/mg/ - Math general

Burnblaze
Burnblaze

What are you reading today, /mg/?

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All urls found in this thread:

veekyforums.com/thread/9604727/science
veekyforums.com/thread/9612214/science
amazon.com/Tensor-Analysis-Manifolds-Dover-Mathematics/dp/0486640396
amazon.com/Tensors-Differential-Variational-Principles-Mathematics/dp/0486658406/
amazon.com/Vector-Tensor-Analysis-Applications-Mathematics/dp/0486638332
amazon.com/Elements-Tensor-Calculus-Dover-Mathematics/dp/0486805174/
amazon.com/Vector-Tensor-Analysis-Dover-Mathematics/dp/0486601099
amazon.com/Applications-Tensor-Analysis-Dover-Mathematics/dp/0486603733
ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20050175884.pdf
veekyforums.com/thread/9612824/science
freevideolectures.com/Course/2721/Algebraic-Topology
mathoverflow.net/questions/66084/open-problems-with-monetary-rewards
en.m.wikipedia.org/wiki/Chain_rule
en.m.wikipedia.org/wiki/Taylor's_theorem

VisualMaster
VisualMaster

reading
not science or math

RavySnake
RavySnake

Just doing some trig derivative problem sets, not too engaging but better than higher derivatives.
I’m doing an independent study on approximating pi, possibly converting it to hex/binary. Any good books on pi?

GoogleCat
GoogleCat

Refreshing Geometric Algebra and Calculus.

I plan to use some of its formalism in my next publication.

It's fascinating because I tried just using a Clifford algebra and quickly ran into issues that made it obvious that a discrete exterior calculus or the geometric calculus would be much simpler

I'm excited.

What do researchers here feel is the more popular/standard field? I tend to prefer the exterior calculus since the ties to differential geometry is already well developed, but the notation of geometric algebra appears to be really easy to work with.

Thoughts?

Methshot
Methshot

Math general
define "Math"

BinaryMan
BinaryMan

I was reading a parsing theory book and having trouble with a proof on (recursively defined) regular expressions' properties. Not sure if properly applying double induction.

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PurpleCharger
PurpleCharger

veekyforums.com/thread/9604727/science
All you need is basic set theory to get started.
I formally doubt this.
veekyforums.com/thread/9604727/science
i find algebra to be more fun
You mean abstract algebra?

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Supergrass
Supergrass

Who ENS here?

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Booteefool
Booteefool

who is the terence tao of the ENS?

MPmaster
MPmaster

For those of you who ascribe to ZF(C), would you care if it was proved to be inconsistent, or just continue using it?

If you cared enough to switch, what system would you use instead?

Spamalot
Spamalot

I formally doubt this.
It is true both formally and informally. It's better to start with topology rather than infecting your brain with stuff like "analysis" which you will ultimately have to purge if you wish to continue studying mathematics.

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girlDog
girlDog

mathematics
This is not well-defined.

farquit
farquit

Mathematics is the study of mathematical structures.

viagrandad
viagrandad

mathematical structures
This is not well-defined.

happy_sad
happy_sad

@9610484
Don't respond to the spammer, retard.

SomethingNew
SomethingNew

spammer
?

takes2long
takes2long

I have a feeling that you're trolling me so I will not follow your advice, sorry.

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idontknow
idontknow

It being formally true is trivial. Just check any introductory book on topology. Some of the shittier ones use examples from "analysis", but that's about it.

TreeEater
TreeEater

But it is.

Sharpcharm
Sharpcharm

But it is.
That remains to be shown.

New_Cliche
New_Cliche

Why do you doubt it? The only reason to """""need""""" anal before topo is that you can then say
oh this is why it works instead of some ridiculous inequality farce i saw earlier
when you see claims familiar from anal proved in a more general sense. It follows that is correct. Have fun studying topo!

t. veekyforums.com/thread/9604727/science

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Stupidasole
Stupidasole

I took an applied math thing but it's all Lagrangian and Hamiltonian systems and I keep getting bogged down in the physicsy things I don't need to know about. I'm becoming one of those people who can regurgitate enough to solve problems but can't understand what's going on.

SomethingNew
SomethingNew

I'm becoming one of those people who can regurgitate enough to solve problems but can't understand what's going on.
Congratulations! You are becoming a true applied "mathematician".

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Methnerd
Methnerd

lmao category ""theorists"" eternally fuming out their arse because the analyst will get employed after their degree whilst they sit on Veeky Forums all day crying. HAHAHAHAHAHHAA

PackManBrainlure
PackManBrainlure

lmao category ""theorists"" eternally fuming out their arse because the analyst will get employed after their degree whilst they sit on Veeky Forums all day crying. HAHAHAHAHAHHAA
cringe

Snarelure
Snarelure

qê wants to be employed by the bourgeoisie
No wonder you can't handle the deep insights of category theorists.

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Burnblaze
Burnblaze

I'm not a "qê "

Flameblow
Flameblow

Did you know category theorists were once banned(informally) from receiving NSF funding because they were huge cunts?

SniperGod
SniperGod

bourgeoisie
This is not well-defined.

RavySnake
RavySnake

NSF
Do you mean MSF? Why would they be funding math?

RumChicken
RumChicken

Sorry for misgendering.

a sociologically defined class, especially in contemporary times, referring to people with a certain cultural and financial capital belonging to the middle or upper stratum of the middle class: the upper (haute), middle (moyenne), and petty (petite) bourgeoisie (which are collectively designated "the Bourgeoisie"); an affluent and often opulent stratum of the middle class (capitalist class) who stand opposite the proletariat class.
Yes it is.

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TechHater
TechHater

an affluent and often opulent stratum of the middle class (capitalist class) who stand opposite the proletariat class.
Not well-defined.

BinaryMan
BinaryMan

because
Your reasoning doesn't seem to make sense here, I'm assuming that's just on the surface level. Could you elaborate how you came to this deep conclusion?

FastChef
FastChef

The proletariat (/ˌproʊlJˈtɛəriət/ from Latin proletarius) is the class of wage-earners in a capitalist society whose only possession of significant material value is their labour-power (their ability to work). A member of such a class is a proletarian. In Marxist theory, a dictatorship of proletarians is for the proletariat, through the proletariat and by the proletariat. This, in Marxist theory, will lead to proletarian self abolition and, thus, communism.
Take the complement of this set.

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New_Cliche
New_Cliche

set
Not well-defined.

Supergrass
Supergrass

This is just a bunch of gibberish, not a well-defined set. Some authors have even gone as far as to call it a "fictional set".

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Sir_Gallonhead
Sir_Gallonhead

Some authors have even gone as far as to call it a "fictional set".
Is that like a "fictitious force" (i.e. actually not fictitious)?

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King_Martha
King_Martha

fictitious force
Please keep this discussion in the proper board: /toy/

Evil_kitten
Evil_kitten

I meant the US National Science Foundation

happy_sad
happy_sad

Yes it is in anarcho-primitivist mathematics.

Is there not a set of humans? Is there not a set of people living in a country? Is there not a set of people living in a country and not owning the means of production?

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kizzmybutt
kizzmybutt

The proper class of humans doesn't contain things which are fictional and not well-defined, i.e., terms/objects/entities such as "proletariat" and "means of production". It also doesn't contain "communists", but the only known proof of this uses "biology" which we don't discuss here.

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Playboyize
Playboyize

The class of humans is in bijective correspondence with a subset of natural numbers, and thus a set. It follows that all those sets are well defined.

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StrangeWizard
StrangeWizard

Read up on the Monte Carlo approximation method for approximating pi.

girlDog
girlDog

I'm trying to find a formula for the number of elements in P1(Z/nZ)

The number of elements in P1(Z/pZ) is obviously p+1 as you have p elements of the form (1:k) and then 1 element (0:1)

It's also obvious that Pn(Z/pZ) has 1+p+...+p^n elements for the same reason as the above.

If I can get a formula for just P1(Z/p^kZ) then I'm done as I can use the Chinese Remainder Theorem to get the answer for all n, but I'm lost trying to get any formula for this.

Any help?

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Lunatick
Lunatick

modern algebra lecture
professor asks class to define the characteristic of a ring
classmate flips to the page in the book with the definition and paraphrases "It's the least positive integer n such that nx = 0 for all x in the ring."
I chime in and say that nx is not necessarily the same thing as n · x, nx is multiplication while n · x is summing x with itself n times.
professor says I'm being pedantic, multiplication is repeated addition. We move on.
as I'm sitting through the rest of the lecture, I think of the ring [math]M_{2}(\mathbb{Z}_{2})[/math].
you can sum the matrices in [math]M_{2}(\mathbb{Z}_{2})[/math], but you cannot multiply them by an integer.
didn't ask professor about this case because too much of a pussy.
Am I being autistic and pedantic, or was the definition given by my classmate valid? I usually don't win when I disagree with professors, but I would like to make sure that lies are not being taught in class.

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Inmate
Inmate

Every abelian group (G,+) is a Z-module with Z x G ---> G given by ng=g+...+g .

Poker_Star
Poker_Star

nx is multiplication
In a ring this is usually written as x^n.
n · x
This is just the [math]\mathbb{Z}[/math]-module action on your ring, usually it is written as nx.

SniperWish
SniperWish

Follow up to this:
it seems the formula is p^k+p^(k-1)
or p^k(1+1/p)

This has confused me somewhat as for Z/4Z I think I can make 9 distinct elements, not 6:
(1:0) (1:1) (1:2) (1:3) (0:1) (0:2) (2:0) (2:1) (2:2)

Any help?

CouchChiller
CouchChiller

Implying topologists actually prove their claims

DeathDog
DeathDog

you can multiply the matrices in M2 by integers, that is scalar multilication. it's the same thing as adding a matrix to itself n times (or the additive inverse of that matrix)

ZeroReborn
ZeroReborn

Mathematics is (by definition) the study of TQFT and string theory and maybe some AQFT over exotic spacetimes.

Stupidasole
Stupidasole

seems like 0:1 and 0:2, 1:1 and 2:2 aren't distinct. 2:0 and 1:0 also but I don't know how you justify it

Supergrass
Supergrass

and maybe I just don't understand your terminology but if 2:2 != 1:1 aren't we talking about a cartesian product instead? i.e. Z X Zn

Crazy_Nice
Crazy_Nice

these are distinct because 2 is not a unit in Z/4Z

Boy_vs_Girl
Boy_vs_Girl

What scares me is that he is even talking about "multiplication" in a group theory context.

The operation nx of the ring isn't necessarily multiplication in the trivial sense.

That Prof is confusing his class.

girlDog
girlDog

What's the best software for making figures of combinatorial graphs?

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kizzmybutt
kizzmybutt

python-networkx

WebTool
WebTool

Well-definiteness is not well-defined.

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Supergrass
Supergrass

yes it is, it's often not well-explained though. well-defined things just fit the labels you use for them, e.g. checking if a map is well-defined is the same as checking if it's actually a map.

lostmypassword
lostmypassword

How do you define the projective line over a commutative ring that is not a field?

Gigastrength
Gigastrength

Proj(R[x,y])

Skullbone
Skullbone

Set theory student here. No one except philosophers and babies first logic class care about the consistency of ZF. The reason is that if ZF is inconsistent everything follows, so the only interesting case is when ZF is consistent. Thus that assumption is implicit when working ZF. Very few set theorists actually care or work with axiomatics, I took a grad set theory course with someone who did work with axiomatics and it was fucking painful. Hurr durr does this set exist well take the power set of the power set of the power set of this set and cut down with comprehension. I do work in effective theory so I could restrict ZF down to Kripke Platek (KP) set theory + omega and everything would carry through.

CouchChiller
CouchChiller

Ok, I see. The problem with the (algebro-)geometric definition is then that [math] \mathbb{P}^1(\mathbb{Z}/p) [/math] already has infinitely many elements - there are not only the points rational over [math]\mathbb{Z}/p[/math] but also other points. But if you restrict yourself to rational points, the question over [math]\mathbb{Z}/n[/math] for general n is somehow weird.

FastChef
FastChef

infinitely many elements
it has p+1 elements

Lord_Tryzalot
Lord_Tryzalot

These are the rational points. But the Proj-construction generally gives more (closed) points (whose residue field is a proper extension field of the ground field).
But if you mean rational points - what do they mean over arbitrary Z/nZ.
Or do you mean something else by Proj? If you mod something out (set-theoretically) of some kind of R^2 you might get the correct object.

Playboyize
Playboyize

Does it matter where you get your undergrad degree? I go a decent public Uni and I am thinking of transferring to a more rigorous private school or an IV league.

BlogWobbles
BlogWobbles

some "decent" public universities have abysmal math programs, especially if you stay off the graduate track
this of course means transferring from such a school would be really hard, because everyone around you would have underlying knowledge that you lack

ZeroReborn
ZeroReborn

is right.
I go to what would be considered an ivy league school if it were in the states and the math program I'm in is a total joke. The honours stream is legit though and will actually prepare you for grad school. Research thoroughly the program you want to be admitted to regardless of the reputation of the uni.

StrangeWizard
StrangeWizard

I went to a pretty shitty undergrad institution but got into a Group I school for grad school. Get good letters of rec, and try to get your name on as many papers before you graduate as you can. I'd also recommend self-studying your dream school's curriculum if your current one isn't challenging you enough.

Lunatick
Lunatick

How did you cope? My courses are terrible so I self study the material from proper books, but having to do all this computational bullshit in the actual class is brutal.

Lord_Tryzalot
Lord_Tryzalot

I haven't started the math program at my school yet. I've completed all the Calc courses and am currently taking Differential Equations. At this point I'm a mathlet. Which is why I was wondering if I should transfer out before I even have the chance to be aware of how shit my school's curriculum is. I plan to self study anyway and to review Spitvaks Calculus book since my school uses Stewart. Could I still lack crucial underlying knowledge if I haven't even seen a real math course yet?

Thank you.

SomethingNew
SomethingNew

this. someone recommend something better for linear algebra

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Inmate
Inmate

If you're not being challenged by the material, use it as an opportunity to work learning a new skill into it.

I took a cryptography course at my old school that wasn't hard, but it was extremely computation heavy. So I taught myself how to code and wrote methods to do all the long calculations for me.

PackManBrainlure
PackManBrainlure

What's a physicist friendly book for differential geometry?

Emberburn
Emberburn

Plotting on how to overthrow my upcoming calculus classes.
Algebra 2 person here, freshman, the only freshman in my class of all sophomores. I already raised the pits of Satan himself upon the class by smoking everyone, which is fun until our teacher counts everything off for not showing work, but hey, I might consider studying pre calculus over the summer just got the heck of it, that way I'll send the class into oblivion.
Then I'll just enjoy senior year.
What am I doing.

Boy_vs_Girl
Boy_vs_Girl

yes it is
That remains to be shown.
well-defined things just fit the labels you use for them
This is not well-defined.

haveahappyday
haveahappyday

hoffman & kunze obviously come on now

askme
askme

you have to be 18 to post here I thought. If this isn't b8 tho just realize now that you aren't special and chances are you won't amount to anything like the overwhelming majority of the rest of us so try to understand that now so you don't end up being disappointed in the future.

Inmate
Inmate

Showing your work is what mathematics is. Don't be a brainlet by thinking you aren't one

TreeEater
TreeEater

mathematics
This is not well-defined.

TurtleCat
TurtleCat

apparently he talks about high school math (algebra/precalculus), not actual mathematics

viagrandad
viagrandad

Thanks for the recommendation. I'm taking a class in this and this book is really confusing.

DeathDog
DeathDog

take a look at the GRE's, that should give you some idea what you are supposed to learn. analysis and algebra are typically 3 semesters each.

New_Cliche
New_Cliche

How did you guys learn numerical/computational math? Any good books? Youtube?

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Supergrass
Supergrass

This is the mathematics general. If you would like to discuss engineering please direct yourself to the engineering thread(s) on /toy/ and elsewhere.

viagrandad
viagrandad

Hey, can someone here answer my question? (veekyforums.com/thread/9612214/science)

Thank you!

takes2long
takes2long

general
Not well defined.

iluvmen
iluvmen

Never mind, it's been answered. Thank you!

massdebater
massdebater

Start with Spivak's calc on manifolds and Schutz's geometry in physics.
Kuhnel's curves surfaces manifolds, Spivak's differential geometry vol 1-2, Lee's smooth manifolds, Milnor's differential topology, Guillemin and Pollack's differential topology, Schlichenmaier's Riemann surfaces algebraic curves moduli spaces, Naber's gauge fields, Nakahara's geometry topology, Baez's gauge fields knots gravity, Gockeler and Schucker's differential geometry

WebTool
WebTool

Isnt Algebra 2 and Trigonometry precalculus? Trig is very easy if you can remember and visualize the unit circle and understand it. Precalc algebra is harder than trig

Methshot
Methshot

Schlichenmaier's Riemann surfaces algebraic curves moduli spaces
That book tries to cover way too much material and ends up not really giving any detail at all.

Inmate
Inmate

Try posting about this in the physical threads located at /toy/.

TalkBomber
TalkBomber

How can I show that every ideal is maximal in the non-standard integers [math]\underline{\mathbb{Z}}^\infty[/math]?

WebTool
WebTool

because no one understood their research

ftfy

TurtleCat
TurtleCat

because they produced no tangible results

ftfy

RumChicken
RumChicken

No one in engineering you mean? Why are you posting about that here?
tangible results
Try asking in the physics threads if you want "tangible" (i.e. understandable by the mentally impaired) results such as the existence of blacks holes and so on.

PurpleCharger
PurpleCharger

Generally it means checking that a relation is functional.

StrangeWizard
StrangeWizard

No need to get mad user.

I meant tangible in an abstract sense, as in lacking results within the field. How many useful connections have actually been made that weren't previously known though other techniques?

Stark_Naked
Stark_Naked

Show any ideal quotient defines a field

Garbage Can Lid
Garbage Can Lid

That's true. I included it because its short and gives a fair intro to complex geometry with good references. I thought about including Bott and Tu and Bredon as well but I think they're too involved.

askme
askme

Hey guys I'm a real brainlet when it comes to maths and am having some trouble trying to solve this problem I have. I want to find the coordinates of B and D in pic related. I have the coordinates of A and C currently and have calculated the length of each edge and the diagonal length.

The problem is it's a 3 dimensional object and it's on a reasonable angle such that A is much deeper than C.

If anyone could point me in the right direction of what they'd do next that would be super appreciated.

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Need_TLC
Need_TLC

Whats a good book about tensors. I can't understand them.
t.physics brainlet

Booteefool
Booteefool

amazon.com/Tensor-Analysis-Manifolds-Dover-Mathematics/dp/0486640396
amazon.com/Tensors-Differential-Variational-Principles-Mathematics/dp/0486658406/
amazon.com/Vector-Tensor-Analysis-Applications-Mathematics/dp/0486638332
amazon.com/Elements-Tensor-Calculus-Dover-Mathematics/dp/0486805174/
amazon.com/Vector-Tensor-Analysis-Dover-Mathematics/dp/0486601099
amazon.com/Applications-Tensor-Analysis-Dover-Mathematics/dp/0486603733
ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20050175884.pdf

Sir_Gallonhead
Sir_Gallonhead

What Topology book would you recommend?

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Soft_member
Soft_member

as in lacking results within the field
That's understandable since it's not a field about "results" in the usual sense.

How many useful connections have actually been made that weren't previously known though other techniques?
What is "useful" to you? Is pretty much the entirety of algebraic geometry, algebraic topology and homological algebra somehow not "useful" and "tangible"? In that case, maybe you should start using the physics threads over at /toy/? Although even their kind would laugh at you for openly claiming such things. So maybe /g/ would be a more suitable place?

Techpill
Techpill

tensors
What do you mean? This isn't standard terminology.

TurtleCat
TurtleCat

Dugundji's book.

Rotman's book on homological algebra.

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StonedTime
StonedTime

Dugundji's
An old dusty Topology book. I knew that you were a troll, you can't do Topology without Analysis.

eGremlin
eGremlin

you can't do Topology without Analysis
No. You in particular can't do topology (with or without an*lysis) and that's understandable given the limits of your brain.

Sir_Gallonhead
Sir_Gallonhead

old dusty
Not an argument.
i knew that you were a troll
How am I a troll?
you can't do topology without anal
Yes you can. Anal serves as a source of examples of how topology can be applied to certain cases, but it is not needed for topology. You can't do linear algebra without analysis either because differential operators are linear?

This.

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farquit
farquit

an*lysis

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Burnblaze
Burnblaze

You say this as a person who did topology before analysis or are you just speculating because you feel like your mathematical maturity didn't play a role because you fail to realize it's importance and just focus on the analysis-aspects?

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Emberburn
Emberburn

I'm sorry about your brain loss. It must have been painful, right?

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Evilember
Evilember

Not him, but he's completely correct and I'm saying this as someone who has never touched any branch of engineering (including analysis).

CouchChiller
CouchChiller

an element in the tensor algebra

Stupidasole
Stupidasole

We used some anal stuff as examples when doing metric space stuff, for example Lipschitz continuity. Otherwise we had no use for anal.

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Garbage Can Lid
Garbage Can Lid

HOME-uh-toe-pee

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askme
askme

Reddit frogs are not welcome here. Refer to /v/ and /r/catalog#s=eddit%2F.

Sharpcharm
Sharpcharm

Ignore the charlatans.

Reddit frogs are very welcome here, friend.

Burnblaze
Burnblaze

This but unironically

Firespawn
Firespawn

Reddit spacing and reddit frogs are not welcome here. Try using proper websites for your kind, one example would be /r/catalog#s=eddit%2F.
"unironically"
Refer to the message above .

TalkBomber
TalkBomber

Errrrrrrrrrrrrr, nope.

If you can't pronounce shit like "homotopy" using only the fact that it's derived from Greek, you are not welcome here.

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SniperWish
SniperWish


Reddit spacing and reddit frogs are not welcome here. Try using proper websites for your kind, one example would be /r/catalog#s=eddit%2F.
(You)
"unironically"
Refer to the message above .
(You)
Errrrrrrrrrrrrr, nope.

If you can't pronounce shit like "homotopy" using only the fact that it's derived from Greek, you are not welcome here.

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CouchChiller
CouchChiller

No one gives a shit faggot. Go drink your soy milk you pathetic kike. You can play all the nintendo switch you want you limpwristed faggot no mudslime yuro or shitskin spic will ever accept you into their commie nigger club

New_Cliche
New_Cliche

veekyforums.com/thread/9612824/science
any takers

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Spazyfool
Spazyfool

This holds trivially, since any class which is a set is finite.

askme
askme

I'm interested in Logic, Number theory, Proof theory and to a certain degree Probability theory.
I'm a physics major.
Using the common division, Algebra, Analysis and Geometry/Topology. Would Algebra be the right way to go?

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Sharpcharm
Sharpcharm

what?

LuckyDusty
LuckyDusty

What are you having trouble with in my post?

PurpleCharger
PurpleCharger

what's a class

viagrandad
viagrandad

Would Algebra be the right way to go?
In what sense are you interested in number theory if you have to ask this?

Boy_vs_Girl
Boy_vs_Girl

what you missed because the question is trivial

viagrandad
viagrandad

Suppose epsilon is smaller than 1 (otherwise, the set is empty or has very few elements). Then there is by archimedean property of the reals, there is some natural number q such that [math]\frac \epsilon 2 q>1[/math]. Hence [math]\frac{1}q<\frac \epsilon 2[/math]. Now, how many natural numbers p(and hence rational) are there such that p/q is smaller than 1? Hint: it's finite

SomethingNew
SomethingNew

All the things you are interested in are completely unrelated, and hence they require literally all the fields you mentioned

Lunatick
Lunatick

Studying for a functional analysis test and reading Rick Miranda's Algebraic Curves and Riemann Surfaces along with Milnor's Characteristic Classes. Miranda's book is a gem.

Ignoramus
Ignoramus

Vilfredo Pareto’s Manual of Political Economy.

Not mathematical enough desu senpai. I liked Irving Fisher’s mathematical investigations a bit more

GoogleCat
GoogleCat

Is pretty much the entirety of algebraic geometry, algebraic topology and homological algebra somehow not "useful" and "tangible"?
Of course those are not useful or tangible.

Nojokur
Nojokur

In what sense are you interested in number theory if you have to ask this?
Presumably the analytic sense.

Lunatick
Lunatick

All the things you are interested in are completely unrelated
This is false.

lostmypassword
lostmypassword

Perhaps to a "computer ""scientist""" such as yourself. Refer to the /g/catalog#s=hetto%2F.

Gigastrength
Gigastrength

"computer ""scientist"""
This is a meaningless notion.

Methshot
Methshot

analytic
And why would he be posting about that in a mathematics thread? Presumably he has read the subject.

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PackManBrainlure
PackManBrainlure

t. literal drooling retard

Sharpcharm
Sharpcharm

Indeed. "Computer "scientists"" such as are meaningless notions.

Firespawn
Firespawn

True. They're too abstract and untangible for me. I'm a black person by the way.

SniperGod
SniperGod

"Computer "scientists""
What do you mean?

RavySnake
RavySnake

Mathematics is that which is studied in Mathematics departments in non-profit academic institutions

kys

BlogWobbles
BlogWobbles

old dusty
do you think theorems change over time, faggot-kun?
dust is also topologically invariant so just discard it

RumChicken
RumChicken

faggot
Why the homophobia?

StonedTime
StonedTime

this fucking thread
We should just call it /shit/. Do you autistic losers EVER discuss mathematics? The thread is literally solid shitposting from post 1 to here.

CouchChiller
CouchChiller

an*lysis

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VisualMaster
VisualMaster

Do you autistic losers EVER discuss mathematics? The thread is literally solid shitposting from post 1 to here.

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DeathDog
DeathDog

See

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ZeroReborn
ZeroReborn

faggot
Why the homophobia, faggot-chan?

eGremlin
eGremlin

I'm a black person by the way.
Why the racism?

AwesomeTucker
AwesomeTucker

What do you mean? How is me being black racism?

CodeBuns
CodeBuns

Hey guys. What are some good algebraic topology books for black people? I find the usual references too hard and abstract for some strange reason.

Nude_Bikergirl
Nude_Bikergirl

What are some good algebraic topology books for black people?
It's not a book, but freevideolectures.com/Course/2721/Algebraic-Topology

farquit
farquit

How is me being black racism?
How is it not?

cum2soon
cum2soon

Mendelson's and Jänich's

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Bidwell
Bidwell

How is black people (me) simply existing somehow racism?

Inmate
Inmate

the complement of the middle class is not the proletariat
unless you consider people like Gates, Trump, and Weinstein to be proles
you know what, fine, i like this definition
leftists are so funny sometimes

hairygrape
hairygrape

Is there not a set of humans?
no. there are only sets of sets. formally all that exists are sets. your entire premise is ill-conditionned

Gigastrength
Gigastrength

formally

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Deadlyinx
Deadlyinx

The class of humans is in bijective correspondence with a subset of natural numbers, and thus a set.
Dunning-Kruger: the post

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PackManBrainlure
PackManBrainlure

This Also check out Lee's "Introduction to Topological Manifolds"

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Carnalpleasure
Carnalpleasure

it's in a ring context; they're talking about characteristics of rings
it's honestly perfectly fine

Sharpcharm
Sharpcharm

all that exists are sets

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Snarelure
Snarelure

How is black people (me) simply existing somehow racism?
Blackness IS racism

Evilember
Evilember

proletariat
proles
This is a meaningless notion.

Firespawn
Firespawn

The Black Body is an ONTOLOGICAL condition. Ontology here is not in the Heideggerian sense of Dasein, but a social formation in which Being, as such, is determined by the system which produces it. Being, then, is defined by the outside. Who you are, or who you think you are, is irrelevant against the condition of Blackness. Blackness is the condition of a body which is labelled as inhuman, uncivilized, etc, and is the figure by which Civil Society is defined against. This opposition of Civil Society being everything which is NOT the Black Body is the way racism perpetuates itself in the status quo, and comes from a long tradition of slavery.

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TalkBomber
TalkBomber

Middle class = petty bourgeoisie, high class or w/e it's called in English are the capitalists. Combine those and you get the non-proletariat.

Are we not sets of atoms in the end? Are atoms not sets of smaller stuff? Eventually we get down to some primitive notion.

What do you mean? There is an injective class function from the class of humans to the set of natural numbers.

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RavySnake
RavySnake

As a Black Body, this is too abstract for me.

WebTool
WebTool

petty bourgeoisie
high class
non-proletariat
all ill-defined

ESL
oh that explains it, you're just retarded.

BlogWobbles
BlogWobbles

Are we not sets of atoms in the end?
no, faggot
of course the literal communist posting in the math general has never been exposed to the most fundamental branch of mathematics
kindly kys

StonedTime
StonedTime

There is an injective class function from the class of humans to the set of natural numbers.
no there isn't. if you'd studied even the most rudimentary set theory or type theory you'd know this to not be the case. instead, you're content to copy and paste buzzwords from wikipedia to impress anonymous faggots on the worst thread on the worst board on Veeky Forums

DeathDog
DeathDog

Hey friend, are you the one that makes the topological friends images?

eGremlin
eGremlin

the set of natural numbers.
The natural numbers object in "[math]\mathbf{Set}[/math]" can be shown to be a proper class.
He is actually correct if you assume that LEM is false.

BinaryMan
BinaryMan

you can't do topology without analysis.
this is kind of true in a sense, but really it's more like they're both intertwined.
think of the Jordan curve theorem for example. most of complex analysis is virtually impossible without it but you have to prove it topologically.

FastChef
FastChef

atoms
Please go back to /toy/

GoogleCat
GoogleCat

I wish. They are by @omnisucker (twitter). These three are the only ones which exist as far as I know.

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StrangeWizard
StrangeWizard

no there isn't. if you'd studied even the most rudimentary set theory or type theory you'd know this to not be the case. instead, you're content to copy and paste buzzwords from wikipedia to impress anonymous faggots on the worst thread on the worst board on Veeky Forums
cringe

Fuzzy_Logic
Fuzzy_Logic

oh that explains it, you're just retarded
Speaking the same language as British island monkeys and Amerimutts makes you the retard here.

faggot
Why the homophobia?
of course the literal communist posting in the math general has never been exposed to the most fundamental branch of mathematics
You mean TQFT? That is not mathematics.

How is there not an injective class function? Collect all humans in a line and label them with consequent positive integers. What you end up is a function mapping every human to a unique natural number, and thus a function from a class to a set. Since it is injective, the class of humans must be a set.

he
Did I permit you to assume my gender?

this is kind of true in a sense, but really it's more like they're both intertwined
False. Anal is an application of algebra and topology.

The category of [math]\mathbb{R}\text{world}[/math] can be used as an example. Read Bourbaki's critique on Proudhon.

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New_Cliche
New_Cliche

He is actually correct if you assume that LEM is false.
no he is not, as the "class" of humans is not a class of any type, neither a proper class nor a set

Stupidasole
Stupidasole

He is actually correct if you assume that LEM is false.
I'm not a "he".

whereismyname
whereismyname

Literally this. Actually, you can even prove a meta-theorem that the definition of an exact sequence depends in a crucial way on analysis.

Illusionz
Illusionz

Speaking the same language as British island monkeys and Amerimutts makes you the retard here.
he said, in English.

Collect all humans in a line and label them
hahahahahHAHAHAHAHHAHAHAHHAHAHAAAAAAAAAAA

Spazyfool
Spazyfool

pretty much the entirety of algebraic geometry
nice meme

Supergrass
Supergrass

By no means an argument.

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Fried_Sushi
Fried_Sushi

th-things aren't an a-a-argument when YOU do them!!
he winged, in English.

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Need_TLC
Need_TLC

Nice damage control, mutt cuck.

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Nude_Bikergirl
Nude_Bikergirl

It's provably a type in the topos [math]D(\mathbf{Ho}(\infty\mathbf{Type}))[/math] which is definable if and only if LEM is provably false.

Booteefool
Booteefool

Exactly what a retard would say.

Spamalot
Spamalot

, you can even prove a meta-theorem that the definition of an exact sequence depends in a crucial way on analysis.
What do you mean?

farquit
farquit

What exactly isn't clear?

SomethingNew
SomethingNew

What exactly isn't clear?
What the "meta-theorem" precisely states

cum2soon
cum2soon

Thank you friend :3

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w8t4u
w8t4u

I am not reading anything. I am doing a really tedious partial derivative Webassign before Spring Break.

Poker_Star
Poker_Star

It states that the notion of an exact sequence in an abelian category is undefinable without having the deep prior notion of an "integral".

Skullbone
Skullbone

I am doing a really tedious partial derivative Webassign before Spring Break.
Why did you decide to tell us about your non-mathematical activities?

ZeroReborn
ZeroReborn

spinors all day everyday

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BinaryMan
BinaryMan

What is cardinality of a set which contains all of the cardinalities?

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CodeBuns
CodeBuns

Burali Forti paradox

Booteefool
Booteefool

contains all of the cardinalities
What do you mean?

VisualMaster
VisualMaster

I'm currently teaching myself abstract algebra.
Is it just me or do all of the interesting results in this field come from other, superior fields? number theory, polynomial algebra, combinatorics, etc.

CodeBuns
CodeBuns

superior fields
number theory
polynomial algebra
combinatorics
Nice b8, m8. I r8 8/8.

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StrangeWizard
StrangeWizard

number theory
That's a branch of algebra.
polynomial algebra, combinatorics, etc.
Haven't heard of those. Not an expert in engineering.

Dreamworx
Dreamworx

What are these interesting "results" you speak of?

Fried_Sushi
Fried_Sushi

That's a branch of algebra.
This is false.

Crazy_Nice
Crazy_Nice

who else /petitbougie/ af here?

Sir_Gallonhead
Sir_Gallonhead

This is false.
This is false.

MPmaster
MPmaster

petitbougie
This is provably not well-defined.

TreeEater
TreeEater

This is provably not well-defined.
The burden of proof is on you.

Emberfire
Emberfire

burden of proof
Refer to /lit/ for the proper place to discuss such topics.

Firespawn
Firespawn

Refer to /lit/ for the proper place to discuss such topics.
Refer to /x/ if you are unable to provide proof of your claims as per the burden of proof.

LuckyDusty
LuckyDusty

Is this a simulation?

JunkTop
JunkTop

most of the less-obvious stuff to me, at least so far. e.g. the structure of a cyclic group is essentially derived from number theory. it's obvious that every group is isomorphic to a permutation group, but the features of permutation groups (e.g. parity) are much less obvious and are proved with more outside math.
compared to those kinds of results, stuff like lagrange's theorem seems really basic
I know I'm still in baby land but I wanna know if this pattern continues -- does most of the insight in abstract algebra stem from concrete examples?

Booteefool
Booteefool

Do you know what makes abstract algebra abstract? You abstract away redundancies like numbers.

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happy_sad
happy_sad

Is this a simulation?
Is what a simulation?

idontknow
idontknow

structure of a cyclic group
lagrange's theorem
features of permutation groups (e.g. parity)
""results""
It's funny how high-schoolers always seem to be the ones writing such laughable posts and yet with a serious tone. I wanna know if this pattern continues -- do most of these people ever become self-aware enough to realize their own retardation?

Techpill
Techpill

Am I in a simulation right now? I demand to be briefed.

GoogleCat
GoogleCat

not every group is isomorphic to a permutation group
every group *embeds in* a permutation group
consider: the order of a permutation group on a set of cardinality n is n!, but there are groups of each prime order

Ignoramus
Ignoramus

I demand to be briefed.
We use "we", not "I".

Dreamworx
Dreamworx

Permutation groups are by definition the subgroups of symmetric groups.

Raving_Cute
Raving_Cute

oh. my bad, probably shouldnt've inferred definitions

Lord_Tryzalot
Lord_Tryzalot

don't listen to the other anons. Group theory is trash. Better speed up to get to the juicy ring/module theory

girlDog
girlDog

Seconding the Lee recommendation, gr8 book altho it doesn't cover some areas of non-directly-manifold-related point-set topology, if you care about that)

Evil_kitten
Evil_kitten

Group theory is trash. Better speed up to get to the juicy ring/module theory
Oh, the irony...

haveahappyday
haveahappyday

Pure maff student here --any tips for an aspiring hs math teacher? I know it sounds gay, but I want to give kids the education I never received.

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Bidwell
Bidwell

Where(which book) can I find levi civita tensors demonstrations in vectors? Like Ax(B.C), determinant, trace, det(I + kA), something like that, not the definition of index.

Techpill
Techpill

the fuck are you talking about, it's completely algebraic

RumChicken
RumChicken

Not really mg material, but don't be that "cool" teacher. That shit killed my desire to show up for geometry. I might be biased though since I was a loner.

BunnyJinx
BunnyJinx

speed up
What do you mean? Are you implying that finite group theory is somehow a prerequisite for studying rings and modules?

Need_TLC
Need_TLC

don't be that "cool" teacher.
Kek, that won't be an issue.

Crazy_Nice
Crazy_Nice

I've often felt the same way but if I'm being honest with myself most people probably wouldn't appreciate the kind of education that I wish I'd had (i.e., most people are not autistic)

Poker_Star
Poker_Star

finite group theory
As opposed to what?

Methnerd
Methnerd

In what sense?

Skullbone
Skullbone

The books the topology guys are recommending you are find, though I would say they're probably going to be too advanced if you're fresh off Spivak (it's not there there's a formal prerequisite for lots of this, it's just you want more mathematical maturity first). It also makes some sense to do a good analysis book first, because such books will do some point set topology in a more simple concrete context, which helps when you generalize later when studying topology properly.
But before you do all that, it's really crucial you do some linear algebra next. It just shows up everywhere and it's a good way to build more mathematical maturity. Hoffman and Kunze is the best linear algebra book in my opinion, but there are lots of good options out there.
After this, for analysis, I think Pugh's book is excellent. Rudin is a more terse alternative with no pictures, so I like it less for self study (it does have good problems though). Since you mentioned Tao, Analysis I covers very similar material to Spivak, so you'd really want to start on Analysis II. After any of these you'd be more than ready to read a point set topology book if you want (Mendelson or Munkres for example).
There's lots of options out there for algebra, like Aluffi, Artin, or Dummit and Foote. I have no strong feelings on these, maybe someone else will.

BlogWobbles
BlogWobbles

I would say they're probably going to be too advanced if you're fresh off Spivak
Post disregarded. Try recruiting people into your organization elsewhere.

RumChicken
RumChicken

In what sense?
As opposed to a term that is not redundant.

ZeroReborn
ZeroReborn

I have no strong feelings on these
You don't have any strong feelings on actual math and yet you seem to be an expert in "undergrad" "analysis" as you guys call it. Maybe you shouldn't be giving advice?

AwesomeTucker
AwesomeTucker

What are some applications of vector spaces which do not have a basis?

Fuzzy_Logic
Fuzzy_Logic

applications
Please go to the physics and engineering threads
/toy/

kizzmybutt
kizzmybutt

it's just you want more mathematical maturity first
And how exactly is someone supposed to develop it by doing engineering problems?
It also makes some sense to do a good analysis book first, because such books will do some point set topology in a more simple concrete context, which helps when you generalize later when studying topology properly.
He didn't state that he was a brainlet who requires crutches to understand simple concepts.
But before you do all that, it's really crucial you do some linear algebra next.
Linear algebra (the mathematical kind) requires basic ring theory and module theory, so it's advisable to learn those first.
After any of these you'd be more than ready to read a point set topology book if you want
He would be more than ready even without reading any of the poisonous garbage you recommended.

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Methshot
Methshot

anime poster
Not even worth reading your shitty post. Why don't you fuck off to /a/ and stay there?

PackManBrainlure
PackManBrainlure

Not even worth reading your shitty post. Why don't you fuck off to /a/ and stay there?
Do you need to swear?

Skullbone
Skullbone

Your kind is not wanted here, simpleton. Proceed to /r/catalog#s=eddit%2F if you dislike the fact that this website is based on anime discussion.

Emberburn
Emberburn

Not necessarily, but if he's taking the usual abstract algebra sequence, then they always start with group theory

Firespawn
Firespawn

none, which is why you want a basis so badly

WebTool
WebTool

So basically you're admitting that you're a redditor then?

BlogWobbles
BlogWobbles

if you havent read all 9 volumes of dieudonne's treaties on analysis what exactly have you been doing with your time? hint: wasting it

someone mentioned that pic was good. pdf on author's website.

ZeroReborn
ZeroReborn

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TechHater
TechHater

none, which is why you want a basis so badly
But what good is assuming you have a basis if you can't do anything else except assume it exists?

Dreamworx
Dreamworx

Every vector space has a basis by the AoC, I don't know what your problem is? you want an explicit basis?

Raving_Cute
Raving_Cute

You don't need AC to prove something which holds trivially.

Harmless_Venom
Harmless_Venom

it doesnt hold trivially for infinite dimensional vector spaces

Lord_Tryzalot
Lord_Tryzalot

Every vector space has a basis by the AoC, I don't know what your problem is?
So every vector space has a basis only if you assume it has a basis. What's the point in making such an assumption?

King_Martha
King_Martha

it is a useful one. Turns a "suppose you have a basis", to "let this set be a basis"

viagrandad
viagrandad

it is a useful one. Turns a "suppose you have a basis", to "let this set be a basis"
Useful for what? "suppose you have a basis" and "let this set be a basis" are functionally equivalent if you can only say "let this set be a basis" by assuming a basis exists.

happy_sad
happy_sad

infinite dimensional vector spaces
This is redundant.

SomethingNew
SomethingNew

redundant
This is not well-defined.

cum2soon
cum2soon

well-defined
This is not well-defined.

Bidwell
Bidwell

This is not well-defined.
This is false.

iluvmen
iluvmen

This is false.
The burden of proof is on you.

likme
likme

It holds by definition of "vector space" for arbitrary vector spaces.

lostmypassword
lostmypassword

arbitrary vector spaces
This is a meaningless notion.

Poker_Star
Poker_Star

Another poster interrupting - you might define "finite dimensional" without a basis: just take "generated by some finite subset" as your definition. Then definite "infinite dimensional" as "not finite dimensional".

Deadlyinx
Deadlyinx

Another poster interrupting - you might define "finite dimensional" without a basis: just take "generated by some finite subset" as your definition. Then definite "infinite dimensional" as "not finite dimensional".
I am not sure what you are trying to imply here.

All vector spaces are infinite dimensional which is why "infinite dimensional vector spaces" is redundant, and "generated by some finite subset" is not remotely equivalent to the definition of a basis.

Skullbone
Skullbone

Ok, I misunderstood your statement.
Can you give a proof that all vector spaces are infinite dimensional?

SniperGod
SniperGod

How so?

TalkBomber
TalkBomber

proof
Refer to /lit/ for the proper place to discuss such topics. I am sure you can find one in any of the standard references (e.g. proofwiki, vixra).

RavySnake
RavySnake

How so?
What meaning does it have?

TechHater
TechHater

The proof can't be shown to exist constructively.

CodeBuns
CodeBuns

constructively
This is a meaningless notion.

GoogleCat
GoogleCat

This is a meaningless notion
This is not well-defined.

Stupidasole
Stupidasole

well-defined
What do you mean?

Spamalot
Spamalot

Can anything which is not "well-defined" be lifted to something "well-defined"? For example the function [math]f: \mathbb{Q} \to \mathbb{Z} [/math] defined by [math] f(\frac{a}{b})=a [/math] which is not "well-defined" since [math]\frac{1}{2}=\frac{2}{4}[/math] but [math]f(\frac{1}{2}) = 1[/math] and [math]f(\frac{2}{4})=2[/math], but can be lifted to a "well-defined" function [math] \tilde{f}: \{ \frac{a}{b} \mid a\in \mathbb{Z}, b\in \mathbb{Z}\backslash \{0\} \} \to \mathbb{Z}[/math].defined by [math] \tilde{f}(\frac{a}{b})=a [/math].

happy_sad
happy_sad

Clearly homotopy should have the same cadence as homology.

SomethingNew
SomethingNew

What do you mean by "well-defined"?

massdebater
massdebater

The formula you gave does define a relation, just not a function. What you can do is show that given an appropriate into the "domain" of the relation, the relational composition of that function with your relation is itself a function; this is your "lift". The function you'd compose with in this case would be (a, b) |-> a/b

likme
likme

s/given an appropriate into/given an appropriate function into/

Playboyize
Playboyize

wait never mind I have no fucking idea what I was thinking, pls ignore this

eGremlin
eGremlin

Maybe look into applied math about something you care about? I am an electrical engayneer who likes machine learning so taking advanced linear algebra with someone who researched applied problems in signal processing/control theory was pretty cool. Of course if you don't give a shit about anything then pure math is cool too.

BunnyJinx
BunnyJinx

hoe moe loe gee

happy_sad
happy_sad

Honest question: why is this general so cancerous?

Bidwell
Bidwell

why is this general so cancerous?
What do you mean?

Sharpcharm
Sharpcharm

Things like this:
This is just from the first half the of the thread and I definitely skipped some. Basically, lots of trolling and elitism about branches of mathematics (inb4 somebody replies in a way that implies analysis isn't "true math"). I just wanna talk about math without 5 trolls responding to every post.

RumChicken
RumChicken

I just wanna talk about math
Like what?

AwesomeTucker
AwesomeTucker

The set [math]\{(a^2,a^3,a^4) | a \in \mathbb C\}[/math] is algebraic since it's the vanishing of [math] (x^3 - y^2, x^2 - z) [/math], right? It's an exercise to find the Zariski closure of this set, and based on how far into the section it is it feels like it shouldn't be this obvious.

CodeBuns
CodeBuns

Ok, let's try this and see what happens.
I'm taking a geometric measure theory seminar this coming semester. Does anyone have any book recommendations, and have there been any recent interesting results to give me some idea of what's being worked on right now?

Illusionz
Illusionz

That's not math

Stark_Naked
Stark_Naked

wow I'm so shocked

Need_TLC
Need_TLC

Does anyone have any book recommendations
The most boring kind of question, are Amazon reviews not enough? Especially when you can download nearly any book instantly

Inmate
Inmate

what is analytic number theory
what are elliptic curves
the absolute state of algebraists

likme
likme

brain damage: the post

lostmypassword
lostmypassword

the definition of a vector space nowhere implies the existence of a basis
go retake undergraduate linear algebra for the third time; maybe you'll learn something this time

Poker_Star
Poker_Star

All vector spaces are infinite dimensional
every day i browse this site i more quickly converge towards suicide

Deadlyinx
Deadlyinx

brain damage: the post
Wrong: the post.

Techpill
Techpill

geometric measure theory
sorry, i thought you wanted to talk about math?

anyways guys what's you're favourite functor/co-functor pair?

Methnerd
Methnerd

mathoverflow.net/questions/66084/open-problems-with-monetary-rewards

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PackManBrainlure
PackManBrainlure

all vector spaces are infinite-dimensional

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Flameblow
Flameblow

Because of a failed jewish biologist spamming. He doesn't even understand what people are talking about here, but tries to act cool by "knowing" abstract non-sense.

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Methnerd
Methnerd

Yeah, just take the equivalence class of being a certain number and project it down to the quotient, but don't expect it to be a homomorphism or anything

Skullbone
Skullbone

Federer. If you can tackle it, you'll be literally god

VisualMaster
VisualMaster

because we are on Veeky Forums

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TreeEater
TreeEater

So is this the homework help thread?

Because I need some help with a statistics question.

I have to use the maximum likelihood rule to determine which classification and object belongs too.

There are two classes of objects, and each object has two measured features.

The question asks you to use the "Naïve Bayes classifier" which is no problem, but all of the examples I have for applying this have the constraint:

Objects are equally likely to be in class 1 or class 2 and are normally distributed.

For this question though, objects are still normally distributed, but objects in class 1 are twice as likely to appear as class 2.

my set of data looks something like:

class 1:
object 1: x=3.4 y=2.3
object 2: x=4.5 y=2.1
...
object 10 ...

class 2:
object 1: x=2.4 y=1.3
object 2: x=3.5 y=1.1
...
object 10 ...

where both sets are the same size. My question is just what do I need to adjust in my calculation to reflect the increased likelihood of being in class 1 vs class 2 if the data sets are the same size?

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Fried_Sushi
Fried_Sushi

your reddit spacing and retarded way of explaining things makes it hard to understand what you want

I have never done anything like this before so you should have clarified some more

Objects are equally likely to be in class 1 or class 2
My question is just what do I need to adjust in my calculation to reflect the increased likelihood
my guess is you simply multiply with the probability

what exactly is the formula you use? I dont know what naive bayes means. so when you have a new object, to guess its class you compare the probability that it belongs tto class 1 or class 2. now if twice as many appear in class 2, you simply add the respective probability multipliers 1/3 for class 1 and 2/3 for class 2 and then pick the one with the higher probability for maximum likelihood

when both are equally likely both are multiplied by 1/2 and since it is the same you can ignore this factor

Need_TLC
Need_TLC

class 1 are twice as likely to appear as class 2
read that wrong
ultipliers 1/3 for class 1 and 2/3 for class 2
should obviously be switched, 2/3 for class 1 and 1/3 for class 2

Skullbone
Skullbone

Ok lads, I wanna be ready for the start of my PhD next September on algebraic number theory/geometry. Recommend me books or a certain progression to be absolutely prepared for anything by the time I get there. Assume I'll work all day starting June.

RumChicken
RumChicken

For Naive Bayes with Gaussian class conditional you need

a) priors for all classes given by b) Estimate the class conditional for each class by estimating the mean of the feature vectors. Since its Naive Bayer you don't need to estimate a full covariance for each class but only the variances for each feature in each class

Sharpcharm
Sharpcharm

so [math]dx[/math] is a purely symbolic representation and not an actual division of differentials?

Why does this work then?
[math]\dfrac{df}{dg} \times \dfrac{dg}{dx} = \dfrac{df}{dx} [/math]

Why does this also appear to work?
[math]f(x) = y[/math]
[math]f(x+dx) = y+dy[/math]
[math]f(x+dx) - y = dy[/math]
[math]f(x+dx) - f(x) = dy[/math]
[math]\dfrac{f(x+dx) - f(x)}{dx} = \dfrac{dy}{dx}[/math]

eGremlin
eGremlin

You need to think of it as an arbitrary change in value locally then all that makes sense

BunnyJinx
BunnyJinx

en.m.wikipedia.org/wiki/Chain_rule
en.m.wikipedia.org/wiki/Taylor's_theorem (first order)

Techpill
Techpill

you can turn it into an actual division if you work in non-standard analysis
ultrapowers are neat

whereismyname
whereismyname

how hard would it be to learn multivariable calc on my own? ive just finished integration at uni.

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