but this struggle of mine is not.

Have a nice day everyone!

>>11570147
Oh yeah, I'm fine with teaching sometimes, I just don't want to be a literal high school teacher.

>>11570181
Maybe I'm still stuck in the undergrad mindset, but it feels a little "wrong" just learn a little bit a subject and then move onto another subject. Even though I've been told over and over that sometimes you only need to read a single chapter of a book I feel compelled to read the whole damn thing. Same thing here, even though I likely don't need all that much category theory, it feels weird to move onto homological algebra without really "getting" category theory. At the moment it almost feels vacuous and without meaning.

>>11568582
> people you think could help you

it is everyone against everyone

>>11570041
Shit like this loses all meaning when even fucking Grothendieck shares the sentiment.

>>11570041
>if you end up with the result
That's a big if. It's massive in fact, since the whole issue ultimately revolves around it.
>b-b-but I can't solve IMO problems fast!!
That was never the argument or the concern, which goes to show he actually doesn't fucking get it, as much as he may pretend to do. Others like Tao also do it, which is why I find him infuriating.

>>11570243
>I may feel useless but this struggle of mine is not.
You're not useless, struggler. Now go fight against the currents of causality.

>>11570041
>if you end up with the result
Well, obviously nobody will judge you if it took you 20 years to solve the RH.
But that really isn't the issue, right?

>>11570181
>I want to be OK with being myself.
Pro tip: Leave 4chan and do something that isn't on the internet.

my major is statistics am i fucked

>>11570041

respect to Him and to his students

Brainlet here. If I have a sequence of complex numbers [math]a_n[/math] and I only know that it is square summable, i.e. [math]\sum_{n=1}^\infty |a_n|^2[/math] is finite, can I still do basic algebraic manipulation with it like
[math](\sum_{n=1}^\infty a_n)(\sum_{k=1}^\infty \overline{a_k}) = \sum_{n=1}^\infty |a_n|^2 + \sum_{n \neq k}^\infty a_n \overline{a_k}[/math], even if [math](\sum_{n=1}^\infty a_n)[/math] could potentially diverge?

>>11570575
It depends, but in general not really, especially not in that equation, since neither side has to exist...

He says it's easy to prove but I can't see how. Help?

>>11569522
>>11569544
>22
>44
wow bros we truly are going to make it

>>11568171
your thumb...

>>11570626
this is pretty obvious, he is just using [math] p(x,y)\geq p(x)p(y) [/math], and the monotone increasing of logarithm functions.

>>11570651
What are you, stupid?

>>11570651
>pretty obvious
[math]p(x,y)\geq p(x)p(y)[/math]
You do realize that this is not true in general, do you?

Is a good way to do research to look through the wikipedia pages on open problems in math, select one that sounds cool and is in a field that you like, and then spend the next few years solving it?

>>11570694
Thats possibly one of the worst ways to do research. You wont last a week like this. The best way is to pick a field youre interested in and just study it. After a while, natural questions will arise that have not been solved yet. Youll understand the motivation behind the questions and will have a much better time researching.

>>11570694
Sounds good to me. Just be sure to read and understand all the existing literature about it. Look for an interesting subproblem and try to solve that first. Then go on from there.

>>11570697
>>11570701
The duality of man

>>11570706
In a way, we were saying the same thing.
Except the other anon prefers to study from outside in, that us, first understand well the whole field, then start on a specific question.
What I have personally known to be of success is to work from inside out. Just focus on a specific question, then learn all the stuff that relates to it.
Pretty sure some successful people have done it one way, some the other way.

Let [math]u_n[/math] be a sequence of real/complex numbers. Does [math]\sum_{n \in \mathbb{N}} u_n[/math] convergent [math]\Leftrightarrow \sum_{p \ prime} u_p [/math] convergent? If not, what are some counter examples?

>>11570746
u_n = 0 if n is prime u_n =1 otherwise disproves <=.

>>11570746
subsequence of convergent sequence converges.
For the other direction, build counter example by taking any prime term of any convergent sequence, and anything that diverge grossly on non-prime indices. Like, 1/p^2 on prime and n on non prime.

>>11570771
>subsequence of convergent sequence converges.
This is about series though a "sub series" is not a subsequence of it's partial sums.
Take the summands 1,-1,1/2,-1/2,1/3,-1/3,... Clearly this sum converges, the "partial series" over 2*|N doesn't though...

>>11569750
Stop playing make believe and be productive.

>>11570771
>>11570746
>subsequence of convergent sequence converges
That's not relevant here. None of the directions hold true.
Counter example is you take u_p_n = 1/n if p_n is the n'th prime and in between you put negative numbers so that the whole sum converges.

>>11568582
shut up faggot

>>11568871
You can end it yourself tranny

>>11568410
my homework

>>11570023
As long as you're young you can hope and dream as much as you want and it might even become true, who knows, but after you reach a certain age and keep failing, most of the times the reason is because you're still clinging to those old dreams, at that point the best thing is to just let it go and simply enjoy life, the truth about this world is that almost no one makes their dreams come true and almost no one is truly happy with how their life turned out to be. If you're young you just won't understand this, but when you get older and older, at some point, you'll remember those words.

>>11570790
my bad, conveniently unread the sum sign.

>>11570629
Trust me when I say we're all fucking making it, no ones getting left behind here

>>11570816
Damn dude, i am getting my 4chan dose to escape reality not to be hit with a double lariat to my soul :/

>>11570262
But do you notice the vicious cycle here? You don't like CT now because it lacks motivation, but to get that you would need to see it applied to stuff. A nice way to get started could be just going through a lot of that homological algebra stuff for example, and seeing how various concepts present themselves there as direct products and sums of modules, (co)kernels, direct and inverse limits, tensor products and hom's inducing morphisms etc. All this can be done using just algebraic methods, and in that sense you don't need to know category theory much at all to see what's going on. However, when you would then take a look at categories themselves, you would see how the right exactness of the tensor product functors is a special case of right adjoints preserving limits, and so on. Then you can also drop truth bombs like how not all epimorphisms in the category of Hausdorff spaces are surjective. I can relate to that book thing, as I used to be the same.

>>11570289
Thanks. I will.

>>11570326
>Pro tip: Leave 4chan and do something that isn't on the internet.
I do other things to, but for some reason I always end up returning here.

>>11570801
Quite rude, yet most true.

>>11569994
Convenience for certain people. There are plenty of situations where I want to refer to the positive integers, and less where I want to refer to the nonnegative ones.

How do I get a math TA gf bros? Most of the ones at my uni are qt tomboys.

>>11570575
If you're asking questions of this caliber, you're not a brainlet. You're thinking.
But the answer is unfortunately no. You can run into some bad stuff if you try to do that. You really need absolute convergence, i.e. that the sum of |a_n| is finite.

>>11570983
That's a man

>>11570846
just be kind and fucking die ok

>>11570983
she's beautiful

>>11571105
Shut the fuck up, he has a brain tumor you insensitive fuck

>>11571213
she's fucking annoying

>>11570846
>But do you notice the vicious cycle here?
Yeah, it's getting a little frustrating. I guess I really just need to dive in and table my discomfort at the moment. Thanks anon.
>>11570626
https://ttic.uchicago.edu/~madhurt/courses/infotheory2014/l2.pdf

>>11571241
No, they aren't (don't assume their gender like that), they're one of the finest users here and a very cute one

>>11569147
Is this [math]SL_2(\mathbb Z/p^2\mathbb Z)[/math] or [math]SL_2(\mathbb F_p^2[/math] ?

how do you feel about QFT?
im considering running a general in which i post the problems from a QFT textbook and we solve them in order. kind of a joint exploration into the subject.

>>11571308
Ugh, meant to type " [math]SL_2(\mathbb Z/p^2\mathbb Z) or SL_2(\mathbb F_{p^2})[/math] "

>>11571331
Best subfield of physics together with General Relativity. It would be nice if everyone helped creating a solutions manual for the famous books like Peskin or Weinberg.

>>11571377
Threadly reminder that set theory and category theory are outdated as foundations of mathematics and we should find a new one if we want to move mathematics foward.

>>11571331
it's not math

>>11569532
Bro is Waterloo that bad? I thought it was one of the top cs Unis? Or is it just a codemonkey factory because of coop?

>>11568255
Please?

>>11571421
Theoretical Physics is practically a subfield of mathematics nowadays.

>>11571377
>>11571399
ZFC in conjunction with Cat theory is the standard and has been tested for decades. There is no reason to change it until we really hit a wall (everything knew discovered leads to some sort of paradox).

>>11571440
Read on homotopy type theory, brainlet. Set Theory has outstayed its welcome, category theory is starting to show its weaknesses as well, we must abandon those primitive foundations if we want to keep moving foward. Can't you see that we've already hit a wall here? When was the last breakthrough in math? The current state of mathematics is stagnation.

>>11571449
>rephrasing basic definitions will lead to a breakthrough in maths
i don't think you actually believe that

>>11571449
This has to be a joke post, right?

>>11571453
>>rephrasing basic definitions will lead to a breakthrough in maths
>i don't think you actually believe that

>>11571475
>>11571453
From my point of view you, who keep clinging to set theory and category theory, are the jokes here.

set theory and category theory are both trash, replace everything with zeta functions as primitives

>>11571105
One day, my friend.

>>11571213
https://www.youtube.com/watch?v=OaTO8_KNcuo

>>11571261
No problemo.

>>11571266
Aww~

>>11571308
>>11571332
[math]\mathbb{F}_{p^2}[/math]

>>11571512
Can you model ZFC in HoTT? If so, what's the problem? If not, why do you prefer such a weak foundation system?

>>11571449
Why would homotopy type theory lead to breakthroughs? What about homotopy type theory will improve the human mind, which is the bottleneck stopping advancement?
IF a human brain can't figure it out in set theory, why do you think we could figure it out in HTT?

>>11571484
>this discussion again

>>11571540
Doesn't matter, if even homotopy type theory fails us then wr must find a new foundation instead of keep relying on those broken and outdated fields.

>>11571533
>Aww~
Marry me i think we were made for each other

>>11571526
very good ed boy

>>11571484
Is the Springer edition good?

There have been some terrible editions of /mg/ in the past but this one takes the cake. Good lord. This entire thread is a piece of shit.

>>11571565
>broken and outdated
How?

>>11571600
Last thread was way worse, it had a debate about sexual education, gay's rights, brain tumors, relationship advice, I thought I was in some other general for a moment.

>>11571602
Because from set theory and category theory we can't move the other fields foward, it stagnated, there's been no breakthroughs, the major unsolved problems are still unsolved, no new fields have been discovered in the last 4 or so decades, mathematics as we know it is dead because our foundation is already outdated, in order to make some progress we urgently need to redefine the entirety of mathematics using HoTT as its foundation.

>>11571600
>>11571614
Fuck zoomers. can't stop talking about sex and fags and trannies.

>>11571620
Name one problem that fundamentally cannot be solved with the current standard systems, namely ZFC and category theory.

>>11571620
But why is it the foundations that are the problem and not the fact that the problems themselves are very difficult?

>>11571638
He won't be able to, he doesn't even know any set theory.

What do we know about the relative sizes of [math]L^p[/math] spaces? For example, is [math]L^1(\mathbb{R})[/math] zero measure in [math]L^2(\mathbb{R})[/math]? What about sequences in [math]\ell^p(\mathbb{R})[/math]?

>>11571614
I'm sorry, I am mixing up this thread with the last one. I was under the impression we were still in the same thread. Well, that one was worse for sure.

>>11571638
There is no way to prove that a given problem fundamentally cannot be solved with the current standard systems, namely ZFC and category theory with the current standard systems, namely ZFC and category theory.

>>11571695
there's no reasonable measure on L^2(R) and L^1(R) is not a subset of L^2(R) so I don't think you know what are you talking about

>>11570846
>Quite rude, yet most true.
You're a tranny I don't want to end up in the 41%.
>>11570983
We need to know more. Are you Chad?

>>11571695
what the fuck do you mean by "zero measure"
there's no measure on the space itself
and anyway, L^1(R) is not contained in L^2(R)
if you look at finite measure spaces, L^p(X) is contained in L^q(X) for all p > q, and is always dense in the q norm because they all contain simple measurable functions.
in counting measure spaces, l^p(X) is contained in l^q(X) for all p < q, and is always dense in the q norm because they both contain all finite support sequences except that none of them are dense in l^infinity(X) because none of them get close to the constant 1 sequence.
these are all topological notions of size, if you want measure theoretic notions you need to define a measure on the L^p spaces themselves (not too uncommon to do)

>>11571682
>He won't be able to, he doesn't even know any set theory.
I'm not a "he".

>>11571721
Then prove it using HoTT

>>11571732
post open throat

>>11571732
Oh so you're a tranny as well as a schizo retard. Dilate on Discord and 41% yourself.

>>11571744
new

>>11571739
lewd

>>11571449
Scholze told us that Homo Kike Theory is a bunch of wank. I'd rather trust him than some autist in /mg/ (except when it comes to Mochizuki sensei).

>>11571565
In the immortal words of Dr. Breen.
"You`ve destroyed so much, but tell me, what is it that you have created? [...] I thought so."

wtf are borel measures on [math]\mathbb{C}[/math]? I literally did no measure theory in my life

MonkaHmm
https://www.youtube.com/watch?v=RiQ5WKUYlD8

>>11571632
It's impossible not to talk about fags and trannies considering they infest the place. Normalfaggotry is just the latest cancer.

>>11571736
I almost want to bonk you again. Does it have to be HoTT?

>>11571620
Give us an example of something one can do in HoTT and not in ZFC + CT.

>>11571512

>>11571837
>Give us an example of something one can do in HoTT and not in ZFC + CT.

Actually make formal the usual principle that two isomorphic structures are equal? Real mathematicians keep doing that but it's dead wrong in ZFC.

>>11571824
Look up Borel measure on wikipedia and ask us if you don't understand something.

>>11571867
Nobody cares

>>11571910
Bwahaha

>>11571867
that's bullshit, you often want to have the distinction between "isomorphic" and "equal"

>>11571872
I need to understand what "the set of all Borel probability measures on [math]\mathbb{C}[/math]" is

>>11571867
This is your brain on HoTT.

>>11571867
>two isomorphic structures are equal
whattu za fuckku is zis shittu

>>11571568
So soon!

>>11571728
Why would you end up in the 41%?

>>11571968
What's the next step in his master plan? He has already snared his opponents using info war by baiting them into a comment section debate.

>>11571916
That's only because your foundation is imperfect.

>>11571998
>Why would you end up in the 41%?
I meant that it seemed that you were admitting to be trans and wished you well. If I haven't an hero'd it's because my friends and family are keeping me hostage in life.
>What's the next step in his master plan?
Crashing this field... WITH NO SURVIVORS

>>11571867
>ZFC can't make formal the notion of set equality
Holy fuck you are retarded

>>11572019
I see. Thanks for the kind thoughts, fellow prisoner of life. Or are you?
>if i haven't an hero'd
>if
Spooky!

>>11572030
Not the same thing.

>>11572033
What are you even talking about then? You have two isomorphic objects, how do you tell if they are the same, you show their underlying sets are the same.

What math is necessary for computer science?

>>11571824
>>11571953
Measure is a function which assigns non-negative numbers to subsets of some space. You should think of it as an abstract notion of volume. Of course it needs to satisfy some fairly intuitive axioms.
A cannonical example is the measure on R which to any interval [a,b] assigns the number b-a.
There are a lot of technical issues in measure theory. For example one cannot expect the measure to always be defined on ALL subsets, only on some smaller collection. A measure is called Borel if it's defined on all open and closed sets.
Probability measure means that the measure of the whole space is 1. This implies that measure of any subset is between 0 and 1 (or is undefined). Now you think of the subsets as events and the measure as the probability of happening.

>>11572041
addition

>>11572056
ok, ok, anything else?

>>11571785
>HoTT is a homo kike theory

Literally HoTT, Set Theory, AND Category theory are all "homo kike theories"

that's what we call a "kosher sandwich"

>>11572069
IUT

>>11572071
*Sigh* all this antisemitism really pisses me more than it should, I come to /mg/ to read and banter about maths but it looks like even this part of 4chan has been infested by the imbeciles of /pol/, I'm honestly thinking of just sticking to the stupid questions thread, math.stackexchange and physicsforum.

imagine catgirls on your dick haha how crazy would that be haha

>>11572038
>You have two isomorphic objects, how do you tell they are isomorphic...
FTFY

>>11572071
There is nothing wrong with jews you Electric Universe faggot

>>11572109
I think it's just a quarantine thing, they'll go away in a few months (I hope)

>>11572109
>>11572129
>>11572137
post nose

>>11572118
Same anon here, I'll stop trolling now. Don't ban me pls.

>>11572069
set theory, logic, easy proofs

>>11572109
just imagine being such a fag that you have to control all the banks and the media and you STILL cant get pussy.

How long would you say it takes to solve an unsolved problem in math, generally speaking, it the person works on it every day for at least 5 hours a day? 3 years? 5 years? 2 years? 10 years?

>>11571825
I've checked out the blog post, but has anybody here started to read his 450 pager or those PhD guys' two papers yet?

>>11571785
Source of what he says about it?

There's quite dismissive talking points of Lurie on the web, if you search for it, but he's also is a closer field

>>11572030
>>11572038
He's pointing to how HoTT's equality is closer to the 1940's universal property idea than the 1900's Extensionality axiom of sets (don't pin me down on those numbers.)
Set theory as foundations, tying to model theory, has auxillary theorems about mathematical objects.
E.g., if [math] (0, 7) [/math] is the pair with first entry zero and second entry seven, does it hold that [math] 1 \in (0, 7) [/math]. Taking set theory seriously as foundations for mathematics in praxis, then answer will typically be yes. The number [math] 1 [/math] is the Neumann ordinal [math]\{ \{\} \}[/math] and the tuple [math] (x,y) [/math] is the Kuratowskipair [math]\{ \{ x \}, \{ x, y \} \}[/math]. So it's easy to prove [math] 1 \in (0, 7) [/math], by extensionality of the sets involved.
Any models will have such artifacts. Of course, such issues never pop up in praxis because indeed nobody but model theories makes use of such characterizations. People tend to think in a typed way (as in, it's apriori eery to even speak of [math] 1 \in (0, 7) [/math] ) and they effectively use only the properties derivable from universal properties, not those of the mathematical foundations.
Equality (the equality sign) in type theory is generally hard and was studied for forever. Equality there allows for substitution. E.g. knowing [math] 3 = 1 +1 +1 [/math] means being able to rewrite [math] (5+3)^2 [/math] as [math] (5+(1 +1 +1))^2 [/math] .
HoTT has isomorphism implying equality. E.g. in a group theoretical context, "(0,1) and addition mod 2" and "(1,-1) and multiplication" can be shown to be isomorphic, and a mathematican will call "that group" "Z_2". But in ZFC he/she doens't have "Z_2"

>>11572174
some problems are not solvable so forever?

>>11572178
Assume the problem is solvable

>>11572178
nothing is unsolvable

>>11572178
And some take thousands of years. For example trisecting an arbitrary angle using nothing but a straight edge and a compass.

>>11572184
This, you just need the right set of axioms to work with.

>>11572187
Not thousands, it took a little more than a thousand years until Gauss did it.

Assume the problem is solvable within your axiomatic system and you system is consistent and it is within to set of problems within your system that are decidable
please everyone you know what im asking

>>11572193
Plato was a BC guy, so 2000 years and more.

>>11572184
you're completely wrong and i cant prove it.

>>11572197
>BC
It's BCE, we don't acknowledge Christ in the academia anymore.

>>11572204
So that's what the E stands for?

>>11572178
Are there problems which can't be solved and also can't be shown to can't be solved.

>>11572200
at least you got double dubs

>>11572211
P=NP comes to mind. people think that p!=np but they cant prove either way so far.

>>11568419
based and misunderstanding of the theory of heigths-pilled

>>11572228
You wouldn't be able to give an example of a theorem that is unprovable and unable to be proven unprovable. You could only prove it in principle.

>>11572182
how can you know a problem is solvable? you might spend years only to find out it cant be, or to find out that it would take the lifetime of the universe to compute the answer. if you can guess how long it will take, then why not just solve it on the spot? the average people work on big problems can be peoples entire careers, where they end defeated by the problem.

>>11572209
Before Common Era

What is good book or books to learn about Catalan numbers and Schröder–Hipparchus numbers? Should I first open basic combinatorics book?
My level of mathematical knowledge is 30% of Khan Academy calculus BC and everything before that except probability and statistics.
I have to say. Some how I was waiting more from calculus. Learning it has been quite anti climatic.
Is there some area of mathematics that has more visual candy and surprising connections to other areas that can be appreciated and understood by someone with low level of mathematical knowledge?

Thank you.

>>11572241
>how can you know a problem is solvable?
You can't son, Gödel showed that some problems simply can't be solved unless we create a new set of axioms, and that's how mathematics move foward, we keep creating more and more axioms and definitions and from those we keep solving more and more problems.

>>11572243
I see. Something new learnt today!

>>11572241
That's why lot of success in this field comes from luck.

>>11572212
you got a 12 straight, thats just as rare.

>>11572204
sounds petty

>>11572280
atheists ARE petty, anon. its why they reject their maker.

https://www.youtube.com/watch?v=ppWPuXsnf1Q
are we hyped bros?

new thread

>>11572312
>>11572312
>>11572312
>>11572312

>>11572317
New thread should only be created when this one died, you fuckers can't wait huh?

>>11572343
Let's be honest, this one wasn't great. It's kinda like 2019, we just want to move on as quickly as possible, it can't be worse, right?

>>11572350
Since Yukari stopped coming here it turned to trash

Does anyone know how anti-foundationalism applies in math? How can you do math without foundations?

>>11572427
Kek wtf, you want to destroy all foundations? Holy shit, that's so absurd that I'm wondering if it could actually be possible

>>11572177
>HoTT has isomorphism implying equality
Indeed, and it sounds perfect.
>>11572350
>>11572355
Greatest /mg/ thread by far.
Because there are a few math gems in this sea of trash. There probably will be some more (and maybe funnies) to toss in or to troll for later.

>>11571728
>We need to know more. Are you Chad?
No I'm a loser with no friends lol

>>11571422
Durrett