/mg/ maths general: cohomologies edition

[Anonymous No.9861124]

talk maths, formerly >>9837232

picture from https://arxiv.org/pdf/1712.03708.pdf
>p-adic geometry
>Peter Scholze
>(Submitted on 11 Dec 2017)
>We discuss recent developments in p-adic geometry, ranging from foundational results such as the degeneration of the Hodge-to-de Rham spectral sequence for "compact p-adic manifolds" over new period maps on moduli spaces of abelian varieties to applications to the local and global Langlands conjectures, and the construction of "universal" p-adic cohomology theories. We finish with some speculations on how a theory that combines all primes p, including the archimedean prime, might look like.

[Anonymous No.9861131]

[eqn]\sf\color{red}{Gook}\; \color{orange{moot}\; \color{yellow}{\bb STILL}\; \color{green}{hasn't}\; \color{cyan}{fixed}\; \color{blue}{the}\; \color{indigo}\TeX\; \color{violet}{tags}[/eqn]

[Anonymous No.9861173]

>>9860149
You're a failure as a mathematician if you can't even solve elementary mathematical problems

[Anonymous No.9861206]

>>9861173
OK. You begin.

[Anonymous No.9861214]

>>9861173
>spending hundreds of hours solving contrived trash problems with no intrinsic value in the problem or the solution except that it's "hard"
you need an insect brain to enjoy competitive math

[Anonymous No.9861270]

>>9861173
you're not even a mathematician!
go back to your physics containment board >>>/toy/

[Anonymous No.9861272]

>>9861124
p-adics are fucking useless fuck off idiot

[Anonymous No.9861347]

I hate this general.

[Anonymous No.9861805]

Are there such things as algebraists? I’ve heard about ring theorists and topologists, but never about algebraists.

[Anonymous No.9861807]

>>9861805
>Are there such things as algebraists?
Yes.

[Anonymous No.9861809]

>>9861807
What do they do? Coming up with theories about algebra or solves some unsolved algebraic problems?

[Anonymous No.9861816]

>>9861809
>Coming up with theories about algebra or solves some unsolved algebraic problems?
Yes.

[Anonymous No.9861842]

>>9861805
Yes, well algebra is pretty big so there are plenty of more specialized terms for people working in algebra (algebraic geometers, representation theorists, ring theorists, etc.)
I think people now called algebraists would be the ones working in things like central simple algebras, quadratic forms, algebraic K-theory, pure commutative algebra etc.

[Anonymous No.9861845]

>>9861842
Cool, thanks friend.

[Anonymous No.9861936]

If I have a group of uncountable cardinality, can it be finitely/countably generated?

I was thinking this because, could an element of an uncountable group generate uncountably many different elements, or maybe the countable nature of cyclic subgroups restrict the generation of elements so that they could never "catch up"

[Anonymous No.9861945]

>>9861936
No. Consider the terms of length n which can be generated using a finite/countable number of generators.

[Anonymous No.9861964]

>>9861945
What about the group Z^N (that is, the N copies of the integers where N are the natural numbers). That group is uncountable but it is countably generated (a 1 generates Z for each term)

[Anonymous No.9861971]

>>9861964
>That group is uncountable

[Anonymous No.9861974]

>>9861964
It doesn't generate it because you're only supposed to use finite sums of the generators while forming the generated set.

[Anonymous No.9861977]

>>9861971
lmao quick to delete your massive blunder, categoryfaggot

[Anonymous No.9861978]

>>9861971
It is tho

[Anonymous No.9861980]

>>9861977
>using N for \mathbb{N}

[Anonymous No.9861982]

>>9861980
tex doesnt work anymore so im not even going to attempt it

[Anonymous No.9861997]

>>9861980
>weebs' reading comprehension

[Anonymous No.9861998]

>>9861997
>>weebs' reading comprehension
Who are you quoting?

[Anonymous No.9863193]

>>9861173
>elementary mathematical problems
I don't see any such problems in that post.

[Anonymous No.9863507]

Prove you're not a brainlet: >>9862425

[Anonymous No.9863601]

>>9861173
You said that last thread.

[Anonymous No.9863603]

Are you ever angry that your mathematical "game" isnt actually real?

[Anonymous No.9863621]

>>9863603
What did he mean by this?

[Anonymous No.9863667]

>>9863621
>he

[Anonymous No.9863711]

>>9863667
Women can't do math

[nigger No.9863749]

7/11 was a part-time inside job

[Anonymous No.9864083]

>the rumor about a mistake in Mochi's abc proof has been deleted
OH NO NO NO NO NO
https://totallydisconnected.wordpress.com/2018/05/09/the-latest-hot-abc-news/

[Anonymous No.9864255]

>>9864083

[Anonymous No.9864329]

Do I need to learn abstract algebra before learning finite vector space linear algebra?

[Anonymous No.9864331]

>>9864329
no

[Anonymous No.9864333]

>>9864331
Phew, thanks friend.

[Anonymous No.9864335]

>>9864329
linear algebra is abstract algebra

[Anonymous No.9864336]

>>9864329
no point unless you wanna be an engineer

[Anonymous No.9864341]

>>9864335
So I do need to learn abstract algebra beforehand?

>>9864336
I want to understand the concept rather follow it blindly

[Anonymous No.9864357]

>>9864341
Both are predicated on a set of axioms. You won't be very knowledgeable about fields in general, but you really don't need to know much about fields beyond the axioms to use them in linear algebra; Linear algebra studies vector spaces and linear maps, which are special types of algebraic structures (but particularly nice ones)
There's no reason to start with abstract algebra unless you have autism and hate the idea of starting with a larger structure before the very smallest, most general interesting one.

[Anonymous No.9864361]

>>9864357
Thanks Anon

[Anonymous No.9864371]

>>9864329
You should learn linear algebra first.
Linear algebra is a subject in its own right, with its own methods and styles of proof. You're doing a disservice to your understanding to try and think of it only as a branch of abstract algebra, even though you technically _could_ approach the subject that way.

[Anonymous No.9864383]

>>9864371
Thanks onii-chan

[Anonymous No.9864394]

>>9864083
Kek

[Anonymous No.9864466]

>>9864394
the eternally doing fine man

[Anonymous No.9864487]

make no mistake: scholze is gonna rip him a new asshole

[Anonymous No.9864500]

>>9864487
This is true but it’s fun to fantasize that Mochi is playing non-equidimensional chess on everyone and already has a 1000 page rebuttal ready which solves four millennium problems along the way.

[Anonymous No.9864540]

>>9861173
thanks for the problems bro

[Anonymous No.9864571]

>>9864083
The plot is getting thicker.

[Anonymous No.9865570]

[Anonymous No.9865677]

>>9865570
You shouldn't have.

[Anonymous No.9866256]

>>9864487
Scholze is a an overrated boipucci.

[Anonymous No.9866280]

>>9866256
Perfectoid spaces are far greater than anything that Mochi pulled out of his ass, before or after IUTeich.

[Anonymous No.9866306]

>>9866280
>Perfectoid spaces are far greater than anything that Mochi pulled out of his ass, before or after IUTeich.
"No!"

[Anonymous No.9866349]

I want to give Peter Scholze a prostate orgasm.

[Anonymous No.9866468]

what are some generalizations of conjectures you think are probably wrong because of being too general?

for me, it's the equivariant tamagawa number conjecture (generalization of birch-swinnerton dyer conjecture)

[Anonymous No.9866548]

I asked in /sqt/ already but they only seem to want to shitpost today

in the coming semesters I'm going to be taking Calculus II and Calculus-Based Physics II: Electricity and Electromagnetism.

Everyone and everything tells me these two classes are brutal.
I can't, however, find much information on why.
All I've been able to ascertain is that integration is a non-trivia PITA and Calc II is all about them, and I assume Physics II involves them a lot too.

Can you guys tell me why people consider these two courses to be difficult so I know what to study up on before I take them?

[Anonymous No.9866551]

>>9866548
>what to study up on before I take them?
Calculus II and Calculus-Based Physics II: Electricity and Electromagnetism.

[Anonymous No.9866555]

>>9866551
thanks I got that
in turn I'm reading up on integration by parts which seems to be a big stumbling block for calculus II, but I haven't found anything else for Physics II

[Anonymous No.9866842]

>>9866555
>>9866548
>i am proficient in the product, the quotient rule was a joke

[Anonymous No.9866879]

I want to shut Mochizuki’s mouth and stroke his cock until he begs me to stop

[Anonymous No.9866881]

>>9866468
Most generalizations of the Hodge conjecture and Tate conjecture don't seem to work. Hell, maybe the basic conjectures are false themselves, or at least "barely true".

[Anonymous No.9866886]

How do I prove that all the numbers in a row of Pascal's triangle are odd iff the row is 2^n-1?

[Anonymous No.9866970]

>looking through random mit materials and see this

Anyone tell me what this is about

[Anonymous No.9866973]

>>9866886
You need to specify n first

[Anonymous No.9866974]

>>9861124
Why do modem mathematicians have such a hateboner for rigor?

[Anonymous No.9866985]

>>9866886
Induction

[Anonymous No.9866989]

>>9866970
Cones

[Anonymous No.9867053]

>>9866970
>sanjoy mahajan
really makes me stink

[Anonymous No.9867098]

>>9866974
because modern math is such a clusterfuck that if everyone was rigorous nobody would get anything done

[Anonymous No.9867109]

>>9866548
The difficulty of those kind of things depends basically entirely on how much of an asshole your professor is.
Most integration is fairly straightforward, but the difficulty level can also be ratcheted up basically indefinitely. Electromagnetism can be made to involve some pretty evil integrals if the guy writing the problems wants it to.

[Anonymous No.9867348]

>>9866879
How will he be able to beg you if you shut his mouth?

>>9866881
>"barely true"
How do you mean?

[Anonymous No.9867417]

>>9867348
>How will he be able to beg you if you shut his mouth?
Exactly

[Anonymous No.9867603]

>>9861124
Anyone know a good introductory textbook on Morse theory? Mostly interested in its applications, but I'm fine with any amount of depth.

[Anonymous No.9867610]

>>9867603
K. Perera, R.P. Agarwal, Donal O’Regan, Morse theoretic Aspects of p-Laplaccian Operators, AMS,
2010.

[Anonymous No.9867611]

>>9864083
Based interuniversal samurai

[Anonymous No.9867624]

>>9867610
Thanks, looks perfect.

[Anonymous No.9867761]

I'm planning to do a book club type thread for Atiyah & Macdonald's commutative algebra, where we discuss week by week each chapter, solve the exercises and share explanations/questions etc. Only problem is that A&M is pretty hard and advanced and requires knowledge of field theory after chapter 5, and some basic topology, and TeX doesn't work(?).

Perhaps I could start instead with a Jacobson's Basic Algebra I thread and cover most of the prereqs. Although it'd be pretty boring for me, but i dont mind that much, i've a lot of free time.

Thoughts?

[Anonymous No.9867782]

>>9867761
>TeX doesn't work(?)
turn off adblock

[Anonymous No.9867793]

>>9866973
N is obviously a natural number you fucking retard
>>9866985
Can you be more specific? Also it's an exercise that I think only uses direct, contrapositive, and contradiction

[Anonymous No.9867819]

>>9867761
>I'm planning to do a book club type thread for Atiyah & Macdonald's commutative algebra
y tho

[Anonymous No.9867904]

>>9867348
>How do you mean?
I mean that most ways to generalize the result ,even slightly, will cause the whole thing to break. It appears this is the case with the Riemann hypothesis according to one of Tao's recent papers.

[Anonymous No.9868137]

>>9867782
testing

[math] \sum\limits_{n=1}^\infty \frac{1}{n^n} [/math]

[Anonymous No.9868200]

>>9866881
>Most generalizations of the Hodge conjecture and Tate conjecture don't seem to work.
I think these suffer from a different issue than being "too general".
The state of understanding around those conjectures is fairly poor compared to a lot of areas, so it's entirely possible that the conjectures suffer not from being too general but from not being the right kind of general, since our understanding is so weak that most guesses are bad guesses.

Many attempts to generalize the Hodge conjecture end up failing because they weren't even formed properly, rather than having a subtle error.

[Anonymous No.9868387]

>>9867782
test
[eqn]\oiiint 0.9999...[/eqn]

[Anonymous No.9868391]

>>9868387
>>9868137
>>9867782
fucking chimoot

[Anonymous No.9868398]

>>9867819
I'm bored and gonna go over it anyways, might need help at some times too and i enjoy helping other peopel (i always answer sqt math q's for example), plus i get to practice a bit for when i teach

[Anonymous No.9868439]

>>9867761
sounds good to me

[Anonymous No.9868449]

>>9866548
Calc II is a breeze, if you're good at math. It's usually just normies who say they had a real tough time with it because they aren't cut out for it.

[Anonymous No.9868457]

Where the fuck do i start reading on motivic homotopy theory?

[Anonymous No.9869434]

>>9868457
You don't.

[Anonymous No.9869541]

>>9869434
Any specific reason or will we leave it at shitposting?

[Anonymous No.9869555]

>>9869541
It's a half-baked field built on some vague ideas Grothendieck had.

[Anonymous No.9869860]

>>9869555
>vague ideas Grothendieck had
Seems awesome. Is it a dead field like KK-theory or is there any progress being made?

[Anonymous No.9869869]

>>9869860
It's as dead as any math theory can be. Only a handful of people ever worked on motives in the first place.

[Anonymous No.9869890]

>>9869869
I only read some vague babbling on motives by Lurie and it sounded interesting. Guess it would be beyond my abilities anyway, i'm just an undergrad.

[Anonymous No.9870593]

>>9869890
>I only read some vague babbling on motives by Lurie
Link?

[Anonymous No.9870627]

>>9870593
iirc, it was on the occasion of Voevodsky's death. Can't be bothered to find it though, i've just recently got to it on my to-do list so i figured i might just ask around.

[Anonymous No.9871062]

"Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose. More of continuity, or less of continuity, more derivatives, and so forth. Indeed, from the point of view of logic, these strange functions are the most general; on the other hand those which one meets without searching for them, and which follow simple laws appear as a particular case which does not amount to more than a small corner.

In former times when one invented a new function it was for a practical purpose; today one invents them purposely to show up defects in the reasoning of our fathers and one will deduce from them only that.

If logic were the sole guide of the teacher, it would be necessary to begin with the most general functions, that is to say with the most bizarre. It is the beginner that would have to be set grappling with this teratologic museum."
—Henri Poincaré, 1899

Found my favorite quote. Math would be boring if it's easy. Really make my dick rock hard.

[Anonymous No.9871230]

Anyone else addicted to mints? I read once that they enhance memory and ever since then I take mints when I study and take tests. I think I'm building resistance because a couple of weeks ago I started to instinctively take two mints at a time like one mint was not doing it for me anymore.

Any known side effects? I mainly do tic tacs by the way.

[Anonymous No.9871396]

>>9871230
>I read once that they enhance memory
sounds like horseshit to me, I love mints as well yet have horrible memory, short term at least. Willing to bet most mint-flavored candy contains little to no actual mint oil, too

[Anonymous No.9871449]

Can I get help with this baby calc problem?

find
lim x --> 0 (cscx - 1/x)

I rewrote it in terms of y, took the ln of both sides and was able to rewrite it as
ln y = lim x-->0 ln(cscx/ (1/x))
which I then rewrote as
ln y = lim x -->0 ln(x/sinx)
raise both sides by e and get
y = lim x--->0 x/sinx
use l'hopital's rule which gives
lim x-->0 1/cosx
which gives and answer of 1. However the back of the book says it's 0, and I'm not sure where I fucked up.

[Anonymous No.9871505]

>>9866280
Scholze has Lang's Glans too far down his throat to do any important work. Programme Builders are wishful thinkers, especially in this case.

[Anonymous No.9871514]

>>9871062
>dude functions lmao

Yeah my man subsets of Cartesian products are totally mystifying.

[Anonymous No.9871532]

>>9871514
I've never taken an analysis course in my life - the post

I've never taken a history of mathematics course in my life - the post

I... am just ignorant about everything - the post

[Anonymous No.9871660]

>>9871532
>history of mathematics course
I mean, I agree with what you're saying but why'd you take that qhen you could just read about it.

[Anonymous No.9871673]

>>9871660
He's a brainlet and needs to hunt for credits instead of taking actual classes.

[Anonymous No.9872938]

[Anonymous No.9873047]

>>9872938
Trivial, define the proximity set of a customer [math] x [/math] as the set of family members, co-workers, and close friends of [math] x [/math]. Then a set of customers [math] O [/math] (in the universe of all potential customers) is said to be open if and only if [math] x \in O [/math] implies that O contains the proximity set of [math] x [/math]. It is a trivial exercise to the marketing 101 student to prove this definition satisfies the axioms of topology.

Now, one of the open problems in Marketing Topology is given a topological space, finding the smallest set of people such that the union of their proximity sets is an open cover of the entire space. We seek to minimize the number of people to spend as little money in ad campaigns, and we seek to cover the entire space to be able to reach every possible customer through the use of "early adopters" of our product.

As you see, all of this is already what marketing people do. All I did was rephrase it in terms of topological jargon. Marketing students are, in fact, some of the greatest topologists of our time.

[Anonymous No.9873285]

>>9873047
jej

[Anonymous No.9873838]

Do differential geometry or differential topology rely on differential equations?

[Anonymous No.9873858]

>>9873838
nope but it would hurt to know about them.
DG is basically glorified chain rule, trust me

[Anonymous No.9873880]

>>9873838
Yes, differential equations are very useful in differential geometry and topology. The Cauchy-Lipschitz theorem ensures that one can use vector fields to construct diffeomorphisms of a manifold satisfying constraints (look up flows and 1-parameter groups of transformations).

[Anonymous No.9874059]

Redpill me on compressed sensing.

[Anonymous No.9874119]

>>9873838
Yes, most results and objects depend on existence of solutions to differential equations over manifolds. You can get away with only knowing the results of existence in first and second order ODEs for some time in DG, but ultimately you're gonna need to know much more about it if you wanna do anything interesting. For example, the Nash embedding theorem or poincaré conjecture both required extensive study of PDEs.

>>9873858
this guy's a retard

[Anonymous No.9874425]

>>9861347
#metoo

[Anonymous No.9874439]

>>9874059
The future is nonlnearity, and compressed sensing is linear.

[Anonymous No.9874803]

>>9866974
I've been reading a lot of real & complex numerical algebra recently. They (somewhat) get around this problem by talking about everything as arrays with different indexing schemes attached to them. Its actually similar to how Arthur Cayley did a some of his work on early tensor algebra. I like it, abstract algebra with a more applied twist. Keep the rigor, but keep it concrete.

[Anonymous No.9875128]

>>9861124
the fuck is a cohomology nigga

[Anonymous No.9875223]

>>9875128
its the 'cis' to a 'trans', if you know what i mean

[Anonymous No.9875337]

TURN ON CNN

https://arxiv.org/pdf/1807.06447.pdf
>A proof of the Riemann Hypothesis via the Nicolas Criterion
>Vincenzo Oliva
>(Submitted on 14 Jul 2018)
>The achievement of this paper is a proof by contradiction of the inequality addressed by the Nicolas criterion for the Riemann Hypothesis, carried out relying on the known fact that it either always holds or both holds and fails infinitely often. We accomplish it showing by induction that if it ever fails, it always does from a certain point onward, which contradicts the aforementioned fact.

[Anonymous No.9875352]

>>9875337
Nothing on the news?

[Anonymous No.9875372]

HOLY SHIT SCHOLZE-STIX BTFO MITSUBISHI IN PERSON
http://www.math.columbia.edu/~woit/wordpress/?p=10436

>>9875337
kek

[Anonymous No.9875445]

>>9875372
>http://www.math.columbia.edu/~woit/wordpress/?p=10436
>‘Report on discussions, held during the period March 15–20, 2018, concerning inter-universal Teichmüller theory (IUTCH)’
>‘Comments on the manuscript by Scholze–Stix concerning inter-universal Teichmüller theory (IUTCH)’
>the manuscript by Scholze–Stix concerning inter-universal Teichmüller theory (IUTCH)
For what reason are none of these three online

[Anonymous No.9875449]

>>9874439
splain

[The Lord No.9875484]

>>9875449
splain you dat?
>nyelo

[Anonymous No.9875502]

>>9875445
probably because it was only written for an audience of no more than ten people, of which they wanted to have a discussion with first before they filled in the details and went public

[Anonymous No.9875764]

>>9875372

no wonder Fesenko is so stressed and aggressive
poor Mochizuki desu, it looks like Fesenko is leeching out of him

[Anonymous No.9875796]

>>9875449
Mathematically, compressive sensing is when you are given a (nonsquare) matrix A, vector y, and you are trying to solve Ax=y. The issue is that there are many solutions x to the system, so you choose x with as many components that are 0 as possible. This is known as the sparsest solution, and that is the one you are looking for in compressive sensing. However, in real life, things may not be so simple. For example, if e is some unknown error term or noise, then the problem turns into solving Ax+e = y, which is nonlinear. This problem has already been considered in the research of compressed sensing, but real life situations require that the measurements that you take might not end up being linear. As a result, compressive sensing does not apply as many situations as you would like as it is right now, unless you do some modifications. So there needs to be more work done in compressive sensing in a nonlinear setting.

https://terrytao.wordpress.com/2007/04/13/compressed-sensing-and-single-pixel-cameras/

[Anonymous No.9875862]

>>9861807
Yo, right here.

[Anonymous No.9875899]

>>9875337
>it either always holds or both holds and fails infinitely often. We accomplish it showing by induction that if it ever fails, it always does from a certain point onward, which contradicts the aforementioned fact.
What.

>>9875372
wew

[Anonymous No.9875925]

I am beginning to think that Mochizuki is right and Scholze will ultimately lose this fight. What do?

[Anonymous No.9875930]

>>9875925
nah senpai Jakob Stix is solid too

[Anonymous No.9875939]

>>9875930
>Jakob Stix is solid too
>https://de.wikipedia.org/wiki/Jakob_Stix
>taught by a gypsy
>Jakob Stix is solid too
"No."

[Anonymous No.9875947]

The glorious samurai of mathematics does not fear a pair of millennial Nazis.

[Anonymous No.9875971]

I thought, I had lost my love for mathematics, but then it came back to me. For two months, I could not do any Mathematics, not any. I was too busy socializing and wasting time with women, but now, I don't know. My heart yearns to go back to it, the urge is irresistible.

[Anonymous No.9875982]

>>9875971
I've never loved math, I'm just good at it.

[Anonymous No.9875991]

"Four most important mathematical reasons explaining the difficulty to study IUT are related to the overall
poor digestion of the Grothendieck heritage by number theorists, to a relatively large distance between anabelian
geometry and IUT and the mainstream directions, to a large number of new concepts in IUT and to its
relatively large volume. A very small number of number theorists have an experience of working with the étale
fundamental group, one of first key objects of anabelian geometry. The Grothendieck heritage, so essential for
IUT, has not been properly digested by very significant part of number theorists. Strikingly naive questions
at the Oxford IUT workshop about why does one need to use categories in number theory is a reminder of
that issue. Galois representations or L-functions, or aspects of the Langlands program, used by many number
theorists, are very far away from key substantial methods of IUT."

#rekt

[Anonymous No.9876011]

>>9875372
Woit siding with Scholze already tells you enough - Mochizuki is right.

[Anonymous No.9876018]

>>9875991
>A very small number of number theorists have an experience of working with the étale
fundamental group

That seems like an incredibly false statement. I don't know a single number theorist who isn't comfortable with etale fundamental groups and etale cohomology.

[Anonymous No.9876019]

>>9875991
rofl
i think it's safe to assume that Scholze and Stix have at least "an experience of working with the étale fundamental group"

[Anonymous No.9876022]

>>9876018
>>9876019
one second apart
>this kills IUT

[Anonymous No.9876024]

>>9876019
Scholze is an exception that proves the rule.

>>9876018
>That seems like an incredibly false statement. I don't know a single number theorist who isn't comfortable with etale fundamental groups and etale cohomology.
That seems like an incredibly false statement.

[Anonymous No.9876028]

>>9876024
go away Ivan
>Scholze is an exception that proves the rule.
well it is Scholze who has supposedly objections to IUT

[Anonymous No.9876032]

>>9876028
>go away Ivan
No, you go away, W*it.

>it is Scholze who has supposedly objections to IUT
Scholze will eventually come around.

[Anonymous No.9876035]

>>9876024
>That seems like an incredibly false statement.

It isn't. Etale algebraic geometry proved itself an extremely valuable tool to number theorists decades ago.

Any modern number theorist would be well versed in it.

[Anonymous No.9876037]

>>9876035
Decades ago... specifically around when?

[Anonymous No.9876040]

>>9876037
In the 70s when Deligne used etale cohomology to prove the Riemann Hypothesis for local zeta functions.

[Anonymous No.9876137]

>>9875971
>I thought, I had lost my love for mathematics, but then it came back to me. For two months, I could not do any Mathematics, not any. I was too busy socializing and wasting time with women, but now, I don't know. My heart yearns to go back to it, the urge is irresistible.

[Anonymous No.9876150]

>>9875223
i got u

[Anonymous No.9876155]

>>9876137
My man, who's your favorite 2hu? Mine is Murasa.

[Anonymous No.9876177]

>>9876032
Scholze just needs to get Mochizuki as his new father figure instead of Langlands

[Anonymous No.9876181]

>>9876018
>I don't know a single number theorist who isn't comfortable with etale fundamental groups and etale cohomology.
You must not know many number theorists.

[Anonymous No.9876190]

>>9876035
number theory is not limited to arithmetic geometry

[Anonymous No.9876237]

[Anonymous No.9876786]

>>9876181
Find me a single modern number theorist who has never used etale stuff in a paper,

>>9876190
I didn't say it was. But a number theorist rarely works ONLY in such a specific topic.

[Anonymous No.9877223]

If I prove that something is turing complete by constructing a machine that can simulate any turing machine, how do I prove my construction correct?

[Anonymous No.9877243]

>>9877223
Is this a trick question?

[Anonymous No.9877277]

>>9876786
>Find me a single modern number theorist who has never used etale stuff in a paper,
Ram Murty
Greg Martin

[Anonymous No.9877288]

>>9877243
No. What do I need to prove to show that the machine actually simulates a universal turing machine?
Some sort of equivalency of configurations?
Halting for the same inputs and producing an equivalent final configuration?
(What's an 'equivalency of configurations'?)

Also, when writing an input to my machine, what kind of calculations am I allowed to do?
For instance, is it allowed to look for a position in memory in my machine that has enough space for the input?
For an extreme, I'm obviously not allowed to just calculate the output with a real turing machine and then write the output to my machine.

I haven't been able to find any papers that actually prove their construction correct either.

[Anonymous No.9877323]

>>9876786
>Find me a single modern number theorist who has never used etale stuff in a paper,
Yitang Zhang

[Anonymous No.9877395]

>>9876786
>Find me a single modern number theorist who has never used etale stuff in a paper,
Waldspurger
Ono (Jr. and Sr.)

[Anonymous No.9877667]

>>9875372
>the "serious problem" STILL hasn't been publicly stated, months later
obviously it's bullshit, scholze is a pussy and a hack

[Anonymous No.9877763]

Never knew mathfags are so toxic. You disappoint me /mg/.

[Anonymous No.9877921]

>>9877277
>>9877323
>>9877395
WRONG

[Anonymous No.9877924]

>>9877921
>WRONG
[citation needed]

[Anonymous No.9878236]

>>9877763
>mathfags are so toxic
The fuck does this even mean?

[Anonymous No.9878245]

>>9877223
>If I prove that something is turing complete by constructing a machine that can simulate any turing machine,
Any turing complete machine can simulate any turing machine.

>>9877288
No, just prove your machine can compute boolean algebras. It doesn't matter if there are memory limitations, the question concerns processing ability, bare minimum processing can simulate anything given enough time.

[Anonymous No.9878247]

>>9878236
That you're white and possibly even male.

[Anonymous No.9878309]

>>9878247
How is that related to toxicity?

[Anonymous No.9878418]

>>9876786
Gerald Tenembaum

[Anonymous No.9878496]

>>9877277
>>9877323
>>9877395
>>9878418
Fucking #rekt, once again.

[Anonymous No.9878508]

>>9875991
This reminds me of that pasta with the number theorist anon complaining about topologists.

[Anonymous No.9878556]

>>9861982
It's the adblock.

[Anonymous No.9878565]

>>9864329
You can learn them in any order you want.
Linear algebra is going to be more familiar, but learning groups and rings before vector spaces also makes sense since a vector space is essentially gluing a group and a field.

[Anonymous No.9879073]

Hey guys I am a kiddo when it comes to mathematics. I took calc 1 and 2 in high school, got a 97 in both, then went to college. Freshman year i just took all my core classes like history, English, fine arts, etc. I'm a compE major with a math minor, so I am taking calc 3 this upcoming semester. Does anyone have a good online review resource for cal 1 and most importantly Cal 2? I remember most of calc 1 but not much of calc 2, although I'm sure reviewing will refresh my memory.

[Anonymous No.9879093]

Teaching myself a linear algebra curriculum and am getting a bit stuck on a basic problem.

How would I prove this? My only idea is to basically set [math]\vec{y} = A\vec{x} [/math] and invert A on both sides... Is this the right approach.
If not, are there any good resources for reading up on linear algebra proofs?

[Anonymous No.9879119]

>>9879093
Nonsquare matrices don't have inverses to begin with, and even if n=m your function will not always be invertible.

Try this: Pick a 3x3 matrix (any one you like) and see what it does to the standard basis vectors (1,0,0),(0,1,0),(0,0,1).

[Anonymous No.9879124]

>>9879093
[math]\mathbb{R}^n[/math] has [math]n[/math] basis vectors, for convenience we can choose the standard unit vectors. If we know the function outputs for the basis vectors we can use that to construct the corresponding matrix. So start we the desired function, find the value of the function at the basis vectors and then use those values plus linearity to construct the matrix.

[Anonymous No.9879235]

Book of Proof solutions.
https://www.people.vcu.edu/~rhammack/BookOfProof/Solutions.pdf

Page 2, problem 51. Is that solution a mistake?

[Anonymous No.9879251]

>>9879073
http://tutorial.math.lamar.edu

[Anonymous No.9879256]

>>9879235
> Is that solution a mistake?
How the fuck should we know when we don't know what problem 51 is?

[Anonymous No.9879266]

>>9879256
>How the fuck should we know when we don't know what problem 51 is?

Sketch the sets of points written above the graph.

[Anonymous No.9879284]

>>9879266
That is indeed the graph for the set [math] \{ (x,y) \in \mathbb{R}^2 \| (y-x)(y+x) = 0 \} [/math].
Again, what is problem 51?

[Anonymous No.9879291]

>>9879284

Does that mean all elements x,y are the real numbers squared? If so, wouldn't the rest of the graph outside of the first quadrant need to be erased since only positive values of x and y can be used to satisfy the equation?

[Anonymous No.9879299]

>>9879291
>Does that mean all elements x,y are the real numbers squared?
What. How would you even reach this conclusion?
When does (y-x)(y+x) equal 0 anon? Think.

[Anonymous No.9879313]

>>9879299

some examples for x,y would be (1,1), (4,4), (9,9)

whenever y = x or y = -x

but I thought it's forcing us to use only positive values for x and y since it says x,y are elements of the real numbers squared. so shouldn't only the first quadrant be graphed?

[Anonymous No.9879318]

>>9879313
[math] \mathbb{R}^2 = \mathbb{R} \times \mathbb{R} [/math]

[Anonymous No.9879320]

By the way, this thread >>9855388 exists for a reason. Let us gossip about Mochizuki in peace.

[Anonymous No.9879330]

>>9879320

ah ok. my bad.

[Anonymous No.9879348]

>>9879330
As long as you understand. . .

[Anonymous No.9879486]

>>9861964
Ok, then how do you make the element of all 1's?
No, idiot, you can't have infinite group operations like infinite sums.

[Anonymous No.9879686]

I'm starting a PhD program this fall anyone got any advice?

[Anonymous No.9879713]

>>9879686
Do research on shit that make your colleagues go “damn that is based”

[Anonymous No.9879762]

>>9867782
Fuck, TeX hasn't been working for months for me and I just thought 4chan was broken.

>>9867761
It's not enough to make sure that ublock is allowing everything. You actually have to disable ublock for the page in order for TeX to work.

[Anonymous No.9880213]

>>9879686
Yeah, you're wasting your time.

[Anonymous No.9880331]

Just started complex analysis and I'm told every smooth function is analytic in C

What are some other nontrivial differences between real and complex analysis?

[Anonymous No.9880375]

>>9880331
Real analysis is much more complex. Doing calculus with complex numbers destroys a lot of structure, e.g. complex differentiable functions are too nice.

[Anonymous No.9880380]

>>9880375
Oh shit, you noted the same thing. Should have read the whole post, not just the question.

[Anonymous No.9880401]

>>9880331
>What are some other nontrivial differences between real and complex analysis?
To expand a bit on what you said, a smooth complex function is analytic in C, but the same is not true for R, namely, there exists non analytic smooth functions on R.

[Anonymous No.9880406]

Why the fuck is this so hard for me. I’m usually good at imagining abstract concepts, why when it comes to variables I can’t do this shit when I can easily do it with numbers.

[Anonymous No.9880410]

>>9880406
It's pretty simple. Numbers and logic use different neurological systems, as in, we use different parts of our brain to process arithmetic and language.

[Anonymous No.9880577]

>>9880406
What are you having trouble with?

[Anonymous No.9880585]

>>9880577
I don’t get how 5a becomes “I will only buy the pants when I buy the shirt.” Ever other one on the page I understand the conclusion to.

[Anonymous No.9880731]

>>9880331
For starters you can integrate around loops (which you can also do in R^2 but whatever). Also, there's a weaker notion of holomorphic function that becomes quite useful called a meromorphic function, where it is 'almost' holomorphic in the sense that it has singularities in discrete sets (ie: not too many closed together). However, it turns out that integration around loops is completely topological and depends only on the number of singularities of the function inside the loop. That is, it doesn't matter what loop you take, just as long as you account for all the singularities inside, you can easily compute your integral.

This makes it very easy to compute hard real integrals. Suppose you're integrating a real function over some interval [a,b] (perhaps infinite too). Then you can create a loop in the complex plane that passes through that interval, and then 'escapes' into the complex plane. Since the integral in the complex plane is topological, one can compute the integral with ease, and then it is relatively simple to compute the real integral by just considering the part that is in the real line.

Another good one are the maximum theorems. Roughly, if a holomorphic function is defined on some open set U, then if there exists a maximum within U, then the function is bounded. There's a lot more cases of these, including if the function is defined in the whole of C.

[Anonymous No.9880736]

>>9880585
I'm writing out an explanation. It's long.

YOU ARE NOT STUPID THOUGH! This is actually really hard and a fucked up translation example that I really think they should stop teaching. It is not only unnatural to get to that interpretation but NO ONE would do that intentionally because understanding why it's correct requires leaning into several counterintuitive gotchas that trip up everybody who takes introductory formal logic.

[Anonymous No.9880742]

>>9880736
I distributed the “not” and flipped the “and” to an “or” canceling the “and” in front of S and come up with “either I will not buy the pants or I will buy the shirt.” Which I guess could also be “I will neither buy the pants nor not buy the shirt.” Anyway I did a truth table and it is true that the only time P is true is when S is true. I’m thinking it’s just a failure of formal logic notation -> language

[Anonymous No.9880744]

>>9880585
looool dont listen to this retard >>9880736 this is actually piss easy lmaoooo

[Anonymous No.9880768]

>>9880742
Yes! It's also equivalent to
>If I buy the pants then I will buy the shirt.

Applying double negations and De Morgan's laws will go a long way with formal manipulation.

The formal approach is easy. It's the 'intuitive natural language' approach that is ridiculously hard. I'll post the full explanation momentarily, brace for a wall of text.

>>9880744
See above.

[Anonymous No.9880769]

>>9880736
It's an essential exercise. And it's also pretty easy.

[Anonymous No.9880772]

>>9880768
>>9880406
>>9880585

1/?

The reasons why it's hard are:
1) Natural language (i.e. English) is hard and sometimes not well suited for formal logic.
2) There are a lot of really confusing gotchas where some terms are used in formal logic in ways that are completely different from how they are used in real life. Blame philosophers.
3) This stuff can be understood on both an intuitive "natural language/real world" level or on a technical/formal level. The former is way harder and it's what they're asking for here.
4) This is also a particularly hard example.

Before we can break it down I need to point out a few big gotchas.


Gotcha #1:

Suppose your professor says:
>'If' you failed the final 'then' you failed the class.
Does this mean that if you did not fail the final then you passed the class? No, you might have failed the class anyways based off of your other marks.

Another way to say this is that the following two sentences are not equivalent
>'If' you failed the final 'then' you failed the class.
>'If' you failed the class 'then' you failed the final.

In notation we write 'if' statements (conditionals) with an arrow pointing from the 'if part' to the 'then part'. Depending on your textbook the notation will be one of the following (the difference is superficial): [math]\Rightarrow[/math], [math]\rightarrow[/math], [math]\supset[/math].
Let:
F: "Failed the final"
C: "Failed the class"
then our sentences become
[math]F\Rightarrow C[/math]
[math]F\Leftarrow C[/math]

For cases where we have statements where the arrow is true in both directions people will use either a double arrow [math]\Leftrightarrow[/math], [math]\leftrightarrow[/math] or a triple equals sign [math]\equiv[/math] and in English they'll write:
>'if and only if'
eg.
>I will pay you 'if and only if' you finish the job.

(cont.)

[Anonymous No.9880773]

>>9880772

2/?

Gotcha #2
The terms 'whenever' or 'when' are sometimes used instead of 'if' to sound "more natural" (but in practice people avoid doing this because it can be confusing).
>'If' I use the restroom 'then' I wash my hands.
>'Whenever' I use the restroom, I wash my hands.
>'When' I use the restroom, I wash my hands.

Similarly
>I wash my hands 'if' I use the restroom.
>I wash my hands 'when' I use the restroom.
>I wash my hands 'whenever' I use the restroom.


Gotcha #3
The case where 'only if' is used by itself totally fucks up EVERYBODY who takes formal logic (and it will continue to fuck you up later on when you least expect it because it's just counter-intuitive as fuck). The way the term 'only if' is used here is not the way you're used to using that word.

To illustrate this concept I will present lots of EQUIVALENT variations of this sentence.
>'If' it rained 'then' the ground is wet.
or put slightly more formally:
Let:
R: "It rained"
W: "the ground is wet"
and the sentence becomes:
[math]R\Rightarrow W[/math].

(cont.)

[Anonymous No.9880775]

>>9880773

3/?

I will repeat the sentence below so you don't have to jump around this wall of text too much (this shit is confusing as fuck as it is).

Think about each pair of sentences and why they're equivalent:

For the first variation we change the position of the 'if' and remove the 'then'.
>'If' it rained 'then' the ground is wet.
The ground is wet 'if' it rained.
It should be easy to see that these are equivalent.

In this variation we negate both sides and change the order of the implication. It's called taking the contrapositive.
>'If' it rained 'then' the ground is wet.
'If' the ground is not wet 'then' it did not rain.
Really think about this one, it's an extremely useful technique.

This variation uses the 'only if' and it is probably easier to understand by comparing it to the contrapositive than the original statement, so I've both here.
>'If' it rained 'then' the ground is wet.
>'If' the ground is not wet 'then' it did not rain.
It rained 'only if' the ground is wet.
Compare this to the formal sentence mentioned above, [math]R\Rightarrow W[/math]. Indeed, 'only if' can be interpreted as a [math]\Rightarrow[/math] when it appears between your statements.

Probably the most fucked up variation involves doing the same as above but rewording it so that it sounds "more natural" (but not really, because in reality it's totally fucked).
>It rained 'only if' the ground is wet.
It 'only' rained 'if' the ground is wet.
DON'T EVER DO THIS!! IT WILL CONFUSE EVERYBODY INCLUDING PEOPLE WITH A BACKGROUND IN FORMAL LOGIC OR MATHEMATICS.

For the final variation we change the position of the 'only if'.
>'If' it rained 'then' the ground is wet.
>'If' the ground is not wet 'then' it did not rain.
>It rained 'only if' the ground is wet.
'only if' the ground is wet, did it rain.
ALSO DON'T DO THIS! It's not nearly as fucked up as the last sentence but still.

(cont.)

[Anonymous No.9880777]

>>9880775

4/4


If it's not clear that 'only if' is counterintuitive, consider a sentence you might here in the real world:
>You can go to the party 'only if' you do your chores.
In the real world people would intend this to be interpreted as
>'if' you do your chores 'then' you can go to the party and 'if' you do not do your chores 'then' you cannot go to the party.
or more concisely:
>You can go to the party 'if and only if' you do your chores.
However, in an introductory formal logic class they will interpret this to mean that
>'if' you can go to the party 'then' you did your chores.
Which is not equivalent (but also not false).

More on 'only if' here:
https://www.quora.com/In-propositional-logic-how-do-the-statements-If-p-then-q-p-only-if-q-and-a-necessary-condition-for-p-is-q-mean-the-same-thing

Now that we have all that out of the way. The problem was interpreting:
[math]\lnot (P\land \lnot S)[/math]
where
P: I will buy the pants
S: I will buy the shirt

The naive reading is:
>It is not the case that (I will buy the pants and not buy the shirt).
In other words:
>It is not the case that I will buy the pants but not the shirt.
This is the same as:
>If I buy the pants then I will buy the shirt.
Converting to only if:
>I will buy the pants only if I buy the shirt.
Rewriting in that TOTALLY FUCKED UP WAY:
>I will only buy the pants if I buy the shirt.
Replacing if with when:
>I will only buy then pants when I buy the shirt.

Of course, don't ever do this in real life. It's confusing as fuck.

[Anonymous No.9880793]

>>9880331
That's really the only and main difference.
Holomorphic functions are essentially polynomials.

[Anonymous No.9880809]

>>9880777
>It is not the case that (I will buy the pants and not buy the shirt).
Okay, if this is how I interpreted the problem I would have got it instantly. Unfortunately the way the author tells us to translate the logical notation to language is using “neither” when given a negated term. Actually looking at it now even in that way and saying “I will not: buy the pants but not buy the shirt.” Implying that the only condition in which the shirt will be bought is when the pants are also bought. It was just the shitty way the author of this book intended for us to translate into english and it’s quite the oversight seeing how you described t in a much easier to understand manner.

[Anonymous No.9880812]

>>9880406
>>9880585
NOT ("buy pants" AND "NOT buy shirt")
i.e. I won't do both of the statements in the quotation marks
This is the same as saying you won't do one or you won't do the other (or you won't do one and you won't do the other as well).

[Anonymous No.9880814]

>>9880772
>>9880773
>>9880775
>>9880777
You're making this a bigger deal than it is.

[Anonymous No.9880816]

>>9880812
yes and distributing that negative and putting an “or” into the mix just makes it a semantical nightmare. I just need to study this enough to completely forego the English interperitation of this shit.

[Anonymous No.9880826]

>>9880816
>I just need to study this enough to completely forego the English interperitation of this shit.
Yes, that's why we use mathematical notation in logic instead of a natural language. Natural languages suck when one is trying to be precise.
Don't worry, it's not your fault.

[Anonymous No.9880829]

>>9880809
I switched shirt and pants in one of the sentences. Oh well I understand now so that’s all that matters.

[Anonymous No.9880831]

>>9880814
I'm the person who wrote all that and you're right. Thank you for mentioning this because it is an important point to make.

All of the 'only if' stuff rarely appears outside of intro formal logic courses. In general, mathematics is typically written using 'if then' statements.

>>9880816
A simpler way to see it might be to note that the negation of
[math]P\Rightarrow Q[/math]
is
[math]P\land \lnot Q[/math]

So the "double negation" is
[math]\lnot (P\land \lnot Q)[/math]

>>9880826
This.

[Anonymous No.9880906]

current vibes

[Anonymous No.9880947]

>>9880906
>write down proof like a first year undergrad
>and by Feit-Thompson....

[Anonymous No.9881167]

>>9880947
big thanks dude couldnt have done it without you

[Anonymous No.9881210]

>>9880331
They are harmonic functions and have shit like this. https://en.m.wikipedia.org/wiki/Maximum_modulus_principle.. Basically, holomorphic os comfy to do PDE ina physicists setting where assuming smoothness is valid.

[Anonymous No.9881369]

>>9881167
Proving the "G is cyclic" part is alright.
Proving the "G is finite" is also alright.
The fact that its prime can be proven by using the fact Z_n is simple if and only n is prime (if n is not prime, take m|n different from 1 and n; n/m generates a subgroup of order m; if n is prime then G can't have subgroups due to Lagrange's theorem)

[Anonymous No.9881421]

>>9881369
thanks dude, i totally didnt post it because i was mocking the poster

[Anonymous No.9881452]

I'm trying to prove the third sylow theorem, in particular that the number of sylow p-subgroups conjugate to a sylow p-group [math]P[/math] (Denoted by [math]N_p[/math]) is [math]N_p \equiv 1 \pmod p[/math]. The book exercise is pointing at this method:

Show that the action of [math]P[/math] on the set of sylow p-subgroups has [math]P[/math] as its only fixed point (easy to show). Then use this and the second sylow theorem to prove the third.

My attempt:

Using the class formula, [eqn]|P|=|Z| + \sum_{H} [P:\mathrm{Stab}_P(H)][/eqn]
where [math]Z[/math] is the set of fixed points (which only has 1 by the above) and the sum runs over the distinct orbits of the action. But from the second sylow theorem, every sylow p-subgroup is a conjugate of the other, so in particular the sum only has one term. If we denote the set [math]P[/math] is acting on by [math]S[/math], then by the orbit-stabilizer theorem, [math]S\cong P / \mathrm{Stab}_P(H)[/math]. But [math]|S|=[P:\mathrm{Stab}_P(H)][/math] is precisely [math]N_p[/math], so I get by the class formula that [math]|P|=|Z| + N_p[/math] and taking [math]\mod p[/math], [math]N_p\equiv -1 \pmod p[/math]. What went wrong here?

[Anonymous No.9881524]

>>9881452
>What went wrong here?
You forgot that the set acted upon is the set of Sylow subgroups, not P

[Anonymous No.9881666]

>>9881524
yes, but by the second sylow theorem, every sylow subgroup is a conjugate of P. A mistake I did make is that the sum does not only have one term, since the orbit is not necessarily contained by the conjugation by elements of P (it would be if the group i used to act it on was G)

[Anonymous No.9881784]

>>9881452
never mind, solved

[Anonymous No.9882672]

>>9875372
>http://www.math.columbia.edu/~woit/wordpress/?p=10436
>comments are locked
fuck wo*t

[Anonymous No.9882674]

>>9882672
http://www.math.columbia.edu/~woit/wordpress/?p=10443
>Recently people have contacted me suggesting I blog about two physics-related topics likely to lead to vigorous debate. I’d begged off in both cases, since engaging in such a debate or moderating it would be on a short list of things I’d most like to avoid doing. This afternoon though, it struck me that there is an excellent, if cowardly, way to deal with this. I’ll mention the two topics briefly here, then shut off comments on the blog and leave town. So, some may find interesting and want to argue elsewhere about:

>One of the PiTP lecturers, Aron Wall, has a blog on physics and theology, called Undivided Looking. Wall’s theological views include thinking he has a pretty good idea about how God wants people to behave, in particular he’s pretty sure that God doesn’t want them having homosexual relations. He wrote extensively about this in a blog entry (now deleted) back in 2015. He’ll be soon taking up a faculty position at Cambridge University, and some people are not happy about this, see for example this statement from the Cambridge University Student’s Union.
>If you’d like to attend an early universe conference this September, one place you could do so is in the Israeli-occupied West Bank settlement of Ariel, where Ariel University is hosting a workshop on Inflation, Alternatives and Gravitational Waves.

[Anonymous No.9882750]

>>9882674
>>googoo gaga big meanies say bad things
How he wasn't kicked out of academia by now is beyond me.

[Anonymous No.9882764]

>>9882674
God, what an obnoxious prick.

[Anonymous No.9882989]

>>9882750
Academia is a joke.

[Anonymous No.9882994]

>>9880731
>then the function is bounded
you mean to say, then it is constant?

[Anonymous No.9883002]

>>9882989
There are legit fields and legit academics trying to do real work instead of shitting out papers for the sole purpose of bloating their h-index.
Wo*t is a butthurt faecal matter that hasn't done anything but shit on legit research in the last two decades. He has no business in academia, even his recent textbook is trash-tier, him teaching future physishits is a crime against humanity.

[Anonymous No.9883119]

>>9882994
i meant to say if it is bounded, then it is constant, yep

[Anonymous No.9883280]

>>9861124
What do you do to maximize the amount of studying you do in one day? I want to be able to do at least 14 hours a day for the rest of the summer.

[Anonymous No.9883289]

>>9883280
Get quality sleep, don't try marathons - have few minutes rest every so often and a run/gym/physical activity around 8 hours in.
If you get stuck, move on to some other topic, no point in spending 14 hours doing pretty much nothing.

[Anonymous No.9883305]

>>9883289
This is good advice.

[Anonymous No.9883306]

>>9882674
What Aron Wall said is literally what any Catholic priest would say which is to say it’s extremely benign and any gay person could easily brush it off. I’m willing to bet that over a course of any random week, Wall is doing more contributions than Woit has done his entire career.

[Anonymous No.9883322]

>>9883289
How often/when do you eat, and what kind of diet is the best?

[Anonymous No.9883397]

>>9883280
For me it's a comfortable environment. I like to read stuff on my bed with music playing.

[Anonymous No.9883451]

>>9883322
I wouldn't overthink diet, i was comfortably pushing 14 hours a day last 3 semesters while on coffee, tea and ramen almost exclusively (not that i recommend this, it certainly isn't a sustainable lifestyle).
Whatever works for you is good enough, just don't eat american portions so you can focus even while digesting.
I usually took a break when i was hungry to the point of distraction.

[Anonymous No.9883455]

Hey guys. Brainlet here. Can anyone help me with a problem. I am working out the provided example in pic related and keep getting the incorrect answer. Here is the formula.

[Anonymous No.9883458]

The sample problem i keep fucking up.

[Anonymous No.9883463]

Solving for the example problem. No matter what Ive tried I get the incorrect answer.

[Anonymous No.9883467]

I figured perhaps it was the dielectric constant in a vacuum was the variable fucking me up so I substituted 8.85E-12 with 8.85x10^((1-2)12) and still not getting the proper answer.

[Anonymous No.9883470]

>>9883455
>>9883458
>>9883463
>>9883467
Wrong thread go here >>>/sqt/

[Anonymous No.9883474]

>>9883455
Not math

[Anonymous No.9883476]

Plz help nerds

[Anonymous No.9883634]

How do I find the sum of series where terms are changing its sign?

(sum from 1 to inf) (-1)^(n-1) / (2 * 3^(n-1))

[Anonymous No.9883680]

>>9883463
Didn't you get the correct answer at the bottom of the page though?
>>9883634
If you sum the alternating terms it's easy to see things cancel out nicely
[math]\frac{(-1)^{n-1}}{2*3^{n-1}}+\frac{(-1)^{n}}{2*3^{n}}=\frac{(-1)^{n-1}}{2*3^{n-1}}(1-\frac{1}{3})=\frac{(-1)^{n-1}}{2*3^{n-1}}(\frac{2}{3})=\frac{(-1)^{n-1}}{3^{n}}[/math]
Just choose n to be the odd integers and sum the geometric series

[Anonymous No.9883698]

>>9883680
Can I do it through Taylor's series?
I remember that 1 - 1/x is (-1)^k * x^k. But I don't know if it could be applied here, since it's the sequence, not the function.

[Anonymous No.9883707]

>>9883698
Yeah, that works too since [eqn]\frac{1}{1+x}=1-x+x^2-x^3...[/eqn] and in this case we choose [eqn]x=\frac{1}{3}[/eqn] Just divide the whole thing by 2 and you're done.

[Anonymous No.9883815]

>>9883634
Split it into two series: positive (odd n) and negative (even n).

[Anonymous No.9884054]

>>9866468
imagine being so delusional that you think you can judge correctness of open conjectures

[Anonymous No.9884059]

>>9867098
I don't think you understood the post.

[Anonymous No.9884117]

>>9878508
please share

[Anonymous No.9884124]

>>9884054
hodge conjecture has already been proven wrong several times in the 1900s for more general statements, and has whittled down to the current one. Many say it's the most likely conjecture to be false (in its current state at least).

[Anonymous No.9884145]

>>9884117
just when you think your theory is safe from the geometrytards, some fucking algebraic topologist comes along and computes homology groups of your structures, for absolutely no fucking reason, and then an entire field of study is based off of that guys 'work', and he wins a fields medal, and everyone forgets about your work

next thing you know, this structure you described to represent an abstract number theoretical concept with no relation to geometry WHATSOEVER is being mutated and eventually it's remembered as some perversion of the original concept with n-dimensional holes for n>27 in some weird n+1 dimensional space

I MEAN IT'S FUCKING NUMBER THEORY, THAT THING WAS INVENTED JUST TO MONITOR IDEALS IN SPECIFIC INTEGRAL RINGS
I FUCKING HATE TOPOLOGISTS

[Anonymous No.9884214]

>>9884145

[Anonymous No.9884318]

How do I prove or disprove this statement: There exist two primes whose difference is 1000.

[Anonymous No.9884351]

>>9884318
proof: 1013 is prime

[Anonymous No.9884380]

>>9884145
You mean closed subschemes of an affine integral scheme?

[Anonymous No.9884383]

When do you think there comes a final decision on Mochizooka? I mean, either approval or rejection by the community

[Anonymous No.9884468]

>>9884383
Probably whenever these >>9875445 are made public

[Anonymous No.9884552]

>>9884214

[Anonymous No.9885354]

>>9884552
The topologist cawing is still more beautiful than the geometer chirping.

[Anonymous No.9886384]

>>9879073
Hey guys, I'm sorry but I'm back again. How important is it to review these two items for cal 3? Is it likely they will have a short review for cal 1 and 2 in the beginning? Is it really necessary to review these two classes individually before taking cal 3? Again, I got a 97 in both in high school dual credit, but my first year at actual university I just did all my core classes to get them out of the way, so its only been a year.

[Anonymous No.9886635]

>>9886384
For Calculus 3 you need to review Linear Algebra and Single Variable Calculus.

Linear Algebra and Single Variable Calculus are the two subjects that you really really need to know extremely well in General.

[Anonymous No.9886965]

Is this accurate?

[Anonymous No.9887048]

Is pure math dead?

[Anonymous No.9887264]

>>9886965
Not really.

[Anonymous No.9887279]

>>9887048

Define

"useful"="brings money (in an relatively easy way)"

yes it is

[Anonymous No.9887280]

>>9886965
As accurate as an arbitrary scale like "abstractness" could get, with the exception of a few memes.

[Anonymous No.9887284]

>>9887048
I'm still here.

[Anonymous No.9887289]

Things discussed here literally do not exist, they are pure memes.

Do not forget to spit on religion thou.

[Anonymous No.9887300]

>>9887289
Define exist.

[Anonymous No.9887673]

>>9887048
Not yet, but the age of idle hedonism is soon over and there will be no room for the pacifist ways of low-t theorists then.

[Anonymous No.9887708]

>>9886965
No.

[Anonymous No.9888033]

>>9861124
I've never been good at math, so I'm trying to retrain myself from the basics. I've picked up Stewart's Algebra and Trig, in addition to Gelfand (and Shen)'s Algebra.

While Stewart is pretty easy and straightforward, I find that a lot of Gelfand's problems kick my ass at any given turn. I get that its his way of developing the reader's mathematical thinking, but it seems that I'm just bad at it and I was wondering if there are any resources or advice I could use to remedy this?

Thanks.

[Anonymous No.9888086]

>>9888033
Polya's books on mathematical problem solving are usually helpful for this sort of thing.

[Anonymous No.9888317]

https://youtu.be/SUGnwvmz6C4

>writes down 5 of an infinite amount of elements of a set
>show algorithm to construct another element of the set, that is not present in the 5 given elements
>?????
>this proves the set is uncountable

Am I retarded? How does this """prove""" that the set is uncountable?

[Anonymous No.9888335]

>>9888317
>suppose for contradiction that the set is countable.
>by definition, that means there exists a function f from the naturals to the set A that is bijective
>write down the number in A that corresponds to f(1), f(2), f(3), .... (to infinity) in a column
>now construct a number n in the following way: its first digit is different to the first digit of f(1), the second digit is different to the second digit of f(2), etc to infinity
>this number n is well defined because the reals consist of all finite numbers that contain a countably infinite decimal expansion
>however, this number is different (by construction) to every single number in the list
>hence n is not in the set A
>but we assumed every n of that form is in A, and the function is bijective
>contradiction

[Anonymous No.9888342]

>>9888317
The set he is writing down is the set of ALL numbers between 0 and 1 that can be written as a combination of 0s and 1s. But no matter how many of these numbers he lists (even an infinite amount), it will never contain the diagonalization. Thus the set cannot be listed and is uncountable.

[Anonymous No.9888354]

>>9888335
>>9888342
>however, this number is different (by construction) to every single number in the list
>it will never contain the diagonalization

Why this is so was the part I didn't get. To explain how "easy" it was to give a counterexample, I decided to write down an example. Then I figured out that it is indeed impossible since you always have at least one digit that is the opposite of the string of digits you want. So that answers my question: yes I am indeed retarded.

Thanks for the help, appreciate it.

[Anonymous No.9889045]

>>9888354
No, you're not retarded, it took old mathematicians dying for that proof to be popularly accepted. Just realize that you've now understood one of the most interesting discoveries that humans have ever made about infinity. Now try to learn about cardinals, ordinals and surreal numbers to continue the journey of mindfuckery and layers of infinity.

[Anonymous No.9889087]

So /mg/ who is going to win the fields medal apart from scholze?

samurais need not apply

[Anonymous No.9889424]

>>9889087
Who cares? It's an affirmative action award now.

[Anonymous No.9889436]

>>9889424
You're just angry you didn't solve the poincare conjecture while black

[Anonymous No.9889442]

>>9889436
Perelman is Russian/Jewish.

[Anonymous No.9889446]

>>9889442
Check your privilege, perelman has deep neanderthal heritage

[Anonymous No.9889514]

>>9889446
A prominent brow ridge and a lot of facial hair makes you a neanderthal now? Cool, it looks like I fit the criteria.

[Anonymous No.9889516]

>>9889514
Be proud of your roots anon

[Anonymous No.9889530]

I wanna do a Math PhD In Combinatorics so I can transition into industry, is this a good plan? Let me know, guys.

[Anonymous No.9889604]

>>9889530
No. Next question.

[Anonymous No.9889927]

Suppose R is a noncommutative ring, and R[X] to be its polynomial ring. Does X commute with elements of R? If it does, surely the evaluation homomorphism gives different answers depending on how you place X.

What about R[X,Y]? Does X commute with Y? Does X and Y commute with R??

[Anonymous No.9889955]

>>9889087
No one that actually deserves it.

[Anonymous No.9889969]

>The 2018 Fields Medal Symposium will honour Maryam Mirzakhani (Fields Medal 2014) and the current and potential impact of her work.
All you need to know. The medal will be awarded to the "underprivileged" members of the mathematical community from now on.

[Anonymous No.9889996]

>>9889927
https://math.stackexchange.com/questions/806119/do-polynomials-make-sense-over-non-commutative-rings/806500#806500

[Anonymous No.9890041]

It's time to move on to a new thread.

[Anonymous No.9890044]

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[Anonymous No.9890052]

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[Anonymous No.9890053]

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[Anonymous No.9890056]

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[Anonymous No.9890060]

[Anonymous No.9891447]

>>9890044
>>9890048
>>9890050
>>9890052
>>9890053
>>9890056
>>9890060
I love math