/sci/ - Science & Math

>>9825089
whats the deal with that no matter what i do, i can´t get to x1=x2=x3

>>9825106
fuck off

Do mathematicians still make advancements with a pen and paper or is everything software-based nowadays?

also, why aren't there more amateur mathematicians out there making progress in math? Math is the one field in STEM where you don't need any labs to make discoveries.

>>9825280
s stands for statistics.

>>9825280
Few innovations in pure mathematical theory are made anymore.

>>9825302
Don't PhD students in pure math make innovations? Aren't there a shitload of PhD students in pure math?

>>9825311
You don't need to be innovative to get a PhD.

>>9825319
But you have to write a PhD thesis, you have to write-up a new idea in math. Isn't that an innovation?

>>9825302
How could someone be this uniformed.

>>9825326
Most are highly derivative pieces of trash

>>9825280
Mathematics requires such a level of specialization in some fields that in order for someone to make a noteworthy discovery in a popular subject (like number theory or analysis) anymore you would need to put in the time and study equivalent to an actual professional who did things legit in the academic system

>>9825358
>derivative
heh.

Revising for my ring theory exam
There is a theorem that, if R is a principal ideal domain then every irreducible element is also prime. Does the reverse implication hold however? Is there an integral domain that is not a PID, but all of whose irreducible elements happen to be prime?

>>9825844
>Does the reverse implication hold however? Is there an integral domain that is not a PID, but all of whose irreducible elements happen to be prime?
What have you tried?

>>9825844
>Does the reverse implication hold however?
prime => irreducible in general
> Is there an integral domain that is not a PID, but all of whose irreducible elements happen to be prime?
this holds on UFDs

Guys! Guys! Guys!

I solved the Riemann Hypothesis!

>>9825844
>Is there an integral domain that is not a PID
No.

>>9825302
t. brainlet who knows nothing about current powerful interactions between analysis, PDE, statistics and machine learning, to name but one aspect of harmonic analysis. Even wavelets alone hold both theoretical and practical significance to study for decades.

>>9825280
Because the amateurs don't have the discipline to study maths for years like professional mathematicians, who have spent most of their life on nothing but maths. So the pros are more likely to get things done, though outliers exist.

My friends, is non-commutative probability legit or is it just a meme? I'm not sure what should I do after finishing my undergrad, I want to do probability but I don't know what in probability is the best to work in.

Should I get Strang or Axler for Linear Algebra?

>>9826763
Both.

>>9825280
very few mathematicians make advancements with computers

>>9826763
Strang is the Stewart of linear algebra

Can someone help me solve this I forgot all my algebra?

a=b+(a x c)

What is a equal to?

t. liberal art graduate

>>9826983
b/(1-c)

>>9825844
Yes, consider Z[x]

>>9826990

Thanks alot

>>9826804
Okay, thank you.

>>9826907
I don’t understand.

>>9827013
Most linear algebra books are either too easy/tedious or too hard, Axler as an introduction for linear algebra is going to be hard, specially if you don't know how to do computations already, I'd recommend checking Strang's book, "Introduction to linear algebra" along with his lectures

https://www.youtube.com/watch?v=ZK3O402wf1c&list=PLE7DDD91010BC51F8

Here's the complete course https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/

After that Axler should be doable, or check "Finite dimensional vector spaces" by Halmos, a pretty fun book, but also not for begginers. Best of luck.

>>9826117
check out pic from Rudin

Thoughts on modern Set Theory as religious belief?

https://www.youtube.com/watch?v=U75S_ZvnWNk

Should I just lie to my parents that I applied for grad schools and failed? I don't think I have what it takes.

>>9826692
How much background in probability do you have? Do you know measure theory? Do you know measure theoretic probability?

>>9826763
Neither. Lang.

>>9826692
just explore negative probabilities

>>9827382
>negative probabilities
Never knew such a thing even possible. Thanks for telling me that.

>>9827067
Will do. Thanks anon

>>9827346
Why?

>Algebra by Gelfand and Shen
>Functions and Graphs by Gelfand, Glagoleva, and Shnol
>The Method of Coordinates by Gelfand, Glagoleva, and Kirillov
>Trigonometry by Gelfand and Saul
>Precalculus by Stitz and Zeager
>Book of Proof by Hammack

will I have to add a geometry book or are those enough to do both Courant & Fritz's and Apostol's calculus books?

>>9827738
>will I have to add a geometry book or are those enough to do both Courant & Fritz's and Apostol's calculus books?
Why don't you try to do them and find out?

>>9827738
Yeah, definitely add 3-5 more high school books to do another high school level book.

>>9827738
Geometry is dead.

>>9827756
my thoughts exactly but if I have to in order to be able to do those calc books I will. thanks, anon

>>9827765
not for me. math, and specifically geometry, is so beautiful! ty for replying

>>9827749
I thought I could save some time asking for people that has been through it before. no worries tho, I'll follow your advice, thanks

>>9827765
Your mom is dead

>>9825089
Is Mochizuki related to Mochizou?

>>9825302
Holy shit, this dumb faggot is even here now? Fuck off you twit.

>>9827212
>Should I just lie to my parents that I applied for grad schools and failed?
Try to tell them the truth.

>>9828125
They would be really disappointed.

any recommended text books for precalc?

mathlet here learning on my own, reading AoPS series but cant afford precalc book, need a different publisher suggested

[eqn]\sf Gookmoot\; \color{red}{\bb STILL}\; hasn't\; fixed\; the\; \TeX\; tags\; on\; /sci/[/eqn]

So I was reading some papers and they started talking about the amount of statistical entropy enclosed by a polytope in a particular region of space. What did they mean by statistical entropy? And for context this had nothing to do with physics.

>>9826907
You take that back.

What is meant by "modulo the action of a groupoid?"

>>9828710
Do you know the orbits when you have a group acting on a set? My guess is that it's the same idea but with a groupoid.

>>9826582
>powerful interactions between analysis, PDE, statistics and machine learning
Machine learning is a python library that multiplies sparse matrices together for a few million iterations. This is literally what deepfakes is.

>>9828739
That helps, thank you.

>>9828782
No problem, my friend.

For any set [math]X[/math], does there exist a non-trivial topology such that for every sequences [math]x_n[/math] and element [math]x_0[/math], [math]x_0[/math] is a limit of [math]x_n[/math] iff [math]x_0[/math] is the unique limit of a proper subsequence of [math]x_n[/math]?

For any set [math]X[/math], does there exist a topology such that for every sequences [math]x_n[/math] and element [math]x_0[/math], [math]x_0[/math] is a limit of [math]x_n[/math] iff [math]x_0[/math] is the unique limit of a proper subsequence of [math]x_n[/math]?

how fucked am for PhD or MS in the US if I got an F in an upper div course because of stupid personal shit

I retook it and got an A, and I also have a C in one, and averaging out my A and F to a C, giving me the equivalent of two Cs, my upper div GPA is currently a 3.87, which I guess is passable. Is that F going to seriously cuck me, though?

>>9827738
all memes

How does /mg/ write its papers? I mean, obviously using [math]\LaTeX[/math], but what editor/environment?

>>9825302
filtered.

>>9829751
Vim.
It's a shit time but I do it because I'm used to it.

>>9826582
fucking wavelets

>>9829751
TexStudio

Dumb question: Why do we talk about reals instead of "describable numbers" (ie anything that we can (finitely) describe)? Every number we ever use is a describable number. It is not possible to talk about a number that isn't describable. They are closed under anything you can talk about so they satisfy all the nice properties of the reals.

You could have a describable powerset too (just talk about all the subsets which can be described).
Why even bother dealing with uncountability?
When does it make sense to talk about things that aren't describable?

>>9829488
discrete

>>9829864
What is a description ?

>>9829882
https://en.wikipedia.org/wiki/Definable_real_number

>>9829883
Then I'm not sure why they would be complete, hence satisfy the Heine-Borel theorem, the mean-value theorem, the extreme value theorem and all those things that we like about the reals.
Certainly those form a field, but the reason we like the reals is because they let us do analysis

>>9829890
Wouldn't every (describable) subset of the describable numbers have a least upper bound (since we can describe it as the least upper bound of that set)?
This should be enough to give completeness right? (or perhaps describable completeness?)

>>9829899
The set of defineable numbers cannot exhaust the suprema of every power-set of definable numbers

>>9829918
I mean, every subset of definable numbers in the power set of definable numbers**

>>9829922
But we forget about the powerset too. We only need to talk about the definable powerset by the same argument that we only need to talk about definable numbers. By this I mean the set of all subsets which can be defined.

We will have definable completeness in that any Cauchy sequence which can be defined has a definable limit.

>>9829890
>>9829925
I thought things might start getting a bit funny when we get to compactness since a Cauchy subsequence of a definable subsequence might not be definable.

However maybe in the proof of the Bolzano–Weierstrass theorem you could choose the left-most valid element in the sequence at each step (in the proof using iterated intervals to construct a Cauchy sequence) to get something which is definable.

>>9829899
>since we can describe it as the least upper bound of that set
We can describe reals as limits of rational sequences, too. Every rational number is describable, so the set of all rational numbers is describable. Is there a reason why [math]\mathbb{Q}^\infty[/math] wouldn't be? If not, then we have all the sequences of rational numbers. We can then take the subset of all the Cauchy sequences of rationals (again describable?) and describe real numbers as limits of these sequences. Or did I miss something? It seems to me that you can do this if you can describe using sup and inf.

>>9829941
You can't describe all sequences of rational numbers.

The set of describable things is countable (since a description is just a finite string of characters). Thus any uncountable set (the reals, sequences of rationals) must have uncountably many elements which cannot be described.

Sidenote: Anyone know why TeX is broken?

>>9829946
By describable you mean actually constructable, right?

>>9826983
a is equal to b+(a·c).

>>9829950
Not if you mean in the sense of straight-edge and compass construction. They don't even have to be computable. From the wikipedia page that other guy linked:
>Informally, a definable real number is a real number that can be uniquely specified by its description. The description may be expressed as a construction or as a formula of a formal language.

>>9829954
Got it, carry on.

>>9829954
Note that we don't even have to believe in real numbers to talk about definable/describable numbers. We can define them using the Cauchy sequence construction from the rationals but only allowing describable Cauchy sequences.

Presumably a bunch of theorems somewhere along the line start to fail since some step might fail to give a unique element when using something non-constructive like the AoC. I'm not sure of any examples yet though.

>>9829864
I don't thin the idea is actually so bad (although maybe the computable numbers could be more useful in some areas), but that would mean that everything called "Analysis" had to be thrown out of the window.
Because I am pretty sure that >>9829890 is correct.

>Then I'm not sure why they would be complete
Am I retarded?
How could they be complete?
Take a Cauchy sequence of rational numbers (all constructible) going to a non-constructable real number (which obviously exists).

>>9829970
They aren't complete but they are describaly complete. That is, any describable Cauchy sequence has a describable limit (since we can describe it as the limit of said sequence). As far as I can tell this is good enough to continue doing analysis as before (probably also requiring definability in later definitions/theorems).

>>9829974
>That is, any describable Cauchy sequence
Oh, so you don't care about completeness, that is rather interesting, you care whether you can describe the series.

But the obvious question is "when is a number describable?", because I fear that a) you will invalidate all of Analysis with that if you are too strict or b) you will just end up with the reals, if you are too loose.

>>9829988
It's like a weaker version of completeness. The idea is that we only care about describable things anyway so we only think about describable Cauchy sequences. I started thinking of this initially because I was thinking about how it's strange that an uncountable amount of the real numbers can't even be talked about (and only a countable amount can).

The loose idea is that something is describable if you can uniquely define it (and show it must exist) in finitely many symbols. You obviously can't end up with all the reals since there are only countably many describable things. I tried to give a construction of the describable numbers based on the real numbers in >>9829962. I'm not convinced it actually gives all the describable numbers though and that we don't run into problems with describable completeness.

>>9830001
>in finitely many symbols
You have to be a bit more specific there, do infinite sums count? If they don't what about pi or e?

>>9830014
Of course they do. You can talk about them in finitely many symbols. The whole point is any counterexample is impossible to describe (and that the majority of the reals are impossible to describe).

Any "real" number you have worked with before is describable (other than some non-constructive, non-unique, abstract number).

>>9830014
>>9830026
(Obviously I only mean convergent sums)

>>9830026
>>9830029
Still what "symbols" count?
You have to be specific.

I hate this general.

>>9830038
Any

>>9830042
(note we are assuming space is discrete and so there are countably many symbols)
>>9830039
Why?

>>9830042
The set of all real numbers is describable in finitely many symbols.

>>9829941
There is an obvious cardinality issue (finite descriptions using finitely a finite alphabet form a countable set, hence you get countably many describable numbers, whereas Cauchy sequences of rationals have the cardinality of R).
A way to see what could go wrong is to realize that there is no reason for a cauchy sequence of describable numbers to be itself describable, hence to converge to a describable number (there is no reason why a typical infinite sequence of rationals should have a finite description, and indeed it does not).

>>9830052
The whole set maybe. Most individual elements are not though.

>>9830071
>The whole set maybe.
So I can describe ALL real numbers in finite symbols, isn't that a problem?

Again, "all symbols" is a REALLY dumb definition, it is completely unprecise and simply unworkable, what makes it worse it isn't a definition at all, it could be literally anything, what makes it even worse is that you don't specify when an arrangement of symbols is a number is }}}()123 a "describable number"?
If you want to have your "describable numbers", define them first, not in some vague terms, but in actual mathematics give a construction or just refer to some constructions already made, read about Computer Algebra if you want to see some examples.

>>9830078
I don't see why that's a problem. By describe I mean uniquely identify. It's possible to uniquely identify a set without being able to uniquely identify each of its elements.

See the first bit of the pic for a formal definition.
I was hesistant to give my own definition since I have never studied set/model theory.

What could be an interesting topic for my master's thesis? I'm a brainlet and I wouldn't want to be dragged into anything too ambitious.

It's supposed to be related to numerical analysis. I kinda enjoy image processing too and did a bunch of courses related to differential equations. Would be cool to combine it all

Pic related are the courses that I did

>>9830090
So when I asked you which symbols you wanted to use why did you say "Any" when clearly you didn't mean "Any"?
But anyway, "This notion cannot be expressed as a formula in the language of set theory.", so you can't even describe what exactly a real number is anyway.

>>9830098
I feel like you're being delibrately obtuse. I said any because I don't have the rigorous set-theoretic backround to give a good answer. It depends what "universe" you are working in, but I thought it was clear enough for an informal discussion. The wikipedia definition seems good to me.
>But anyway, "This notion cannot be expressed as a formula in the language of set theory.", so you can't even describe what exactly a real number is anyway.
That's not what it is saying. It's saying you can't describe what it means to be describable.

>>9830106
Forgot to add, https://arxiv.org/pdf/1105.4597.pdf seems like a pretty good discussion

>>9830106
>I feel like you're being delibrately obtuse.
Not really, I just wanted to know what "describable" means the wikipedia article already mentioned that it was vague and I just wanted to hear which definition you are using, I didn't think that was too much to ask.
I was genuinely interested if there was some a way to not sacrifice all of Analysis and still get a less abstract base field then the real numbers.

>I said any because I don't have the rigorous set-theoretic backround to give a good answer.
Neither do I, but "Any" seems like a bad answer nevertheless.

>That's not what it is saying. It's saying you can't describe what it means to be describable.
Yes, that is what I was getting at. (sorry for the typo, I meant "describable" not "real").

>>9830108
Looks interesting.

>>9830039
I love you too friend

>>9830097
Try the Mandelbrot set or fractal geometry.

How much work has been done on chromatic homotopy theory already?

Does anyone have the inside scoop on who's writing the disproof of iut and when it will be published?

>>9830677
Yes. I am one of the 3 people involved. The preprint should be out by September at the earliest. We're still ironing out some details and waiting for replies from Mochizuki.

(I am serious, by the way.)

>>9830677
>Does anyone have the inside scoop on who's writing the disproof of iut and when it will be published?
don't hold your breath

>>9830708
>Yes. I am one of the 3 people involved.
Iwanttobelieve.jpg
>Mochizuki
Has he given you any indication of what he thinks about it yet? This has to be devastating blow to his ego. Also, have you gotten any crazy emails from Fesenko yet?

>>9830709
The argument against IUT is pretty air-tight as far as I'm concerned. But we're trying to be polite.

>>9830729
>Iwanttobelieve.jpg
Just in case you are dumb enough to believe him (I just can't be sure with these threads being what they are nowadays), would anyone big enough to bring Memezuki down ruin his reputation by posting Chinese pedophile cartoons?

>>9830729
Mochizuki is pretty slow to respond. I don't want to speculate as to his mental state.

>Also, have you gotten any crazy emails from Fesenko yet?
Crazy? No. We did correspond though.

>>9830733
Mochizuki's reputation is pretty solid. This one mishap won't change that. We all make mistakes.

>>9830738
I meant his proof, not him as a person.

>>9830734
Why wait for his response at all? Why not just put the preprint online and let him respond whenever he has the time?

>>9830746
It's common courtesy and standard practice.

>>9830751
I mean, he's had close to 10 years to locate the error. Will a couple of more months really help?

>>9830760
We want to clarify certain arguments with him. We don't expect him to patch things up now. Time is not really an issue for any of us since this isn't the main thing we're working on right now.

>>9830106
My problem is that describability is a priori only a metamathematical notion, and a very abstract one at that.
Even though it is intuitively obvious to you that "four times the sum of the (-1)^k/(2k+1) for k >= 0" and "the first positive zero of the sine function" are both descriptions of the same number, I would be really interested in seeing a reasonable mathematical definition of "description" that recognizes these two examples as descriptions and assigns to such a description the real number it describes. How do you decide if it exists ? If it defines a unique number ? For a typical English sentence, this can be an actual mathematical problem for humans.
Computability is a much more manageable notion, because you set a formal language, give limits to what you can compute etc. Describability is not well-defined and it leads to the semantics problems we see in this thread (is a number describable if it belongs to a describable set ? etc)

>>9830766
>We don't expect him to patch things up now.
Is there any part of iut that can be saved or is the whole thing bust?

40+20 = 6(100-T)

110 or 90?

>>9830786
90

>>9830783
It's mostly a dead end.

>>9830117
Thanks for questionning me on this stuff btw. I did a bunch of reading and it obviously is important to be specific.

Opinions on this book? Will this book help me to become a better problem-solver?

>>9831214
>Will this book help me to become a better problem-solver?
Why don't you read it and find out?

>>9831215
It's too wordy Anon. Very different from other problem books like Titu Andreescu's and Larson's. I just want to know whether it's worth the time.

>>9831221
If you've already read Titu and Larson, then there might not be much else left for you in this book. Polya's first text has a lot of nice heuristics, but you've probably already learned them else where. It is still a fun read. Polya has a two volume set after this which may interest you though. Another two volume set called "challenging problems with elementary solutions" is also nice.

>>9831233
Thanks friend

>>9831221
I never understood how anyone likes Andreescu's books. He has the biggest boner ever for gross artificial problems that nobody in their right mind would either want to solve or care about the answer to.
What kind of person really wants to shuffle around a 17-symbol inequality for an hour until you find a form that you can club to death with AM-GM?

>>9831242
But I like it. Fuck you.

>>9825302
filtered

>>9831242
You encounter much more complicated problems as a mathematician all the time. Fiddling with a 17-symbol inequality for an hour until you find a form you can solve with a known heuristic is good practice.

Proof by exhaustion is an insult to mathematics

>>9831884
"No!"

>>9831884
Suck my dick.

>>9830708
>Yes. I am one of the 3 people involved. The preprint should be out by September at the earliest. We're still ironing out some details and waiting for replies from Mochizuki.
Which part of this is wrong?
http://www.kurims.kyoto-u.ac.jp/~motizuki/2018-02-02%20Tan%20---%20Introduction%20to%20inter-universal%20Teichmuller%20theory%20(slides).pdf

>>9831935
(fixed link)
http://www.kurims.kyoto-u.ac.jp/~motizuki/Tan%20---%20Introduction%20to%20inter-universal%20Teichmuller%20theory%20(slides).pdf

>>9831935
I don't know. Which part of your brain is rotten for you to pick mathematics as your major?

>>9831973
Something tells me this isn't the original poster.

How specific should I be in my motivation letter when addressing my project? PhD stuff.

>>9831987
No one actually reads those. Except maybe in cases where there is fierce competition for PhD positions (which is very rarely the case in mathematics) and the committee has exhausted all other means of differentiating between candidates.

You can write whatever the fuck you want (within reason, like, don't send them dick pics).

>>9832169
Really? I was told to send a motivation letter and my CV by a chemist who's in charge of the natural sciences' PhD business, so I can't ask him what the mathematicians really want to see. If I pick one or two names from the list of faculty with research topics and throw in something related to those people's research, it should be enough?

>>9832169
shut up if you have no idea what you're talking about

>>9832288
don't fucking ask for advice here, what are you doing? do your research, many department websites have guides for how to do this shit. talk to your advisor, or at least some faculty in the actual field

>>9832468
Shut your fucking mouth.

>>9832288
The main thing everyone cares about is whether you have what it takes to do research. So they'll first look at your academic performance and everything else at their disposal that can tell them you have the right brain. The 'motivation letter' bullshit is used for exactly the purpose I outlined above. It's there mostly to please the bureaucrats. I advise you to contact the professor you want to do your PhD with beforehand (and if you have not decided on one, to look for one) and decide all the details together. See who's available at the university you're interested in, and hit them up with an email.

You will be on the bottom of the list of every professor if you use the method you're using now; a guy to fill a quota.

>>9832468
I have tried, but I have mostly just found advice on how to apply for psychology or a master's program. No harm is done by asking here, so go deepthroat a knife.

>>9832489
I'll try that. Thanks!

if anime/touhu, at least make it math

>>9832609
>if anime/touhu
How about no?

>>9826763
[Hoffman and Kunze] and/or Lang
Strang only if you are brand new to linear algebra.

>>9832700
>Lang
"No!"

>>9826983

b = a - (a*c)

https://youtu.be/ELGQe91LL0E

>>9832635
>>if anime/touhu
>How about no?
How about no?

>>9832743
No weebshit here.

>>9825302
>!!tbkOPmI7bEB
filtered

>>9832714
What's the difference between p-adic K-theory on p-adic rings and K-theory on p-adic rings?

>>9832949
I don't know much about this stuff but just from looking at the video description it seems like the distinction isn't between [p-adic K-theory of p-adic groups] and [K-theory of p-adic groups] but between [p-adic K-theory of p-adic groups] and [l-adic K-theory of p-adic groups] (where l != p, because of invertibility issues):

>The original proof of Grothendieck's purity conjecture in étale cohomology (the Thomason-Gabber theorem) relies on results on l-adic K-theory and its relation to étale cohomology when l is invertible. Using recent advances of Clausen-Mathew-Morrow and joint work with Bhatt and Morrow, our understanding in the complementary case of p-adic K-theory of p-adic rings has reached a similar level. In particular, we can express p-adic étale K-theory in terms of the cohomology theories of integral p-adic Hodge theory, such as the prismatic cohomology discussed in Bhatt's talk.

similar sounding to what goes on here:
https://en.wikipedia.org/wiki/%C3%89tale_cohomology#%E2%84%93-adic_cohomology_groups
>Étale cohomology works fine for coefficients Z/nZ for n co-prime to p, but gives unsatisfactory results for non-torsion coefficients. To get cohomology groups without torsion from étale cohomology one has to take an inverse limit of étale cohomology groups with certain torsion coefficients; this is called l-adic cohomology, where l stands for any prime number different from p.

>>9832714
Interesting stuff, but oh boy are his clothes horrible!

>>9832949
Looks like p-adic k-theory is a step up in chromatic tower of k-theory.

https://ncatlab.org/nlab/show/chromatic+homotopy+theory

>>9832999
Checked, and it looks like Scholze started lifting. Pretty plump chest and thicker arms than the last time I saw him.

>>9832969
>>9833006
Thanks, this was helpful.

>>9833013
His liftings of maps is finally paying off.

What's an interesting Banach space that's completely unlike R^n or a space of function on R^n? E.g. something descrete where the norm isn't effectively measuing the distance of a flat continuous space. E.g. something descrete or more abstract?

>>9833030
Lp spaces?

>>9833030
Falls under functions spaces on R^n.
Let me ask a related wonderance of mine: Metrics are relevant in fields very different than R^n stuff (think of the Hamming distance in coding and information theory) and topology is too, but the Banach theory with all its general problems seem in the end really only be appied to solve equations in functional analysis (including applications for PDF's and integral equations). Is there interesting things to be said for e.g. topics closer to combinatorics, algebra and computer science?

>>9833067
Assuming you meant to reply to me, Lp spaces are defined on an arbitrary measure space. Not just R^n.

Can Mochizukifags please stop kissing the ground that Mochizuki walked? Jesus Christ, you assholes should stop searching for meaning in Mochizuki’s farts.

>>9833092
t. Scholzefag

>>9830635
The general theory is pretty well developed, but there is still a ton of open problems.

Also there is the motivic version, which is likely less developed and probably even more interesting.

>>9833097
I see. Would it be worth doing research on, though?

>>9833101
I think so. You get to blend together homotopy theory, algebraic geometry, and number theory.

>>9833106
That sounds pretty nice. Thanks for your reply.

>>9828765
>Algebraic topology is just drawing arrows
If you took few minutes to read a non-meme ML paper, you'd find that CS faggots are finally getting their feet wet with KK-Fredholm and index theory. Fun stuff.

Name me ONE(1) black mathematician, I’ll wait.

>>9833169
I legitimately can't off the top of my head. Tbh I can't remember the last time I had a math class with a black person in it.

Plenty of asians/indians, some persians, some girls. No black people.

>>9833169
That super duper tiny rectangles girl?

>>9833169
There's a black guy I play vidya with sometimes who's doing a physics PhD.
That's the closest I've got.

>>9833169
https://en.wikipedia.org/wiki/Hidden_Figures_(book)
:^)

>>9833169
https://twitter.com/math3ma?ref_src=twsrc%5Etfw&ref_url=http%3A%2F%2Fwww.math3ma.com%2F
Dirac was also black

>>9833169

Robert Lee Moore was black. I can attest to this fact by how he called his fellow black men "nigger"

>>9833013
why is this place so fucking gay...

>>9834007
>gay
Why the homophobia?

>>9834007
>homophobia

>>9833872
>https://twitter.com/math3ma?ref_src=twsrc%5Etfw&ref_url=http%3A%2F%2Fwww.math3ma.com%2F
She is obviously mixed race, or some kind of asian. A slightly olive skin tone [math] \neq [/math] black.

>Dirac was also black
>WE WUZ MATHEMATICIANS N SHIET

>>9834009
>cringe normalfag cringe meme
cringe

>>9834013

>>9834017
Stupid frogposter.

Does real analysis cover geometric centroids?

>>9834019
Stupid animeposter

>>9834009
>>9834008

>>9834035
>source: libraryofhate.wordpress.com/
Come on anon, this is embarassing.
I tried looking at a few of the "sources" on that website. I got an amazon link to a book from 1979 (no page/chapter citation), a paid medical article (again no section cited) with an abstract that didn't mention the claim, an article on someone's blog citing other non-scholarly articles (this claim actually looked true to me but I'm not going to go through 7 links to check).

>>9834035
thinkplant.png

>>9832745

>>9834050
>I got an amazon link to a book from 1979 (no page/chapter citation)
But remember, the authors are named Bell and (((Weinberg,))) so it's all automatically false anyway

:/

>>9834050
>>9834056
Not him, but just interested.
The first claim is most definitely true, even just because it is so vague:
https://en.wikipedia.org/wiki/Domestic_violence_in_lesbian_relationships
"67.4% of lesbian women reported experiencing intimate partner violence only from female perpetrators.[8]"

For the second claim we have about 163 Million males according to the YouGov poll https://d25d2506sfb94s.cloudfront.net/cumulus_uploads/document/isqcugzp6d/tabs_OPI_Kinsey_Scale_20150813.pdf
5% of males are homosexuals.
So the average HIV diagnosis rate between 2011 and 2015 per 100.000 for all males according to these numbers is https://www.cdc.gov/hiv/pdf/library/reports/surveillance/cdc-hiv-surveillance-report-2016-vol-28.pdf 32,964/1630 = 20.2;
Just considering gay people we get 26,052/(1630*0.05) = 319.7.
So the claim "gay men are more then 60 times more likely to have HIV then straight men" seems to be more then true, if you consider new diagnoses between 2011 and 2015.

I have some doubt about the other claims on there, especially the number of partners of homosexual men, which seems to be ~3 times more then heterosexual men.
If there is any specific claim on there, you can just do your own research, the numbers should be somewhere on the internet.

>>9834089
What's wrong Anon?

http://www.math.columbia.edu/~harris/otherarticles_files/perfectoid.pdf

>>9834058
Weebs are the new normies. Crunchyroll kappa lmao xD

>normie
I want normalfags to go and stay go.

>>9833169
Piper Harris.

>No matter how much you study, you'll never understand all of modern mathematics
>You'll never make important contributions to numerous and disparate fields
>They'll never be a disambiguation page on wikipedia for "Anon's Theorem"

>>9834278
I think you mean Piper Harron. And she's no mathematician.

>>9834304
Then give up Anon. At least you tried.

>>9834306
Oh right, my bad. She's the liberated mathematician. One could even argue that she is a trans-mathematician: all her merits may seem like something, but deep inside she is a mathematician.

>>9834304
>he does math for glory and recognition and not for fun
Just end your pathetic existence.

>>9834342
>>he does math for glory and recognition and not for fun
I'm not a "he".

>>9834347
Sure, son.

>>9834366
Your not my dad

>>9834367
Yet I have fucked your mother.

>>9834370
So have I, does that make me my own father?

>>9834372
No, that only makes you a pervert.

Can we please talk about Inter-universal Teichmüller theory again? This is math general for crying out loud.

where I can get precalculus (algebra and trigonometry and geometry and precalculus) workbooks for free?

>>9834392
Libgen.io is your friend

>>9834379
>Can we please talk about a theory that literally none of the people in this thread understand?

>>9834522
>>Can we please talk about a theory that literally none of the people in this thread understand?
Who are you quoting?

I've had a few interpretations that seemingly all lead me astray, so excuse me asking for some help on a random problem.

What's the probability that (with a fair six sided die) I roll the same number more than once in n die rolls?

>>9834548
I believe it would be six times one minus the probability of rolling a given number once minus the probability of not rolling a given number at all. I don't want to work that out but I think that's what you're looking for.

I does one cure akrasia?

>>9834304
Most math is shit. You should be able to understand a pretty large fraction of the stuff you actually want to learn.

can anyone here please help me with this, I'm literally lost

translation in my next post

>>9834895

>>9834895
>>9834896
>>>/g/

>>9834895
>>9834896
Lost with what? it literally tells you what to do

>>9835074
I'm stumped my man, could you help I'd appreciate it

>tfw only more trivialities fixed in the latest IUT update

http://www.kurims.kyoto-u.ac.jp/~motizuki/2018-06-28-iu-teich-revisions.txt
>Inter-universal Teichmuller Theory I
>Inserted a missing space in the first display of Remark 4.9.1, (i)

>Inter-universal Teichmuller Theory II
>In the second display of Remark 3.6.4, (iv), inserted the word "portion"

>Inter-universal Teichmuller Theory III
>Corrected misprints in the Introduction ("regarded a positive real multiple" ---> "regarded as a positive real multiple", "but rather with]" ---> "but rather] with")
>Added an additional reference at the end of Remark 3.3.2, (i)

>Inter-universal Teichmuller Theory IV
>In the discussion immediately following the first display of Step (v) of the proof of Theorem 1.10, replaced the phrase "the tensor product of log-shells under consideration" by more precise notation (2 instances)

>>9835086
Which part are you stuck on? Is the expectation that you write your own method to calculate eigenvalues or can you use a library?

>>9835109
my own method no library

>>9835137
e is an eigenvalue of A if the dimension of the nullspace of A-eI is positive (I is the identity operation.) A-eI having a nullspace of dimension at least one is equivalent to A-eI having non-maximal rank, which is equivalent to the determinant of A-eI vanishing. Thus you just need your program to find, given arbitrary fixed integers x,y,and z, all e such that det(A-eI)=0. Hell, it's a 3rd degree polynomial in e so you can even compute the roots exactly.

>>9835183
ok thanks my man I'm on it

I'm studying to test out of the 2nd semester undergrad modern algebra course at my school and it's fucking hell.
>takes me two or more days to finish a section of the textbook (Fraleigh) and complete a respectable amount of practice problems
>some sections rely heavily on material that we barely covered in the first semester course, which means I need to take a day off to learn a previous chapter
Don't know if I can make it. Can anyone recommend some video lectures in modern algebra? I think they might help me pick up the pace.

>>9835191
>Can anyone recommend some video lectures in modern algebra?
What exactly does your '2nd semester undergrad modern algebra course' cover?

>>9835200
Copied and pasted from pdf, so formatting looks like shit:
Groups.
•Group actions and their orbits, the orbit-stabilizer theorem and the orbit counting formula (erroneously) attributed to Burnside and Polya counting.
•If time permits, some of the following: conjugacy class sizes, the class equation, and
the fact that nontrivial
p-groups have nontrivial centers. Also the Sylow existence
theorem and the simplicity of the alternating group [math]A_5[/math] can be included here.

Linear algebra.
•A quick review of vector spaces, bases and dimension, linear transformations and their
matrices, eigenvalues and eigenspaces.
•Minimal and characteristic polynomials and the Cayley-Hamilton theorem.
•Nilpotent linear operators and the Jordan canonical form.
•Linear functionals and dual spaces.

Fields.
•Algebraic extensions, finite degree extensions and minimal polynomials. Multiplicativity of degrees of extensions.
•Adjoining a root of a polynomial and existence of splitting fields. Repeated roots
and formal derivatives. Uniqueness of splitting field. (Needed for uniqueness of finite
fields.)
•Finite fields, existence and uniqueness.
•Discussion of geometric constructions. The impossibility of trisecting an angle, squar-
ing a circle and doubling a cube. The construction of regular
n-gons.

Module theory.
•Modules, submodules, module-homomorphisms and factor modules.
•Modules over PIDs and the fundamental theorem of abelian groups. (See the remarks
below.)
•The rational canonical form for linear operators.

Galois theory (brief introduction)
•Galois groups.
•Solvability by radicals.

>>9835191
If you are time constrained the you probably have to treat theorems as black boxes, unless the proofs are instructive. Look at the problems for a given chapter before reading the chapter. As you read, try and solve the problems.

Can you really finish this book with just high school knowledge of mathematics?

>>9835255
>Can you really finish this book with just high school knowledge of mathematics?
Why don't you try it and find out?

>>9835342
Fine

>>9835213
Fuck that's a lot. We covered about that much in two semesters of algebra. How do you possibly go into any detail?

I have done this problem 5 different ways, and every single time I get:

1/b^1/8

BUT THE BOOK SAYS THE ANSWER IS:

1/b^7/8

The book is wrong. I swear the book is wrong! (This isn't homework, I'm tutoring someone in intermediate algebra) Please tell me that the book is wrong.

>>9835364
>I'm tutoring someone in intermediate algebra
Why are you tutoring someone else if you can't simplify it yourself?

>>9835369
I just told you what the answer was, I am just posting to confirm that the book is wrong.

>>9835364
Seems to be 1/b^8 but it's 0200 h in the morning, just plug it into wolfram to be sure.

>>9835364

is it true that if a^(2n) mod b = 0 then a^n mod b = 0, where a, b, n are natural numbers?

>>9835394
Try these: a=4, b=8, n=1.

>>9835394
never mind

>>9835394
>is it true that if a^(2n) mod b = 0 then a^n mod b = 0
No.

>>9835401
I proved that if a^(2n) mod b = 0 then a mod b = 0 for b=2,3 when n=2 but I was wondering if this was generally true for all b or for higher n (obviously when b<=a)

>>9835418
i meant to say when n=2, as in a^2

>>9835421
dumb fucking faggot n=1

>>9835418
Try a=12, b=9 and n=1. Obviously, a^(2n) = 9*16, but a^n is not divisible by b.

>>9835423
so what are the bounds on a and b?

>>9835385
>>9835386
Thanks for confirming. I should email the author of this book.

>>9835441
Damn, is she the author?

>>9835443
Yeah, WWYD?

>>9835444
I'll give her 20 children

>>9835435
I don't know.

>>9835448
me neither

>>9835445
and here I thought this board was run by lolis

>>9825089
[eqn]1+1=\window[/eqn]

Please be patient with me, I'm just starting to learn matrix from Michael Artin Algebra. But this is wrong, right?

>>9835453

>>9835461
What you mean?

>>9835467
The product of multiplication is wrong, right?

>>9835468
Yeah. Looks wrong to me

>>9835473
Thanks buddy.

>>9835450
It holds when b is any prime, but, as my example shows, it can fail even when b is a squared prime. Maybe for b a product of two distinct primes. That does, indeed, hold:
Let p and q be distinct primes. If a^2n = kpq, for some k, n, suppose p does not divide a^n. Then it must be the case that a^n = mp^(1/2) for some integer m, so the square root of p is an integer. This can't happen, so p divides a^n. Similarly, q divides a^n, so pq divides a^n.
Could it hold for a finite product of distinct primes?

>>9835518
Any finite product of distinct primes*

>>9835518
probably holds iff b is squarefree

hello /mg/
if i was a mathlet who wanted to teach himself multivariable calc/linear algebra out of ap calc bc, what book should i start with?

or should i just do books on proofs so i can make the long, hard trek to do the meme books on the wiki

>>9835561
Do it all. In one hour. If you can't, you're a brainlet.

>>9835564
brainlets need to learn too pal

Who'se the Tom brady of Math?

>>9835608
me desu senpai

>>9835575
I'm not your pal buddy.

>>9835096
I guess that's a sign that the supposed 'specific and serious error' doesn't actually exist

>>9835518
It works iff b is squarefree.
You know it holds for primes and always fails for a power of a prime greater than 1. Any b can be broken up into these pieces via the chinese remainder theorem

>>9835561
if you want to go hard and do a more rigorous approach, I would recommend reading a book like Hammack's book of proof and then Hubbard's Unified Approach book. I only just started reading it, but it seems very well written. It teaches MV calc and LA and shows how they can be used together. You might want to do an overview of MV calc first though unless you're really good at math.

>>9835229
The problems have been the greatest time sink, so far. I have not tried solving them while I read, though. Seems like it would help, thanks for your input.
>>9835360
I thought this was standard for a 2nd semester algebra class. How many semesters of algebra did they offer at your undergrad college?

>>9825089
Can you check my book list https://pastebin.com/raw/xsG00eL1

I know is big, I want to put every book in its correspondent folder and separate according level, "beginner", "intermediate", "advanced", etc. Also any recommendation in what to include or remove is welcome.

>>9835762
>https://pastebin.com/raw/xsG00eL1
not science or math

>>9835773
Sorry discard >>9835762
The correct mathematic book list is this https://pastebin.com/raw/SF6JbbAK

Reposting again with the correct link.

Can you guys check my book list https://pastebin.com/raw/SF6JbbAK

I know is big, I want to put every book in its correspondent folder and separate according level, "beginner", "intermediate", "advanced", etc. Also any recommendation in what to include or remove is welcome.

>>9835782
now this is autism

>>9835782
Remove:
>Algebra. Springer, (Graduate texts in mathematics 211) Serge Lang (2002).djvu
>Undergraduate Algebra. Springer, (Undergraduate texts in mathematics) Serge Lang (2005).djvu
>Complex Analysis. Springer, (Graduate texts in mathematics 103) Serge Lang (1999).djvu
>Problems and Solutions for Complex Analysis. Springer, Rami Shakarchi, Serge Lang (2008).djvu
>Real and Complex Analysis - Rudin W. 1987.djvu
>Real and Functional Analysis. Springer-Verlag, (Graduate texts in mathematics 142) Serge Lang (1993).djvu
>Basic Analysis of Regularized Series and Products. Springer-Verlag, (Lecture notes in mathematics 1564) Jay Jorgenson, Serge Lang (1993).djvu
>Undergraduate Analysis. Springer, (Undergraduate texts in mathematics) Serge Lang (1997).djvu
>Problems and Solutions for Undergraduate Analysis (Undergraduate Texts in Mathematics). Springer, Rami Shakarchi, Serge Lang (1998).pdf
>Basic Mathematics - Addison-Wesley series in introductory mathematics. Serge Lang (1971).djvu
>A First Course in Calculus 5th Edition - Springer. Serge Lang (1986).djvu
>Introduction to Linear Algebra. Springer, (Undergraduate Texts in Mathematics) Serge Lang (1985).djvu
>Algebraic Number Theory. Springer-Verlag, (Graduate texts in mathematics 110) Serge Lang (2000).djvu
>Principles of Mathematical Analysis, Rudin W. 1976.djvu

and take this out of the group theory folder
>An Introduction to Galois Theory.pdf

>>9835782
Thanks for the list friend. "A Problem Book in Algebra" by V. A Krechmar is a really good elementary problem book.

>>9835794
Are Serge Lang and Rudin really not worth it?

>>9835809
>Are Serge Lang and Rudin really not worth it?
Why don't you read them and find out?

>>9835811
I did, found Lang quite enlightening.

>>9835782
delete all the books you're not currently using

Please help me /mg/. I've found a math text that I desperately want to read, but it's 1000 pages long, only available in PDF form, and for some reason it causes errors when I try to upload it to my kindle or online printing services. How do I read this thing??

https://www.seas.upenn.edu/~cis515/linalg.pdf

>>9835816
Maybe is a virus.

>>9835816
>How do I read this thing??
looks fine on my monitor

>>9835819
>>9835820
It works fine on my laptop, but I need a way to either get it onto my kindle or print it out, neither of which are working. Neither Staples or Office Depot would accept it.

>>9835824
Maybe convert it to epub with Calibre?

>>9835830
I tried converting it to mobi already, but it spat out mangled garbage. I'll try epub.

>>9835832
Your other chance is convert all pages to individual pictures with something like imagemagick.

>>9835824
What about Adobe Acrobat?

>>9835809
they're not even worth the space on your hard drive

>>9835834
Trying this right now. I'm getting 150mb pdfs that are really blurry.

>>9835857
The goal is to not have to read all 1000 pages on my laptop.

>>9835816
>>9835894
Sweet jesus, I finally got it to work. It was the glitchy images at the very front of the pdf causing the issues, so cut out everything before page 5 and then it worked when I uploaded it to my ereader. Time to git gud numerical analysis.

I want to do my PhD in the University of Paris (Paris VII is the one with the math program, right?). Academically speaking, what do I need to do in order to get in?

I wasn’t born to learn mathematics. I was born to solve them.

>>9836322
Paris VI, VII, XI and Polytechnique all have excellent pure math programs (VI and VII work inside the same group called IMJ-PRG, XI does its own thing).
For applied math, you can also look at Polytechnique and Paris-Dauphine for example.
Academically, you only need an MSc.
That being said, you have to contact the professors you want to work with individually to see if they would be inclined to. There are no PhD programs where you "get in" and then choose an advisor.
The way it usually goes in France is that during the last year of your masters, you ask one of these guys (preferably with excellent grades and some references) to supervise your masters thesis during the spring semester and, if they accept, they will probably keep you as a PhD student (but ofc you should ask them for both).
I also need to point out that non-funded PhDs in science/math are prohibited here, hence even if you find an advisor, you have to secure funding in order to actually enrol, which can be tricky for pure math.

Please, what is Pythagoras' Theorem to the nearest five decimal places?

>>9836370
a^1.99999 + b^1.99999 = c^1.99999

>>9836365
Thank you Anon! Do you know if they ask for a DELF diploma or something related?

>>9836365
Do they require fluency in French there?

>>9825354
>uniformed

>>9835809
Don't listen to him. Rudin is tough, but worth it.