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/sci/ - Science & Math


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6351632 No.6351632 [Reply] [Original] [archived.moe]

Is there anything that can give me a good understanding between the relationships in all of mathematics? I'm not talking about the different branches of mathematics (as depicted in the picture), but about the different definitions and theorems.

It always helps me tremendously to see the "bigger picture" of something. It does not even need to be arbitrarily accurate, even black boxes might do the job. Something that gives me an understanding that "these are the fields, over fields you have vector spaces, if you add operation X to Y then you get Z (where Z might be rings or whatever)"

And all of this in form of a picture, kinda like a mind map. To get an idea of how it all works together.

Like you could have a bubble representing the set of all real numbers, then you draw a line to the vector space over R and the line reads addition and scalar multiplication.

>> No.6351640

>>6351632
>about the different definitions and theorems
I think you're going to have to define this better. Pretty much all of mathematics involves "proofs," if that's what you're asking. If you want to be just a mathematician, in general, you will need to be good at proofs.

>> No.6351643

>>6351640
no, this doesn't need any proofs

I just want to have a mind map of all the relation ships, this doesn't have anything to do with actually learning this shit

it's more about seeing what is a subset of what and what is needed where and what plays a role somewhere else

>> No.6351650
File: 25 KB, 450x450, morph.png [View same] [iqdb] [saucenao] [google] [report]
6351650

>>6351640
I found an example of what I'm talking about on wiki

you see, this is only for homomorphisms, but I want this for pretty much every (important) definition and theorem that exists in mathematics all on one picture

>> No.6351670

I forgot to mention it in the first sentence lol

I just want a fucking picture of everything, a circuit layout of mathematics so to speak

dozens of bubbles each reading a definition or a theorem and all of them intertwined and each line connecting from one bubble to another shall read what operation is needed to get there, or what makes this generalization possible

kinda like the pic in the OP, only bigger, more detailed and instead of branches actual information

>> No.6351721

>>6351632
>It always helps me tremendously to see the "bigger picture" of something.
same here op. bumping.

>> No.6351724

>>6351650
Mathematics is simply way too large to be encompassed in a single diagram or picture. Yes even if you just look at "important" theorems and statements.

>> No.6351728

>>6351632
>It always helps me tremendously to see the "bigger picture" of something
Couldn't agree more OP. For me, context turns a mathematical subject from something completely tedious to deeply interesting.

>> No.6351731

>>6351724
how can this be true if a picture can be arbitrarily large and all of mathematics has been written on a finite amount of papers?

>> No.6351731,1 [INTERNAL] 

Op you already have an idea of what you are looking for so you should make it yourself and fulfill your destiny for the benefit of all mankind

>> No.6351733

@OP: If you write me an email with what you want and who who are (education wise) in the next couple of minutes, I might have information for you.

>> No.6351741
File: 6 KB, 755x459, pic.png [View same] [iqdb] [saucenao] [google] [report]
6351741

>> No.6351745

>>6351733
I don't want to use my private email address for people on 4chan

I study physics

>> No.6351758

>>6351745
>I study physics
hehe, same here.
Some years ago I decided to strategically learn math and so I'm actually working on a project which does pretty much what you describe in your post and I even visualize it in a grpah. Should have sent me an email, but I also just used 10 minute mail. In any case, I can say I stated here
http://en.wikipedia.org/wiki/Mizar_system
(although I don't use that language and designed a system which lets me go in different subject more easier - and more importantly, as you yourself argue, I concentrate on mathematical objects, not proofs)

>> No.6351767

Sounds like you want Category theory of some sort.

Unfortunately it's too esoteric and difficult for a non-math person to access, so you'll have to build up to it. But basically it's like a branch of meta-mathematics where you look at similarities between "categories" of objects (like all topological spaces, commutative rings, etc.).

>> No.6351773

>>6351745
What do you think this is, /b/?

>> No.6351812

>>6351758
I will just have to do it on my own then I guess, alternatively you could just upload a picture of it here

also tried 10min mail, but it doesn't allow you to send emails

it's just the way my brain works, I will build this picture in my head in years to come anyway, but I thought I'd just ask and see if I can get a glance of it, I just feel uncomfortable moving around in systems I don't know how big they are

mathematics is like a house I entered, but everything is still so unfamiliar (just recently finished babby rudin) that I cannot even see the walls yet, it'll take some time for me to settle in, but as I get more and more comfortable, everything will come to me naturally and as I get better and better I start to see all the relations and by the time I reach perfection the house will be a sphere - it's my dream for it to become one, but my one lifetime is not enough, but it will most definitely become a cogwheel

if that makes any sense

>> No.6351825

>>6351773
i am a /b/ro, so i am ready to fuck him up just because you said that. feel free to share email pal. kek

>> No.6351850

>>6351632
That picture is terrible. Axiomatic set theory should be in the center. Algebra, topology and analysis should sit just outside of it. Calculus should be an infinitesimally small circle connected to analysis.

Maybe, there could be charts that show systems of mathematics developed from category and type theory.

>> No.6351969
File: 1.00 MB, 218x228, retarded.gif [View same] [iqdb] [saucenao] [google] [report]
6351969

>>6351650

In the middle: Autism.

I always new it, we're teh beest!

>> No.6351990
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6351990

>> No.6352006 [DELETED] 

Hate to break it to you OP but if you want to be spoonfed, I doubt you'll find it here. I've never seen such a chart and while it would be neat, I don't think it exists.

>> No.6352007

>>6351812
I know the feel, I also always saw that something more is lacking and climbed down the formal ladder to comprehend stuff better. I learned a lot of logic, set theory and computer science in the process. And I fell in love with the category perspective and the type theory insights on processes as well.
That said, I can really recommend these sets of lecture notes, particularly the first one
http://www.personal.psu.edu/t20/notes/

In which semester are you?

>I cannot even see the walls yet
there are a lot of walls:
http://msc2010.org/kwicindex.pdf

>> No.6352124

>>6351850
I would say recursion theory should be in the center.

>> No.6352164

>>6351850
>infinitesimally
iswydt

>> No.6352706

>>6352007
I just finished only my first semester

>> No.6352710

>>6351990
this is p good btw

>> No.6352721

>>6351632
I was toying with the idea of doing something exactly like that. (mostly with physics though)

Just creating a giant web of what is all derived from what, and you would be able to see on the edges of the web what is an axiom. You could see how different sets of axioms can make up a single theory.

Or where there are gaps in derivations, or what rests on weak foundations due to too many approximations etc...

I thought it would be cool to make it into a website, and allow people to make contributions..

a man can dream...

>> No.6352749

>>6351767
And still doesn't do any of what OP wants.

OP, you might want to start out by asking for something in one very specific area. Like "undergrad algebra". Then you might actually find something.

>> No.6352757
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6352757

The big fields are algebra, geometry, and analysis. Also, there's foundations and computing science. They're all intertwined in ways not particularly insightful macroscopically.

>> No.6352760

>>6352757
this is exactly not what OP wanted

there isn't a single definition or theorem on there, into the trash it goes

>> No.6352873
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6352873

Don't overthink it, nerds. Math is linear.

>> No.6352878

>>6352873
OP wants something similar to this

>>6351990
only that this doesn't have enough detail, where is the set of bounded functions, continuous functions, uniformly continuous functions, differentiable functions, and so on and so forth

for every important axiom, definition and theorem in existence

>> No.6353037

>>6352721
>>6352878
For proofs there is ProofWiki of course, and one could try to sort the theorems there.
A similar question was asked here
http://math.stackexchange.com/questions/90578/what-is-an-efficient-nesting-of-mathematical-theorems
but no good answers.

>> No.6353448

bump

>> No.6353465
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6353465

>>6351632

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