/sci/ - Science & Math

what to study over summer after calc 2??

>>10727710
>what to study over summer after calc 2??

>>10727663
What is the biggest number? i think its infinity to the power of infinity XD

>>10727725
>What is the biggest number?
However many times I've fucked your mother.

>>10727710
watch gilbert strang's MIT OCW lectures on Linear Algebra. they're amazing. alternatively, watch the OCW lectures on calc 3. but i'd recommend lin alg.
here: https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/
do the problems and the exams too

>>10727725
i think it's infinity (knuth up-arrow infinity times) infinity xD

>>10727782
thank you

>>10727784
you're welcome

>>10727725
Sasquatch and Big Foot

>>10727710
Touhou.

I guess at most one false proposition should be of interest then

Can anyone help me with a commutative algebra problem?

I have a graded ring, with a homogeneous Ideal, say J. Let [math] F = F_0 + ... + F_t \in J : F_d \in S_d [\math] for all d. I want to show that each [math] F_i \in J [\math] for each i.

I tried inducting on the homogeneous components of F, but it didn't really seem to work.

Any goys have ideas?

In terms of Mathematics, how far does the general use of it in life go in terms of it being applied to science?
People spend their whole lives and thousands of dollars immersed in Mathematics, trying to get their PHDs. But how much of the stuff that they're learning is actually useful?

>>10727988
>apply the definition of an ideal to get F in terms of J's generators
>decompose the coefficients
>apply distributivity
>apply gradedness

>>10728000
Who cares?

>>10728021
My trips and dubs do.

>>10728024
Fuck.

>>10728033
There we go. My dubs demand answers.

>>10728000
I wake up in the morning and the first thing I remember is that I have my goddamn doctorate in mathematics, this results in an immediate rush of endorphins and testosterone which will last for the rest of the day. I then get to work writing down the proofs to the theorems that I solved in my head last night. After that I fuck my 10/10 wife while thinking about my research. I then leave without eating breakfast since I no longer require sustenance. Next follows morning lectures gracing plebs with some invaluable insight into my mind and its firm grasp on the most important field of study in human history. The rest of the I spend developing various mathematical structures on blackboards, the results of which will applied to curing all cancers and building thermodynamically efficient cold fusion reactors. As the day winds down I ponder my surreal existence, I have to dig up my degree to remind myself of the reality that I do in fact have a PhD in mathematics. Finally I fall asleep holding my doctorate and 300k salary slip in my arms.

And then I do it all again.

I've been reading up on group rings and group algebras, and was curious about something.
So the group algebra [math]\mathbb{R}[\mathbb{Z}_2][/math] is isomorphic to the split-complex numbers [math]\mathbb{R}[x]/(x^2-1)[/math]. OK, looks good, let's double the dimension. What is group algebra [math]\mathbb{R}[\mathbb{Z}_2\times\mathbb{Z}_2][/math] isomorphic to? I know that it looks like the multiplication for quaternions but with all of the minus signs switched to pluses.
Anybody got any clues?

>>10728086
Similar to split complex, but you have a and b, a^2=1, b^=1, ab=ba.

>>10728110
So is it pretty much the quaternions but all of the imaginary units commute with each other and square to 1?

>>10728143
Yes.

>>10728144
Thanks dubs.

>>10728086
So I had a hunch that this might be one of the Clifford algebras [math]\mathcal{C}\ell_{p,q}(\mathbb{R})[/math] for [math]p+q=2[/math], but it turns out that the only such Clifford algebras are either the regular quaternions or something called the split-quaternions, where one of the imaginary units squares to [math]-1[/math] while the other two square to [math]1[/math].
I just wish I knew what other names [math]\mathbb{R}[\mathbb{Z}_2\times\mathbb{Z}_2][/math] goes by so I can finally satiate my curiosity.

>>10727988
Depends. There's a vast difference in how applied different types of maths are. One can spend their whole life studying something that can be applied like Encryption, optimisation, PDEs, etc and this is inarguably "useful".
Something more abstract probably won't have applications to anything outside of more maths. However, you could argue that it is "useful" for its own sake in the same way poetry, literature, film, etc are "useful".

>>10728355
Meant for >>10728000

>Someone asks a math question on /sci/
>never took the subject
>quickly review the intro chapter
>answer the question
>poster thanks me
>feel smart despite failing all my math classes in real life

What writing utensil do you use for doing math? I have a mechanical pencil that came in a pack, but I want to get something different. I like writing small notes and was thinking about something less than the .5mm lead I am using now. What should I get?

>>10727725

See: 1:18 of https://vimeo.com/13497928

>>10728394
>What writing utensil do you use for doing math?
latex

>>10728394
>What writing utensil do you use for doing math? I have a mechanical pencil that came in a pack, but I want to get something different. I like writing small notes and was thinking about something less than the .5mm lead I am using now. What should I get?

I use 0.5mm 2B lead with a Pentel GraphGear 500 and a "hi-polymer" eraser, on unruled B5 Muji notebooks. Writes extra dark and erases perfectly.

>>10728405

btw, the Muji notebooks are a ripoff if you buy them online on Amazon. They have brick & morter stores where they are $1.50 a notebook, although not always in stock.

>>10728409
Have you see those rotating mechanical pencils that spin the lead as you write so you don't get angles? Are those just a meme?

>>10727782
What make Gil Strang a good higher level math professor?

Is Sal from Khan academy a good higher level math teacher?

Anyone else studying topology this summer?

>>10728811
>studying
>summer
have sex

>>10728811
yep, 3-manifolds

>>10728811
I'll need to know some sheaves, schemes and homological algebra if I want to enter a phd. So yes.

>>10728867
Why not both?

What are some good talks on the interwebs? I mean math talks, not TED.

>>10728923
>IHES
>Institut Henri Poincaré
>Stanford lecture collections
>Harvard Math
>Graduate Mathematics

>>10728485
gil strang is not a higher level math professor, as far as i know he pretty much only teaches low level undergrad math
no, linear algebra is not "high level"
strang shows enthusiasm and pure childlike joy for some of the most simple, dry mathematics in finite dimensional computational linear algebra. it's like he acts like an engineer who doesn't get why diagonalization or such is obvious, but unlike an engineer he absolutely loves it for its pure mathematical beauty and elegance. of course he actually gets it, but in lecture he acts differently that even gets all the mit engineering brainlets excited. this is why his lectures are great for people who have taken calc alone, because college calc is soulless and strang's linear algebra has soul.
sal is a horrible god awful "higher" level math teacher (by which i mean anything above calculus) because he pumps out shit for people who need facts to be repeated 5 times and need idiotic amounts of exposition. sal is a great high school level teacher, because most high schoolers are pathetic morons who literally cannot cope with the simplest of abstract ideas.

>>10728811
there are plenty of types of topology. i was thinking of studying some differential topology but that might not happen now.

>>10729100
yikes

Undergrad math major here. When will I be able to understand this?

What is going on here?
I cant even.

>>10729190
understand it? after freshman year of undergrad math
understand every word in it fully? maybe after 3 years of undergrad math, 4 if you leave some alg geo and alg top for the end.

>>10729198
that's clearly the quadratic formula. they probably fucked up and meant to write a root sign in place of the division sign.

>>10729203
>clearly
Thanks mate, that works out.

>>10729190
You can grasp the gist of the problem with babby linear algebra, and his retarded approach to the k=n-1 case with some knowledge of hodge theory, which is masters/phd stuff.
I say retarded because he could just average the norms.

>>10729257
what are you on about
you just need to pick which side you have the vector on

>>10729190
>take an orthonormal base of R^n
>fix an order on it
>orthogonalize the first element of the base in relation to the all the elements
>if non-zero, done
>otherwise repeat
Apparently it's unsolvable, tho.
Does anyone have any idea why this wouldn't work?

>>10729274
Nevermind.

>>10729198
>what is latex

>>10729304
I can dig up the contact info of the manufacturer from the datasheet so you can send that quality comment to them.

>>10727663
daily reminder that if you are a weeb, you stand no chance

>>10729378
*if you are not a weab
i haven't slept in 20 hrs

Was Gödel the Terry A. Davis of mathematics?

>>10729416
>Gödel
>Terry A. Davis
Who?

>>10729416
No, Bishop.

>>10729416
>Was Gödel the Terry A. Davis of mathematics?
Gödel was a logician, not a mathematician.

>>10729387
Cringe

>>10729378
I wonder if Cedric publishes articles while waiting for HxH to come back from hiatus.

>>10729378
Birth of a theorem is an amazing and wonderful book which I sadly have yet to finish. I must have almost finished it. He just plops whole pages of latex into the book and you can either skip over it and it wont matter, cause he'll tell you before or after what the importance is in more readable terms. Or you can really work through it and follow his journey through the mixed norms and ridiculous bounds and so forth. It's so much fun.

>>10728811
No, but I am studying some algebra in preparation for algebraic topology

>>10729610
algebra is garbage

>>10728018
Here's my attempt, sorry it's a rough draft

>>10729634
Seems correct.
>>10729610
>studying algebra for algebraic topology
If it isn't homological algebra you might as well stop.

What's the latest on our boy Mochizuki?

>>10729634

>red pen

autism

>>10729708
>What's the latest on our boy Mochizuki?
He's looking forward to his IUT conferences
http://www.kurims.kyoto-u.ac.jp/~motizuki/project-2020-english.html

>>10728405
>using a mechanical pencil that isn't kuru toga

>>10728475
no they're the real deal
get one

>>10727663
How do I compute the Steenrod algebra of a sphere?

>>10730033
What have you tried?

>>10730038
Posting on 4channel.

>>10730063
Try posting harder.

I'm just getting in topology. What is the intuitive conceptualization of topological spaces in general? Is a topology just a set that maps certain point to eachother, meaning they are "connected"? Is Euclidean space a topology?

>>10730159
>What is the intuitive conceptualization of topological spaces in general?
A generalization of metric spaces. Most concepts defined in analysis can be defined with axioms and without requiring a metric, which makes way to more (general) examples.
>Is a topology just a set that maps certain point to eachother, meaning they are "connected"?
"no"
>Is Euclidean space a topology?
Yes, because it's a metric space. The definition for open space in metric spaces matches with the axioms for open sets in topology. Basically every metric space is a topological space, but the inverse isn't true.

>>10730159
Think of it as a "black hole" of sorts. It's intuitively very large and very connected, but not fully and not necessarily in all parts of the black hole.

>>10730190
>inverse
Mathematicians say "converse".

>>10730190
So generalizing "distance"? Is there a difference between a metric on a set and a measure on a set?

>>10730205
>Is there a difference between a metric on a set and a measure on a set?
No. Obviously.

>>10730208
I clearly spell out the difference between these things and the DNC emails here:
>pastebin com/LbDk56Es

what are some topologies that's can't be generated by a metric on a set

>>10730205
Yes, obviously.
The Hausdorff measure is induced by a metric, but other than some special cases I don't know a canonical way to induce a metric from a measure.
>>10730215
Sierpinski.

>>10730205
"no"
it's generalizing the concept of metric space (emphasis on space), without using a metric
>>10730198
in french we say inversement
>>10730215
a set with more than two points and the trivial topology

>>10730220
>"no"
What do you mean by the "quotes"?

>>10729378
>if you are a weeb, you stand no chance
This. Glad to see some meaningful stuff on this horrendous general.

Measure is a generalization of area, distance etc

A topology is a generalization of "nearness" "neighborhood" etc

Is this correct

>>10730258
>>10730258
No.
A measure is a generalization of volume.
Am topology is a generalization of convergence that doubles as a tool for detecting conectedness.

>>10730266
At last I truly see

>>10727663
How do you guys optimize your study routines?

I want to make the most of this summer and learn as much as possible. Ideally I'd like to study 12 hours every day, but I don't think this is sustainable. Is there anything that helps you guys stay focused for extended periods?

I like arithmetic triangle groups

>>10730352
9 to 5 from Monday to Friday, 11 to 3 or 4 on weekends :)

Any one knows how much category theory and generating functions should I know before getting into combinatorial species?

>>10730159
You should think of general topology as the most barebones conceptualization and abstraction of geometry, and nothing else. You need not know almost anything about these topologies on sets. You could as well just think of every space you encounter and Hausdorff and paracompact (ie not "too big") or second countable and get away with it. Even in Algebraic geometry where you don't get Hausdorff, there's still a "pseudo-Hausdorff" desirable property. Whenever a teacher draws a picture on the board, it's a (para)compact Hausdorff visualization.

Essentially, you're either doing proper geometry, or simply infinite combinatorics, and no in between.

>>10730352
Don’t do that, absolute waste of time if you aren’t already engaged with this kind of thing. 4-6 hours a day is more than enough to work through multiple textbooks

>>10730258
Does the indiscrete/trivial or discrete topology tell you anything about nearness?

In the discrete topology, every point is the same distance apart. In the indiscrete, every point is near to every other point.


As this points out >>10730641, you should be thinking, "how does a Hausdorff paracompact space behave?"

In essence, you can think of open sets as how the "majority of the space behaves", or the "generic neighbourhood". This is in fact how it's looked upon in algebraic geometry - here, open sets are very large - any single open set 'intuitively' covers almost all the space, and essentially dictates how the space looks like 'generically'. Most people care about things that exist in an open set. For example, singularities can exist only outside of an open set, or more generally, 'bad' behaviour does too.

This is actually how it works too in compact spaces. Only finitely many open sets are needed to tell you all the information about the space, and this generally is why compactness is such an important property.

Am I fucked as a pure mathematician if I never got to participate in something like, for example an IMO?

>>10730750
no. contest math is nothing like academic math

>>10730763
thanks anon, my fragile spirit needed that.

holy fuck this topology discussion is moronic
A METRIC SPACE IS A SPACE WHERE YOU CAN FIND OUT HOW FAR APART TWO POINTS ARE
IT IS A SET WITH DISTANCES

A TOPOLOGICAL SPACE IS A SPACE WHERE I CAN TELL YOU WHICH POINTS ARE CLOSEISH TO A GIVEN POINT
IT IS A SET WITH A MORE GENERAL NOTION OF CLOSENESS

A METRIC SPACE IS A TOPOLOGICAL SPACE BECAUSE NUMERICAL DISTANCES GIVE YOU A NOTION OF CLOSENESS

A MEASURE SPACE IS TOTALLY UNRELATED. A MEASURE SPACE IS A SET WITH A NOTION OF SIZE. IN A MEASURE SPACE ONE CAN THINK ABOUT LENGTH, AREA, OR VOLUME, ETC, BUT NEVER DISTANCE.

MANY TIMES ONE DEALS WITH TOPOLOGICAL MEASURE SPACES. BUT THE MEASURE AND TOPOLOGY RARELY INTERACT VERY WELL, IF AT ALL.

Please.
Stop spreading misinformation.

>>10730833
To clarify one point, one CAN talk about distance in a metric space equipped with a measure. I mean that in a PURE measure space with JUST a measure there is ABSOLUTELY NO notion of distance or of closeness.
There are measure isomorphisms between R, or say the unit interval, with some PRETTY NASTY ASS SETS.

>>10730352

Probably not feasible while you're still a student, but G.H. Hardy and Poincare only worked 4 hours a day:

>In fact for most of his life his day, at least during the cricket season,
>would consist of breakfast during which he read The Times studying the
>cricket scores with great interest. After breakfast he would work on his
>own mathematical researches from 9 o'clock till 1 o'clock. Then, after
>a light lunch, he would walk down to the university cricket ground to
>watch a game. In the late afternoon he would walk slowly back to his
>rooms in College. There he took dinner, which he followed with a glass
>of wine. When cricket was not in season, it was the Australian cricket
>scores he would read in The Times and he would play real tennis in
>the afternoons.

>>10727986
CEASE

>>10730625
>Any one knows how much category theory and generating functions should I know before getting into combinatorial species?

I was thinking about this myself today. I just started reading Peter Doubilet, Gian-Carlo Rota, and Richard Stanley, "The idea of generating function" (MR403987), and have also been meaning to dip into pic related Lawvere and Rosebrugh (although it's about modeling the the ZFC and the category of sets axiomatically, it is for undergrads and builds up the category theory material from scratch.

>>10730750
>pure mathematician
As opposed to what?

>>10730220
Where are my french mathematicians at?

>>10730961
>As opposed to what?
Applied mathematician

>>10727710
george simmons differential equations

>>10730837
Kek, someone saved the pic I posted of that discrete math student's quiz I graded

>>10730912
Same with Dieudonné, he would work consistently 4 hours a day in the morning and that would be it. I think Kazhdan or Margulis (don’t remember which one) would only work something like an hour and a half a day

I wish Jacob Lurie was my heart, so he would be pumping inside me 24/7

>>10730912
They could have afforded it
We have to compensate intelligence with knowledge though

>>10729190
What is he even saying? ELI5?

What is so bad about research in Langlands program or L-functions? Should I go for motives and algebraic cycles instead? Pic not really related.

>>10730912
4 hours of hard, focused mathematical work each day is very good. the rest of the time you spend mulling over things in your head and thinking about what you're researching anyway, which is a lot of the work.

>>10727988
Is there a way to get that equation to not show up as plain text?

>>10731195
>eli5
it's time for you to go back to r/math
in any case he's saying that if you have a function which continuously varies over k-tuples of orthonormal vectors in R^n, then how would you get from it a function which continuously varies over orthonormal bases in R^n? like, so that k of the vectors are the ones from the original function.
you can think of it like "completing the bases in a nice way".
another way to think of it is that you have a continuous function f which is valued on n x k orthonormal matrices, and you want one which is continuous and is valued on n x n orthonormal matrices such that the first k columns are the same as those of f.

>>10731537
you did backslashes for your [/math] tags. i know, it's stupid since latex uses backslashes.

>>10727988
why does shit like this not show up in latex for me anymore, just plaintext

>>10731545
Jesus, alright thanks. Are you a PhD student?

>>10731573
lol no i'm going into 3rd year undergrad
all you need to do to understand that post is take a linear algebra class and maybe an analysis class

My shit CS uni left out Linear Algebra.
How do I learn it by myself online? Something easy for brainlets would be appreciated.

>>10731695
>>>/sci/sqt

>>10731716
?

> Hey guys I got a cool idea
> NOPE, ERDOS ALREADY DID IT

>>10731501
>What is so bad about research in Langlands program or L-functions?
It's a pretty eclectic field with a lot of overhead, not many job offering (though not much competition), and abstract enough that's it's pretty difficult to make any reasonable headway in a short amount of time, which could be bad for securing tenure unless you go to a school which properly appreciates the work.

If I study 8~12 hours everyday for 3 weeks will be sufficient to refresh algebra/precalc and learn calculus 1? What textbook should I use?

The exam cover log, functions with trig identities/ equations (it's a mix of early calculus with algebra II), and the only hardests questions is asking to derive a function of parabola, vector geometry, and some integral. It's pretty similar to IB Math HL.

How do I know if I need to be worried about differential geometry?

I was going along doing algebraic geometry and it is going pretty good, but you see diff geo mentioned a lot and I don't even know what I don't know about that field.

Any fans of Bredon here? I don't know much topology yet, but I'd love to work through this book someday.

>>10732382
This is a great book imo! You don't need to know much topology to work through it.

>>10731973
Try studying actual math then.

>>10732122
Some subfields like complex algebraic geometry rely on differential geometry. A lot of it also comes down to the fact that differential geometry gives a more concrete realization of certain concepts in algebraic geometry. Vector bundles, for example, are common in differential and algebraic geometry, tangent for differential, ample for algebraic. Another one shows up on the wiki page for sheaves
https://en.wikipedia.org/wiki/Sheaf_(mathematics)#Sheaves_on_manifolds
So while differential geometry may not be a strict prerequisite, there's a lot of conceptual overlap and it might be beneficial to understand the different realizations

>>10727782
>>10727710
Second for linear algebra. I didn't really pay attention in lin alg I and II and it almost killed me in statistics this term.

>>10728811
I fucking hate topology.

>Mochizuki's anabelian variation of ring structures and formal groups
>Kirti Joshi
>(Submitted on 17 Jun 2019)

>I show that there is a universal formal group (over a suitable (non-zero) ring) which is equipped with an action of the multiplicative monoid [math]\mathcal{O}^\triangleright[/math] of non-zero elements of the ring of integers of a p-adic field. Lubin-Tate formal groups also arise from this universal formal group. If two p-adic fields have isomorphic multiplicative monoids [math]\mathcal{O}^\triangleright[/math] then the additive structure of one arises from that of the other by means of this universal formal group law (in a suitable manner). In particular if two p-adic fields have isomorphic absolute Galois groups then it is well-known that the two respective monoids [math]\mathcal{O}^\triangleright[/math] are isomorphic and so this construction can be applied to such p-adic fields. In this sense this universal formal group law provides a single additive structure which binds together p-adic fields whose absolute Galois groups are isomorphic (this anabelian variation of ring structure is studied and used extensively by Shinichi Mochizuki). In particular one obtains a universal (additive) expression for any non-zero p-adic integer (in a given p-adic field) which is independent of the ring structure of the p-adic field (this is also inspired by Mochizuki's results).

>>10733201
https://arxiv.org/pdf/1906.06840.pdf

>>10730033
Consider what the Steenrod squares [math]Sq^1[/math], [math]Sq^2[/math] do to the generator [math]x[/math] of the mod 2 cohomology algebra of [math]S^n[/math] (trivial exercise).
>>10731153
God same. Wish he'd classify the bordism groups of my asshole while panting.

>>10728811
I'm going to take the exam in like, 2 hours.
It fun shit! Having to imagine shit in 4d is not that fun tho

>>10733207
Kill yourself.

>>10732114
>If I study 8~12 hours everyday for 3 weeks will be sufficient to refresh algebra/precalc and learn calculus 1?
Why don't you try it and find out?

>>10733535
>Kill yourself.
Are you ok?

How do I generalize this form?

>>10733629
let y be the infinite form of that expression. then
y = (y-1)/3 => y = - 1/2

>tfw you dont know tex commands and shit to make this pretty :(

>>10733637
>let y be the infinite form of that expression
That's not very rigorous of you.

>>10733629
Define the operator [math]Q(x)=(x-1)/3[/math]
Set [math]Q*(x)= lim ~ Q^n(x)[/math] as n goes to infinity.
My bad, I forgot the Tex for the infinity symbol.

>>10733916
>I actually have to use ^*
Bleh.

>>10733916
>n goes to infinity
Why would n "go" to infinity? Infinity is not a place.

>>10733207
What tf is a Steenrod algebra?

Why is everyone at my uni so unrigorous? They're constantly drawing pictures and vaguely talking/handwaving about intuition, but when I ask them to properly define their intuition, they either change the topic or just leave the conversation altogether. Should I just transfer somewhere else? What's a good place which won't suppress a sharp and inquisitive mind, but instead let it flourish? (I'm in the US).

any fellow mathfags here have some suggestions for a blockchain reference? I don't want any normie-tier shit, I'm primarily interested in the mathematics

>>10734111
>fellow mathfags
>blockchain
Nice try at fitting in, /g/-tard. Fuck off to your containment board.

>>10734112
I want to learn about the mathematics blockchain cryptography, suck my balls. Who the fuck cares about fitting in on an anonymous board? You're probably a fucking biologist, why don't you fuck off and go measure some squirrel dicks or whatever you faggots do

>>10734119
Read Mochizuki's IUT and you'll get a good grasp of the fundamentals of blockchain ;)

>>10734119
>You're probably a fucking biologist
>Who the fuck cares about fitting in on an anonymous board?
Obviously you do.

>>10734130
No faggot I just want a fucking resource should I go ask /biz/ or can you fucking brainlets handle it?

>>10734119
>mathematics blockchain cryptography
Any mathematician reading this will think that it's gibberish. Study how actual mathematicians talk before trying to desperately fit in on a thread on some third-rate Chinese cartoon forum.

>>10734132
>you brainlets
>"you"
Ah, so the truth is unveiled.

>>10734134
mathematics OF blockchain cryptography sorry for the typo, I hope I haven't offended you since you're obviously a galaxy-brain nigger who has never made a typo

>>10734136
just give me a fucking resource, I recently completed an intro to cryptography class and I want to learn about blockchain crypto shit because it's the only area of mathematics you can talk about at parties and still hope to get laid

>>10734119
Reminder that underage people who just learned about swear words aren't allowed to post here.

>>10734137
>mathematics OF blockchain cryptography
Any mathematician reading this will think that it's gibberish. Study how actual mathematicians talk before trying to desperately fit in on a thread on some third-rate Chinese cartoon forum.

>>10734111
>blockchain
Not math.
>>>/g/sqt
>>>/wsr/

>>10734149
Ok I'll go ask /biz/ you literal gamer word

>>10734142
>I
Mathematicians use "we".

>>10734150
cryptography is math, and I'm asking about a specific cryptographic application

>>10734152
I guess the solution to my problem is left as an exercise for the reader

>>10734157

you have no cock

>cryptography
Start by learning abstract algebra

>>10734142
>it's the only area of mathematics you can talk about at parties and still hope to get laid
Not true. We have parties where we talk about algebraic geometry with 2-dimensional females all the time.

>>10734163
I'm not that cryptofaggot but I'm self studying algebra this summer, I've taken proof based linear algebra and I'm using Aluffi Chapter 0. Should I complement it with another book?

>>10734157
We guess the solution to our problem is left as an exercise for the reader*

>>10734163
I know enough about cryptographic algorithms and groups and shit, I don't need to study all of abstract algebra. I am interested in a specific application of cryptography

>>10734171
Suck our balls

>>10734169
>proof based
>self studying
As opposed to what?
>Should I complement it with another book?
No, clearly one book is enough to cover all of "abstract" algebra.

>>10734174
>cryptographic algorithms
>groups and shit
>I don't need to study all of abstract algebra
>specific application of cryptography
Fuck off to >>>/g/ with this garbage. Do you need to be constantly reminded that subhumans like you aren't welcome in this thread?

>>10734177
Stop trying to playing it smart, I'm asking because the sections on Galois Theory seem rather small compared to other books and also speaks nothing about Representation Theory you dumb fuck

>>10734181
>the sections on Galois Theory seem rather small compared to other books
>speaks nothing about Representation Theory
You're the one trying to play smart here by pretending to ask questions you don't already know the answers to.
>you dumb fuck
Rude.

>>10734168
>algebraic geometry
>>10734181
Galois theory isn't exactly the most extensive subject, but I've seen Morandi recommended a lot.
You might want to also go through Serre's Course in Arithmetic.

>>10734180
Yeah, I don't give a fuck about 90% of abstract algebra shit and I don't fucking care. My focus is statistics, mainly. I swear to God /sci/ is the gayest board on all of 4chan. I'll go ask /g/ or /biz/ since you brainlets are obviously stalling because you don't have a link to a reference.

@10734190
>I don't give a fuck about 90% of abstract algebra shit and I don't fucking care
>statistics
Fuck off to >>>/g/ already, you retarded animal.

>>10734192
ok have fun with your little cohomology groups virgin

>>10734190
>you don't have a link to a reference.
See [math](1)[/math] where Mochizuki-sensei explains the application of Alien copies to chain complexes (a more general/complex version of a blockchain).

[math](1)[/math] http://www.kurims.kyoto-u.ac.jp/~motizuki/Alien%20Copies,%20Gaussians,%20and%20Inter-universal%20Teichmuller%20Theory.pdf

Would Grothendieck still do Math if he was born in the 21st century?

>>10734204
yeah I'm aware of the IUT meme but thanks anyway

>>10734209
>I'm aware of the IUT meme
Clearly not, as you haven't even read that paper yet.
>thanks anyway
What's the deal? Are you too feeble-minded to actually understand the topic you're asking a reference for? Fuck off to >>>/lit/ or >>>/g/ with this pseudo-intellectualism.

>>10734206
He'd probably contract a retarded form of autism from one of the retards in the 21st century, I don't know how exactly this would affect his ability/desire to do math though.

>>10734211
lol shut up nerd

Here is something I discovered through a randomized program I wrote. At first, I saved the picture but forgot the algorithm and it took me a long time to figure out how to generate it again.

This picture is what you get when you plot [math]Wt(\vec{x}\ XOR\ \vec{y})[/math]

where "[math]Wt[/math]" is the hamming weight and the pixels are colored based on the PARITY of the result.

I have seen plots like these before in the literature. You can see that it really only depends on the parity of [math]Wt(3*\vec{x})[/math], which is a single variable boolean function. I suspect that plotting [math]f(\vec{x^y})[/math] where f is an arbitrary boolean function always generates a pretty picture, so it isn't that special

>>10734217
So much this. I am feeling so based right now... Kek!

>>10734218

I fucked up every latex in this post but IDGAF

>>10734218
>randomized program I wrote
>algorithm
Cool. Blog about it on >>>/g/.

daily reminder that none of you nerd virgins will ever be full professors. You'll toil endlessly as temporary hire instructors making less $ than a burger king manager. Have fun teaching pre-calc to undergrads for the rest of your lives.

>>10734218
>I have seen plots like these before in the literature.
What "literature"? Why have we, as a mathematician, never seen this "literature" before? Could it be, perhaps, that your shitpost has literally nothing to do with the subject of this thread?

>>10734237

In a paper about bent boolean functions

> Why have we, as a mathematician, never seen this "literature" before?

Because you're hacks and don't actually read mathematical papers? You tell me chieftain.

>>10734245
Didn't even read your post. I can already tell just by the formatting that it was written by a non-mathematician.

>>10734236
This story seems awfully detailed... I'm sure even you can make it, anon. Don't lose the magic in your heart.

>>10734251

Seething weeb go fuck your mother

>>10734134
>>10734152
>>10734237
>>10734251
Do you have a preferred name or can I call you writingfag?

>>10734281
>writingfag
Who?

>>10734267
Please vent your Oedipus complex pseudo-intellectual pseudo-philosophy at >>>/lit/. We discuss mathematics here, as you can notice by looking at the "subject" field of this thread.

>>10734261
I'm not gonna make it. You're not gonna make it. None of us are gonna make it. You will never be a professor. You will never hold hands with a girl.

>>10734313
>You will never hold hands with a girl.
Wrong. Even you can achieve that if you make the effort to properly understand and channel your autism.

>>10734454
t. someone who has never held hands with a girl

>>10734587
If that makes you feel better. Just know that even for an autist like you there's some hope.

>>10727710
Calc 3.

>>10734236
le epic blackpill

>>10734206
He didn't do math in the 20th century

>>10734086
It's the graded algebra over [math]\mathbb{Z}_2[/math] of stable cohomotopy operations.

>>10735717
The superalgebra of stable cohomotopy operations?

>>10735736
>superalgebra
No. It's graded over [math]\mathbb{Z}_2[/math], not graded by [math]\mathbb{Z}_2[/math].

>>10735745
>graded over, not by
I was joking earlier, but is that actually standard notation?

>>10735748
Huh?

>>10727663
I'm trying to compute the homology of [math]K=K(G,1)[/math] using the path space fibration [math]\Omega K \rightarrow PK \rightarrow K[/math] and the Serre spectral sequence.

[math]\Omega K=K(G,0)[/math] is just a discrete set of [math]\# G[/math] points, so its only nontrivial homology group is [math]H_0(\Omega K)=\bigoplus_{\# G} \mathbb{Z}[/math]. So everything on the [math]E^2[/math] page is zero outside the [math]q=0[/math] row. I can get at least the first two groups there using Universal Coefficients and the Hurewicz map.

Now each diagonal [math]t=p+q[/math] on the [math]E^\infty[/math] page is supposed to give a filtration of the group [math]H_t(PK)[/math] whose homology I know since [math]PK[/math] is contractible. The problem is, the way the [math]E^2[/math] page is set up (pic related), there is no way for the groups in the [math]q=0[/math] row to vanish. This implies [math]\bigoplus_{\#G} \Z \cong \Z[/math] for instance, so something must have gone wrong here. Any thoughts/suggestions?

How do i stop fucking up basic arithmetic

>>10735879
id also like to know

>>10735805
is this image cursed

>>10735879
Just stop doing basic arithmetic in the first place.

>>10730837
>>10731102
>>10731102
Holy fuck, did some sperg really write that down on a quiz?

>>10735954
No, that's what we call a "Yukari".

>>10736147
Yeah, dude got zeros on every single quiz for either writing complete nonsense or nothing at all, and didn't turn in a single homework assignment. I think he was a computer information systems major.

>>10733930
You can't be fucking serious.
Get the fuck out of here nigger.

>>10735879
practice
a lot of practice, that's basically it

>>10733207
trannies should be banned from math.

>>10736193
>trannies
Why the transphobia?

>>10736193
>trannies
Where? I only see a faggot wanting to be fucked real hard in that post.

>>10727663
i am hazy on this notation. Am I supposed to interpret it as

[ U(AeF) U B ] - [ U(AeF) U A ]?

or

[ U(AeF) ] U [ B-A ] ?

>>10736218
>i am hazy on this notation
Why do people do this? You could just honestly ask what that notation means. There's no need to pretend that you're "hazy".

Is there an efficient way to draw or generate the adjacency matrix of the Cayley graph of a finite simple group?

>>10736167
Why the niggerophobia?

>>10736223
I forgot to say it but I know the set of generators

>>10736220
okay. What does this notation mean? As far as I know U(AeF) is the set x such that x is an element of A for some A in F. Or {x|x e A for some AeF} right? What I don’t understand is how to interpret that in this notation where it’s juxtapositioned next to B - A

>>10736232
>>10736220
sorry again.
>As far as I know
I meant “As far as we know”
and
>What I don’t understand
I meant “What we don’t understand”.
Please help

>>10736232
Intuitively speaking, the bottom notation [math]A \in \mathscr{F}[/math] is what you intuitively "run through" to get each set [math]B - A[/math] in the union [math]\bigcup_{A \in \mathscr{F}} (B - A)[/math] over all elements of [math]\mathscr{F}[/math].

>>10736223
>efficient way
Sorry, not a programming thread.
>draw
Sorry, not a drawing thread.
>adjacency matrix
Sorry, not a statistics/engineering thread.

>>10736264
I'm so sorry that you can't get into interdisciplinary work :((( not everyone can be a researcher

>>10736325
>interdisciplinary work
Sorry, this isn't an interdisciplinary thread.

>>10736328
got me

>>10736325
>I'm so sorry that you can't get into interdisciplinary work
Seems like a cheap attempt at giving your shitty field more "legitimacy" by associating it with math, when it in fact has literally nothing in common with math. That's a usual tactic employed by the less secure and less intelligent /g/-tards. You can now proceed to fuck off to >>>/g/.

>>10736332
>"τbh fαm"
Sorry, this isn't a facebook thread.

>>10736214
>wants to fuck dudes
>anime avatarfagging

the diagnosis is autogynephile tranny, infa 99%

>>10736335
Yeah I guess trying to improve bounds on the diameter of the Cayley graphs of dihedral groups using representation theory isn't related to math, my bad won't happen again

>>10736340
>>wants to fuck dudes
be fucked by a dude*
>>anime avatarfagging
Touhou avatarfagging*
>diagnosis
>autogynephile tranny
Refer to the nearest medical thread.

>>10736346
>isn't related to math
At least you have enough sense to understand this. Too bad you didn't realize that before shitting up this thread with your programmer vomit.

>>10736347
>be fucked by a dude
A cool one at that.

>>10736347
>hey I'm autistic!

autism spectrum disorders correlate non trivially to transexualism

>>10736357
I'm still not sure whether I would like him to breed me or if I would like to see him moan like a little bitch

>>10736358
>>hey I'm autistic!
Who are you quoting?
>correlate
We say "map" around here.
>transexualism
Refer to the nearest philosophy/medical thread.

>>10736357
no, like most category theorists he is on the autism spectrum (watch any of his interviews) and publishes only the sort of dispensable erudition which will be forgotten inside of a generation. Good only for churning out piles of meaningless results only cited by other autists.

Underrated math trans king

>>10736370
>dispensable erudition
Pseudo-intellectual /lit/tard detected.

>>10736370
Holy fucking shit, Lurie is doing some of the most interesting work in higher category theory and derived algebraic geoemtry rn, his work on function fields is pretty dope too

>>10736370
>which will be forgotten inside of a generation
At least his work will last for a generation (actually more, but a subhuman such as yourself couldn't possibly see this), unlike the meaningless pseudointellectual garbage you wrote up right now, which will only last for a single 4channel thread.

>>10736377
its literally from an einstein quote, brainlet.

>>10733168
>>10733172
>>10732122
>>10731695
>>10731195
brainlet

>>10736370
What did you just say, sissy-boy?

>>10736156
You should have written on his last quiz just how much of a brainlet faggot he is and told him to drop out.
What a waste. His rest energy could have been better spent powering a nuclear factory than being in such a shitty bound state.

>>10736381
Imagine being this devastated

>>10736382
I could tell, it sounded just like what some low-brain-power physishit would say.

>>10736382
>quoting that dumbass

>>10736392
>muh Tesla hurr durr

>>10736389
I smoke weed too, my Based Kekerino. It just gives you such an epic feeling like you're being based and redpilled and epically breaking all the societal rules, doesn't it?...

>>10736386
>he *doesn't* have a fields medal because all his work is in useless tripe meaningful only to other purveyors of effete abstractions

>effete abstractions
> useless tripe
>purveyors
>>>/lit/ pseudointellectualism is that way.

>>10736396
Hmm just because Lurie isn't part of your fucking ponzi scheme plotted by jews doesn't mean that his work isn't relevant, besides that you wouldn't understand it

>>10736396
I too am investigating the ontological nature of the meaning of black holes right now. I find it to be such a fascinating and deep topic, aptly suited for my keen and sharp mind.

>>10736402
Those farts must smell real nice.

>>10736399
lurie is literally a jewish name
>not knowing this
good goy

>>10736407
I'd let Lurie fart in my face and shit on my chest any day of the week

>>10736397
>>10736402
>getting triggered by some words used correctly

guys, it's ok if english isn't your first language.

anons, what do you do when you forget part of a formula when taking an exam?

>>10736408
Luriestein

>>10736407
I am not like those individuals you mention. I am really intelligent and I am being really intelligent right now in my investigations. I am trying to peer in into the true depths of the cosmos, while you study useless tripe conjured up by the purveyors of abstract nonsense like "higher category theory and derived algebraic geoemtry and "function fields"". Pfft, I laugh at you... I truly do...

>>10736420
>projecting this hard

>>10736413
dont Memorize the formula... iF your going to memorie it also learn how to rederive it... in case you forget it you can work it out during the exam tough... you might lose a lot of valuable time...

>>10736420
true depths of the cosmos

>>10736425
No, truly, as in having the ontological and philosophical property of being true. I am truly an intellectual individual and I am deep into my studies regarding the true nature of black holes and the empirical ontological truth they surely hold beyond their event horizons, or "beyond their depths", to put it in simpler terms you might understand.

>>10736433
No need to make such a big deal about black holes.
Black holes are the way they are because God made them that way.
So easy and simple, no need for all this heavy thinking.

>>10736433
wow event horizonSSSS!!!!1 hehe thanks for explaining it in simpler terms i almost got lost hehe sorry for not being a smart individual like you hehe

>>10736436
Pfft... How pathetic you are being right now by appealing to completely ficticious and trite fallacies like construction by this "God". I am an intellectual being and clear thinker, thus I will search for the real truth myself, I do not need this "God" of yours to help me in my pursuits of the truth. After all, I am not a mere purveyor of mere dispensable erudition which will be forgotten and lost to the deep abyss of a black hole (figuratively) inside what is not even a single generation, as some of my detractors might have you believe.

>>10736253
okay so help a brainlet out here. If Im considering all the sets in F either way, what is the difference between these two? are these two sets equal, since its (B-A)?

>>10736468
just unpack it, say that F contains two elements, [math]A_{1}[/math] and [math]A_{2}[/math] then [eqn]\bigcap_{A\in F} (B-A) = (B-A_{1})\cap (B-A_{2})[/eqn]
and so on

>>10736468
The first one intuitively has [math]all[/math] those [math]x \in B[/math] which are [math]not[/math] in [math]any[/math] of the various [math]A \in \mathscr{F}[/math]. Now consider the intuitions behind the second set being a union and you'll see the difference.

>>10736493

Is there a place on the internet where recent progress on grothendieck standard conjectures is being tracked? I've found a math overflow question, but it has no updates since 2015.

>>10736703
My house. You have to be cute to come over though.

>>10736703
nlab maybe?

>>10736468
come on dude, you're just throwing shit at the wall and seeing what sticks.
recall the definition of set minus. [math] B - A = B \cap A^c [/math] where the c means complement.
Then what is [math] \bigcup_{A \in F} (B - A) = \bigcup_{A \in F} (B \cap A^c) [/math] ? (Try DeMorgan's Laws.)

>been away for a few days
>suddenly /mg/ is filled with coping physishits and autistic categorytards
wtf??

>>10736787
>been away for a few days
I'd prefer it if you kept it that way. Can't stand subhuman vermin.

>>10736370
>he is on the autism spectrum (watch any of his interviews)
So? How does that prevent him from being "cool"? Seems like you're on the autism spectrum too, except on the low-functioning side.

>>10736789
what, you've missed me "spilling the tea" that algebraists are fucking morons and not real mathematicians, and that analysis is the only true type of math?
you missed that, didn't you? you fucking alg geo shitter.
>>10736796
the thing that prevents him from being "cool" is his inhuman obsession with abstract garbage which literally no one with a modicum of respect in the mathematical community gives any respect or credit.

>>10736878
>real
>true
>type
Refer to >>>/lit/.

>>10736878
I am your rightful ruler.

>>10736884
apparently i'm not the biggest "schizo" in /mg/ anymore. thanks for taking the attention off me and making these other troglodytes recognize that "hey, that guy's not crazy at all, this is what a REAL crazy person looks like". they're pointing at YOU, YOU FUCKING PSYCHOPATH!!!

>>10736896
>i'm
>that guy
Who?

>>10736907
>Who?
Who are you quoting?

>>10736913
Essentially, yes.

>>10736907
The local village clown who fancies himself as a "schizo" for some reason.

>>10736940
i'm not a schizo, nor do i fancy myself as one. i'm a mathematician, and you're not. it's that simple.

any of you nerds make full professor yet? didn't think so

>>10736992
>I
mathematicians use “We”

>>10736992
>i'm
Whom?

>>10736725
Nope

>>10736703
I am not cute unfortunately, but I can print touhou pictures and glue them to my face

>>10734313
lol chill bitch its supposed to be fun if youre gonna shit around bout not having money and bitches then go fuckin full chad mode do whatever u wanna do and dont give up ffs

>>10737016
where did we say we were a mathematician?

Are p-adic and [math]\ell[/math] -adic the same?

>>10737220
you'll never be a professor. At best you'll be a part-time instructor or go code-monkey for the NSA

>>10736193
this

>>10737296
The point of [math] \ell [/math]-adic is that it isn't p.

Guys, I'm messing around with greedy algorithms here but I'm bad at combinatorics so I need your help. I need to know if the local optimal choice my program makes is actually the global optimal choice. What's the mathematical model I should use for that? It's the continuous knapsack problem, if that helps.

new thread >>10737655