/mg/ - math general

[Anonymous No.11340981]

Happy Birthday Mordell :)
elliptic curves edition
Why aren't you learning about elliptic curves and L-functions?

[Anonymous No.11341019]

>>11340981
God this board is dead.

[Anonymous No.11341083]

Elliptic curves are really nice. I haven't touched them since I was doing some Number Theory stuff a long time ago but if I recall correctly John Stillwell had an introductory article on them. I'll look for it

[Anonymous No.11341088]

Yeah, it's on Jstor and scihub

[Anonymous No.11341129]

>>11341019
Couldn't you wait for the other thread to reach 310 replies like a normal person?

[Anonymous No.11341138]

oh, genus one :3

[Anonymous No.11341143]

>>11341129
Can't you suck my dick you mathfag.

[Anonymous No.11341237]

How do I master geometry? Is there a proven way to improve visual thinking?

[Anonymous No.11341266]

>>11340981
what do you guys think about mathematical logic and set theory and modal theory and shit

[Anonymous No.11341269]

>>11341237
just lean to say how your results are geometric even if you are just doing a bunch of algebraic calculations

[Anonymous No.11341334]

>>11341143
>mathfag
Why the homophobia?

[Anonymous No.11341337]

>>11341237
>How do I master geometry?
What have you tried?

[Anonymous No.11341767]

>>11341337
i tried poncelet theorem

[Anonymous No.11341795]

>>11341767
Have you ever done any work in CAD? I found that over the years, as I try to model more and more complex designs/objects, my ability to fix unsolvable geometries has improved tremendously. I've also gained a lot of intuition when it comes to knowing what parameters to define to achieve a desired geometry, plus CAD is just fun

[Anonymous No.11341974]

why would you make a new thread before the other has reached bump limit? why didn't you even have the courtesy to link the new thread? fucking idiot.

[Anonymous No.11342897]

>>11341334
Why the gayness?

[Anonymous No.11343405]

Anyone have suggested books for geometric group theory? I already have some exposure to the theory of mapping class groups and teichmüller space if that helps.

[Anonymous No.11343424]

>>11343405
>geometric group theory
isn't that lie theory?

[Anonymous No.11343439]

>>11343424
Lie theory contains examples of ggt, for sure. Geometric group theory, in general, is the study of actions of groups on topological spaces as homeomorphisms and the quotients obtained therefrom.

[Anonymous No.11343451]

How come after Hilbert and Godel, all german mathematicians were shit?

[Anonymous No.11343534]

> the only woman in my differential geometry class dropped it

[Anonymous No.11343535]

>>11341266
I think there's some unaccessed potential in modal logic w.r.t. common mathematical problems.
Set theory ought to be carved out by now - I doubt it's feasible to do something interesting there, for the common mathematican. As opposed to the above.

>>11343451
Sounds quite wrong. The French had a good run, but e.g. Scholze is german. It's not like there's so many outstanding people from after the war to now to pick from. Their mostly either from the continent around the US or France.

[Anonymous No.11343543]

>>11341143
>>11341019
>"math books by women is a mistake" OP brainlet detected

[Anonymous No.11343639]

>>11343535
>It's not like there's so many outstanding people from after the war to now to pick from
Most members of Bourbaki are outstanding

[Anonymous No.11343682]

>>11343543
Not OP but sure.

[Anonymous No.11343771]

>>11343439
Serre's book on trees as an intro

[Anonymous No.11343780]

>>11343639
Most of them are also French

[Anonymous No.11343783]

>>11343534
good for her I fucking hate DG

[Anonymous No.11343866]

>>11340981
the virgin elliptic-curves-understander
>knows the proof of the weil bound by heart, using stepanovs method AND bombieris method
>insufferable nerd
>achieves minor improvements on the weil bound in fields of large characteristic with sparse polynomials or some shit that no one cares about anyways
>result he worked on for years only gets cited by a survey article with 12 overfull latex boxes written by shparlinski in russian, somehow published in the soviet mathematical journal years after the collapse of the soviet union

the chad elliptic curve non-understander
>gets tons of citations by restating difficult problems in the term of certain exponential sums, that he then bounds "trivially" using the weil bound
>hasnt even read the proof of the weil bound
>doesnt even know how the bound on exponential sums is related to elliptic curves
>when told "if you look at the corresponding curve, it has tons of points", answers in a nonchalant way "is this good or bad?"
>has never considered polynomials in 2 or more variables

[Anonymous No.11344907]

>proof by abstract nonsense

[Anonymous No.11344909]

>>11340981
>Why aren't you learning about elliptic curves and L-functions?
Are they useful in in any area related to Probability Theory?

[Anonymous No.11345341]

Are there examples of infinite perfect fields of characteristic non-zero?

[Anonymous No.11345361]

>>11345341
The algebraic closure of [math]F_3[/math]?

[Anonymous No.11345728]

How much do tenured math professors make?

[Anonymous No.11345798]

>>11345361
It need not always exist though. I'm asking for a true infinite perfect field of non-zero characteristic.

[Anonymous No.11345867]

>>11345341
>asking for examples that are given on the wikipedia page

[Anonymous No.11345984]

given two commutative linear maps A and B over the complex numbers, how do you show that they must have at least one common eigenvector and can you construct such a vector?

[Anonymous No.11346004]

>>11345728
Probably like 140K-200K max.

[Anonymous No.11346175]

>>11345984
1. A has an eigenspace Ker(A-tI)
2. B leaves Ker(A-tI) invariant
3. Find an eigenspace for the restriction of B to that subspace

[Anonymous No.11346184]

>>11341237
do geometry proofs, try coxeter, kiselev or bergers books they’re quite good.

[Anonymous No.11346198]

>>11341795
also seconding this, have real visual representations of complex structures is essential for developing internal visualizing capacities. I wasn’t able to understand vector calc beyond plug and chug and weird disparate analytical notions until I started looking at transformations visually.

[Anonymous No.11346549]

What is a good book for proofs? A lot of math doesn't click for me until I go over the proofs. I'm at a calc 3 level of math comprehension. I want to like go over most of the proofs I would've already used.

[Anonymous No.11346565]

>>11346549
>book for proofs
>i want to go over most of the proofs I would have already used
not the same thing, for the first you should pick up a book on elementary math that employs proofs and try to solve as many exercises as possible instead of wasting time learning disjointed nothings from various mathematical subjects in a "proof book" for CS majors. The second, you should read the wiki page linked in the sticky thread at the top of the front page of this board.

[Anonymous No.11346669]

>>11346565
Was more looking for something more like what you described. Just put in better words than I did. And yes I am very much aware of the wiki. Any recommendations?

[Anonymous No.11346715]

This is driving me nuts lads, can someone help me with this?
Define the Tropical Numbers as
[math]\mathbb{T}=\mathbb{R}\cup\{-\infty\}[/math]
let
[math]``a+b"=\max(a,b)[/math] for [math]a,b\in\mathbb{T}[/math]
and let
[math]``c\times d"=``cd"=c+d[/math] for [math]c,d\in\mathbb{R}[/math]
Define a tropical polynomial as
[math]P(x)=``\sum_{i=0}^d a_i x^i"=\max^d_{i=1}(a_i+ix)[/math]
and let a tropical root be an [math]x_0[/math] such that
[math]P(x)=``(x+x_0)Q(x)"[/math] where [math]Q(x)[/math] is a tropical polynomial

What would the roots of [math]``ax^2+bx+c"[/math] be? I figured out the [math]``ax+b"=``(a)(x+ba^{-1})"[/math] case but the order two case is giving me trouble.

Some things to note:
[math]``0x"=``x"[/math]
[math]``ax+bx"=``(a+b)x"[/math]
[math]``x+0"\ne``x"[/math]

[Anonymous No.11346757]

>>11345798
>[math]\overline{\mathbb{F}}_3[/math] need not exist
What did he mean by this?

[Anonymous No.11346762]

>>11346715
>it's a whole new level of bad notation
>it's so obfuscating anon literally can't solve basic maths
Amazing.

[Anonymous No.11346763]

>>11346762
From what I can tell this is the standard notation actually lmao

[Anonymous No.11346882]

>>11346715
I think I got it actually
if [math]``c"\ge ``b^2"[/math] then
[math]``x^2+bx+c"=``(x+\sqrt{c})(x+\sqrt{c})"[/math]
(tropical square rooting would be the same as taking one half)

If [math]``c"<``b^2"[/math] then
[math] ``x^2+bx+c"=``(x+cb^{-1})(x+b)"[/math]
I don't there's a way to do it without those conditionals though

[Anonymous No.11347084]

>>11340981
https://arxiv.org/abs/math/0609210v1

[Anonymous No.11347314]

>>11347084

fuck off mark

[Anonymous No.11347493]

>>11346669
Taos Analysis 1.

[Anonymous No.11347692]

>>11344907
>proof by unreadable gibberish

[Anonymous No.11347766]

>>11341266
I'm not much of a logician but it's an area I want to explore more. There's a ton of interesting work done by philosophers that uses modal logic. For my taste, modal metaphysics kind of goes off the deep end at a certain point, but I'm very curious about epistemic logics and applications in AI and knowledge management systems.

[Anonymous No.11347854]

Consider a prime p, a p-th root of unity [math]\zeta_p[/math], and the cyclotomic extension [math]\mathbb{Q}(\zeta_p)/\mathbb{Q}[/math].
This is a cyclic Galois extension of degree [math]p-1[/math].
The Galois group G is isomorphic to [math]\mathbb{F}_p^*[/math] (the isomorphism maps [math]j \in \mathbb{F}_p^*[/math] to the automorphism [math]\sigma_j[/math] which satisfies [math]\sigma_j(\zeta_p) = \zeta_p^j[/math]).
For any divisor [math]d[/math] of [math]p-1[/math], [math]\mathbb{F}_p^*[/math] has a unique subgroup of size d, namely [math]H_d := (\mathbb{F}_p^*)^{(p-1)/d}[/math].
So there is a corresponding subfield [math]K_d \subseteq \mathbb{Q}(\zeta_p)[/math].
Finally, let [math]s := \sum_{j \in H_d} \zeta_p^j[/math]. How do I prove that [math]\mathbb{Q}(s) = K_d[/math]? I can see that [math]s \in K_d[/math], but I can't do the other inclusion.

[Anonymous No.11348194]

>>11347854
>>11346715
>>11343866
I think I'm just not good enough for math. I literally don't even know how to begin tackling these problems ie. I will never make it as a postgrad.

[Anonymous No.11348358]

>>11343866

> certain exponential sums

mmmmm daddy I love it when you drop that phrase

[Anonymous No.11348389]

Is field theory and galois theory legitimate? How do I into it as a highly intelligent person?

[Anonymous No.11348399]

>>11348389
They are gay

[Anonymous No.11348841]

Fuck discrete probability

[Anonymous No.11348917]

>>11347854
H_d is cyclic and s is the sum of its generator's powers, then use summation formula for the geometric series and you are done

[Anonymous No.11349223]

>>11348841
Counting measure is trivial.

[Anonymous No.11349475]

>>11345798
are you one of those guys who don't believe in algebraic closures?

[Anonymous No.11349697]

>>11348389
>Is field theory and galois theory legitimate? How do I into it as a highly intelligent person?

[Anonymous No.11349814]

>>11347854
um bro we did this in high school lol you're not gonna make it

[Anonymous No.11350633]

sad general hours, bois

[Anonymous No.11350639]

>>11346669
Basic Mathematics, Lang
Calculus, Spivak; Calculus Vol. I-II, Apostol; Introduction to Calculus and Analysis Vol. I-II, Courant

Spivak, Apostol, Courant in descending order of difficulty. When finished with at least Spiv or vol I of the other two books attempt Principles of Mathematical Analysis by Walter Rudin. You can find pdf/djvu of these books on libgen.is

[Anonymous No.11350654]

>>11346669
For multivariable Calculus you could use Spivak’s Calculus on Manifolds, it sucks cock in spite of how great Spivak’s other books are; Munkres’, Analysis on Manifolds, requires explicit knowledge of introductory Real Analysis and abstract Linear Algebra; CH Edwards, Advanced Calculus of Several Variables, somewhat easy compared to the first two but is rigorous, theorems are all stated correctly, gives you a crash course in basic Lin Alg and does not require learning Analysis first; Loomis and Sternberg, Advanced Calculus, very abstract introduces calculus on Normed Linear Spaces, heavily dependent on exercises to the point where many proofs in other advanced calc books are shifted there, lucid interesting discussion of vector space theory throughout the book, archaic formatting and style of teaching, I would recommend using it as a reference text with something else as your main resource. Zorich Mathematical Analysis Vol I-II most closely resembles L&S and Tao’s books in scope and detail and is much more readable than Spivak’s Calc on Manifolds but Zorich writes for physics students and with an inelegant approach to his statement of certain proofs. Edwards is the smoothest transition I think w/Rudin accompanying it.

[Anonymous No.11350660]

>>11346669
For Linear Algebra use Lax’s Linear Algebra and its Applications or Hoffman&Kunze’s book. The others are inadequate and written either inefficiently or for retarded people, you will end up like /mg/ not knowing anything at all about the topic if you don’t learn it the hard way.

[Anonymous No.11350748]

Which are the places in Europe that do more research in analysis/pdes?
I'm searching for graduate schools for next year.

[Anonymous No.11351237]

>>11350748
France?

[Anonymous No.11351381]

>>11340981
What math should I study before college this fall? I shouldn't have went for a marketing major...
I stopped really paying attention to math in 6th grade and coasted off my friends through honors classes in high school until my 4 year Army stint for college monies.
Pls help

[Anonymous No.11351525]

>>11351381

[Anonymous No.11351566]

>>11351381
i gave tutorials for math for business classes and these are the things that i think are helpful:

solving systems of linear equations using gaussian elimination; calculating derivatives and simple integrals by hand; determining maxima/minima of functions; familiarity with equations and so on (expanding, factoring etc.)

everything else is not necessary or will be repeated so you need not bother learning it.

(on a side note: while i recognise that the education system in the us is fucked up, joining the us army is bad considering the atrocities that are being committed/have been committed by it. but i know the system is designed to lure poor people into the army which is just fucked up)

[Anonymous No.11351819]

>>11351566
>that last bit
joining the US army cant be much worse than paying a lifetime of taxes to it, can it? and while i agree with your moral assessment i doubt everyone would.

[Anonymous No.11351932]

Is there a known real function whose graph is dense in R^2?

[Anonymous No.11351950]

>>11351932
BTW I know discontinuous linear maps have that property, I'm asking if there exist such a function where we can explicitly compute f(x) for any x.

[Anonymous No.11351951]

>>11351525
Ty
>>11351566
Ty
Though the Army isn't one person or one instance. Personally I have held migrant children for parents, fed families, and helped people with everything from heat injuries to heart attacks. You'll find other people serving with mesh lining in their stomach from after shrapnel injuries and others with compartment syndrome taking on extra weight while already carrying a hundred pounds of equipment. A lot of good people do great things. At the end of the day the only way to stop those moral objections is for good people to step up and prevent or end them.

[Anonymous No.11351966]

>>11351932
https://en.wikipedia.org/wiki/Peano_curve
>inb4 only covers the unit square
Adapting the construction is left as an exercise to the reader;

[Anonymous No.11351969]

>>11351966
>graph
Aaaaaaaah.
No, obviously fucking not, are you retarded?
Literally the definition of continuity.

[Anonymous No.11352105]

Quick
statistics or pure math?
statistics: guaranteed internship and well paying job
pure math: more interesting

[Anonymous No.11352247]

>>11352105
Both?

If you have to pick one only do pure math if you really, really love it and are not overly concerned about finding eomployment immediately after.

[Anonymous No.11352289]

>>11343866

funny yet brutal

[Anonymous No.11352869]

>tfw don't understand how to derive equations using the von Bertalanffy eq.
life is hard in brainletville

[Anonymous No.11353226]

[Anonymous No.11353228]

>>11351951
>says Ty in response to the meme image
that was obviously not sincere you idiot. back to r/learnmath

[Anonymous No.11353314]

https://www.nytimes.com/2020/01/30/science/math-villani-paris-mayor.html
/our guy/

[Anonymous No.11353683]

>>11353226
Why is the motivating context for the creation of this image?

[Anonymous No.11353776]

What are the most philosophical fields of math? Is category theory fairly philosophical?

[Anonymous No.11353979]

>>11351932
no idea, but that's an interesting question. ask on reddit, not in this shithole

[Anonymous No.11353993]

>fibration, quiver, gerbe, sheaf, fiber bundle, stack, braid

are mathematicians crypto-fascists?

[Anonymous No.11354015]

>>11353979
Feel free to leave whenever.

[Anonymous No.11354023]

>>11354015
no, why, I love it here

[Anonymous No.11354033]

>>11354023
Clearly, if reddit is better you should go enjoy yourself that.
Also, I think this is what he wants: https://en.m.wikipedia.org/wiki/Conway_base_13_function

[Anonymous No.11354037]

>>11353993
based

[Anonymous No.11354693]

I have a random variable [math]Z=X\wedge 1[/math] where [math]X[/math] is a random variable. What does the [math]\wedge[/math] symbol means? I suppose it means something like "and" but I'm not sure in this context.

[Anonymous No.11354867]

(Ignore top blog post if you dont care)
Wanted to become a math teacher ever since I was a kid, fucked up my teenage years by doing coke and partying. I'm now in my early twenties going back to school. The problems im doing are fun and not that hard but i am severely paranoid that I'll fall victim to a filter in university where i wont be ''smart'' enough. Especially when I look through these threads and see concepts and theories i cant even begin to understand

What are some topics that I should be weary of that are big filters in universities?

[Anonymous No.11354925]

>>11354867
>Especially when I look through these threads and see concepts and theories i cant even begin to understand
don't worry, if you want to be a HS teacher you won't ever come across these theories at uni.

[Anonymous No.11354973]

This is backwards, isn't it?

[Anonymous No.11355115]

>>11354693
it means >>11354867
min

[Anonymous No.11355117]

>>11354693
It means min

[Anonymous No.11355310]

tits-pingpong lemma ehehehe

[Anonymous No.11355346]

>>11354973
No it's correct.

Let B_i and T_i be balls and topologies corresponding to the metric p_i.

Take an open set U in T_1 and let x be an element of U. Then, by definition, there is an eps>0 s.t the ball B_1(x,eps) is a subset of U. Now for any epsilon, if p_2(x,y)<eps then p_1(x,y)<eps. Hence the ball B_2(x,eps) is a subset of the ball B_1(x,eps). Thus, since U contains an open ball B_2, U is in T_2.

[Anonymous No.11355387]

ultra based /10

[Anonymous No.11355391]

>>11355346
Thanks.

[Anonymous No.11355404]

What level of math would stochastic processes and stochastic calculus be considered? Upper year undergraduate? Graduate?

I don't see any type of stochastics in the math guides and I'm wondering what a path would look like. I've done first year calculus and have just started linear algebra (for a point of reference)

[Anonymous No.11355428]

>>11343534
welcome to DG, enjoy your stay :^)

[Anonymous No.11355432]

>>11355404
Can't hurt to try it, depends on the person honestly.

[Anonymous No.11355513]

Where can I learn 'concepts' like hyperbolics, logarithms, etc outside of my textbook? I don't quite get it and I really want to learn how their mechanisms outside of "Do X when Y", any other text/book/guide/video would be appreciated!

[Anonymous No.11355635]

Could anyone check if the explanation in red is correct? I was looking at the solution manual and they did this but I didn't know the reason and tried to explain it myself.

[Anonymous No.11355645]

>because -5 doesn't exist, we can just "negate" it by plugging in it's negator reciprocal

[Anonymous No.11355654]

>>11355635
It's correct, but it's poorly explained.

[Anonymous No.11355676]

>>11354867
"Filter" courses filter lazy people, not brainlets. You don't need to be a gigabrain to get a bachelor's degree; if you're smart enough to want one in the first place you're smart enough to finish it if you put in the time.

The parts of mathematics that require legitimate intelligence/talent are not the "learning stuff from a textbook" parts.

[Anonymous No.11355763]

>>11355645
>>11355654
Is there a resource/explaination to it? I know it's probably off by a mile but I don't have the name/procedure of doing it sorry.

[Anonymous No.11355772]

>>11355763
>Is there a resource/explaination to it? I know it's probably off by a mile but I don't have the name/procedure of doing it sorry.
The formula for integration by susbtitution?

[Anonymous No.11355776]

>>11355763
you're finding an anti-derivative. if you differentiate your answer, and you get what you started with, it's correct.

[Anonymous No.11356234]

>>11353314
he's my math husbando

[Anonymous No.11356240]

>>11354867
If you have a clear goal, and know what it means to make mistakes in your life, you'll get wherever you want. Especially if what you want is a bachelors in math for the purpose of teaching high school.
Remember, you're taking those electives later in your degree not because you want to do research in them, but because you want to be able to get that bright but misguided kid in your class really really excited about abstract math. Think of it that way and stay motivated!

[Anonymous No.11356244]

>>11355635
I mean sure, but the right way to think about this is "-1/s du = 1/t^2 dt, so I can replace 1/t^2 dt with -1/s du in the integral."

[Anonymous No.11357185]

are there any non-empty posets that do not have a totally ordered subset?

[Anonymous No.11357200]

>>11357185
>the poset is non-empty, so it contains some x
>{x} is a totally ordered subset

[Anonymous No.11357231]

>>11357200
that's what I thought

[Anonymous No.11357739]

always struggled with algebra because i could never find 'the big picture' of things. always just seemed like an accumulation of things with properties that 'just worked'. am i retarded?

[Anonymous No.11357804]

>>11357739
satisfying patterns should be enough motivation
its nice that it doesnt rely on outside observations and can be replicated/justified on the back of an envelope

[Anonymous No.11357829]

>>11357804
what patterns do you speak of?

[Anonymous No.11358141]

contemplating subgroups of frobenius complements.

[Anonymous No.11358234]

give me your best number theory books for undergraduate and graduate level

[Anonymous No.11358237]

>>11358234
Weil.

[Anonymous No.11358373]

is this going to be fun?

[Anonymous No.11358456]

>>11358234
What kind of number theory do you like? Algebraic, analytic, geometric?

[Anonymous No.11358555]

>>11358373
nope

[Anonymous No.11358887]

>>11343451
Witt, Teichmüller, Hasse, Krull, Siegel...

[Anonymous No.11358891]

>>11345341
Any algebraically closed field of positive characteristic.
Note that you can also take any infinite field K of characteristic p > 0, and add the p-power roots of all elements of K. Then this new field will be perfect.

[Anonymous No.11358892]

>>11358234
Bordelles, Arithmetic Tales

[Anonymous No.11359609]

I need to find the maximal perimeter of the triangle [math]A=(1,0), B=(\cos(x),\sin(x)), C=(\cos(y),\sin(y))[/math]. They first ask me to define a function on the set [math]\{(x,y)\in [0,2\pi ]^2|x\leq y\}[/math]. So I define the function computing the perimeter using [math]x[/math] and [math]y[/math] the the euclidean norm. Sadly searching for critical points is harder than expected, any idea? I feel like I should use another equation for the perimeter.

[Anonymous No.11359616]

Anyone can recommend me some differential geometry books that focus on all the bundle jargon? So far I've read DoCarmo and skimmed through a few others and all of them don't go beyond defining tangent bundles and maybe cotangent bundles.

[Anonymous No.11359635]

>>11359609
Nevermind, I think I found the solution, it's way easier when using trig identities to reduce the expression...

[Anonymous No.11359650]

>>11359616
Bundle Fumble by Bob Mundell.
Literally any "geometry for physics" or "differential geometry for physics" book. Physicists love bundles.
There's also Tu's Differential Geometry, that one's good.
But what you should do is learn the differential geometry of curves and surfaces.

[Anonymous No.11359826]

>>11359635
Ok so I'm stuck solving this: [math]\sin(y)\sqrt{1-\cos(x)}+\sin(x)\sqrt{1-\cos(y)}=0[/math] for [math]0\leq x < y \leq 2\pi[/math] and I can't solve it.

[Anonymous No.11359830]

>>11359826

[Anonymous No.11359851]

Will be taking newbie undergrad analytic geo next semester. Any books that I should read as the prime heterosexual force of a pure mathematician I aspire to be?

[Anonymous No.11359867]

>>11359851
>heterosexual
Not gonna make it

[Anonymous No.11359892]

>>11359830
I don't want an half baked solution, I just want a small hint on how to solve it.
Well I think I'm not working on the right direction because finding critical points is harder than I thought, maybe the function I'm trying to find the critical points is not the right function, here is the original problem if someone have an idea: >>11359609

[Anonymous No.11359902]

>>11359867
I'm being quite ironic, buddy

[Anonymous No.11359907]

>>11359892
>I just want a small hint on how to solve it.
Don't try to do both points at once. Fix B, and then look for the maximum perimeter of triangles with AB as a side.

[Anonymous No.11359915]

>>11359907
The exercise forces me to use a function of two variables and finding the maximum (we are studying critical points in functions of multiple variables).

[Anonymous No.11359928]

>The exercise forces me to use
yikes

[Anonymous No.11359931]

>>11359915
did you try taking a derivative

[Anonymous No.11359936]

>>11359931
Yes and searching for the partial derivatives to be equal to zero leads to these kinds of equations: >>11359826

[Anonymous No.11359938]

>>11359915
Then do this, and get the chord lengths via trig

[Anonymous No.11359949]

>>11359936
>Can't solve it
>cos(y) = 1 and sin(y) = 0
>Can't solve it

[Anonymous No.11359954]

>>11359949
That's clearly not the only solutions, y=2pi-x for all x is also a solution.

[Anonymous No.11360395]

>expand out the formula and simplify
>it says I'm wrong
>don't see how
>enter the formula into a math solver, letting [eqn]y=\Deltax[/eqn]
>get the same result I put in
???

[Anonymous No.11360405]

>expand out the formula and simplify
>it says I'm wrong
>don't see how
>enter the formula into a math solver, letting
[eqn]y = \Delta x[/eqn]
>get the same result I entered as an answer
???

[Anonymous No.11360415]

If this young man expresses himself in terms too deep for me, then what a very singularly deep young man this deep young man must be!

[Anonymous No.11360421]

Can all distributions be simulated by the uniform distribution?

[Anonymous No.11360447]

>>11360405
are you trying to ask a question or something

[Anonymous No.11360465]

>>11360447
how is that not the answer?

[Anonymous No.11360471]

>>11360465
why are you squaring a delta and not a delta x?

[Anonymous No.11360696]

>>11340981
I need to learn everything there is to know about the adjoint representation of [math]\mathrm{SU}(n)[/math]. In particular, I know that given the usual [math]\mathrm{Ad} : \mathrm{SU}(n) \to \mathrm{Aut}(\mathfrak{su}(n))[/math], we have that [math]\mathrm{Ad}(\mathrm{SU}(n)) = \mathrm{SU}(n) / \mathbb{Z}_n[/math] (i.e. projective [math]\mathrm{SU}(n)[/math]), which is an [math](n^2-1)[/math]-dim. subgroup of [math]\mathrm{SO}(n^2-1)[/math]. I want to understand this subgroup of [math]\mathrm{SO}(n^2-1)[/math]: for instance, exactly what kinds of SO transformations are being excluded?

If anyone has any good references, I would be very grateful. I'm not well-versed in Lie theory, so I don't know where in the literature to look. (Although I found 2 mathoverflow posts that were not very helpful...)

[Anonymous No.11360953]

>>11360471
Oh, it was just a dumb typo. Thanks

[Anonymous No.11360960]

What was the point of substituting here instead of just doing
[eqn]\lim_{x\to 0} \frac{sin(4x)}{x} = 4(\lim_{x\to 0} \frac{sin(x)}{x}) = 4(1) = 4[/eqn]?

[Anonymous No.11360966]

>>11360960
Am I being trolled here

[Anonymous No.11360992]

>>11360966
no I'm just stupid

[Anonymous No.11361072]

>>11360960
sin is not linear
In general, [math]\sin(4x) \neq 4\sin(x)[/math] and [math]\sin(x+y) \neq \sin(x)+\sin(y)[/math]

[Anonymous No.11361139]

>>11343451
WWII and the continued rape of the German people.

[Anonymous No.11361144]

>>11353314
That Dr. Villani he's an odd one.

[Anonymous No.11361148]

>>11360415
Please don't post this fraud who hides behind the Japanese language barrier ever again.

[Anonymous No.11361180]

>>11360421
bump

[Anonymous No.11361204]

>>11351932
you mean space filling curves?

[Anonymous No.11361225]

>>11340981
>NEW THREAD
>>11361210
>NEW THREAD
>>11361210
>NEW THREAD
>>11361210
>NEW THREAD
>>11361210

[Anonymous No.11361304]

>>11361225
>literally 150 replies in
Baboon tier.

[Anonymous No.11361314]

>>11361304
just ignore it anone

[Anonymous No.11361316]

>>11361225
based
>>11361304
>>11361314
cringe

[Anonymous No.11362309]

Bump.

[Anonymous No.11362325]

>NEW THREAD
>>>11361210

[Anonymous No.11362449]

Give me your best graduate-tier [math]\mathbb{R}[/math]-analysis book for someone who never touched [math]\mathbb{R}[/math]-analysis.

[Anonymous No.11362556]

Hello, math noob here.
Can you rec an entry level math book that explains complex ideas and the history of mathematics?

[Anonymous No.11362591]

>>11362556
infintesimal was fun
cant remember how much it taught

[Anonymous No.11362634]

>>11362449
Here you go gigachad, my best joke recommendations.
https://link.springer.com/book/10.1007/978-3-030-33143-6
https://link.springer.com/book/10.1007/3-540-28890-2

[Anonymous No.11362691]

https://www.scribd.com/doc/233602815/Barnetts-Identity-Pdf1

Can anybody who knows a bit about the algebraic geometrical aspects of quantum loop gravity break this down for me? I cant understand how he says you can use the corollary of [1] to prove this result

[Anonymous No.11362695]

>>11362691
Yukari faggot im specifically asking for your help

[Anonymous No.11362713]

>>11358373
I really like this book, but I'm not a huge fan of algebra. I like analysis and geometry

[Anonymous No.11363324]

>>11362634
These seem like fine books. Where's the joke?

[Anonymous No.11363347]

>2020-02-05
>・(Papers) Revised version (list of revisions):
>The Mathematics of Mutually Alien Copies: from Gaussian Integrals to Inter-universal Teichmuller Theory.
http://www.kurims.kyoto-u.ac.jp/~motizuki/Alien%20Copies,%20Gaussians,%20and%20Inter-universal%20Teichmuller%20Theory.pdf

[Anonymous No.11363349]

>>11363324
>Where's the joke?
Axler.

[Anonymous No.11363549]

This is an NxN square matrix with N ones in it. Does it have some sort of name? Can I represent it with an N bit number, or does it have to be N^2? I want to just get a large integer and turn it into one of these matrices with one-to-one correspondence between the int and the matrix, I'm currently thinking just a series of fixed-width numbers, each saying the place of the ones (so pic related would be (00, 03, 02, 06, 07, 05, 01, 04) but all concatenated, and probably in binary with only enough width to contain the largest number. But I'm pretty sure this isn't very bit-efficient.
Google searching just gets me "matrix full of ones" and "identity matrix".

[Anonymous No.11363563]

>>11363549
>Does it have some sort of name?
The one you posted is a permutation matrix, but not all matrices with N ones are like that.
>Can I represent it with an N bit number
Convert an NxN matrix to a N^2 vector and you can write your matrix as the vector of length N containing the indices of each 1.

[Anonymous No.11363580]

>>11363549
Oh and the will only be a single one in each column, only a single one in each row.

>>11363563
So yeah a permutation matrix is exactly what I'm looking for, thanks.
>Convert an NxN matrix to a N^2 vector
Isn't that not as efficient as it could be? For example, counting the number of zeroes between each 1 would give you N numbers of log2(N) length on average, so that's N*log2(N). The method I stated in my previous post is also N*log2(N), or at least I think it is. Suddenly bigO notation makes more sense to me.

[Anonymous No.11363680]

>>11363580
Wait a minute, the number of possible permutations is the same as the ID number of the last possible one, hence if the number of possible combinations is an f(N) bit number, then f(N) bits is all that is required to uniquely identify any single one of the combinations. But there are N! permutations of an NxN permutation matrix. And N! increases quicker than N*log2(N), so it doesn't really make much sense.

[Anonymous No.11363696]

>>11363680
Well doing some work on 3x3 permutation matrices tells me that storing the number of 0s between 1s or the position of each 1 give me larger numbers than N!, so I guess it wasn't N*log2(N) after all.

So I need to write an algorithm that converts a number from 1 to N! (actually from 0 to N! - 1) into a unique permutation matrix. And the permutation matrices I'll be working with will be rather large (N=204 for a moderate example) so I can't just iterate through a bunch of them.

I've seen these matrices with numbers next to them, but I can't seem to find how they're numbered, so I'll attempt to assign each matrix its own unique ID number or power rating or whatever i should call it. I think multiplying this matrix with an N-long vector and squaring/summing the result, or multiplying it by another NxN matrix and taking the determinant/summing the result is a potential method to get what I'm after. I'll test it with 2x2s and then 3x3s on paper before coding anything. Probably with non-binary matrices.

[Anonymous No.11363720]

>>11363696
Shit, just calculated that 200! isn't a small number, and I'd need to do parallel mathematics on 1200 bits at once, without easily being able to split it up. I'm getting way more permutations than I need of the possible encoding matrices, such that the encoding matrix is exponentially more difficult to guess than the encoded binary.
I'll ditch the matrix idea and figure out some other method, unless I can make an easy way to generate a unique 200x200 permutation matrix with a much smaller seed, one in the realm of 150b, not 150B.

[Anonymous No.11363739]

I don't know if any anons remember but I asked about how to find a function where the derivative is the inverse of the function.
I found the solution. It's ((phi+)^(phi-))*x^(phi+). Where phi+ is the positive value for the golden ratio (1.618...) and phi- is the negative (-0.618...).
I thought it was a nice solution

[Anonymous No.11363777]

>>11363324
Axler is
>open access
and has funny formatting.
Jost has an autismo title.

[Anonymous No.11363928]

>>11362634
AXLER PUBLISH A NEW TEXTBOOK???? NOICE
It's good, right?

[Anonymous No.11364036]

Babby's first differential geometry question here. How do I show that the "set of solutions to an equation" (i.e., a curve) is a subset of a given parameterization? The idea is to show that given

[math]\gamma(t) = ( pcos(t), qsin(t) )[/math]

to show that this is an ellipse given by

[math]x^2/p^2 + y^2/q^2 = 1 [/math] for p > q > 0

I've shown that [math] Image(\gamma) \subseteq C[/math] but showing that [math]C \subseteq Image(\gamma) [/math] seems more difficult. In the first case, you just substitute in the parameterization to the equation that defines [math]C[/math], in the second case, so far I've tried talking about the curve is closed, and the parameterization is periodic, which implies... something something the solutions to the equation of the curve is a subset of the values given by [math]\gamma(t)[/math] in our parameterization.

[Anonymous No.11364075]

>>11363739
I found [math]y(x) = \sqrt{2(x+c)}[/math] as solution to the differential equation [math]y^\prime = y^{-1}[/math].

[Anonymous No.11364186]

>>11364036
use the fact that (cos(t),sin(t)) can be Defined as the set of solutions to x^2+y^2=1

[Anonymous No.11364187]

>>11364186
or to make it clearer: z^2+w^2=1

[Anonymous No.11364492]

>mfw my supervisor said I may be able to publish my first paper soon

[Anonymous No.11365060]

>>11364036
you need to use the fact that any point on the unit circle can be expressed as ( cos(t), sin(t) ). this is something which can be taken for granted, given that it's one of the possible definitions for sin and cos, as >>11364186
said.

[Anonymous No.11365186]

If I do a statistical test asking if a null hypothesis H0 is rejected using a statistic K (which must be bigger than a critical CriticalK), and p is bigger than alpha, can I never reject H0?

I.e. is the p value comparison against alpha always required?

I.e. if p > alpha, can I never reject H0 with that test (even if K>CriticalK suggests H0 should be rejected)?

[Anonymous No.11365432]

/mg/pill me on quantum computing

[Anonymous No.11365438]

>>11365432
it's a meme

[Anonymous No.11365508]

>>11364075
yeah but that's the reciprocal not the inverse. The inverse is a reflection in y=x.
Eg the inverse of x^2 is x^0.5

[Anonymous No.11365521]

>>11360421
Not practically.
https://en.wikipedia.org/wiki/Inverse_transform_sampling

[Anonymous No.11365626]

Does this pass /sci/ peer review?
https://www.dropbox.com/s/v3ll8johs4v20jm/Analysis%20of%20Unique%20Numbers%20Generated%20By%20Interaction%20of%20Sets.pdf

[Anonymous No.11365677]

>>11365626
>dropbox

[Anonymous No.11365682]

>>11365677
Is dropbox not a respectable journal?

[Anonymous No.11365800]

did you guys ever wake up to find that all your desire to learn mathematics was just gone. like not that you couldn't do it anymore but you just couldn't be bothered to study it. halfway through problems I start asking myself who cares, it doesn't matter, I want to go work on an oil rig and never talk about anything even remotely intellectual ever again

pls help

[Anonymous No.11365893]

>>11365800
See a doctor, express your lack of motivation

[Anonymous No.11366110]

>>11365800
Yeah

[Anonymous No.11366132]

>>11365682
/thread

[Anonymous No.11366150]

>>11365626
No. Abstract starts with "This paper discusses..." but on scrolling I can see no discussion.

[Anonymous No.11366198]

>>11365800
happened for me and all physics except for electronics, but was gradual enough that I didn't notice it, it's just like my desire to learn got directed somewhere else
if it's really sudden for you I can only assume some sudden hormonal imbalance

[Anonymous No.11366200]

>>11365800
If you've been working continuously for a very long time, you probably need a good sized break where you don't think about mathematics at all.

[Anonymous No.11366204]

>>11365800
Yes

[Anonymous No.11366205]

>>11366200
>where you don't think about mathematics at all
is that even possible, i don't think a day has gone by when nothing mathematical has popped into my head since i started getting into maths when i was 16

[Anonymous No.11366533]

>just finished a test
>wondering if a question was actually an if and only if and I didn't notice
FUCK
I mean, the way back is literally trivial, surely he won't get on my ass about it.

[Anonymous No.11366855]

want to learn topology, what books do you guys recommend? a friendly professor said starbird and su's topology through inquiry was good

[Anonymous No.11366903]

do bases and subbases generate different topologies on a set X?

[Anonymous No.11366975]

>>11366855
If you were gigachad, I'd tell you to read Arkhangel'skii and fill in all the proofs.
But you aren't, so I really don't know any good general topology books that I can actually recommend.

[Anonymous No.11367012]

>>11366855
I for one have started reading Munkres (very) recently and can only really say good things about it.

[Anonymous No.11367098]

>>11366533
Depends how autistic the t.a. is.
>>11366903
They both are defined for a particular topology so it's fixed from the start.

[Anonymous No.11367137]

Is it a waste of time to TeX my own set of notes based on an already short set of lecture notes ? (they're 60 pages) I don't know why I feel so compelled to do so, maybe I'll just make a crash course in general topology or a little quick review document.

[Anonymous No.11367150]

>>11367137
Literally print out a copy of the first half of
Arkhangel'skii, it's ~100 pages long and was basically written to be a reference in general topology.

[Anonymous No.11367157]

>>11365521
oooohh right forgot you could do that
thanks mate!

[Anonymous No.11367263]

I did this completely schizophrenic proof for a problem in a test, and I'm worried my professor will feel concerned for my mental health. Should I email him about it?
>how schizophrenic
Basically, picture a proof that doesn't work, makes no sense, but every few lines echoes a correct proof. Not like it was copied badly off the internet, but like the author hadn't slept for a week.
>how did that even happen
I had slept badly, my blood was low on coffee and I was in a hurry, so I didn't review anything.

[Anonymous No.11367283]

>>11367263
>Should I email him about it?
No. Just make sure you do it consistently so that he begins to pity you and takes you under his wing.

[Anonymous No.11367301]

>>11367283
I really don't want to be under his wing, tho.

[Anonymous No.11367504]

>>11367301
keep up the schizo proofs and throw in some demonic scrawlings in the margin
post updates

[Anonymous No.11367539]

I'm going to be taking honors abstract algebra next semester and they use D+F, but I want to learn the material now and over the summer to have a big head start. What book do I use that's the best and most rigorous for non-brainlets?

>herstein
>aluffi
>artin

[Anonymous No.11367627]

>>11367539
I liked (((Herstein))).

[Anonymous No.11367652]

Why is combinatorics so based?

[Anonymous No.11368011]

>>11367539
>most rigorous
Cringe. Just try all off the books and find out for yourself. All of them are respectable choices and it's not like one of them is going to be enough.

[Anonymous No.11368590]

>>11367301
Then transcend and take him under your wing instead.

[Anonymous No.11368598]

what you guys think of this oc

[Anonymous No.11368628]

>>11367263
> Basically, picture a proof that doesn't work, makes no sense, but every few lines echoes a correct proof
every other undergrad in my class writes like that, business as usual

[Anonymous No.11369731]

sorry to shit it up with an elementary algebra question, but can someone help me prove this?

I penciled it out by breaking the summation down into terms in a sequence, x_1^2y_1^2 +... + x_1^2y_n^2, for each sequence in each summation, and it seems like it's true, but that's a bit insufficient and a nice elegant proof would be 11/10

also asked here, where it'd probably better be answered.
>>11369714

TIA

[Anonymous No.11369762]

>>11369731
Break the summation on the left into two cases, i<j and i>j

[Anonymous No.11369820]

>>11364492
Nice one!
Hopefully me too soon

[Anonymous No.11369837]

>>11368598
Made me laugh

[Anonymous No.11370187]

>>11369762
like this? or am I missing some detail? srry i know this is stupid. is the choice of using sum i>j or sum i<j arbitrary or what?

[math]
\sum_{i>j}(x_i^2y_j^2 - x_iy_ix_jy_j) + \sum_{i<j}(x_i^2y_j^2 - x_iy_ix_jy_j) +
[/math]

thank god this websites anonymous

[Anonymous No.11370260]

>>11370187
>like this?
Yep. This is the right starting point.
>is the choice of using sum i>j or sum i<j arbitrary or what?
I'm not sure exactly what you mean by this. The two sums mean different things (which should be clear from how summation notation works).
I think you're onto the correct idea though. You want to relabel (swap i and j) one of the summations.

[Anonymous No.11370286]

>>11370260
what i meant was like maybe, but probably not, sum_{i < j} = sum_{i > j}, so it doesn't matter which you use in the original inequality.

what do you mean about the relabeling? any other tips to mvoe the problem forward?

[Anonymous No.11370294]

>>11370286
>sum_{i < j} = sum_{i > j}
You can't just do this, the sums aren't symmetric in how they treat i and j
What you can do is swap i and j everywhere inside one of the summation terms since they are just arbitrary labels.

[Anonymous No.11370405]

General integration question:
How do you know within like a minute which method to use?
(Like conjugate, completing the square, trig identities, splitting up a fraction, etc)
I just get stumped every time and get lost on what to do.

[Anonymous No.11370427]

>>11370405
Practice

[Anonymous No.11370559]

>>11365800
happened to me in the middle of a graph theory course t bh

[Anonymous No.11370693]

>>11370294
>What you can do is swap i and j everywhere inside one of the summation terms since they are just arbitrary labels.
like dis

[math]
\sum_{i>j}(x_i^2y_j^2 - x_iy_ix_jy_j) + \sum_{i<j}(x_j^2y_i^2 - x_iy_ix_jy_j)
[/math]

?

please place the next breadcrumb on the table

[Anonymous No.11370700]

>>11370693
>crumbs
in other words, I don't know how to combine these sums of different indices to arrive at what was originally shown here: >>11369731

[Anonymous No.11370832]

Anyone knows some twitter account, blog or whatever like the @mathvisuals telegram channel??
Its so helpful and I want more

[Anonymous No.11370843]

>>11370405
recognize the patterns, try out possible substitutions and parts splits in your head to see what they'll get rid of.

[Anonymous No.11370984]

Should I go for a math degree?

[Anonymous No.11371003]

>>11370984
If you have to ask if you should do something you don't want to do it badly enough to succeed anyway.

[Anonymous No.11371297]

Phew. I was worried all the stuff I did this weekend was wrong. I simply forgot that the loop space functor is contravariant. Don't mix anorexia and maths. It is a combination both addictive and mistake inducing.

PS. I just realised the reason behind my self esteem problems. I don't believe in gods, and thus I don't believe in myself.

[Anonymous No.11371406]

>>11371297
*covariant, fuck.

[Anonymous No.11371409]

>tfw just managed to solve an extremely technical problem I've been dealing with for nearly 6 month now
it was basically some fucky arithmetic problem, looking as unnatural as they come, yet the solution is extremely simple (as has a simple, but non-obvious form)

[Anonymous No.11371412]

>>11371297
Are you a female? You sound like a bit of a whore.

[Anonymous No.11371414]

>>11371297
eat
no arrows are not food
reversed arrows are also not food
coffee and sweets do not count as food
eat a steak

[Anonymous No.11371429]

>>11371414
I ain't got no time to feed.

[Anonymous No.11371430]

>>11371297
>I don't believe in gods, and thus I don't believe in myself.
become the god you worship

[Anonymous No.11371433]

>>11371412
t. incel

[Anonymous No.11371435]

>>11371409
cute meem mind if I steal it?

[Anonymous No.11371446]

>>11371297
>I don't believe in gods
cringe.

[Anonymous No.11371483]

>>11371435
id's all urs fren

[Anonymous No.11371505]

Make it better, /mg/.

[Anonymous No.11371556]

>>11371297

Microwaveable rice, some eggs, and vitamin+mineral pills. Lowest effort, palatable, and will give you all the nutrients you need (carbs, prots, fats and everything nice).

If you're the kind of moron that is anorexic because they "care about how their body looks", rather than pure laziness, I'd suggest you don't do math. "Good looking body" AND "anorexia" is as clear-cut a contradiction as they come.

PS: M2F ?

[Anonymous No.11371559]

>>11371483
mmmm thanks
i shall use it to pleasure myself and other like-minded individuals

[Anonymous No.11371563]

>>11371556
Fuck off.

[Anonymous No.11371795]

>>11371430
mcride pls go

[Anonymous No.11371851]

>>11370693
>>11370700
still stuck, will some wise mg wizard pls halp?

[Anonymous No.11371890]

>>11371505
It's just not good.

[Anonymous No.11371894]

>>11371433
LOL. Yes you are a woman.

[Anonymous No.11371898]

Do you have any ideas on finding closed formula for [math]\sum_{k=0}^{l} \binom{n}{k}[/math], where [math]l<n[/math]? Or maybe convince me that it's impossible

[Anonymous No.11371963]

>>11371795
I meant it unironically, not even memeing

[Anonymous No.11372003]

>>11371898
Choosing k out of n is like choosing k-l out of n and then choosing l more out of n-(k-l).
So that sum has some pretty simple recursion relations and should have closed form.

[Anonymous No.11372020]

>>11371898
I don't think there's a closed formula
Search google, it's such a simple statement that surely a thousand people have already thought about it

[Anonymous No.11372038]

>>11372020
Wiki has a lot of closed formulas for many sums of binomial coefficients, yet it states that there's no closed formula for partial sums. I think that if there would be such a formula it would end up there

[Anonymous No.11372112]

>>11371898
You can prove it is "impossible" by running it through Gosper's algorithm. If you are willing to work through a couple pages of technicalities any book with a chapter on hypergeometric summation will discuss this, but it's a technical theorem and there's no lower-level "intuitive" reason why it should be impossible, afaik.

[Anonymous No.11372123]

>>11371505
make it better by deleting it
stop trying to force endless hordes of zero creativity rip-off wojak memes you braindead motherfucker

[Anonymous No.11372315]

I'm taking a babby's first complex analysis class and I'm looking at holomorphic functions
If f(z)=2x+ixy^2 where z=x+iy, I found that f was not entire because it failed to satisfy the cauchy riemann equations. The question further asks if there are any points where the function is differentiable and I concluded that it was never differentiable. Am I correct?

[Anonymous No.11372372]

>>11372315
>holomorphic
oh yeah keep saying it~~~ it makes my dick ROCK HARD
mmmmm holo....holomorphic..... yeeeahh....

[Anonymous No.11372373]

>>11372372
I'm just trying to understand man

[Anonymous No.11372524]

>>11353683
to destroy 1/2 of all mathematics, so there is no motivation

[Anonymous No.11372567]

>>11372315
It depends what you mean by differentiable. It is R-differentiable everywhere as a map from R^2 to R^2 (since it has polynomial components), but it is not C-differentiable (ie. holomorphic) at any point

[Anonymous No.11372915]

>>11371563
If your goal is to give your boyfriend a gumjob before the age of 30, just keep what you're doing and glorifying your mental illness (anorexia).

Otherwise, I'd suggest you at least begrudgingly take part of the advice, and swallow the vitamins to avoid scurvy. Last person I knew who glorified anorexia ended up in a wheelchair, barren, toothless and hairless. Real sexy she looked, like a 24 year old cancerous grandma. Yum.

But hey, not eating is really cool and quirky and unique right ? and a good basis for a healthy identity to boot !

baka u_u

[Anonymous No.11372930]

Just a quick reality check: Suppose [math]R, S[/math] are unital rings and [math]S[/math] is a mutual-sided module over [math]R[/math]. Then, for mutual-sided [math]R[/math]-modules [math]M, N[/math], we have [math] S \otimes_R (M \otimes_R N) \cong (S \otimes_S S) \otimes_R (M \otimes_R N) \cong (M \otimes_R S) \otimes_S (S \otimes_R N) [/math], right?

>>11372915
Who's glorifying anything___? Eat some merde.

[Anonymous No.11372948]

>>11372930
So you're asking if the tensor product commutes with base change?
Because it does, according to wikipedia.

[Anonymous No.11372954]

>>11372948
Good. Thanks.

[Anonymous No.11373039]

>>11365800
I'm in that state right now. Worked Last half of the year like madman. What tilts me is the inability to learn the subject deeper fuck that and fuck university for forcing me to learn a lot of different subject that I have no interest in learning to and Will most definetely not use in the future like Game theory when Im focusing on differential equations.

[Anonymous No.11373422]

Is measure theory the epitome of autism?

[Anonymous No.11373431]

>>11373422
Getting there, but not quite. The rule is that the more set theory invades your math the more autistic everything becomes. General topology (beyond the first 50 pages of an algebraic topology book) is substantially worse than measure theory. Pure set theory is the true pinnacle.

[Anonymous No.11373489]

>>11373431
Based

[Anonymous No.11373628]

>>11363739
Anon solved this back when you posted it.

[Anonymous No.11373717]

>>11372123
today i had an idea for a meme (not the wojack poster), the idea is trump rambling off some garbage in his iconically way of speaking, somehow generated using some artificial speech software (probably already exist) and overplayed onto a vid of him talking. could be really funny but i haven’t thought of any good dialogue yet, maybe a trumpy spin on that “chain rule is my specialty” pasta

[Anonymous No.11373718]

>>11371851
sadbump :((

[Anonymous No.11374404]

>>11343534
That's pretty weird. In all the classes I've taken, women were the most present in geometry/topology. Algebraic geometry, homotopy theory (like the Quillen/Lurie style shit, the ultra-abstract shit) and abstract algebra (Lie algebras, representation theory and whatnot) courses as well as combinatorics are usually full of the most physically disgusting (obviosly all male) human beings you will ever encounter from my experience.

[Anonymous No.11374418]

>>11350748
The ENS in Lyon is good. As far as Paris is concerned, I'm studying here right now and there aren't THAT many PDE courses... I think there's a few people in Paris 13 and a lot of applied mathematicians. Generally in Paris the PDE-ists are somewhere on the spectrum between the pure and applied math. A lot of places in Germany are strongly PDE-ish, Bonn and Berlin have good schools obviously. I assume Cambridge and Oxford have strong PDE departments although I have no idea.

[Anonymous No.11374419]

>>11340981
I don't give a fuck about useless stuff. I could be learning about how to reduce intermodal dispersion in my experiment instead.

So long, Autismos...

[Anonymous No.11374425]

>>11347084
>University of Colorado

yuck

[Anonymous No.11374776]

why do we even care about Kähler Manifolds?

[Anonymous No.11374854]

>>11374776
https://www.youtube.com/watch?v=2rjbtsX7twc
Manifolds must be Kähler.

[Anonymous No.11375331]

Why can't we use the diagonal argument to show that computable numbers are uncountable?

[Anonymous No.11375342]

Hello math bros, hobbyist A.I. developer here
What would be your reccomendation for a book on game theory for a guy who has good all around knowledge/grasp on math but isnt a mathematician?

[Anonymous No.11375343]

>>11375331
if follows directly from the uncountability of R

[Anonymous No.11375513]

>>11375331
Computable reals are those whose digits are enumerated by Turing machines. There are only countably many Turing machines, so only countably many computable reals. You should look at the proof of the recursion theorem, the existence of fixed ponts of computable functions, the proff is characterized as a diagonalization that fails.

[Anonymous No.11375718]

what's your favorite topology?

[Anonymous No.11375758]

>Hello, I am Urysohn's lemma. Why do you pester me?

[Anonymous No.11375777]

>Why yes, I am the class of the tautological bundle on the Riemann sphere. How could you tell?

[Anonymous No.11375790]

>My secret? I read up on the periodic complex cobordism spectrum.

[Anonymous No.11375808]

>Me? I'm a étale topological groupoid.

[Anonymous No.11376017]

>>11373422
Only because it's horribly motivated as a way to measure more sets. Measure theory is fundamental in many high level areas as without it you couldn't construct more examples besides your usual autistic ones. It's fundamental in rigorous quantum theory, pde theory, probability and stochastic processes. It's such a powerful tool that most people only get to see in grad school when you realize you need it.

[Anonymous No.11376064]

Mathlet here, going through James Stewart's precalculus. I can hardly do the algebra, I mean I understand it conceptually but working out the problems is far more difficult then I'd like. I want to master precalc topics so I can finally learn calc this year. Early 20s, there's hope for me right? Wasn't really pushed to study math hard in high school and didn't take it too seriously because I didn't understand it was the most important subject in relation to the sciences. Finding it really hard to get motivated. Not trying to blog, just need a good push. Is there a discord or irc channel for studying maths?

[Anonymous No.11376107]

>>11374419
>Useless
>Couldn't make this post without Elliptic-curve cryptography

[Anonymous No.11376246]

>>11376064
there’s #math on irc, but shitposting here and in sqt is comfiest

[Anonymous No.11376249]

>>11373718
depressedbump

[Anonymous No.11376345]

I don't get the standard complex of a group ring. How does it provide any interesting homology if it's exact? Shouldn't the whole homology be trivial in degreed higher than 0?

[Anonymous No.11376520]

>>11376345
Yes, but that is precisely the point. What you compute is the (co)homology groups of modules over that ring.
These are defined as [math]H_n(G,M) = Tor_n^{\mathbb Z[G]}(\mathbb Z, M)[/math] and [math]H^n(G,M) = Ext_{\mathbb Z[G]}^n(\mathbb Z, G)[/math].
To compute them, you start from the exact sequence you mentioned and apply the [math]\cdot \otimes_{\mathbb Z[G]} M[/math] or [math]Hom(\cdot, M)[/math] functors to get a possibly not exact complex, the (co)homology of which is what you seek.

[Anonymous No.11376564]

>>11376520
Oh shit, now I see. So it is exact over the base ring, but not necessarily over the group ring, and that is what you use when you take the Tor. Cheers!

[Anonymous No.11376904]

new bread when? :3

[Anonymous No.11376914]

>>11376904
die ^___^

[Anonymous No.11377065]

>>11377064
new
>>11377064