/mg/ maths general: literal hack edition

[Anonymous No.9657809]

talk maths

prev >>9647362

[Anonymous No.9657824]

redpill me on differential equations

[Anonymous No.9657866]

>>9657824
ordinary or partial?

[Anonymous No.9657871]

>>9657809
Where to start? Number Theory? Graph Theory?

[Anonymous No.9657876]

>>9657866
partial

[Anonymous No.9657886]

>>9657871
>Where to start?
Where to start what?

[Anonymous No.9658409]

>>9657809
>my adviser's life work is applying basic graph theory to some obscure chemistry problem no one cares about
What the fuck? Is this what happens when you get a math PhD?

[Anonymous No.9658501]

please do not disparage mac lane sama

[Anonymous No.9658616]

will be here for awhile, willing to help someone understand / solve something relating to calculus. Not an expert but I want an excuse to read my textbook.

[Anonymous No.9658684]

>>9658409
For you, maybe. Why did you choose him as your advisor? Plan ahead, maybe?

[Anonymous No.9658689]

>>9658409
Depends on the field, but as a general rule, you shouldn't expect most people (or even most mathematicians) to care about what you do

[Anonymous No.9658852]

>>9658409
>graph theory
>math
What did she mean by this?

[Anonymous No.9658976]

>>9658852
> Something too concrete to understand

[Anonymous No.9659037]

>>9658976
That unironically looks a bit like Mochizuki's latex art.

[Anonymous No.9659060]

>>9658409
>graph theory
You mean topology?

[Anonymous No.9659529]

How do you guys respond to the doom and gloom of the current state of academia?

I was reading this thread, https://news.ycombinator.com/item?id=16725368#16727307, and it's got me down a bit. I study math in my free time, I like doing math. So doing it professionally in grad school seems great, but if it's as bad as some say (terrible living conditions due to being overworked, underplayed, commuting, no family time, etc) I simply would no longer be interested in doing it professionally. Is academia just as bad for math as it is any other field?

[Anonymous No.9659979]

>>9659529
We've had people say similar things in /mg/. This shit scares me.

[Anonymous No.9659981]

>>9659037
And sounds like ass. Some parts in it are literally impossible to play.

[Anonymous No.9660173]

>>9659529
The strong does what he wants while the weak suffers what he must.

[Anonymous No.9660318]

>>9660173
largely irrelevant, the strong in this case is the institution

[Anonymous No.9660488]

>>9659529
>https://news.ycombinator.com
Try making a thread at >>>/g/.

[Anonymous No.9660664]

>>9660488
god SHUT UP about redirecting everything to /g/, why the fuck would I post a thread about the current of academia over there instead of here?

you're probably just mad that CS fags are cucking you out of employment

[Anonymous No.9660672]

>>9660664
I'm sorry to inform you that C"S" garbage isn't everything. You're posting a website called "Hacker News" on a board about science and math in a thread about math. But "hacking" is clearly neither of those things. So I'm just telling you to discuss hacking at >>>/g/ where it is appropriate to do so.

[Anonymous No.9660700]

>>9660664
Just ignore him, anon. He's the same fag that calls everyone an engineer and says that mathematics is not well defined

[Anonymous No.9660701]

>>9660700
>Just ignore him, anon. He's the same fag that calls everyone an engineer and says that mathematics is not well defined
I'm not a "he".

[Anonymous No.9660749]

>>9660700
>He's the same fag that calls everyone an engineer and says that mathematics is not well defined
Wrong. The guy who says that is a subhuman engineer himself.

[Anonymous No.9660899]

>>9660672
>implying a websites content is limited by it's name
>implying that thread and the comments within aren't on topic
>implying cryptography and other select elements of hacking aren't mathematical
Many of the commenters in said thread had supposedly even attended grad school for maths themselves.Further, once again, the thread would've been useless at /g/, since they are a consumerism board, not a board to discuss academia, you dunce.

>>9660700
sorry to disappoint you, anon

[Anonymous No.9661003]

how you structure your study time? do you divide into modules like review, exercises, read/watch/digest new material (and explore tangents, etc), try to solve problems, etc? I'm interested in how professionals would coach and structure a math study routine, might they do it similar to how a pianist trains by splitting the study time into modules?

Personally, I usually just open up the text and try to get through it, with occasional reviewing, but I'm trying to find a system I like to put into place, and think the modules I outlined above should work great.

[Anonymous No.9661107]

a few questions regarding the macro state of math:

every year, the lowest hanging fruit are picked. where is mathematics right now? has it been in somewhat of a plateau since the 1800-1930s?

what is the front line of modern research looking at? what are some good resources for someone who can't understand cutting edge mathematics in the fine technical detail, but is interested in the "ELI5", "for dummies", etc boiled down synopsis of it and what the results imply, the context, etc?

why does discrete math exist? why arne't the topics covered like traditional math texts (as in, study graph theory, study combinatorics, study etc etc rather than a lump sum)? I assume discrete math = math that's applicable to CS, but why is this distinction so blurry? why isn't math for CS like math for mathematicians?

and lastly, do you keep up with developments in math pedagogy and utilize the fruits of this field?

[Anonymous No.9661155]

>>661107
look up the works of the most recent fields medalists to find out

I'm not aware of any source which translates it ELI5 except the articles that come out right after such people won it

[Anonymous No.9661163]

>>9661155
>a few questions regarding the macro state of math:
>every year, the lowest hanging fruit are picked. where is mathematics right now? has it been in somewhat of a plateau since the 1800-1930s?
>what is the front line of modern research looking at? what are some good resources for someone who can't understand cutting edge mathematics in the fine technical detail, but is interested in the "ELI5", "for dummies", etc boiled down synopsis of it and what the results imply, the context, etc?
>why does discrete math exist? why arne't the topics covered like traditional math texts (as in, study graph theory, study combinatorics, study etc etc rather than a lump sum)? I assume discrete math = math that's applicable to CS, but why is this distinction so blurry? why isn't math for CS like math for mathematicians?
>and lastly, do you keep up with developments in math pedagogy and utilize the fruits of this field?
Since the cringy post got deleted.

[Anonymous No.9661181]

>>9661163
>why isn't math for CS like math for mathematicians

Same reason why math for business majors isn't like math for mathematicians

[Anonymous No.9661190]

>>9661155
>follow field medalist
Ok, thanks. The lack of an ELI5 is probably a good thing anyway, but I don't have a lot of breadth as it is (only intro analysis and algebra, so it's probably foreign unless in an analogous fashion).

Why was it cringe?

[Anonymous No.9661192]

>>9661181
I was going to ask for a more serious explanation, but CS has really turned into a four year "programming bootcamp" degree hasn't it? I'm just consistently off put by how many relentlessly shit on all forms of CS, since from what it seems it's an active and fruitful field for a (relatively) pure mathematician - and before CS, a number theorist, statistician, combinatorist (or so) was not nearly as 'in demand'.

[Anonymous No.9661300]

>>9657809
I'm self studied in mathematics, but only have a formal education in engineering.

I'm applying to applied math programmes. Most of them are attached to engineering institutes or some other computational department, but some of the more interesting projects are attached to mathematics departments. I was wondering what real mathematicians consider proof of proficiency in math fields. Currently my only tangible proof is publications (in applied- not pure math journals) which apply results from pure math fields I studied (in some cases extending ("relatively") popular theorems to more general spaces).

Will professors be offended if I claim to have a background in these fields (most of which are postgraduate level)? I feel that if I make no mention of it they will think my background is insufficient unless they read my publications and letters of recommendation in detail.

[Anonymous No.9661303]

>>9659979
Listen. At the end of the day regardless of the statistics there are many people who still make it. Whether it's getting the all coveted faculty position or a high paying job with interesting projects, there are at least 1 in 5 graduates who get it. And regardless of your current position you can be one of those 5.

If you get caught in the trap you'll be stuck in a depression void instead of focusing on giving your best to make it.

The only solution is to ignore all the depression posting and keep working and be optimistic. Lie to yourself if you have to.

[Anonymous No.9661369]

>>9661303
Giving your best doesn't matter if you don't have the brain power. Effort cannot make up for being a brainlet.

[Anonymous No.9661441]

>>9661369
Right, but most of us in these stories aren't brainlets.

There are countless people who graduated top of their class, went to top grad-schools and still can't find a good job afterwards or get stuck in eternal postdocs.

[Anonymous No.9661468]

>>9661369
Sure it can, you get to btfo all the smart-but-lazy faggots who don't realize that half of intelligence is being intelligent enough to fucking apply yourself.
>I'm really smart but doing bad at x
Yeah well if you were so smart you'd be smart enough to find a way to stop being bad.

[Anonymous No.9661553]

>>9661468
You come across as pretty stupid. Dyslexic?

[Anonymous No.9661581]

>>9661468
Yeah look, we're talking about people who were top of their class and at least smart enough to get into gradschool.

Those are the people that are struggling. The ones who were fucked to begin with got some low to mid tier job and planned their lives around it.

[Anonymous No.9661656]

How would I show iii) here? x is obviously a set and I'm not allowed to use Choice

[Anonymous No.9661683]

>>9661656
Explain your notation please.

[Anonymous No.9661702]

>>9661683
Px is the set given by the axiom of power set and Ux the set given by the axiom of union. I wasn't aware that the notation was a bit nonstandard

[Anonymous No.9661733]

>>9661656

Axiom of regularity.

[Anonymous No.9661757]

>>9657871
Set theory

[Anonymous No.9661793]

>>9661656
Choice is actually provable assuming ii) holds.

[Anonymous No.9661824]

>>9661003
2 hours of work followed by 30-60 mins of relaxation. I got the idea from reading Poincaré's wikipage. He believed that his subconscious would solve the problems for him while he did other things. I specifically avoid hobbies doing those breaks, since my subconscious might work on those rather than on the maths I want it working on.

If I want to summarize what I've learned I just pick or think of two or three hard problems or results and use the solution as a summary, keeping in mind that the audience of my proof is me in the past who didn't know anything about the topic and me from the future who has forgotten all about it.

[Anonymous No.9661912]

>>9661793

It is not. C is independent of ZF.

[Anonymous No.9661925]

>>9661656
If the powerset of x was an element of x, then you would get [math]x\in \mathcal{P}x \in x[/math]. It is elementary to show that [math]a \in b\in a[/math] can't occur with any sets.

[Anonymous No.9661934]

>>9661925
It's elementary with the axiom of foundation.

[Anonymous No.9661935]

>>9661925
Gah, that was a total brainfart! What you would get is that [math]\mathcal{P}x \subset x[/math], so [math]|\mathcal{P}x| = 2^{|x|} \le |x| < 2^{|x|}[/math], unless you have the axiom of regularity as a tool from which it follows immediately.

[Anonymous No.9661979]

>>9659529
trample the weak, hurdle the dead

[Anonymous No.9662079]

>>9661935

You have to have the axiom of regularity, or you can't meaningfully define cardinality of sets.

[Anonymous No.9662099]

why do you like math

[Anonymous No.9662113]

Anyone able to help with this? I want the contours to show inside the region plot.

The only output I'm getting is:
"no interpretation available"

Goes for pic included AND the sample given by mathematica.

[Anonymous No.9662140]

>>9662079
It is not certain whether that anon is doing things properly or just doing some naïve introductory thing. Thus, it is possible that cardinalities are included in his toolbox but axioms are not.

[Anonymous No.9662157]

>>9662099
God wills it.

[Anonymous No.9662366]

>>9661303
being ignorant isn't a good solution

[Anonymous No.9662676]

>>9661824
>I specifically avoid hobbies doing those breaks

What do you suggest doing then?

[Anonymous No.9663027]

>>9661824
I do something similar. I work until a natural stopping point (anywhere from roughly 30 minutes to 2 hours, roughly). My break then last about 10% of the time spent studying. But I intentionally use the break 'productively', if you will, to get my conscious mind off it. Usually I do some calisthenics, practice guitar or read some poetry, those more passive hobbies, so at the end of the day I still had a sufficient practice session/workout/etc in. In the back of my mind the concept still rolls around, and I come back with a fresh perspective. Often a problem will begin forming a breadcrumb trail in my mind that leads me to the solution once I return.

But at any rate, I was more looking for how people divvy up their spent studying. As in, on a daily basis, do you allow x amount/percent of time for review (give take some error margin), y amount of time for new material, z amount of time for exercises/problem solving, etc etc..? I try to review in the AM and PM, before anything and after everything else, respectively. Other than that I just kinda go through the text in a chronological order, reading supporting texts via Wikipedia or watching lectures via YouTube as necessary, but it feels very unstructured to meander around as such, so I think I'm going to implement a more modulized approach.

[Anonymous No.9663039]

can someone give me a swift rundown on tensor algebra?

[Anonymous No.9663045]

>>9663039
Tensors are not the same as tensor fields which are not the same as tensor fields on manifolds if you are a confused physicists. If you are a math fag, it's just multilinear algebra.

[Anonymous No.9663054]

>>9663039
Let [math]M[/math] be a module over a unitary ring [math]R[/math]. Define [math]T^n (M) = \{ m_1 \otimes m_2 \otimes \cdots \otimes m_n\ |\ m_1, \dots, m_n \in M\} [/math]. Then you want to have that [math]T^m (M) \otimes T^n (M) \cong T^{m+n} (M)[/math], and define [math]T(M) = \sum\limits_{n=0}^\infty T^n (M)[/math].

[Anonymous No.9663073]

>>9663045
>it's just multilinear algebra
alri', cool.
>>9663054
thanks.

[Anonymous No.9663087]

brainlet here, any takers on this >>9663035

[Anonymous No.9663179]

>>9663087
>doesnt post the theorem
>doesnt explain the notation
cmon bruh

[Anonymous No.9663181]

>>9663179
>>9663087
although just looking at it its relatively trivial what you want

left as exercise

[Anonymous No.9663191]

>>9663179
it's common notion in linear algebra and projective geometry, "bruh"

[Anonymous No.9663192]

>>9663087
fine ill bite

clearly the span of B'C is is the line spanned by the vector (0,1-c,1). It is a easy exercise that any two lines in the projective plane must intersect at a unique point. Now note the second equality of BC'.

[Anonymous No.9663273]

https://arxiv.org/pdf/1804.03275.pdf
>Developments in Topological Gravity
>Robbert Dijkgraaf, Edward Witten
>This note aims to provide an entrée to two developments in two-dimensional topological gravity – that is, intersection theory on the moduli space of Riemann surfaces – that have not yet become well-known among physicists. A little over a decade ago, Mirzakhani discovered [1,2] an elegant new proof of the formulas that result from the relationship between topological gravity and matrix models of two-dimensional gravity. Here we will give a very partial introduction to that work, which hopefully will also serve as a modest tribute to the memory of a brilliant mathematical pioneer. More recently, Pandharipande, Solomon, and Tessler [3] (with further developments in [4–6]) generalized intersection theory on moduli space to the case of Riemann surfaces with boundary, leading to generalizations of the familiar KdV and Virasoro formulas. Though the existence of such a generalization appears natural from the matrix model viewpoint – it corresponds to adding vector degrees of freedom to the matrix model – constructing this generalization is not straightforward. We will give some idea of the unexpected way that the difficulties were resolved.

[Anonymous No.9663283]

>>9663273
me on the right

[Anonymous No.9663297]

>>9663273
Not math.

[Anonymous No.9663301]

>>9663297
define "math"

[Anonymous No.9663305]

>>9663301
No

[Anonymous No.9663310]

>>9663301
I would define math as [You need a 4chan Gold Account ™ to view the contents of this post. Please put your credit card information in the name field to process your order].

[Anonymous No.9663340]

>>9663305
How do you know that it's not math?

[Anonymous No.9663346]

>>9663340
Mind your own business

[Anonymous No.9663374]

can analysis be developed on anything other than the field of real numbers?

[Anonymous No.9663378]

>>9663374
p-adic analysis
complex analysis

[Anonymous No.9663386]

>>9663378
fug

[Anonymous No.9663402]

Anyone understand divisors on Riemann Surfaces? They look like formal linear combinations; some people say they're a generalisation of the integers since the divisors with the equivalence class given by difference is the principal divisor of a meromorphic function. On the riemann sphere there's an isomorphism to the integers.

Basically I have no idea what these divisors are, nor how to think about them. Help would be appreciated

[Anonymous No.9663422]

>>9663378
wait, how do you define a limit in complex analysis? I haven't taken it yet, but I've been told there is no meaninful order of [math]\mathbb{C}[/math], so how can this work?

[Anonymous No.9663439]

>>9663422
limit from all directions, similar to how you would in R^3

[Anonymous No.9663516]

>>9657809
https://xavierleroy.org/stuff/categories.html

[Anonymous No.9663525]

>>9663516
Not math.

[Anonymous No.9663542]

>>9663422
Use your imagination moron.

[Anonymous No.9663599]

>>9662099
It's the best.

[Anonymous No.9663660]

>he doesn't study 12 hours a day 7 days a week
it's like he doesn't even want to git gud

[Anonymous No.9663922]

>>9663273
>>>/sci/pg

[Anonymous No.9663927]

>>9663525
Kindly fuck off chink. It's math related, unlike your physics shit. Fucking leaf.

[Anonymous No.9663938]

>>9663927
>chink
Why the racism?

[Anonymous No.9664114]

>>9663422
>meaninful
What do you mean by "meaningful order"?

[Anonymous No.9664116]

How does one show that the collection of free groups forms a dark set?

[Anonymous No.9664136]

>>9663422
The same way you define a limit in any topological space.

[Anonymous No.9664138]

>>9664116
The fuck is a dark set?

[Anonymous No.9664139]

is mac lane a hack ?

[Anonymous No.9664189]

>>9662676
For example housework, walking/strolling, cooking/eating, physical exercises, reading, listening or playing music, and just things in general that don't require too much cognitive ability. Try to find some activities that reduce stress for you. You can have time in the day for your hobbies and distractions (4chan, movies, or whatever), but not during those breaks.

>>9663027
>mount/percent of time for review
0
>amount of time for new material
30% or lower
>amount of time for exercises/problem solving
70% or higher

[Anonymous No.9664193]

>>9664189
actually I spend a lot of time reviewing nearing the end of a course (or important chapter), which is to say I make summaries

[Anonymous No.9664500]

>>9664139
>is mac lane a hack ?
Very.

[Anonymous No.9664598]

>>9664138
A collection which is too big to be a set but too small to be a proper class. So in some sense it's "dark" or "off the radar".

[Anonymous No.9664639]

>>9664189
>strolling
>physical exercises
>reading
>playing music
>cooking
>eating (if you're fat)
How are these not hobbies

[Anonymous No.9664644]

>>9664639
More importantly, how is there no "(if you're fat)" after cooking?

[Anonymous No.9664650]

>>9664644
maybe you cook healthy stuff and/or just do it for the sake of cooking rather than eating

[Anonymous No.9664661]

>>9664650
Anything food related is fatness except not eating.

[Anonymous No.9664671]

>>9664639
Eating and cooking aren't my hobbies. Strolling isn't really a hobby but more related to the listening to music idea. The rest I agree are pretty much hobbies yeah.

[Anonymous No.9664673]

>>9664661
Anorexic anon detected

[Anonymous No.9664690]

is the annihilator on a vector subspace analogous to the kernel?

[Anonymous No.9664701]

>>9664598
So in other words, it doesn't exist.

[Anonymous No.9664707]

>>9664690
That gorilla is very brave. If I could not see through the water I would be afraid that some fish or some snake is going to bite my dick.

[Anonymous No.9664712]

>>9664707
you must be brave for replying to me without an answer

[Anonymous No.9664749]

Aubrey de Grey is smart!
https://plus.google.com/+TerenceTao27/posts/QBxTFAsDeBp

[Anonymous No.9664750]

is a tensor really a "3d" matrix like the normies tell me?

[Anonymous No.9664751]

>>9664750
No.

[Anonymous No.9664754]

>>9663402
You can think of a divisor D as a bunch of points with multiplicities attached. They are a handy way to formulate and manipulate conditions on orders of vanishing of functions (or sections of line bundles) on Riemann surfaces, which is something that pops up all the time

[Anonymous No.9664760]

>>9664750
over a field, pretty much (or "n-d" matrix), but there's not much intuition to be gained by thinking of it that way. moreover, they don't multiply like matrices do

[Anonymous No.9664780]

>>9657809
Why was Mac Lane a hack? Why did the National Science Foundation not fund category theory until just a few years ago?

And as much as it pains me to say it what is your opinion on applied category theory? What's the best way to poach category theorists to work on applied category theory? I've got enough funding to support a mathematician forever, but can't seem to find any category theorists.

[Anonymous No.9664808]

>>9664780
>applied category theory
You mean math? Otherwise I don't see how something being "applied" is relevant to this thread.

[Anonymous No.9664812]

>>9664808
>Otherwise I don't see how something being "applied" is relevant to this thread.
What do you mean?

[Anonymous No.9664815]

>>9664812
He's a physics grad student that is notorious for shitposting in this general. Ignore that post.

[Anonymous No.9664817]

>professor said to row reduce instead of take determinant
>take the determinant anyway

[Anonymous No.9664818]

>>9664812
Don't reply to the spammer.

[Anonymous No.9664825]

>>9664815
>He's a physics grad student that is notorious for shitposting in this general.
I'm not a "he".

[Anonymous No.9664848]

>>9664825
Frankly you're not anything. Never have been, never will be.

[Anonymous No.9664889]

how do you study for your exams /mg?

[Anonymous No.9664898]

>>9664889
>exams

[Anonymous No.9664901]

>>9664889
>exams
Which school for brainlets do you go to?

[Anonymous No.9664908]

>>9664898
>>9664901
ah yes, the neets have taken the bait.

[Anonymous No.9664918]

>>9664848
>Frankly you're not anything. Never have been, never will be.
What do you mean?

[Anonymous No.9664924]

>>9664918
What do you mean?

[Anonymous No.9665018]

How do you prove the Plücker embedding is injective?

[Anonymous No.9665025]

>>9664780
I get the impression that most mathematicians don't like pure category theory.

[Anonymous No.9665042]

>>9665025
It's reasonable that a non-mathematician would get such an impression.

[Anonymous No.9665057]

>>9665018
It preserves dimensions.

[Anonymous No.9665084]

>>9665042
I'm literally doing a PhD right now. Everyone in my department thinks it's just a neat trick to prove rep theory stuff.

[Anonymous No.9665093]

>>9665084
It's reasonable that everyone in a "physics" department would think that.

[Anonymous No.9665094]

>>9665042

Category theory brings nothing new to the table. Like universal algebra its just a way to unify commonly occurring concepts. I don't see why people think its a valid replacement for ZFC.

[Anonymous No.9665095]

>>9665084
>most mathematicians
>Everyone in my department
What did he mean by this?

[Anonymous No.9665097]

>>9665093
why so eternally mad that your field of study is the literal poo of mathematics.

[Anonymous No.9665098]

>>9665094
>Category theory brings nothing new to the table.
What exactly would you consider to be something new? Perhaps that's the case in "physics", but you should discuss that elsewhere.
>I don't see why people think its a valid replacement for ZFC.
I don't see why """people""" think it's meant to replace ZFC.

[Anonymous No.9665102]

>>9665098
"putting" ""words"" """in"""" """"quotes"""" doesn't strengthen your argument.

[Anonymous No.9665103]

>>9665097
Why is algebraic geometry the "poo of mathematics"?

[Anonymous No.9665105]

>>9665102
Something trivially true doesn't need strengthening.

[Anonymous No.9665106]

>>9665103
Because it's not what I study.

[Anonymous No.9665110]

>>9665105
>trivially true
Explain why it's trivial and explain why it's true.

[Anonymous No.9665113]

>>9665110
It's trivial that physics garbage should not be discussed in a place not meant for discussing physics garbage.

[Anonymous No.9665117]

>>9665113
very bias argument. I reject your claim.

[Anonymous No.9665119]

>>9665095
Where are all these category theorists? I actually like category theory, but no one here (Pacific NW) does.

[Anonymous No.9665120]

>>9665094
>thinking that people care enough about axiomatic set theory to replace it
The philosophy threads are over at >>>/lit/.

[Anonymous No.9665123]

>"Z"
>""F""
>"""C"""

[Anonymous No.9665128]

>>9665119
>Where are all these category theorists?
Do you mean geographically? Just look up where all the mathematicians are. They can usually be found somewhere nearby.
>but no one here (Pacific NW) does.
That's a common occurrence in physics departments.

[Anonymous No.9665137]

>visit /mg/
>very little maths actually being discussed
woah....

[Anonymous No.9665147]

>>9665098

I'm not the PhD guy. I'm a mathematician. Regardless, the ad hominem of "physics" tells me you seem kind of defensive, so I'm sorry that you can't handle other people having different perspectives on category theory.

[Anonymous No.9665153]

>>9665120

Clearly you haven't gone to departmental colloquia on logic in the last few years.

[Anonymous No.9665155]

>>9665137
As expected of "physicists"

[Anonymous No.9665156]

>>9665147
>I'm a mathematician.
What are you doing in a physics department then? What do you study exactly?
>I'm sorry that you can't handle other people having different perspectives on category theory
I've actually acknowledged the existence of the physics perspective on category theory in the very post you're replying to.

[Anonymous No.9665157]

how do I prove ∞-groupoids are equivalent to the topological spaces?

[Anonymous No.9665162]

>>9665128
I'm doing a MATH PhD. All the algebraicists here don't like category theory.

[Anonymous No.9665163]

>>9665162
algebrashits*

[Anonymous No.9665164]

>>9665157
It follows trivially from the definitions.

[Anonymous No.9665167]

>>9665164
no it doesn't

[Anonymous No.9665171]

>>9665162
>I'm doing a MATH PhD.
That doesn't say much. What exactly do you study?
>algebraicists
You could just as well say "mathematicians" instead. There isn't a real difference.

[Anonymous No.9665181]

>>9665153
Yeah, I don't browse /lit/.

[Anonymous No.9665189]

boring thread. time to study my algebra in peace, far away from you lot.

[Anonymous No.9665195]

>>9665171
I'm technically pre-PhD. I wanted to do universal algebra, but no one here does that. I'm probably gonna have to choose between rep theory or algebraic topology.

[Anonymous No.9665215]

I hate this general.

[Anonymous No.9665225]

>>9665195
>I wanted to do universal algebra
Thanks for confirming that people can safely ignore anything you have to say on the matter.

[Anonymous No.9665238]

>>9665225
What's wrong with that?

[Anonymous No.9665239]

>>9665137
>maths
Not well defined.

[Anonymous No.9665240]

>>9665215
>I hate this general.
Why?

[Anonymous No.9665243]

>>9665147
>I'm not the PhD guy. I'm a mathematician.
Mathematicians use "we", not "I".

[Anonymous No.9665244]

>>9665238
There is nothing "wrong" with it just like there is nothing wrong with fields of study like biology or anything else not used in mathematics. It's just that these things belong elsewhere.

[Anonymous No.9665245]

>>9665243
Sorry, mathematwecwean.

[Anonymous No.9665246]

>>9665195
>universal algebra
does anybody unironically do this in 2018 ?

[Anonymous No.9665249]

jaded autists

[Anonymous No.9665259]

>>9665244
What is used in mathematics?

[Anonymous No.9665264]

>>9665189
>>9665167
>>9665157
>>9665137
based gorillaposter

[Anonymous No.9665270]

>>9665259
This is too broad of a question to have a non-tautological answer.

[Anonymous No.9665323]

>>9665270
>This is too broad of a question to have a non-tautological answer
What do you mean?

[Anonymous No.9665332]

>>9665323
What do you mean?

[Anonymous No.9665421]

>>9665018
Easiest way is to write the obvious inverse, once you figure out what property have the elements of the image, duh

[Anonymous No.9665435]

>>9665421
>obvious

[Anonymous No.9665444]

>decide to study maths to feel like less of a brainlet (already have STEM degree but it wasn't maths and I've forgotten all of it anyway)
>start going through section on line integrals in maths for engineers and physicists textbook
>SO fucking boring

Is this normal? I want to feel like less of a brainlet but studying maths with no purpose is boring.

[Anonymous No.9665454]

>>9665444
>gets bored studying boring material
study algebraic geometry. that'll make you shoot hot cum all over your notes.

[Anonymous No.9665461]

>>9665435
I don't think we need to spell out things you can find in any book or that a person who knows about Plucker embedding should do as a 10m exercise. gn

[Anonymous No.9665475]

>>9665461
REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

[Anonymous No.9665489]

>>9664750
Its an n dimensional cubical lattice. But because you cannot geometrically manipulate that shit as clear and there are many thing important to discuss that go beyond matrices, you should tale it with a real handfull of salt.

[Anonymous No.9665514]

P(W|M) = 0.95
P(W|M') = 0.25
How the fuck do I find P(M) what the fuck?

[Anonymous No.9665526]

>>9665514
w*m=0.95
w-wm=0.25
w=0.25+0.95
w>1
are you sure you're dealing with a P here?

[Anonymous No.9665551]

>>9665526
I kept getting this im going crazy, the question is:

Miss Marple next turned her little grey cells to The Butler. Simply because he was a butler,
Miss Marple thought it was a 50/50 chance that he was the murderer; it was just as likely
that he was the murderer as that he wasn’t. But then Harriet the Housekeeper, who had
delivered the tea, volunteered that as she rushed past the kitchen on the way to the adjacent dining room to investigate all the noise, she had seen The Butler vigorously washing his
hands... (Harriet wondered aloud if he might have been washing blood off his hands?)
Miss Marple asked for more tea as she thought about this new information. She trusted
Harriet’s account of what she had seen, but The Butler was a known cleanliness fanatic —
while vigorous handwashing at that late hour might seem a little odd, she thought that if
he had not been murdering Sir Humphrey next door there would still be a 25% chance that
he would be washing his hands like that anyway. On the other hand, if he had just been
murdering his boss, it was very likely, say 95%, that he would have been cleaning his hands
as if his life depended on it (which it just might!). How does Miss Marple update her probability that The Butler is the murderer?

[Anonymous No.9665753]

>>9665514
P(W|M)=P(W & M)/P(M) -> P(W & M)=0.95P(M)
P(W|M')=P(W & M')/P(M') -> P(W & M')=0.25P(M')=0.25(1-P(M))=0.25-0.25P(M)
P(W)=P(W & M)+P(W & M')=0.95P(M)+0.25-0.25P(M)=0.25+0.7P(M)
-> P(M)=(P(W)-0.25)/0.7

[Anonymous No.9665792]

>>9665246
You have a few people in order theory and lattice theory that could still be classified as doing universal algebra. The universal algebra program was subsumed by category theory.

[Anonymous No.9665891]

>>9665444
>>9665454
Hey integrals are fun mate.

[Anonymous No.9666320]

>>9665444
>line integrals
>for engineers and physicists textbook
What even makes you think that you're studying math?

[Anonymous No.9666326]

>>9666320
define "math"

[Anonymous No.9666359]

>>9666326
Try asking around at >>>/lit/. They would probably be able to do so ontologically speaking.

[Anonymous No.9666465]

>>9665454
This, but unironically.

[Anonymous No.9666486]

>>9666465
Nothing compares to algebraic curves and surfaces. Only faggots like their stuff linear.

[Anonymous No.9666505]

>>9657824
ODE are love
ODE are life
...
I hate engineering

[Anonymous No.9666734]

If I am to use the existence of an Eilenberg-Mac Lane space for any group [math]G[/math] and any positive integer [math]n[/math] in a category theoretical text, but the sources I am using don't contain any references to such spaces, must I provide a proof or cite some source with the proof of existence, or can I just explain briefly what they are and omit the details? I am not requiring anything else than their existence, so I can use them for classifying purposes.

[Anonymous No.9666743]

>>9665891
integrals are fun if you are the kind of person who likes row reducing 10x10 matrices

[Anonymous No.9666747]

>>9666734
Provide references for the full exposition and sketch an outline of the proof to the degree that it is relevant to your own work. If you don't use any arguments from the proof simply state "we know that..." and then slap a reference to the article with the result.

[Anonymous No.9666772]

>>9666747
Thanks. I'll do the latter one. Even though these generals are shitty, not all posters are.

[Anonymous No.9667373]

Why are monoids so beautiful lads?

[Anonymous No.9667379]

>>9667373
They aren't. Algebra cannot be beautiful by itself.

[Anonymous No.9667385]

>>9667379
>algebra

[Anonymous No.9667539]

>monoids

[Anonymous No.9667608]

tell me about de rham cohomology

[Anonymous No.9667625]

>>9667608
Take a smooth manifold, consider its smooth covariant tensor fields, restrict your attention to the alternating ones, define the exterior derivative and notice that it gives rise to a cochain complex. Now, call the differential k-forms closed if their exterior derivative is 0, and call them exact if they are images of differential (k-1)-forms. The kth cohomology group with the real numbers as its coefficients is now the quotient of the subgroup consisting of all the closed k-forms with respect to the subgroup consisting of all the exact ones.

[Anonymous No.9667637]

>>9667625
thanks

[Anonymous No.9667647]

>>9665157
What is you definition of ∞-groupoid?

If it is the common definition of just a Kan Complex, then it is pretty easy.

[Anonymous No.9667679]

G'day boys, is it ever useful to define an inner product like this:

[eqn] (f,g)_K = \iint_{\Omega \times \Omega} K(x,y) f(x) g(y) \ \mathrm{d} y \mathrm{d} x [/eqn]

[Anonymous No.9667683]

>>9667679
I don't think that is an inner product in general.

[Anonymous No.9667689]

>>9667683
Any references on this? What kind of properties does [math]K(x,y)[/math] need to satisfy? I'm working on the torus [math]\mathbb{T}^d[/math], so I was thinking of doing something with the Fourier transform [math]\widehat{K}(\xi,\xi')[/math]. Any other ideas?

[Anonymous No.9667704]

>>9667689
I mean first of all the definition of (f,f) isn't obvious.


If (f,f) is give by ∫K(x,y)f(x)f(y)dyxdx , then you would need K(x,y) non-negative.

[Anonymous No.9667718]

>>9667704
Yeah it would be like an infinite dimensional analog of a positive definite matrix. It would also need to be symmetric [math]K(x,y) = K(y,x)[/math]. I can't believe no one has ever looked at these things. Surely there must be a reason inner products like these are not widely used?

[Anonymous No.9667834]

Are Hatcher's exercises and examples hard or am I just really fucking stupid?

[Anonymous No.9667861]

>>9667834
Hatcher's just a bad author

[Anonymous No.9667902]

>>9667718
>I can't believe no one has ever looked at these things.

Might be that you can just re-normalize the basis factors to get a simple L^2 product and that's why. But for kernels like that, check out Fredholm anything and kernel anything.
https://en.wikipedia.org/wiki/Fredholm_theory
I mean it can't be an accident you guys also chose K as letter to represent it. Or in this direction
https://en.wikipedia.org/wiki/Hilbert%E2%80%93Schmidt_integral_operator

What I'm also immediately reminded of is considering a positive differential operator, e.g. some Laplacian, Fourier trasnforming the vectors/functions and thus getting a function kernel. Or generally any positive observable in quantum mechanics

>>9667689
https://en.wikipedia.org/wiki/Pontryagin_duality
?

[Anonymous No.9668023]

What even is equality? How is it defined for everything if there is no universal set for it to be defined on?

[Anonymous No.9668085]

>>9667834
hatcher is weird. and his treatment of cohomology is horrid.

[Anonymous No.9668094]

>>9668023
In logic as a binary predicate with some minimal requirements (such as that for any terms x and y, we have that x=y has the same truth value as y=x) and then for each theory, you set up an axiom to derive equality statements.

In a set theory, usually you set up an axiom
∀X. ∀Y. [∀z. (z∈X ⇔ z∈Y) ⇒ X=Y]
saying you can prove, for any two sets X and Y, that when for each item (usually also set) z it's the case that z is in X if and only if it's also in Y (i.e. when they share elements), then X and Y are equal. The allquantors that are part of this definition range over any set in the domain. The domains of discourse is not necessarily part of the model (i.e. also a set).

Here's a list of a few theories - they will usually all come with their own rule to extent equality (beyind the logic rules, like symmetry or transitivity)
https://en.wikipedia.org/wiki/List_of_first-order_theories

One is Robinson arithmetic, in which the x's and y's are not sets but numbers. You must view this syntactically

∀x. ¬ Sx = 0
∀x. ¬ x = 0 → ∃y Sy = x
∀x.∀y. Sx = Sy → x = y
∀x. x + 0 = x
∀x.∀y. x + Sy = S(x + y)
∀x. x * 0 = 0
∀x.∀y. x * Sy = (x * y) + x.
(where, basically, Sx:=x+1)
So for example, using 0 for x and the first axiom, we can prove that "0+1 is not 0" is true.

But of course some theories are more expressive than others and so some may argue you really only need equality for sets and then do modeling.

In other logics, e.g. Matrin-Löf dependent type theory, equality comes with much more rules (computational ones). It's really up to you.

[Anonymous No.9668117]

>>9668085
May does it right. Fuck playing with simplices, just define it axiomatically.

[Anonymous No.9668146]

Real Analysis, Number Theory, or Intro to Nonlinear Optimization.
Which one do I do first to become math fags like you guys asap.

[Anonymous No.9668169]

>>9668146
The last one requires the first one and the last one is also very much on the applied side (as opposed to the fags here). Hardly anyone enjoys number theory in isolation I think and if you do analytic number theory (muh zeta function), then you need the first one also. So there you go.

[Anonymous No.9668175]

>>9668169
I've just basically finished my proof intro class and linear algebra. I want to self study some topics before next semester. Recommendations?

[Anonymous No.9668184]

>>9668175
Algebra chapter 0 and Tao analysis

[Anonymous No.9668255]

>>9664750

In plain english, no, i.e. the kronecker product of an mxn (A) and pxq (B) matrix is an (mp)x(nq) matrix. But you should think of this as a matrix of blocks where each block is B scaled by the corresponding element of A.

I like to think of it in terms of programming (spoiler alert: I'm a brainlet). The tensor 'class' arranges elements of some type T into a grid. For a rank-1 tensor (matrix), T is scalar; for rank 2, it's a matrix, etc.

Tensors themselves are defined pretty abstractly but if you play around with the kronecker product on a few matrices it'll make sense in like 1-2 examples.

[Anonymous No.9668258]

>>9668117
someone that is reading hatcher isnt particularly ready for may...

[Anonymous No.9668265]

>>9668023
equality in the most elementary level (that is, in ZFC) in mathematics is that two sets are equal if and only if they contain the same elements. Since one constructs the naturals, reals, etc out of ZFC, then the definition is somehow translated to your more familiar definition or sense of equality.

[Anonymous No.9668269]

>>9668175
algebra chapter 0 is not good for a first look at algebra to be honest, but its the best for a second. Real analysis is really important in general, especially as an introductory course, because it teaches you of proper rigour. So I would suggest Tao analysis (I'm assuming you know calculus), otherwise Dummit and foote for algebra is good too.

[Anonymous No.9668329]

>>9668258
I read May but have read Hatcher. Although I had already done differential & algebraic geometry.

[Anonymous No.9668332]

>>9668329
have never read*

[Anonymous No.9668334]

Why is [math]\frac{x}{x} = 1[/math] when [math]\frac{x}{x}[/math] is undefined at [math]x = 0[/math]?

[Anonymous No.9668391]

>>9668334
analytic continuation

[Anonymous No.9668435]

>>9663273
Nice. In a private one-on-one chat a colleague of mine was telling me about how he discovered the relationship between ribbon invariants and Feynman diagrams, and how he was sad that it's already a thing. Then I told him that TQFTs could be built with ribbon graphs and he became less sad.

[Anonymous No.9668772]

>>9664780
Get universities to teach undergrads category theory. They will have to eventually.

Or, give mathematicians a crash course in it.

What's your domain?

[Anonymous No.9668805]

>>9667902
>https://en.wikipedia.org/wiki/Fredholm_theory
Very nice anon, thanks

[Anonymous No.9668809]

>>9668334
The function f(x) = x/x is undefined at infinity and at 0.
It's undefined at infinity because 1/f(x) = x/x is undefined at zero.

This doesn't answer your question or anything, I just wanted to say something.

[Anonymous No.9668855]

>>9668809
I want to talk to you

[Anonymous No.9668945]

>>9668269
>Real analysis is really important in general

[Anonymous No.9668960]

>people actually talking math in the last couple dozen posts or so
>in /mg/
Oh, wow...!

[Anonymous No.9668971]

Is there a reasonable procedure to construct a ring around an arbitrary finite abelian group? I'm having trouble thinking about how associativity restricts possible choices.

[Anonymous No.9668991]

>>9668971
The group ring over [math]\mathbb{Z}[/math]? It works for arbitrary groups.

[Anonymous No.9668993]

>>9668960
I don't see any math discussion there, only some questions about integrals or other such bullshit.

[Anonymous No.9668996]

>>9668435
>he discovered
I highly doubt that anyone who associates with dog-eaters can ""discover"" anything.

[Anonymous No.9669070]

Ok /mg/, fess up: how long is your erect dick?
Don't lie, this is very important.

[Anonymous No.9669111]

>>9669070
About 17-18 cm. Why?

[Anonymous No.9669113]

>>9669111
Mine is only 14cm.

[Anonymous No.9669135]

>>9669070
7.1 inches and im just under 5'8, nothing to brag about but i certainly wasnt jipped

[Anonymous No.9669267]

We back.

I'm constructing a type theory modelled by presheaves on symmetric monoidal preorders.

[Anonymous No.9669271]

https://www.amazon.com/dp/311037949X

Thoughts on this book?

[Anonymous No.9669277]

>>9669267
"why"

>>9669271
I don't know it, but it seems suitable.

[Anonymous No.9669286]

>>9669277
Formal verification of imperative programs.

[Anonymous No.9669292]

>>9665025
What exactly is pure Category Theory? I've heard it doesn't even have any results except Yoneda Lemma.

It seems just like handy definitions without much strucutre. Like it needs other math to make sense.

[Anonymous No.9669307]

>>9669286
Refer to the >>>/g/hetto/.

[Anonymous No.9669317]

>>9669307
Type theory and category theory are not really /g/ material, lad.

[Anonymous No.9669320]

Serious question: if you don’t go to a top 10 Uni for grad school, is it even worth trying to become a Math Professor to do research?

[Anonymous No.9669328]

>>9669320
Not that great desu, even in my run of the mill state school most tenured faculty come from top 15 schools or so.

[Anonymous No.9669330]

>>9669328
So what do all these people do with PhD’s from Unis that are in the 30-50 rank?

[Anonymous No.9669338]

>>9669330
eternal adjutants, occasionally get a job at a mid tier school. Rest go into industry I guess.

[Anonymous No.9669355]

>>9669286
Okay then what do the products represent.
On a semi-relate note, I'm playing with the thought of setting up a database/protocol where people upload types together with algorithms that compile for them. A Merkle kind of tree, or rather a bipartite graph. The idea came as I have friends who do a startup where they let one put out jobs and pay for done jobs (using cryptos). I'm thinking of a (more academic) experiemnt on how to aid the job completion (by having strong types that decribe the program in full and then have the job taker / coder provide something that compiles)

>>9669292
Maybe you can count one, two statements about Kan extension. And yes, raw cats are more of a language and people don't look at (non-higher) category theory like they e.g. look at groups so much.

[Anonymous No.9669358]

>>9669317
I don't see any type theory or category theory in "Formal verification of imperative programs.".
Take your programming filth to the >>>/g/hetto/ where it belongs.

[Anonymous No.9669359]

>>9669355
>On a semi-relate note, I'm playing with the thought of setting up a database/protocol where people upload types together with algorithms that compile for them. A Merkle kind of tree, or rather a bipartite graph. The idea came as I have friends who do a startup where they let one put out jobs and pay for done jobs (using cryptos). I'm thinking of a (more academic) experiemnt on how to aid the job completion (by having strong types that decribe the program in full and then have the job taker / coder provide something that compiles)
see >>9669307

[Anonymous No.9669365]

>>9660701
>tehehe I'm a girl btw
fuck off

[Anonymous No.9669370]

>>9669286
>>9669355
Wrong thread on the wrong board.
>>>/g/

[Anonymous No.9669378]

>>9669317
>lad

https://img.4plebs.org/boards/tv/image/1502/07/1502072508811.jpg
can't post images so pretend this image was attached

[Anonymous No.9669379]

>>9669355
>>9669286 was in response to "why", not about the book.

>>9669358
You don't see type theory or category theory in constructing type theory based on particular categorical models?

[Anonymous No.9669381]

>>9669379
I don't see type theory or category theory in discussing the kind of programming filth you want to do using category theory or type theory. There is a special containment board for your kind to engage in the discussion of programming filth. So keep it contained to that board.

[Anonymous No.9669384]

>>9669379
If you don't stop reyplying to the >>/g/ poster, I'll have to assume you're more stupid than him. Rule number one: Don't get trolled. 100% ignore abbraive posts.

[Anonymous No.9669390]

>>9669384
>Don't get trolled
Since when is referring programmers to the correct board for programming discussion considered trolling?

[Anonymous No.9669392]

>>9669390
Are you ok?

[Anonymous No.9669405]

Who’s the current greatest living mathematician?
And why is he so?

[Anonymous No.9669495]

>>9669405
I'm not a "he"

[Anonymous No.9669508]

>>9669405
tao and any other answer is ridiculous

[Anonymous No.9669512]

>>9669405
Peter scholtz

[The Lord No.9669513]

>>9669405
>>9669495
>>9669508

[Anonymous No.9669520]

>>9669508
I'm pretty sure he was asking about mathematicians.

[Anonymous No.9669522]

>>9669520
And I’mpretty sure he was asking for answers from people who know what they are talking about ;)

[Anonymous No.9669526]

>>9669522
Exactly. So I don't see why >>9669508 even bothered to post a non-mathematician.

[Anonymous No.9669531]

>>9669526
go ahead and google Terence Tao

[Anonymous No.9669535]

>>9669531
He's a pretty well-known guy so I doubt there is any need to google him. I fail to see how that makes him a mathematician though.

[Anonymous No.9669548]

>>9669535
stop shitposting

[Anonymous No.9669553]

>>9669405
Serre

[Anonymous No.9669558]

>>9669405
Grothendieck

[Anonymous No.9669687]

>>9665094
>>9665098
>>I don't see why people think its a valid replacement for ZFC.
>I don't see why """people""" think it's meant to replace ZFC.

HoTT

[Anonymous No.9669700]

>>9669687
How does one ``replace" something which isn't being used? How is HoTT category theory? You seem to be confused by basic words.

[Anonymous No.9669706]

>>9669700
ZFC isn't being used?

HoTT types are infinity groupoids.

[Anonymous No.9669713]

>>9669706
It isn't being used in the field this thread is about. Perhaps you could discuss its uses in fields such as philosophy over at >>>/lit/.
>HoTT types are infinity groupoids.
I see. So set theorists are category theorists now since sets are 0-groupoids.

[Anonymous No.9669721]

>>9669713
>I see.
Mathematicians use "we", not "I".

[Anonymous No.9669942]

How much trust is there in expressions that you get from wolfram and other symbolic computing languages?

I'm at the point where it might straight up take me weeks of equation manipulation to do these results by hand, but plugging values into simplified final expressions I get from my code matches what I already suspected, so I wonder if I have to dig through and figure it out myself or if what I've got is good enough.

[Anonymous No.9669954]

>>9669942
>How much trust is there in expressions that you get from wolfram and other symbolic computing languages?
0 from wolfram because closed source.

[Anonymous No.9669963]

>>9669721
>We see.
brainlet

[Anonymous No.9669972]

>>9669954
In that case, what would you do?

[Anonymous No.9669974]

SOMEONE EXPLAIN THIS SHIT.
His example for the Euler–Mascheroni constant is just:
x > x + 1 if you increase the value of x enough

https://www.youtube.com/watch?v=4k1jegU4Wb4

[Anonymous No.9669984]

>>9669713
Kill yourself you fucking piece of shit. God dammit I wish I could strangle you through my monitor. Why does /sci/ have no mods.


I'm so fucking mad right now. Fucking waste of oxygen.

[Anonymous No.9669986]

>>9669721
Die motherfucker. Go grab a noose, tie it around your neck, and hang.

[Anonymous No.9669995]

>>9669721
>highschool freshman who thinks he's a mathematician

[Anonymous No.9669997]

>>9669995
>>highschool freshman who thinks he's a mathematician
Who are you quoting?

[Anonymous No.9669998]

>>9669984
>Kill yourself you fucking piece of shit. God dammit I wish I could strangle you through my monitor. Why does /sci/ have no mods.
>I'm so fucking mad right now. Fucking waste of oxygen.
Can you take your bad attitude elsewhere?

[Anonymous No.9670001]

>>9669997
the post I was replying to, obviously, you retard

[Anonymous No.9670103]

>>9669998
Get cancer.

>>9669999

[Anonymous No.9670105]

>>9670000

[Anonymous No.9670131]

is conjugation an operator

in my coursebook the lecturer sometimes manipulates the bar notation the same way you would other operators

do i go to a brainlet uni

[Anonymous No.9670157]

>>9669512
Interesting, he looks good. What is he up to these days?

[Anonymous No.9670161]

>>9670131
step 1: write down your favorite definition of "an operator".
step 2: check if the map from x to the conjugate of x fulfills it.

And step 3, revise your mindset and way to look at math. You seem to have set up some ill barriers. You make the rules.

[Anonymous No.9670320]

>>9670131
an operator is a linear map T: V-> V. It is easy to check conjugation is an operator. QED

[Anonymous No.9670345]

>>9670320
Conjugation is a nice endomorphism, and thus I'd call it operator.
If you want to restrict yourself to vector spaces and that over (a subfield of) the reals, then okay.

Semi-related, maybe the symmetric monoidal category guy wants to talk about dagger category. I only ever see Baez fap over it, but not sure where it goes. Did he manage to say interesting things using them in his quest for reframing stochastic processes questions. I generally like the topic.

[Anonymous No.9670352]

>>9670345
>reframing stochastic processes questions
Wrong thread. Wrong board.

[Anonymous No.9670364]

>>9670345
>maybe the symmetric monoidal category guy wants to talk about dagger category
I had a change of mind and I'm currently reading https://arxiv.org/pdf/1410.1716.pdf and some other stuff to try and create a new system for geometric and locally-stochastic étale stock trading. That's off-topic for this thread, though. Would you like to move to >>>/biz/ to discuss this further? I'll make a thread if you want.

[Anonymous No.9670374]

>>9670364
That at least looks like a nicely set text, but if you jump around so much you'll never get nowhere - and you know it.
As a side note, I'm also very interested in commutative algebra, or more concretely the representations of functions over Z_2^n -> Z_2 (and there are some results in Boolean algebra that suggest polynomials are the way to go).

>>locally-stochastic étale stock trading
lel.
As for /biz/, I actually wrote a bot who trades on Bittrex. However, getting involved with start-ups is really the way to go.

[Anonymous No.9670457]

>tfw wasted my entire life by not learning math

[Anonymous No.9670472]

>>9670374
>if you jump around so much you'll never get nowhere - and you know it.
I've thought about this deeply and realized that I need to develop a geometric theory of stock trading before I can proceed with my other goals.
I have defined a family of functors [math]\mathscr{B}^n : \mathbf{Stc}_{fppf} \to \mathbf{Qcoh}(\mathfrak{X})[/math] ([math]\mathscr{B}[/math] for "bitcoin"). Where [math]\mathbf{Stc}_{fppf}[/math] is the category of [math](2,1)[/math]-sheaves on the stochastic site and [math]\mathfrak{X}[/math] is a certain space which classifies blockchain transactions that I have created using inspiration from classical applied probability theory. These functors (conjecturally) admit étale covers by locally algebraic Banach spaces and thus (should) have very interesting higher cohomology. I'm hoping to actually prove this by the end of the month and find a way to compute the cohomology. My preliminary work suggests that [math]H^2(\mathbf{Btc},\mathscr{B}^1)[/math] is already encoding a lot of deep information about the blockchain. I also get the feeling that this is somehow related to TQFT but I'm not really experienced in that area to say much at this point. Do you know of any good elementary references?

>I actually wrote a bot who trades on Bittrex
Same here. I'm thinking that my current work might actually help me do this more effectively if I can manage to internalize it in the economic topos.

[Anonymous No.9670515]

>>9670472
That's a nice clusterfuck there. Do people look at (n,m)-sheaves etc. (2 and 1 here) because it gets too complicated if you take n to infinity, or do you get something out of it that you don't in the infinite case. On the nLab, or when I peek into Luries stuff, it seems they really push for the infinite case.
And why would you need anything etale here? If I had the time, I'd get familiar with combinatorial species and I think that's where the applications of cat framework end, pretty much, for anything resembling real world data bases.
Granted, I don't believe you for a second, but in case this thought crossed your mind before you posted, what would there be to classify when it comes to the blockchain transactions? The protocols are compact and self-contained and predictable (only metadata really being the timestamp). And most "transactions" are not even on the chain, all the exchanges obviously write their own database and only do transactions if somebody wants to withdraw to another address. Pic related, the biggest wallets are the exchanges and they keep it mostly on a few addresses. When you trade with someone there, nothing moves. You'd not get too much out of studying the chain. Besides, if you were to pull something like that off, restricting you to BTC would be quite the mistake I think. Finally, most of the interesting action on the chain will be invocations of dApps.
On that note, I've deployed what I think is the first and only Turing complete smart contract (the contract itself is programmable and it's not "just" the virtual machines that are part of the nodes)

https://youtu.be/CAUo5aNmvz8

[Anonymous No.9670538]

>>9670345
>>9670364
>>9670374
>>9670472
>>9670515
Refer to >>>/b/ and >>>/g/.

[Anonymous No.9670821]

>>9670345
>Semi-related, maybe the symmetric monoidal category guy wants to talk about dagger category. I only ever see Baez fap over it, but not sure where it goes. Did he manage to say interesting things using them in his quest for reframing stochastic processes questions. I generally like the topic.
What's that got to do with anything?

[Anonymous No.9671057]

The dagger operation as conjugation

[Anonymous No.9671257]

>>9671057
monoidal categories = categories of processes
dagger = time reversal

[Anonymous No.9671532]

>>9670472
where do i start before I can learn about functors?
go through rudin and dummit&foote?

[Anonymous No.9671755]

>>9671532
>rudin
You can safely ignore anything to do with "real analysis" if you don't care about engineering.