/mg/ - Mathematics General

[Anonymous No.11711046]

Previously >>11703907

Talk maths

[Anonymous No.11711072]

Much better.
Sorry for the impoliteness earlier.

[Anonymous No.11711074]

how does the Lie group connect with its Lie algebra, and what is the interpretation/how do you motivate the Lie bracket? I just can't put it all together...
https://en.wikipedia.org/wiki/Lie_group%E2%80%93Lie_algebra_correspondence

[Anonymous No.11711078]

If you haven't started studying advanced mathematics by age 16, give up right now.
You will never be successful. Forget about it, honestly.
24 is not the cutoff. 24 should be about when you get your PHD.

[Anonymous No.11711088]

>>11711072
you're welcome, it's a pleasure to shitpost about math with you in yet another /mg/ thread (done in the right way this time).

[Anonymous No.11711102]

>>11711078
>16 - start preparation for the IMO
>17 - Gold Medal, anything below that should make you ashamed
>18~21 - College and Masters
>21~24 - PhD
>25~30 - Research
>30 - Fields Medal
that's the path towards victory.

[Anonymous No.11711110]

>>11711102
it should be the standard for anyone serious about mathematics.

[Anonymous No.11711128]

>>11711102
>16 - start preparation for the IMO
if you didn't win gold at the IMO all 4 years you're NGMI

[Anonymous No.11711133]

>>11711074
Lie algebra = linearized Lie group
linearized stuff = easier stuff
I know you've heard this ten times already, but it's the truth

[Anonymous No.11711147]

>>11711074
Exponential map. I never understood the tengeant space stuff.

[Anonymous No.11711165]

>>11711147
>I never understood the tengeant space stuff.
how can one understand *anything* about lie groups and lie algebras without understanding this ?

[Anonymous No.11711166]

Now that the dust has settled, who was the best mathematician of the 20th century and why was it Serre?

[Anonymous No.11711177]

>>11711165
I mean I get the definition, I pretty much figured out the intuition behind it, and can do exercises about it, but it just feels weird to me. Like what the fuck is the tangent space of the set of antisymetric matrices supposed to be? I can compute it but it just feels unnatural to me to speak about an object like that.

[Anonymous No.11711181]

>>11711166
>Serre
Huh? It's pretty much agreed that Grothendieck was the greatest by far, man singlehandedly took AG to a whole 'nother level

[Anonymous No.11711182]

>>11711147
It's just asking where [math] f(x) = \int^x f'(x) [/math] holds apart from f with codmains R.

[Anonymous No.11711194]

Is this a good place to ask a math question because I'm an absolute brainlet?

[Anonymous No.11711199]

>>11711194
So am I. Go on and ask.

[Anonymous No.11711212]

>>11711181
Serre did the same thing to AT, was the youngest fields medalist of all time and also worked on AG. Read the Serre-Grothendieck correspondence, you'll see Serre keeps correcting Grothendieck all the time.

[Anonymous No.11711236]

>>11711199
Well then. To start off I'm doing an art project and I need a combination calculated for me.

I have 3 blocks of wood with 4 illustrations painted on each side (16 sides/illustrations total). When these 3 blocks are put together side by side they create 1 "big illustration" (4 big illustrations). BUT I can switch the places of the blocks meaning I create a new "big illustration". The question is how many big illustrations can I create by switching around the blocks and flipping their illustrated sides.

[Anonymous No.11711237]

>>11711177
>tangent space of the set of antisymetric matrices
Anti-symmetric matrices aren't closed under multiplication, so I think you mixed things up there a bit.
Anyway,
https://youtu.be/gBMdTSXhYsY

[Anonymous No.11711248]

>>11711177
it's hard to picture a Lie group as a space, but you can picture it acting on a manifold. then you'll see there's geometry behind everything, even
>what the fuck is the tangent space of the set of antisymetric matrices supposed to be?
this

[Anonymous No.11711249]

>>11711236
192.
If the blocks remain fixed, there can be 64 possible illustrations if they are arranged in three spaces, 4 possible options for each space. But you can rearrange these, so have 64x3 = 192

[Anonymous No.11711259]

a stupid question but why are toroids not constructed out of spirals instead of rings? wouldnt it have better mathematical properties than a conventional torus construction? I only see crazy conspiracy youtubers talk about this but for example from a 3D modelling point of view, I can see a lot of uses for it.

[Anonymous No.11711263]

>>11711249
can't you rearrange 3 blocks in 6 different combinations?

[Anonymous No.11711271]

>>11711263
oh, yeah
just do the same thing and multiply by 6 notn3

[Anonymous No.11711274]

>>11711259
what could one conspire about, there?

[math] R_A=\begin{bmatrix} \cos \theta_A +k_{A,x}^2 \left(1-\cos \theta_A\right) & k_{A,x} k_{A,y} \left(1-\cos \theta_A\right) - k_{A,z} \sin \theta_A & k_{A,x} k_{A,z} \left(1-\cos \theta_A\right) + k_{A,y} \sin \theta_A \ k_{A,y} k_{A,x} \left(1-\cos \theta_A\right) + k_{A,z} \sin \theta_A & \cos \theta_A + k_{A,y}^2\left(1-\cos \theta_A\right) & k_{A,y} k_{A,z} \left(1-\cos \theta_A\right) - k_{A,x} \sin \theta_A \ k_{A,z} k_{A,x} \left(1-\cos \theta_A\right) - k_{A,y} \sin \theta_A & k_{A,z} k_{A,y} \left(1-\cos \theta_A\right) + k_{A,x} \sin \theta_A & \cos \theta_A + k_{A,z}^2\left(1-\cos \theta_A\right)\end{bmatrix} [/math]

[Anonymous No.11711364]

teehee :3 i'm an anime girl :3 i like homology because i am homosexual :3

[Anonymous No.11711365]

>>11711274
cool I understand some of those symbols lol

can you give me something I can paste into wolframalpha?

actually let me get straight to the point:

https://www.youtube.com/watch?v=kxuU8jYkA1k

is this useful or gibberish?

[Anonymous No.11711402]

>>11711365
Is this /x/ on psychadelics?

The formula wasn't tory related.

But I have this 4u

https://youtu.be/FavUpD_IjVY

[Anonymous No.11711410]

>>11711402
give it a chance.

the least crazy use I can find for it is to maybe modell a functioning 3dimensional gear system pic related

[Anonymous No.11711412]

>>11711074
The Lie algebra is a linearized version of the group. You can think about it as the tangent space to the group at the identity or, equivalently, as the space of left-translation-invariant vector fields on the group.
Differentiating the multiplication map at the identity gives you the addition map on the Lie algebra.
The Lie bracket is the analog in the Lie algebra of the commutator map [math](g,h) \mapsto ghg^{-1}h^{-1}[/math] in the group. It can be interpreted as a literal commutator if you think of elements of the Lie algebra as vector fields (or derivations).

You go from the group to the algebra by differentiating at the identity. You can go the other way around using the exponential map.

[Anonymous No.11711413]

>>11711402
btw I've already seen those vids, good artist

[Anonymous No.11711483]

>>11711078
I don't want to be successful anon. I just want to understand as much as I possibly can.

[Anonymous No.11711511]

>>11711483
this

[Anonymous No.11711514]

>>11711212
Serre's also just enough of a good guy to lure you into believing you can change him, but bad enough to never really do, at least not in any meaningful way

[Anonymous No.11711517]

>>11711483
>>11711511
Understanding is the nicest success.

[Anonymous No.11711762]

How do you place commas? I was unsure about it and read some guides... now Im placing qay too many commas. Are you supposed to relax the rules for math?
>Let A, and, for all C, let B.
>Assume, without loss of generality, that A(x), where x is B.
These sentences are retarded.

[Anonymous No.11711795]

>>11711762
The first sentence is meaningless. The second one is bearable.

[Anonymous No.11711800]

Can you motivate divisors of curves please, I am so lost

[Anonymous No.11711802]

>>11711762
Let A and B be abelian groups, and let C be a Serre ring containing them. Assume, without the loss of generality, that X is a space having A and B as its second and third homotopy group, respectively, for otherwise...

[Anonymous No.11711803]

>>11711762
I have a natural tendency to comma-splice way, way too much.
The only thing I've found that works for me is to write normally at first with a hojillion commas and then read through my text and try to remove as many as I possibly can, leaving only the ones that absolutely need to be there.

The only comma in either of those examples I would consider keeping is the one after A(x) in the second line. Everything else can go.

[Anonymous No.11711827]

>>11711762
The gramatically correct way to spell out "if and only if" is "if, and only if," but I've never seen that done in a textbook, and similarly, I dont often see WLOG used correctly. You can always change the sentence structure to avoid comma overusage or simply ignore grammar rules in sensible locations. It helps if you abbreviate commonly used phrases in this sense, such as using iff or WLOG. For example, you could say:

>assume (WLOG) that A(x), where x is B.
>assume (without loss of generality) that A(x), where x is B.
>assume WLOG that A(x), where x is B.
>WLOG, assume that A(x), where x is B.
>assume for x=B that A(x), WLOG.

[Anonymous No.11711855]

Why is algebra and topology so fucking trendy these days? Is analysis a dead field or something?

[Anonymous No.11711892]

>>11711855
I think your basic assumption is faulty. Algebra and topology being popular doesn't mean analysis is not popular too.

And really pure algebra is not a booming thing. There seem to be a lot of algebraists because algebra completely pervades almost all of math, especially geometry and topology, but if you look at the algebra group of most faculties you'll see almost all of them are doing algebraic something or somethingical algebra. You won't find many people who just say "I'm a group theorist".

[Anonymous No.11711929]

>>11711855
PDEs is the most published subject in AMS journals.

[Anonymous No.11711942]

Reminder that mathematics is the best form of escapism from this cursed world.

[Anonymous No.11712046]

>>11711078
The truth is N. Bourbaki destroyed you before you had a chance. Nobody who did his start in the last twenty or thirty years will get to something deep and insightful. You will end up being a paper pusher playing syntax games until you retire or sell you soul and start to become a computer nerd.

[Anonymous No.11712160]

sneed

[Anonymous No.11712260]

>>11712046
>Bourbaki destroyed you before you had a chance.
How exactly?

[Anonymous No.11712501]

>>11711795
Agreed. I used to do the same thing as you. Now I dont put enough commas and go back to add some in here and there.

[Anonymous No.11712515]

>>11711942
based

[Anonymous No.11712536]

>>11712046
anons I really love math for it's philosophy and aesthetics, but finding other mathematicians interested in this aspect seems rare where I am. all the profs are just dry technical nerds ever optimizing their ability to make estimates or whatever. occasionally in classes I'll catch glimpses of what I love, like algebraic topology had some really interesting ideas in fundamental groups and covering spaces etc, but of course the profs glossed over the big ideas in favor of techniques.

is this because I'm not at state school (graduate) and not around the greats? where do I find this?

[Anonymous No.11712560]

Anybody feels intimidated by combinatorial results? I for the life of me will probably not be able to work on shit like Haruhi problem or Chromatic number.
I feel like there are sudden, huge leaps of logic behind them that I can't just slowly follow (like I do with analysis). Yes I understand the proof. But how do you come up with the proof, I have no idea.

[Anonymous No.11712568]

>>11711046
Which books do you guys recommend for learning differential geometry? For reference, I've finished a course on algebraic topology (hatcher, everything up to and including all of the singular homology stuff) and a differential topology course (no book, but we covered almost everything in Lee's book up to de Rham cohomology). I can't find a consensus on which books are good, with do Carmo (Riemannian book) and Lee (riemannian manifolds) being the canonical recommendations. Does anyone have experience with Loring Tu'd diff geo book? Thank you!

[Anonymous No.11712573]

>>11712536
Can you expand further on your thoughts? I don't quite understand what you mean.

[Anonymous No.11712581]

>>11712560
>Chromatic number
EXTREMELY elementary shit that follows from the inclusion-exclusion principle. If this devastates you then don't look at the 4-color theorem.

>Haruhi problem
I don't know much about this actually

As long as you can break the proof down to manageable sub-cases, computers can do most of the work. Of course, if you have no idea how to break it down, then you're screwed, but that takes practice.

[Anonymous No.11712582]

>>11711046
beautiful! :D

[Anonymous No.11712585]

bros I want to get into machine learning and have concluded the math I need to learn to truly understand it is multivariable calc, linear algebra, probability and statistics.

does that sound right? that ordering also looks like it's appropriate, I have a feeling getting calculus out of the way is going to be the biggest leap and the rest can follow

[Anonymous No.11712590]

>>11712536
Just get into set theory

[Anonymous No.11712594]

How can I get into differential geometry? I'm an engineer btw

[Anonymous No.11712600]

>>11712585
I have a friend doing a PhD in statistics and works in machine learning. You will most definitely need multivariable calc, linear algebra, probability and statistics. It'll also be important to learn some Real Analysis, up to measure theory and Lebesgue integration (for some reason, my friend uses this stuff a lot). Make sure to learn Linear Algebra reallyyyyyy well, my friend usually asks me questions about this stuff pretty often (I recommend Axler's Linear Algebra Done Right). As for the order you listed, I'd maybe try and learn linear algebra and multivariable calc at the same time since sometimes ideas form linear are useful in multivariable calc (such as when doing surface/line integrals).

[Anonymous No.11712604]

what math do I need to learn so I can rotate y=x^2 by 90 degrees? or any parabola by any degree about any axis

[Anonymous No.11712605]

>>11712585
Yes.
You only need basic things in each category by the way. Somebody tells me the last time someone actually used anything beyond 2nd order derivative in ML (that is also useful).
I don't even think they use integral apart from proving some basic probability results.

[Anonymous No.11712607]

>>11712590
>yes get into set theory, the most aesthetic (autistic) area of math

[Anonymous No.11712610]

Which branch of math is the hardest? Which can help me get a Field medal the most easily?

[Anonymous No.11712619]

>>11712610
>Which branch of math is the hardest?
Whatever you're personally worst at. Talent for mathematics can vary wildly even from subfield to subfield.
>Which can help me get a Field medal the most easily?
Stay away from combinatorics/graph theory. Probably foundations too. Pretty much any other option is just as good as anything else.

[Anonymous No.11712622]

>>11712610
In my opinion, algebraic geometry is the hardest branch of math. For reference, I know a grad student at a top school (top 15 for math) who said that algebraic geometry was wayyy harder than the research-level algebraic topology he's done. Additionally, sometimes grad students are even told not to specialize in algebraic geometry since it will take an extremely long time just to even catch up to the research literature! If you're aiming for a fields medal, I'd maybe say it would be easiest to win a medal if you're working in PDEs. I don't really know, though, I'm just an undergrad.

[Anonymous No.11712623]

>>11712581
I was having a crisis when I read the new proof of the Sunflower conjecture.

[Anonymous No.11712625]

>>11711942
True, but still cope.

[Anonymous No.11712626]

>>11712604
https://en.wikipedia.org/wiki/Rotation_(mathematics)

The equations are on this page :)

[Anonymous No.11712636]

>>11712536
Aesthetics in math is like porn. You want to view it, but it's not good for you and the people around you.

[Anonymous No.11712641]

>>11712600
>>11712605
thanks frens, I'm on the case

[Anonymous No.11712646]

>>11712619
Why the combinatorics/graph theory exclusion? I'm curious.
>>11712622
Yeah my friend told me it is hard.

[Anonymous No.11712647]

>>11712641
These results are important findings for therapeutic options in cocaine addiction suggesting treatment therapies with adenosine antagonism at high doses to block the euphoric effect associated with increased DA release.

thanks fren

[Anonymous No.11712655]

Wikipedia cannot satisfy my curiosity about category theory anymore. Does anyone have a good read about the topic? I'm a CS student.

[Anonymous No.11712668]

>>11712625
>cope
Yes, that’s the point.

[Anonymous No.11712686]

>>11712646
>Why the combinatorics/graph theory exclusion?
The biggest reason is that you have to do a specific big thing to get a Fields. maybe you've pushed forward a theory substantially or you proved a huge theorem. Combinatorics doesn't really work like this; mostly, combinatorial problems are bite-sized and don't have big sweeping consequences other than being interesting when you solve one. There are a few exceptions to this though, mostly things that come from parts of algebra that people actually care deeply about (combinatorics is extremely useful in representation theory, for example).

Another reason is credit. Combinatorics is quite collaborative compared to other parts of math. Even if 15 of the bite-size problems above can be assembled into a huge breakthrough, those chunks will often be done by 6 different people in 10 different author arrangements rather than all by one dude hiding in his office. The way people work doesn't lend itself to one guy hogging all the glory for a discovery. It's not a bad thing, but bad if you want a big shiny medal for you and you only.

[Anonymous No.11712702]

Let [math]H[/math] be a Hilbert space.
Let [math]A:H \rightarrow H[/math] be a normal operator.
Does it follow that
[eqn]\bigcap_{\lambda \in \mathbb{C}} im(A - \lambda I) = \{0\}\textrm{ ?}[/eqn]

[Anonymous No.11712718]

>>11711855
Not at all. Algebra is trendy on internet undergrad forums because algebraic topology and algebraic geometry have the reputation of being really hard and people who don’t know any better think that this reputation makes these areas more interesting.
In real life, there are more analysts than «algebraists», as this anon points out >>11711892 . Not many people specialize in the study of algebras or quadratic forms and things like that.

[Anonymous No.11712743]

>>11712655
read maclane
if you can't read maclane, you don't know enough math to learn category theory yet. stop trying until you know more math or risk joining the 41%.

[Anonymous No.11712801]

>>11712585
>does that sound right?
You are missing numerical analysis and Fourier analysis.
And other things, like abstract algebra, ODEs and numerics of ODEs might pop up.
But you don't need to go too deep in any of those.

>I have a feeling getting calculus out of the way is going to be the biggest leap and the rest can follow
If you have multi variate calculus and linear algebra you can understand what a FNN is, that is the single most important thing.

>>11712605
>What are neural ODEs

[Anonymous No.11712811]

>>11712536
I'm sure youtube has everything you want to know about the big math ideas. If you want to be a mathematician and not a mere spectator, you must become comfortable with all the machinery and technicalities. Also, I think you have a bad attitude. Even the machinery and techniques can be beautiful.

[Anonymous No.11712940]

https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminar
>Zhenkun Li (MIT)
>Instanton Floer homology and the depth of taut foliations
>Sutured manifold hierarchy is a powerful tool introduced by Gabai to study the topology of 3-manifolds. The length of a sutured manifold hierarchy gives us a measurement of how complicated the sutured manifold is. Also, using this tool, Gabai proved the existence of finite depth taut foliations. However, he didn’t discuss how finite the depth could be.
>Sutured Instanton Floer homology was introduced by Kronheimer and Mrowka and is defined on balanced sutured manifolds. In this talk, I will explain how sutured instanton Floer homology could offer us bounds for the minimal length of a sutured hierarchy and the minimal depth of a foliation on a fixed balanced sutured manifold.
>The seminar takes place on Zoom (see information below) every Tuesday at 16:00 CET (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).
Just reminding.

[Anonymous No.11713163]

>Got a bunch of books on functional analysis
>I'm used to solving exercises to see if I understand the theory
>Some books have exercises, some don't
>None have solutions

What do I do? How do you go about studying grad topics without solving exercises? They didn't teach me this in undergrad

[Anonymous No.11713174]

>>11712702
Yes.

[Anonymous No.11713178]

>>11713163
Read Haïm Brézis

[Anonymous No.11713240]

>>11711046
Does anyone here have any opinions on what to read for a graduate level in regards to theoretical computer science or mathematical subjects to read about related to that topic?
I have found some books that look interesting, but before I go spending $150 on hard copies, I want to know more about what /mg/ thinks.

[Anonymous No.11713256]

>>11713240
>buying books
What is this, 1850? Why don't you also read parchments while you're at it?

[Anonymous No.11713266]

Anyone else use matlab?
I dont need it for my degree but I think I might download matlab just for fun and to better my understanding of maths and compsci

[Anonymous No.11713276]

>>11713256
Hard copies are always easier to read.
Research shows that you read faster and have better absorption rates on paper.
Ereaders are somewhere between a computer screen and a book.
Screens are bad because of the strain caused by the lights in the monitor (even with blue light filters). As it is direct light with your eyes rather than indirect (like with a lamp).

[Anonymous No.11713296]

>>11713256
>>11713276

[Anonymous No.11713303]

>>11713174
can you elaborate?
i came up with a proof which uses the spectral theorem
>>11713163
just post the exercises here

[Anonymous No.11713327]

>>11712718
>In real life, there are more analysts
analysis is dead, people work in subfields of Analysis like Functional analysis, harmonic analysis etc, but real and complex Analysis are finished, you won't find anyone working on those fields anymore.

[Anonymous No.11713338]

>>11712655
Riehl, category theory in context

[Anonymous No.11713342]

>>11713296
what a fucking faggot, everyone in the academia reads from pdfs these days, the main income of Springer is not even people but libraries, no one is using books anymore

[Anonymous No.11713351]

>>11713327
>complex Analysis are finished
Aren't there still some lads working in value distribution, families of meromorphic functions and spaces of holo/meromorphic functions?

[Anonymous No.11713352]

>>11712655
https://youtu.be/hEW42ARKNoE
https://gist.github.com/Nikolaj-K/282515e58c1c14de2e25222065f77a0a

[Anonymous No.11713356]

>>11713342
that's false. You have no idea what you're saying.
I read both when I can afford it.
pdfs for papers, conferences, journals and paper for books I care about or books I want to keep as a long term reference.

Plus you're being autistic with your tunnel vision. My question wasn't tell me your opinion on how people should be reading, but if anyone in this thread had any insights as to what is decent theoretical computer science reading material (sci google site has nothing).

[Anonymous No.11713370]

>>11713342
I have met exactly one professor in my life who didn't read paper books, and he's a literal assburger so he barely counts. Everybody has a giant shelf of books in their office.
Most people I know prefer paper so much that when they need to read a paper they go to the department printer and print a hard copy of it.

[Anonymous No.11713383]

I just saw some argument using the fact that minimal primes exist due to Zorn's lemma... Is this even true for arbitrary commutative rings with 1? There's no guarantee an intersection of primes is going to be prime, right?

[Anonymous No.11713399]

>>11713383
actually wtf, cant believe Ive lived thus far without knowing intersections of chains of primes are prime

[Anonymous No.11713402]

>>11713327
>>11713351
I don't think complex analysis is totally dead. There are 3 profs in my department who have it listed as their research area. I have no idea what they actually do though, I'm not an analcyst.
There's also analytic number theory, which as far as I know is mostly complex-variable stuff and is still thriving.

Pure real analysis is probably much closer to dead.

>>11713383
>There's no guarantee an intersection of primes is going to be prime, right?
An arbitrary intersection? No, no guarantee.
But it's using Zorn's lemma, it's going to be talking about the intersection of a chain of prime ideals ordered by containment. It will still be prime in this case.

[Anonymous No.11713406]

>>11713276
Reading from the screen has really started to take a toll on my eyes, but the only glasses that would be good for me are pretty much what would make me look like some concentration camp nazi doctor. The world is ugly, maybe it's better to become blind.

>>11713383
Zorn is about chains, always. Instead of rechecking your ring theory, recheck Zorn.

[Anonymous No.11713407]

>>11711102
>Loose Field Medal because white man
>cry
https://www.youtube.com/watch?v=2BclyVYo0Tc

[Anonymous No.11713412]

>>11711078
If you are not virgin. No chance
https://www.youtube.com/watch?v=2BclyVYo0Tc

[Anonymous No.11713413]

>>11713406
>concentration camp nazi doctor
You need to learn german then so it's not as bad.

[Anonymous No.11713414]

>>11713407
>Loose Field Medal because white man
6 out of the last 12 fields medalists were white dudes
7 if you think iranians are white

[Anonymous No.11713421]

>>11713412
based channel

[Anonymous No.11713422]

>>11713414
Yeah so 50%, despite white mathematicians representing 90% of the contributions to mathematics.

[Anonymous No.11713425]

>>11713422
I would bet you a testicle that if you summed up all the papers on arxiv you would get one hell of a lot less than 90% white people

[Anonymous No.11713431]

>>11713413
I knew it back in the days. I'm fairly sure I could relea... nein... vier und zwanzig Jahre...

[Anonymous No.11713433]

>>11713266
>Anyone else use matlab?
I have used matlab extensively.

>I dont need it for my degree but I think I might download matlab just for fun and to better my understanding of maths and compsci
Matlab isn't great and I seriously recommend against using it in any way whatsoever if avoidable, for multiple reasons.
What goes for it, is that for the purpose of interacting with certain mathematical objects it is pretty well designed and has an enormous, consistent library with great documentation.
What goes against it is:
- It is closed source and you will be stuck in a proprietary ecosystem
- It is a *horrible* language for everything that isn't, on some level, matrix manipulation
- - String handling is a fucking joke and abysmally bad
- - It diverges heavily from the way other programming languages work, focusing on single scripts which invoke single functions, as opposed to the creation of a single program. That makes the things you learn in MATLAB uniquely non-transferable and thus in short unsuited to "better my understanding of maths and compsci".
- - - This also means it lacks (well, it *has* them, but you will never find out about them because you are not supposed to use them) a few absolutely essential features which you would find in about any other language, e.g. defining custom types
- - Ridiculously slow for everything that isn't Matrix manipulation

Thing I would recommend are:
- Python with numpy, if you are interested in numerical Analysis
- Haskell, if you are interested in (computational) Algebra

[Anonymous No.11713435]

>>11713425
Yeah and that doesn't mean anything since most papers on arxiv are 1)garbage and 2)completely useless.
Just look at relevant mathematicians. 80% white, 15% Asian, 5% other.

[Anonymous No.11713437]

>>11713327
>analysis is dead
Well, yes. Since all the big questions have basically been answered.
But calling analysis "dead" because it has been developed quite substantially and people moved onto things which aren't real analysis like PDEs, FA, etc. but which are fundamentally based on real analysis, seem to be missing the point.

[Anonymous No.11713438]

>>11713435
define "relevant"

[Anonymous No.11713440]

>>11713383
>an intersection of primes
Nah. See, for example, [math]\mathbb{R}[x, y][/math] and the [math]x[/math] and [math]y[/math] ideals.

For a chain it's completely different.
If [math]ab[/math] is in the intersection, then there are exactly two possibilities. Either every [math]I[/math] in the chain contains both [math]a[/math] and [math]b[/math], in which case both are in the intersection, or some ideal contains [math]I[/math] only [math]a[/math], in which case primeness implies that, for any [math]J \subseteq I[/math] also in the chain we have [math]a \in J[/math], since [math]b \notin J[/math], and then [math]a[/math] is in the intersection, or the same for [math]b[/math].

[Anonymous No.11713441]

>>11713440
>>11713402
>>11713406
lads, please, i already realized my retardedness in the next post >>11713399

[Anonymous No.11713442]

>>11713433
Python's really good to know at some level if you're interested in math because it also has Sage.
A lot of Sage code/documentation is of very dubious quality since it's basically just open-source scripts written by mathematicians in the process of their own research, but the other side of that coin is that Sage has unique libraries to work with a ton of niche, often research-level stuff and many of those libraries are ripe for contributions if you're interested in adding your own code.

[Anonymous No.11713443]

>>11713441
My bad, I thought it was someone else commenting.

[Anonymous No.11713444]

>>11713441
nigger I replied 20 seconds after you posted
my page didn't even refresh before I clicked send

[Anonymous No.11713477]

>>11713438
I know them.

[Anonymous No.11713487]

>>11713433
Based. Matlab can suck my dick and so can mathematica. It’s crazy how bad proprietary math software is t b h

[Anonymous No.11713500]

Why are you studying algebra haha?
Just use the quadratic formula lmao haha :)

[Anonymous No.11713530]

decided to teach myself math
high school level algebra making me feel like a brainlet
integrals man

[Anonymous No.11713564]

>>11712811
retard I'm in a graduate program. I'm ok doing hard technical stuff.

>>11712590
no. just because it's historically had philosophers involved doesn't mean other math isn't interesting to me.

>>11712573
for me the goal of math is understanding. sometimes it's clear we are learning new ways of viewing the world or understanding a subject

in my algebraic topology example fundamental groups show that the configuration of "holes" in a space characterize it. this is further made interesting by covering spaces which pull apart those holes into an analagous surface. so it tells you a lot about what is actually a topological feature and it's interesting to think about what the covering space is for another space.

when I was taught this nobody told me any of that, they just told me how to calculate stuff and prove its a covering space.

however sometimes its clear that a prof is studying something not because it has explanatory power but because nobody else cares. or rather the only people that care are the others in that fields. they estimate the upper bound on some function ever more accurately, etc. it's just a technical skills that literally has no bearing on anything other than being a math professor. (and I don't mean "doesn't have application")
does this help?

[Anonymous No.11713578]

>>11713564
>when I was taught this nobody told me any of that
if you were actually taught an entire algebraic topology class without anyone ever drawing some loops on a donut you should seriously consider going and asking for a refund from whatever university gave you your cracker-jack degree

[Anonymous No.11713648]

>>11713422
haha, owned, white people are so proud of their 'intelligence', but proportionally they contribute less than people of color, shut a slap in the face

[Anonymous No.11713679]

Steins;Gate is the most /sci/ anime ever, they even talk about relativity, string theory, astronomy and three of the main characters are STEM students.

https://youtu.be/IH18z1SSN2U

[Anonymous No.11713714]

Wow, cool, thanks for pointing out that obscure media

[Anonymous No.11713716]

>>11713648
you don't understand anything do you? Fields medal is political, just like the nobel prices

[Anonymous No.11713717]

>>11713714
I've never seen anyone talking about Steins;Gate here, I'm in ecstasy after watching it, I need to recommend it to everyone in /sci/.

[Anonymous No.11713719]

Who watch mathgirl?

[Anonymous No.11713726]

>>11713716
How's the fields medal political? Can you question the work and contributions of the recent winners? I really doubt it. Also, only the literature and peace Nobels are political, but no one cares about them anyway.

[Anonymous No.11713730]

>>11713719
>eceleb shit
enjoy your ban

[Anonymous No.11713732]

>>11713716
Thats not why he's wrong dumbfuck, he's wrong because white mathematicians don't represent even close to 90% of "the contributions to mathematics".

[Anonymous No.11713734]

>>11713730
She not popular only 10 views

[Anonymous No.11713756]

>>11713719
is that a girl (girl)?
Does (he) she actually do any mathematics or just talk about it like someone else?

[Anonymous No.11713763]

>>11712568
Most introductiory differential geometry books are more about differential topology than geometry.
A nice aesthetic choice is to read Sarge - Differential Geometry and supply with Lee for some more aspects of differential topolgy and classical results. All books you mentioned are fine, it's mostly up to personal taste and which aspects you are most interested in.

[Anonymous No.11713764]

holy shit, this guy studies 10h per day, wtf, if I could manage that I think I could genuinely get into an Ivy League or some shit

https://youtu.be/cIVGp0SVAKw

[Anonymous No.11713773]

>>11713719
what's her research area? What college did she go to?

[Anonymous No.11713774]

>>11713763
>not recommending do Carmo
discard his opinion, everyone

[Anonymous No.11713789]

>>11713763
I meant Sharpe of course.
>>11713774
> Do Carmo
yawn

[Anonymous No.11713805]

>>11713764
Theres a difference between being a robot med student rote learning various facts and learning for actual understanding in mathematics.
Poincare worked 4 hours a day. Most mathematicians only do a few hours of serious work a day, 10 hours of good quality work is almost impossible (maybe for some short period of time once you have an idea for a major result)

[Anonymous No.11713818]

>>11713805
Yeah, while you're thinking 4h is fine, there's an asian or indian studying 12h a day in an Ivy League or there's a math 55 student doing nothing all week but eat, sleep and solve lists

[Anonymous No.11713825]

>>11713764
I don't know what it's like studying medicine personally.
But I have a few friends that are quite far into med, and they say it's not the difficulty that's the issue, it's all the memorisation you have to do when to comes to certain things.
Mathematics & related areas (computer science, physics), is more about complexity and depth. This is where your intelligence is important. For slightly above average people like me, it takes us a while to study some concepts where it takes someone who is way above average, maybe an hour to do it nearly perfectly.

My memory of key facts is not great unless I have insight into the underlying concepts, from which I can derive the fact or thing I'm trying to answer a question for. This makes me a good problem solver but terrible at exam or test situations where I have to memorise the conclusion over the premise(s) needed to get to that conclusion.

I would be shit at med, but I'm okay at coming up with solutions to things.

[Anonymous No.11713851]

>>11713679
>relativity, string theory, astronomy
Neither science nor math.

>three of the main characters are STEM students.
Not mathematicians.

Also, stop posting my waifu.

[Anonymous No.11713861]

>>11713719
I am not insane enough to fall for e-girls.
YIKES

[Anonymous No.11713864]

>>11713851
it's heavily implied okabe's a mathematician, also compsci is a subfield of math

[Anonymous No.11713868]

>>11713864
>it's heavily implied okabe's a mathematician
It is?
He clearly seems to go into the direction of engineering, at least from the entire subtext of the show.

>compsci is a subfield of math
Far too little of a compsci degree has anything to do with math to make that meaningful.

[Anonymous No.11713873]

>>11713773
Undergrad

[Anonymous No.11713910]

>>11713327
That's an odd thing to say. Everyone works in subfields. Nobody studies algebra or analysis or probability or geometry per se. They work in more or less tiny subdomains of these (that usually do not fall squarely into one category or another).
PDE is one of the most active (and broad) areas in math and it is very much "real analysis".
For current complex analytic areas of research, you could talk about complex geometry or holomorphic dynamics, both very active topics of research.

[Anonymous No.11713923]

>>11713873
Now answer this. Why would I waste my time hearing a dumb undergrad, moreover a woman, who therefore has an understanding of math that is ten times lower than mine, when she isn't even remotely attractive?

[Anonymous No.11713936]

>>11713774
Lee's book on Riemannian manifolds is better than do Carmo. nothing personnel, do Carmo is great, but it's an old book and has been surpassed.

[Anonymous No.11713950]

>>11712568
Lee > do Carmo
Lee and Tu are uncomparable, both are good but they go in different directions

[Anonymous No.11713974]

Can I read dieudonne's entire treatise on analysis without anything other than it?

[Anonymous No.11713994]

>>11713726
Saying that the Fields medal is political does not necessarily the merits of the winners. Of course they are brilliant. But there is no shortage of brilliant mathematicians.
Maybe not hundreds, but you can be sure that, every four years, there are dozens of plausible candidates.
How do you figure they pick four people out of 30 geniuses, each one at the top of their respective field, all working in completely different areas ?
There has to be some kind of non-mathematical input.
The same thing happens when unis recruit professors. Certainly not all applicants are equally skilled, but be sure that there are always more outstanding candidates than there are positions.
Now 'political' does not mean PoSt-MoDeRn-NeOMarXisT AgEnDa, but there is definitely some shady stuff going on.
For universities, there is definitely office politics involved: If the number theory team had their pick 3 years in a row, then the uni might not recruit a number theorist that year (unless he is Scholze-tier ofc). If the guy is outstanding AND knows people on the team, that can be a plus, etc.
For the Fields medal, there are similar concerns: area of research (probability theorists used not to be very fashionable for example), country of origin, age (Scholze could have had his medal a long time ago but people thought it good to let him wait and give it to older people who would not get other chances), and others.

[Anonymous No.11713995]

>>11713936
>>11713950
shut the fuck up brainlet, do Carmo is the Rudin of Differential Geometry, while Lee is more like the James Stewart equivalent.

[Anonymous No.11714002]

>>11713974
Yes, but Schwartz is better

[Anonymous No.11714020]

>>11713726
Saying that the Fields medal is political does not necessarily detract from the merits of the winners. Of course they are brilliant. But there is no shortage of brilliant mathematicians.
Maybe not hundreds, but you can be sure that, every four years, there are dozens of plausible candidates.
How do you figure they pick four people out of 30 geniuses, each one at the top of their respective field, all working in completely different areas ?
There has to be some kind of non-mathematical input. It cannot be completely neutral.
The same thing happens when unis recruit professors. Certainly not all applicants are equally skilled, but be sure that there are always more outstanding candidates than there are positions.
Now 'political' does not mean PoSt-MoDeRn-NeOMarXisT AgEnDa, but there is definitely some shady stuff going on.
For universities, there is definitely office politics involved: If the number theory team had their pick 3 years in a row, then the uni might not recruit a number theorist that year (unless he is Scholze-tier ofc). If the guy is outstanding AND knows people on the team, that can be a plus, etc.
For the Fields medal, there are similar concerns: area of research (probability theorists used not to be very fashionable for example), country of origin, age (Scholze could have had his medal a long time ago but people thought it good to let him wait and give it to older people who would not get other chances), and others.
In addition, whatever the criteria, prizes, and especially Fields medals, have a political effect on the world of mathematics. Whomever you give a Fields medal to will get very wide exposure. Their university and their country will be in the spotlight; their area of expertise will become very fashionable.
These choices carry a very heavy weight.

[Anonymous No.11714028]

>>11714002
>Schwartz
Who?

[Anonymous No.11714030]

>>11714020
This.
I'm a baby when it comes to mathematics, but I see this exact pattern everywhere.
What "sends the right message" behind "good intentions", is more important then the work you did.
As you said, they are all brilliant, but there is motive for the selection not to be fair.

[Anonymous No.11714065]

>>11713923
I want to know her, help her with math problems, seduce her.
Then I want to get in her beds, fuck her hard enough, let her enjoy the pleasure of being cummed inside while screaming "I'm on 10% of your intelligence, please let me conceive your genius child".
Then dump her.
Isn't that normal?

[Anonymous No.11714074]

is the growth rate of the area of a circle defined by the line
y=pi x^2

[Anonymous No.11714107]

>>11714020
I'm not reading all that fearmongering bullshit, sorry, but you should know that your mentality is pathetic, grow up, study more, then come back here with an actual good post

[Anonymous No.11714122]

>>11714107
What mentality ?

[Anonymous No.11714129]

how do i find a non linear function for a table of values? let's say i have the tables, i know its 2nd polynomial
1 2 3 4 x
2 4 8 16 f(x)
is there a rule to find a function for it or at least some computer program?
sorry for broken english i am ESL

[Anonymous No.11714143]

>>11714129
If I understand correctly, given a certain number of values the function takes, you want to know the explicit definition of the function? For polynomials of a given degree you can, via Lagrange interpolation. I think it might also be possible with rational functions.

[Anonymous No.11714144]

>>11714107
What mentality ? All I said is that there is no way to choose 4 people among all mathematicians under 40 that are uncontroversially the best of their field, if only because there are a lot more than 4 areas of mathematics and each one has a couple of people that are way above everyone else. Obviously the jury's taste is involved. This is not fearmongering, it is literal arithmetic.

[Anonymous No.11714156]

>>11714129
>is there a rule to find a function for it or at least some computer program?
This is called "interpolation" there are millions of ways to do it.
The simplest one being to "just connect the dots" on the graph.

[Anonymous No.11714162]

>>11714074
No. The area of a circle is pi*r^2, this the growth rate is it's derivative, 2*pi*r.
If you recognize that it's circumference, congratulations, because that is exactly what it is and has to be.

[Anonymous No.11714169]

>>11714107
>I'm not reading all that fearmongering bullshit
That is a shit mentality.
If you get challenged on your ideas and fall back to calling it "fearmongering", you have the awful mentality.

Either be willing to defend your ideas, or change them.

[Anonymous No.11714170]

why is apostols calculus the best calculus text ever? when I took Calc 2 4 years ago I had issues understanding /visualizing integrals for volumes and the prof gave me the same rather unmotivated proof of the integral my calc1 teacher gave us, and it was no help.
but apostol? there is no ambiguity, I have no issues visualizing, and Im halfway thru the book and I haven't once used a calculator
wtf?

[Anonymous No.11714258]

Family mathematicians, academics? No? Well then, that means you just have to learn from the greats. Read Grothendieck, Milnor... You know Serre became Big S because he was bullied in school and was forced to to older kids' homework? See what I'm saying?
Listen, the key is to just relax. Don't worry about your research output, don't worry about what the other guys are thinking. You're attracted to maths for a reason. You believe that, right?

[Anonymous No.11714262]

>>11714258
Just remember: if you aren't published by the time you're 24, you are never ever going to make it.

[Anonymous No.11714273]

>>11714258
There are no two words in the english language more harmful than 'Algebraic Geometry'.

[Anonymous No.11714288]

>>11714162
thanks
the real q I'm tryna wrap my head around is
why does a circle with half the area of another circle have more than half the radius if the growth rate is linear?

[Anonymous No.11714302]

>>11714288
"The growth rate of what with respect to what ?" is the question you should really be asking
The growth rate of the area is proportional to the square of the radius so, if the areas of two circles differ by a factor of two, their radii differ by a factor of sqrt(2)

[Anonymous No.11714309]

"The growth rate of what with respect to what ?" is the question you should really be asking
The area grows proportionally to the square of the radius so, if the areas of two circles differ by a factor of two, their radii differ by a factor of sqrt(2)

[Anonymous No.11714335]

>>11714273
>doing AG in english
>not doing it the way it was intended, in French
ngmi

[Anonymous No.11714352]

>>11713719
they cant match this man

[Anonymous No.11714354]

How do I get a range of items in a list in LaTeX? I.e. a list of this structure:
a)
b)
c-e)
etc. ?

[Anonymous No.11714365]

I heard about someone doing a masters thesis on platonic solids (in math, not philosophy).
What is there to learn about them? Is there some advanced graph theory hidden relatet to them?

[Anonymous No.11714368]

>>11714352
Although he's wrong about the reals, he's right that universities lack rigor when it comes to justifying stuff we do in high schools. More time needs to be spent in translating the basic results we learn in highschool to theorems in the proper rigorous framework that you learn about in university.

[Anonymous No.11714371]

>>11714354
why not just do
\item [a)]
\item [c-e)]
?

[Anonymous No.11714376]

>>11714335
Imagine learning or being born in a country that speaks mumble rap
yikes

[Anonymous No.11714382]

>>11714376
imagine not mumble rapping while investigating the chemical geometry of platonic solids

[Anonymous No.11714400]

>>11714376
Hey, canadian french isn't mumble rap...

[Anonymous No.11714414]

Relearning trigonometry by myself.
Phi Φ suddenly appears as part of the major identities without explanation.
Is it just a different variable for radian or?

[Anonymous No.11714429]

>>11714143
>Lagrange interpolation
i am not sure if that's what i was looking for but thanks anyway. to put in a different way what i want is what function would give these values in the table for example [math]f(x)=x^2+x+4[/math] given that i already know it's 2nd degree polynomial
>>11714156
>The simplest one being to "just connect the dots" on the graph.
how would that tell me what function would give these values? it wouldn't even help me know what degree polynominal it is for something higher than 3rd

[Anonymous No.11714442]

>>11714414
That or the golden ratio.

[Anonymous No.11714456]

Are there any open problems which reduce to asking something specific about a specific finite graph?

[Anonymous No.11714458]

>>11714414
it is a very common name for an angle (along with theta and psi)

[Anonymous No.11714463]

>>11714429
You could use least-squares

[Anonymous No.11714470]

>>11714442
>>11714458
thanks

[Anonymous No.11714473]

>>11714376
>Imagine not speaking the language of Pascal, Descartes, Laplace, Legendre, Galois, Cauchy, Fourier, Jordan, Poincaré, Schwartz, Dieudonné, Cartan (father), Cartan (son), Serre, Grothendieck, Connes, etc...

[Anonymous No.11714481]

>>11714456
Any open problem in category theory, graph theory or combinatorics.

[Anonymous No.11714485]

>>11714473
Never speak the language of mine or my son ever again.
- Élie Cartan

[Anonymous No.11714523]

>>11714473
The french they spoke is very different than modern french, which is pure mumble rap.

https://youtu.be/rD--OdhdJfg

[Anonymous No.11714529]

>>11714371
Thanks bro

[Anonymous No.11714576]

>>11714523
>The french they spoke
The french who spoke? Because everyone in the list from at least Galois and onward spoke modern french. And before that there was no such thing as standard french because it was standardized at that time, before everyone spoke a different dialect.

[Anonymous No.11714604]

>>11714481
>>11714456
Don't know if
>Any open problem in category theory, graph theory or combinatorics
comes down to
>something specific about a specific finite graph

Even something concrete like
>Is there any odd natural number that's the sum of its positive divisors (as in 6=1+2+3, but for an odd number)?
is an existence question and not about a particular object.

But here's a bunch of open graph theory problems:
https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics#Graph_theory

[Anonymous No.11714605]

>>11714576
Liar! Modern french, as shown in the video (in the last seconds or so) has only begun to take shape after the second half of the 20th century, probably due to the huge immigrant influx that happened after WW2, out of that last very few (if any) spoke the mumble rap we hear these days.

[Anonymous No.11714625]

>>11714605
Well Serre certainly speaks like that, and he was born in the 1920's IIRC. Every recording (e.g. pétain or de gaulle) of the first half of the 20th century shows that they also spoke modern french.

[Anonymous No.11714649]

>started how to prove it back in january
>finishing chapter 3 today
I'm not gonna make it brahs

[Anonymous No.11714657]

>>11711046
wtf does ANY of that mean

[Anonymous No.11714662]

>>11714657
It's basic algebraic topology

[Anonymous No.11714702]

>>11714481
Give one (1) example.
>>11714604
None of the unsolved problems seem to be about a specific finite graph: all of them seem to be much more general.

[Anonymous No.11714745]

>>11712743
>>11713338
>>11713352
Thanks!

[Anonymous No.11714759]

>>11714702
All of them.

[Anonymous No.11714762]

>>11714649
That's plenty of progress, we're proud of you

[Anonymous No.11714765]

>>11714456
>>11714702
i don't think you're going to find something like this
there are problems like "compute the ramsey number r(5,5)" which essentially boils down to examining the colorings of a finite number (like 5 or 10) of certain graphs
but i'm not sure i would call that a serious mathematical problem

[Anonymous No.11714769]

>>11714762
I'm not proud of him, he's a dissapointment. I had great hopes for anon.

[Anonymous No.11714778]

>>11714288
the growth rate is linear. the larger the circle the faster the area increases. the area itself is quadratic

[Anonymous No.11714794]

>>11714258
>You know Serre became Big S because he was bullied in school and was forced to to older kids' homework?
Was Serre, dare I say it, /sqt/'s guy?
>>11714473
>Connes and Serre are literally still alive
>in anon's head, Connes goes to the store and talks to Algerian immigrants working there in archaic french

[Anonymous No.11714823]

>>11714702
If you want a non-natural example, you can translate SAT problems to a questions of weights on vertices.

[Anonymous No.11714860]

>>11714762
this is a pathetic progress, I'm too fucking lazy holy shit

[Anonymous No.11714873]

Proof there's no largest integer.
Hard mode: No induction allowed.

[Anonymous No.11714877]

>>11714873
suppose there's a largest integer n. then consider n+1. that's it.

[Anonymous No.11714880]

Prove there's no largest integer. Hard mode: No induction allowed.

[Anonymous No.11714888]

>>11714877
>>11714880
Sorry, you were quick. Corrected a typo.

Also, I don't think that's it. What do you think you have shown?

[Anonymous No.11714898]

>>11714880
>No induction
You mean no third removed. No induction is ebin n+1.
For no third removed, I think you can set [math]A[/math] as the set of natural numbers which aren't the largest natural number and show that [math]A= \mathbb{N}[/math] (by induction).
Then again, no third removed is fucking finicky.
>>11714888
>Also, I don't think that's it.
Das literally it.

[Anonymous No.11714901]

>>11714888
I shown that there was no largest integer.

[Anonymous No.11714915]

>>11714898
>>11714901
>Das literally it.
>I shown that there was no largest integer.
How so?
If I study your prove, I conclude that the largest number, call is u has the property
u+1 = u

[Anonymous No.11714922]

>>11713240
>theoretical computer science or mathematical subjects to read about related to that topic?
The old 'canonical' topics are the discrete math primer (lovasz and combinatorics, diestel / bollobas and graph theory), the basic complexity results in arora / barak, your favorite linear algebra book, a year's sequence of abstract algebra, and being more than comfortable with CLRS. After that, it really depends on your subfield - people interested in deterministic algorithms related to databases would do more combinatorics and algorithms reading, those in learning theories would do more analysis, those in comp. geometry and topology would do..well, you guessed it, etc..

TCS is one of those fields that's rapidly growing in both reach and depth. A lot of people get in because of the discrete math, while a substantial amount of others use more "structure based" mathematics like topology to study complexity, automata, etc etc.. Hell, even analysis of algorithms and complexity theory now has analytic combinatorics for powerful average case analysis and solving harder classes of increasingly common questions, and that entire study is based on transfer theorems in complex analysis.
So the best answer I can give is probably to go through the undergrad canon for math and then pick up whatever you need / like for subfields you're interested in.

[Anonymous No.11714923]

>>11714915
Which is a contradiction, since such a statement would imply that 0 = 1.
That's the whole point.

[Anonymous No.11714938]

>>11713240
>>11714922
Oh i should mention that unlike math, TCS is young enough that it doesn't have big 'tomes' of all the novel progress and results from TCS involving more than just discrete math. A lot of the results are locked behind reading more papers since many of the greats from TCS were professionally trained in math first.
So it's really not a meme when I tell you that reading more research papers and having the math undergraduate canon + whatever graduate level mathematics interests you is the best way to go about CS. There's a bunch of low hanging fruit, but if you want to find hard problems, there are plenty of deep, difficult questions you can ask about computation.

[Anonymous No.11714946]

>>11714923
You seem to say that [math] u+1=u \implies 1=0 [/math], but I'm not sure if I understand why that would necessarily be the case.

[Anonymous No.11714963]

>>11714946
substract [math]u[\math] on both sides

[Anonymous No.11714969]

>>11714365
bump

[Anonymous No.11714972]

>>11714963
well I fucked up but you get the idea

[Anonymous No.11714999]

>>11714972
Define substract.

No don't, I'm trolling. It's a dead end, but this has been going for too long.

>>11714969
Did wikipedia not help?
Interesting how you get to that idea, too.

[Anonymous No.11715019]

>>11714969
People make master's theses out of anything. Some have really majestic and pompous subjects, some just write out how to prove some formula for [math]\pi[/math]. It could simply be that the whole idea was to show that there are no other platonic solids. If you are in just to get a degree, why do too much work if you can do less and look for a job at the same time? It is, of course, more fun to do it on something you like, and I could imagine someone doing a low effort master's thesis on platonic solids because it is still a classical thing to study those, and hence potentially appealing to someone. It could, also, be the case that there is some graph theoretical etc. stuff there, but I don't know. I'm not saying this person was after low hanging fruits, I'm just saying that most people don't necessarily find it worth the effort of writing 60 pages of ground work just to modernise the proof of a deep result.

[Anonymous No.11715130]

>>11714794
>tfw Serre is 93

[Anonymous No.11715272]

>>11715130
and still sharp as a tack
https://youtu.be/dxRDEuuko-o

[Anonymous No.11715342]

In optimization theory / convex things, one often encounters the support function of a convex set: [math]\sup_{x \in C} \langle y, x \rangle[/math]. It comes up naturally in a many different settings, it's related to things like dual norms in vector spaces, and in general it's a pretty commonly encountered quantity. Is there a general terminology for the "opposite" function, [math]\inf_{x \in C} \langle y, x \rangle[/math]? Of course, this is just the support function in the direction of [math]-y[/math], but I am curious what it tells about the relation between [math]y[/math] and the set [math]C[/math].

I don't have any specific question, this function just came up in some bounds that I've been deriving and I got curious if it has any "meaning" or if it comes up in some other settings that might be of interest.

[Anonymous No.11715440]

Can anybody tell me what solubility means in the context of congruences?

[Anonymous No.11715441]

So ugly:

[math] j(p)-j(q) = \left({1 \over p} - {1 \over q}\right) \prod_{n,m=1}^{\infty}(1-p^n q^m)^{c_{nm}} [/math]

[Anonymous No.11715539]

>>11715440
Never mind, sorry for the brainlet question.

[Anonymous No.11715562]

>>11715539
I forgive you.

>>11715441
What is this j?

/gnmg/

[Anonymous No.11715647]

FUCK THIS SHIT I DONT FUCKING GET IT someone help me please. What kind of a question is this?
I need to prove it by using contrapositive, and if I take
P -> Q as contrapositive then it is ~Q --> ~P.
then it is basically "if x/sqrt(x stuff) = y/sqrt(y stuff) then x = y". What the heck am I supposed to do here to manipulate the equation to get x=y? The answer is logically obvious but I dont understand the process.

[Anonymous No.11715691]

>>11711046
If I have [math]f'(u)=-D_x\log g(x)[/math] can I obtain a formula for [math]f^{(n)}(u)[/math]? I want to be able to write these higher order derivatives down without a bunch of calculation each time.

[Anonymous No.11715711]

>>11715647
if x isn't y can't u just use the baby 0 identity to show x-y isn't 0?

[Anonymous No.11715713]

>>11715441
is that for circles and trig functions?

[Anonymous No.11715727]

>>11715711
The book I got the question from tells me to use contrapositive to prove the statements. If the baby 0 identity you mentioned is used within the contrapositive proof, please clarify further as I don't know what you are referring to.

[Anonymous No.11715743]

>>11713764
The only mathematician I know who worked 10 hours a day was Grothendieck. Poincare was only 4, Hardy worked only 4 maximum and then played cricket for the rest of the afternoon, and I think that's the rule rather than the exception.

[Anonymous No.11715772]

>Relearning trigonometry by myself

Learn rational trigonometry instead, it just werks

[Anonymous No.11715779]

>>11715647
Literally just square both sides and cancel and show the only solution is when x^2 = y^2

[Anonymous No.11715816]

>>11715779
Amitabha, I humbly bow before your big brains.

[Anonymous No.11716055]

How long do you do math a day?
How long do you spend time on a problem? I feel like the longer I get stuck on one, the less likely I can do it.
Do you cycle from problem to problem?

[Anonymous No.11716149]

>>11715772
Is it more useful/efficient or is it just easier to learn?

[Anonymous No.11716211]

>>11713789
I've never heard about Sharpe's book, though it seems to have good ratings on Amazon. What's your experience with the book and why do you recommend it? For reference, I think I'm mostly interested in differential geometry because I'd like to understand Perelman's proof, gauge theory, and Yang-Mills.

>>11713950
If my intent is to learn gauge theory, Yang-Mills, and other physics-y stuff, would you recommend Tu's diff geo book over John Lee's book? One thing I didn't really like about Tu's book is that the exercises seem very easy.

>>11713995
What's your argument for do Carmo being better than John Lee's book? I'm not asking this in a hostile way, I just want to make a good decision on which book to work through.

[Anonymous No.11716302]

>>11716055
>How long do you do math a day
During college semesters, I can do math for like 5 hours. By doing math I mean working with two other friends on problems, trying problems on my own, and reading through textbooks. However, during breaks I can really only do like 1-2 hours of semi-deep work.

>How long do you spend on a problem?
I can usually spend hours on problems. On homework assignments, I can usually stick to a problem for 5 hours. If I don't solve it by then, I'll ask a friend for a hint.

>Do you cycle from problem to problem?
Yep. If I get stuck on a problem, I'll usually skip around to other problems and just cycle through them like that. I usually find that this helps, especially if you're doing problems from homework or textbooks, since sometimes ideas from other problems can help.

[Anonymous No.11716422]

>>11713648
>drastically lower population than non-whites
>significantly more contributions
There's that nigger inferiority complex again. Must suck.

[Anonymous No.11716581]

>>11716211
>If my intent is to learn gauge theory, Yang-Mills, and other physics-y stuff, would you recommend Tu's diff geo book over John Lee's book? One thing I didn't really like about Tu's book is that the exercises seem very easy.
definitely Tu. if you want into gauge theory, you need principal bundles. Lee doesn't touch them at all.

[Anonymous No.11716591]

>>11711102

More realistic scenario that applies to 99.999999% of this board

>>16 - realize you couldn’t even make it to nationals
>>17 - graduate highschool
>>18~21 - graduate community college
>>21~24 - attempt graduate degree at bottom tier university, crash and burn, drop out
>>25~30 - work menial job
>>30 - full time wage cuck
>>that's the path towards life.

You will soon realize what type of people browse 4chan if you haven’t already (hint not field medallists) . And then you will realize you’re one of them.

[Anonymous No.11716596]

>>11716581
Sounds good, I'll make sure to use Tu then. I appreciate the help. Do you have any other book recommendations for getting into gauge theory/yang-mills or general advice on learning the material?

[Anonymous No.11716668]

>>11714880
Assume N is the largest integer. N+1 > N by definition, a contradiction.

[Anonymous No.11716674]

>>11715691
>can I obtain a formula for f(n)(u)f(n)(u)?
Yes, it is zero, as the right hand side of f'(u) is independent of u.

[Anonymous No.11716691]

>>11716674
I think the question pretty clearly seems to be aimed at chain rule being repeatedly applied.
>>11715691
So [math]\frac{\partial x}{\partial u}=-\frac{1}{g(x)} [/math] and you're asking how to quickly get [math]f''(u), f'''(u), \dots[/math], is that right?

[Anonymous No.11716700]

>>11716691
>I think the question pretty clearly seems to be aimed at chain rule being repeatedly applied.
How so?
f'(u) does not depend on u you can't just make up some dependence.
f''(u) is very clearly zero.

Of course, this probably wasn't what was meant, but I won't spend my time trying to guess the question...

[Anonymous No.11716704]

>>11716700
what's the point of even responding to that question then lmao

[Anonymous No.11716708]

>>11716704
>what's the point of even responding to that question then lmao
To get the person to think about the question he was asking, realize that it doesn't make sense and then ask the actual question.

Telling a person "this question doesn't make sense, let me guess what you mean" is usually less helpful then just demonstrating that they need to reconsider the problem.

[Anonymous No.11716730]

>>11716708
While that's somewhat fair, I suppose since it was a fairly simple question in my opinion I felt no need to fill in pretty obvious blanks since this only really makes sense in one nontrivial case.

[Anonymous No.11716732]

I thought I was good at maths and then I entered this thread

[Anonymous No.11716740]

>>11716732
I thought I was bad at maths and then I entered /sci/ lmao

[Anonymous No.11716745]

>>11716730
I had the experience that often when people ask badly formed questions it isn't the result of just a typo, but a genuine misunderstanding.
Clearing up that misunderstanding, if it exists, should be the first step to a solution.

I really do not like guessing what people mean, that very easily leads to confusion on both sides.

[Anonymous No.11716758]

>>11715562

https://en.wikipedia.org/wiki/Monster_Lie_algebra

[Anonymous No.11716775]

>>11716055
>How long do you do math a day?
Actively 4 hours or more, subconsciously all the time.
>How long do you spend time on a problem?
As long as it takes.
>Do you cycle from problem to problem?
A few problems under work all the time so I can try to make progress on one if I can't do that with another.

>>11716758
Thanks.

[Anonymous No.11716784]

>>11716745
I'm not disagreeing with you, I just think in this case it's pretty clear. I see no other reasonable interpretation there so I don't think I was really guessing much.

[Anonymous No.11716828]

>>11711046
Guys where is yukarifag? You know, that guy that always posts about physicists working with mathematicians and uses touhou avatars. I want to be an epic geometer like him. He is my idol.

[Anonymous No.11716942]

>>11716828
>He
He is not a he.

[Anonymous No.11716966]

https://homepages.warwick.ac.uk/staff/Samuel.Le-Fourn/contenu/Reflexions_mathematiques/GianCarloRota.pdf

[Anonymous No.11716979]

>>11716055
>both answers are above or equal to 4
LITERALLY HOW.

[Anonymous No.11716980]

spent today learning about imaginary numbers and solving cubic equations with them
brainlet but comfy :)

[Anonymous No.11717007]

>>11716942
Wait wtf I didn't know this. Is yukarifag trans or a biological woman?

[Anonymous No.11717014]

>>11717007
Yes.

[Anonymous No.11717020]

>>11717014
You didn't really answer whether if yukari was trans or biologically a woman...

[Anonymous No.11717021]

>>11717020
>>11717007
How new are you.

[Anonymous No.11717023]

>>11717020
Do you really think there would be a single femanon posting in these threads, cis or trans?

[Anonymous No.11717024]

>>11717023
Clearly she's not posting anymore.

[Anonymous No.11717025]

>>11717021
I started browsing this site this past December. I am not asking this question in a hostile manner.

[Anonymous No.11717026]

https://bookauthority.org/books/new-algebraic-geometry-books

Here's a list of new books (last 2 years) in Algebraic Geometry.
Do anybody recommend any of them?

[Anonymous No.11717028]

>>11717024
>she
She is not a she

[Anonymous No.11717029]

>>11717026
>(You?)
Yes.

[Anonymous No.11717030]

>>11717025
>I started browsing this site this past December.
Well, that explains it.

>I am not asking this question in a hostile manner.
I am not accusing you of that.

[Anonymous No.11717033]

>>11717023
It's not very rare to encounter trans women in STEM fields. I wouldn't be surprised if a non-trivial percentage of /sci/ posters are trans...

[Anonymous No.11717035]

>>11717033
Can you point one out though? Without an example it is just speculation.

[Anonymous No.11717036]

>>11717007
Pretty sure Yukarifag is a homosexual cisgender male who occasionally looks through heterosexual Yukari doujins for crops.
>>11716211
>gauge theory, Yang-Mills
I think you might want to swap Lee/do Carmo by Jost's Riemannian Geometry and Geometric Analysis, in that case.
>last chapter is literally about QFT
I haven't read that book in particular, but I've read some other Jost stuff, so it should be good and largely geared to what you want to do.

[Anonymous No.11717041]

>>11717030
Ok, I highly doubt anyone knows yukari's gender so I guess I was just being dumb. I still want to one day be an epic geometer like yukari that has masterful command over TQFT and gauge theory.

[Anonymous No.11717045]

>>11717041
I would suggest that you rather take a random hobo on the street as an idol, but you do you...

[Anonymous No.11717046]

>>11717041
>>11717036
Yukarifag's been doxxed here and yes, he's a male.

[Anonymous No.11717047]

>>11717046
>Yukarifag's been doxxed
Source?

[Anonymous No.11717052]

>>11717036
>I think you might want to swap Lee/do Carmo by Jost's Riemannian Geometry and Geometric Analysis, in that case.
Thank you. It doesn't seem like Jost's book is very popular for some reason, but I will make sure to check it out. What about Tu's diff geo book? Also, do I have the adequate background for Jost's book (>>11712568)? What about Bott-Tu's book on algebraic topology, would that stuff be useful/is it a good book? Sorry for asking so many questions.

[Anonymous No.11717060]

>>11717029

what

[Anonymous No.11717062]

>>11717046
Wasn't that a meme?
>>11717052
Other anon has already responded about Tu.
>do I have the adequate background for Jost's book
It literally starts out by recalling what a topology is.
>What about Bott-Tu's book on algebraic topology, would that stuff be useful/is it a good book?
The differential forms in algebraic topology one?
Probably. I've seen it shilled here before, so I'd wait until someone who's read it provides input.

[Anonymous No.11717065]

>>11717062
>Wasn't that a meme?
Nah I'm pretty sure that's him.
>>11717047
Not gonna reveal it. If you're interested in it go look yourself.

[Anonymous No.11717091]

I'm doing question on differentiation and volume
I know how to do the question but I don't understand it. What does differentiation have to with finding the volume of a box with algebraic lengths?? Isn't differentiation just for finding the slope of curves

[Anonymous No.11717100]

>>11717091
stupid questions go in the stupid questions thread >>11689206

[Anonymous No.11717101]

>>11717091
>What does differentiation have to with finding the volume of a box with algebraic lengths??
Nothing. Just multiply the lengths of the sides together to get the volume.

[Anonymous No.11717104]

>>11717091
>What does differentiation have to with finding the volume of a box with algebraic lengths??
In short, nothing.
But in some sense differentiating the change in volume gives you the circumference of an object.

[Anonymous No.11717108]

>>11717104
The volume of a cube is a^3.
The surface area of a cube is 6a^3.
3a^2 != 6a^3.

[Anonymous No.11717113]

>>11717108
3 is pretty much 6

[Anonymous No.11717118]

>>11717101
>>11717104
the box's width is 10-2x and length is 16-2x. height is x and we have to find out what x is.

[Anonymous No.11717119]

>>11717113
I am guessing he got this (completely wrong) idea from the curious relation that d/dr(area of a circle of radius r) = circumference of a circle of radius r.
It's also true for spheres in general, I think (but not other shapes).

[Anonymous No.11717132]

Hmm this is curious...
Looking at this page
https://en.wikipedia.org/wiki/Volume_of_an_n-ball
specifically pic related.
Couldn't the same argument be used for a 3d cube? After all, the volume of a cube is the union of concentric boundaries of smaller cubes.
Is there a mistake here or am I not seeing something?

[Anonymous No.11717135]

>>11717108
Please notice that I said "in some sense", which means that literally differentiating the formula for the area and expecting the surface area to come out is probably not going to work.
But, noticeably it works for a circle and it would also work for your example if you used the right definition of "in some sense".

>The surface area of a cube is 6a^3.
This is also false, it is 6a^2, yes I know that I am petty.

If you are curious about the "in some sense" look at https://en.wikipedia.org/wiki/Minkowski_content..

[Anonymous No.11717143]

>>11717108
If det(A) is the volume spanned by the column vectors of A, then

[math] \frac{ {\mathrm d} }{ {\mathrm d} t} \det A(t) = {mathrm {tr}} \left( C_A(t)^T \, A'(t) \right) [/math]

where [/math] C_A [math] is the cofactor matrix of A.

That's incidentally related to [math] \det \exp (tA) = {\mathrm e}^{ {mathrm {tr}} (tA)} [/math], which we discussed in >>11711177 (special matrix groups having generators with zero trace, i.e. special transformations leaving the volume invariant)

[Anonymous No.11717150]

>>11717108
If det(A) is the volume spanned by the column vectors of A, then

[math] \frac{ {\mathrm d} }{ {\mathrm d} t} \det A(t) = {\mathrm {tr}} \left( C_A(t)^T \, A'(t) \right) [/math]

where [math] C_A [/math] is the cofactor matrix of A.

That's incidentally related to [math] \det \exp (tA) = {\mathrm e}^{ {\mathrm {tr}} (tA)} [/math], which we discussed in >>11711177 (The special matrix groups, e.g. rotation, having generators with zero trace, i.e. special transformations leaving the volume invariant)

[Anonymous No.11717151]

>>11717143
Can you please fix your TeX? I can't read this. Before posting there is a TeX button on the top left where you can see how it will come out when you hit post.

[Anonymous No.11717156]

>>11717151
huh, I never clicked that TeX button

[Anonymous No.11717157]

>>11717150
Ok and how does that relate to what we're talking about?

[Anonymous No.11717169]

>>11717150
Does the right thing come out?

>>11717157
Well, he is differentiating a volume.

[Anonymous No.11717195]

>>11717118
>the box's width is 10-2x and length is 16-2x. height is x and we have to find out what x is.
This has absolutely nothing to do with differentiation, that's purely algebraic.

[Anonymous No.11717198]

>>11717157
If A=diag(t, t, t), then C_A=E(t^3/t=t^2·E and the volume of the cube has growth rate of dt^3/dt = (d/dt) det(A) = tr{C_A · t'} = 3 t^2
It's the formula how a spanned evolving volume grows.
(The surfaces are then given as norm of the normal vectors, a bunch of (-1)^n are involved, but those are part of the C_A matrix.)

[Anonymous No.11717209]

>>11717198
put differently, it's the translation from the derivative of det(A) (the volume) to the derivative of the edges A characterizing said volume.
I mean it's just fyi to see there's a general relation. Coordinate changes additions are given by the Jacobi matrix, but you probably know that one.

[Anonymous No.11717215]

>>11717132
It will absolutely work, the issue is that circle is expressed in terms of Radius, but the sphere is expressed in terms of edge length.
Another volume for the cube is (2*r)^3, here r is dist(Cube,0). Differentiating gives 6*(2*r)^2, which is exactly right.

You are dropping a constant since your scaling is "twice as fast" as it should be.

[Anonymous No.11717223]

>>11717215
>>11717132
To say the same thing. Imagine a cube with side length r and Radius r-epsilon and then shift the cubes to a common vertex, the distance on the other side will be 2*epsilon, which is why the constant 2 is missing in the original formula.

[Anonymous No.11717226]

>>11717047
Throw Rapcak in the archive.
Fuck if I know if it's real.
>>11717065
Kinda unreasonable to actually expect him to find that.

[Anonymous No.11717230]

>>11717226
>Throw Rapcak in the archive.
>Fuck if I know if it's real.
Thanks.

[Anonymous No.11717231]

i'm in the midst of choosing education. thinking of going for a BSc then MSc in statistics. is this smart? don't have the necessary prerequisites for any pure STEM program, i'm soon to be 24 and want to start ASAP, but still thinking the broader knowledge you gain from i.e a mathematics or engineering program is preferred to the very specific knowledge a MSc in statistics gives me, even though i want to work with AI, ML, big data etc in the future. any thoughts?

apologize if this is the wrong thread...

[Anonymous No.11717235]

>>11717223
What do you mean by a radius?

[Anonymous No.11717240]

>>11717235
Sorry, I meant:
Imagine a cube with side length s and another with side length s - epsilon and then shift the cubes to a common vertex, the distance on the other side will be 2*epsilon, which is why the constant 2 is missing in the original formula.

[Anonymous No.11717268]

>>11717231
Is there really such a thing as a BSc in statistics? That seems too specialized for a BSc, but I am not sure...

I have to say that for NNs statistics is not the main focus and they involve a very broad spectrum of mathematics, which can easily involve real analysis or numerical analysis or even abstract algebra.
There is nothing inherently wrong with specialization, but with things like machine learning, the mathematics you need are usually quite broad and being very proficient at statistics might gain not gain you all that much.

If the BSc in Mathematics does not hinder you to get a MSc in statistics later, I do not see much reason to specialize from day one, but these are just my thoughts.

[Anonymous No.11717278]

>>11717240
>the distance on the other side will be 2*epsilon
What? How?

[Anonymous No.11717287]

>>11717118
>>11717195
https://www.dummies.com/education/math/calculus/how-to-use-differentiation-to-calculate-the-maximum-volume-of-a-box/

[Anonymous No.11717291]

>>11717287
>maximum-volume
Totally irrelevant to your problem.
Ignore the article, it has absolutely nothing to do with your question.

[Anonymous No.11717297]

>>11717268
yeah, here are the specific programs,

https://liu.se/studieinfo/program/f7ksa/4482

https://liu.se/en/education/program/f7msl

the first link, the BSc program, is rather trivial since it's only in swedish, but the masters program from the 2nd link in english is the natural follow up to bachelor. it sounds really interesting, but as you say - i'm not sure if there are enough raw maths courses to get the real deep understanding that's required.

i don't have the required pre-requisities for a BSc in mathematics either, and that would postpone my studies with 1 year.

[Anonymous No.11717304]

>>11717278
I am retarded and can't express myself correctly.
Let's try again in the 2D case.
Take a square of side length s, inside that square is another square which is epsilon away on all sides from the other square.
Now, move the inner square towards the vertex of the outer square, the distance on the other side will be 2*epsilon.

And because we have that "2" there, the factor when we differentiate is wrong, since we should consider is *not* square of side length s and a square of side length s-epsilon, but instead we should use the frame work described above.

[Anonymous No.11717311]

I LIKE NONNEGATIVE CURVATURE AND I CANNOT LIE

[Anonymous No.11717318]

>>11717297
actually, heres the BSc in english too,

https://liu.se/studieinfo/en/program/f7ksa/4482

[Anonymous No.11717321]

>>11717311
Do you like the kurwature of Polish spaces?

[Anonymous No.11717323]

>>11717321
No, I don't really like autistic measure theory.

[Anonymous No.11717330]

>>11717321
I like negative polish space.

[Anonymous No.11717342]

>>11717323
Quite ableist of you, but I don't like it either.

>>11717330
Giggled a bit, good post my friend.

[Anonymous No.11717354]

>>11717330
oof

[Anonymous No.11717357]

>>11717297
>>11717318
Well, for me it looks like they are hitting the important points you will be needing eventually anyway, namely linear algebra, real analysis and multi variable calculus.
Obviously in a real math degree you would see much more "deep" mathematics, but I do believe that you would get adequate preparations to have some decent understanding about ML.

[Anonymous No.11717374]

What would [math]D_{10}[/math] mean? Symmetry group of regular decagon, symmetry group of regular pentagon, 10th derangement number... Anything else?

[Anonymous No.11717401]

>>11717374
There's also a series of simple Lie groups/algebras which are denoted [math]D_n[/math] .

[Anonymous No.11717429]

>>11717226
>Rapcak
Yukari is polish and lives in Poland, that's all I'll reveal though, he's not that guy

[Anonymous No.11717437]

>>11717374
A dihedral group, but there's a problem: [math]D_n = \mathbb{Z}/n\mathbb{Z} \rtimes \mathbb{Z}/2\mathbb{Z}= D_{2n}[/math], with the n or 2n depending on the author.

[Anonymous No.11717489]

How exactly is the group operation on an abelian variety generally defined?
I know it for elliptic curves, but otherwise, for an entirely generic variety, how do I know how to get from two points to a third? What's the definition of the multiplication?

[Anonymous No.11717584]

>>11717374
Besides >>11717401 it could also refer to the Dynkin diagram directly or the root system.
And I'm basically being anal, but still.
>>11717437
What did he mean by this?

[Anonymous No.11717688]

>>11717584
>What did he mean by this?
That depending on the author you can have [math]D_{10}[/math] be [math]\mathbb{Z}/5\mathbb{Z} \rtimes \mathbb{Z}/2\mathbb{Z}[/math] or [math]\mathbb{Z}/10\mathbb{Z} \rtimes \mathbb{Z}/2\mathbb{Z}[/math].

[Anonymous No.11717706]

>>11717688
Anon (>>11717374) already wrote that [math]D_{10}[/math] might mean symmetry group of decagon or pentagon.

[Anonymous No.11717721]

>>11717706
Quite observant of you. The anon was asking what it is, and I only read up to that point.

[Anonymous No.11717762]

>>11711147

er, isn't that obvious to everyone?

[Anonymous No.11717808]

>>11717357
alright, thanks a bunch for your time & answers!

[Anonymous No.11717820]

bros...

[Anonymous No.11717826]

>>11717820
are we gonna make it? 24 is getting closer...

[Anonymous No.11717881]

How do I gain more mathematical knowledge? I sucked off a couple of math trannies and the only thing I learned is that I can not steal their knowledge through this.

[Anonymous No.11717966]

>>11717826
for me it was like 19-21 and now its all gone

[Anonymous No.11717978]

>>11717881
>math trannies
Do these even exist? I've never seen one.

[Anonymous No.11718038]

>>11717978
You're posting in a thread full of them.

[Anonymous No.11718124]

>>11717881
learning cohomology theory, one glitchy feminine penis at a time

[Anonymous No.11718131]

>>11717881
>sucked off a couple of math trannies
That's your problem. You should be sucking off actually talented mathematicians.
I'm a heterosexual cisgender male, right, but I've thought long and hard about this, and depending on my mood and exact context, I might be willing to let a man blow me while I close my eyes and imagine it's a girl. I postulate that the same applies to some of your professors and peers, some of whom might be outright gay or bisexual.

[Anonymous No.11718320]

>>11718038
Am I really?

[Anonymous No.11718342]

>>11718320
Yes! UwU

[Anonymous No.11718445]

>>11718342
Prove your degeneracy.

[Anonymous No.11718502]

>>11718445
I finger my ass every night and can't cum if I'm not thinking about getting cocks in my butt

[Anonymous No.11718570]

>>11718502
That doesn't necessarily make you trans.

[Anonymous No.11718586]

>>11718570
but it makes me a degenerate
I used to crossdress when I was younger too

[Anonymous No.11718641]

>>11718586
>I used to crossdress when I was younger too
post pics

[Anonymous No.11718653]

>>11718641
I was underaged

[Anonymous No.11718656]

>>11718502
>>11718586
Bro just post your discord account and we'll believe you're a tranny.

[Anonymous No.11718795]

>>11718653
And?

[Anonymous No.11718832]

>>11718795
It's illegal to request pedopornography on an american website

[Anonymous No.11718904]

>>11717489
It's just an unspecified operation. It can be anything as long as it satisfies the group axioms.

[Anonymous No.11718913]

Is it weird to have romantic feeling for your professor?
I only chose to work in some niche topics because he's handsome af.

[Anonymous No.11719003]

>>11718653
even better
I didn't say post nudes

[Anonymous No.11719022]

>>11717489
this is very much like asking "what's the group operation on a group generally defined?"

[Anonymous No.11719752]

Finished my precalc book that was recommended to me here. I also taught myself some logic and set theory.
Where should I go from here? Linear algebra, calculus?

[Anonymous No.11720146]

>>11716732
wyd? Theres only really been book recommendations. If you saw what Yukari would post, then you would feel bad