/sci/ - Science & Math

>>9571696
I had this guy for calc 1. Couldn't read a god damn thing he wrote on his projector slides.

Could graph theory be applied to find a winning strategy for a car chase?

http://losangeles.cbslocal.com/video/channel/322-cbs2-live-newscasts-and-breaking-news/

>>9571981
No, but you could use coding and algorithms

>>9571667
Sorry, I'm not mentally diseased.

>>9572311
>implying

>>9572316
So what are you trying to achieve again?

>>9572334
Since you're too autistic to understand, I'm saying you are mentally diseased
It's not funny when I have to explain it anon

>>9572337
You're trying to claim that I'm a "platonist" or an "intuitionist". Neither of these hold since I'm not mentally diseased.

>>9572412
t. Actual retard
You think I'm the same person, who followed you from that thread?
>you're too autistic to understand
This statement still stands, and is amplified by the proof you have just willingly provided

>>9572433
>You think I'm the same person
It's a post made by the same account so it doesn't really matter.
>This statement still stands
How so? I'm neither of those things, nor am I mentally diseased.

>>9572535
>nor am I mentally diseased.
Your posts signal otherwise.

definitive texts for precalc?

For calc you hear about stewart, apostol, spivak

for lin alg, theres axler, strang and a bunch of others

For analysis you hear about tao and rudin

are there any books like those for precalculus?

>>9572545
The doctors signal otherwise.

>>9572606
>The doctors signal otherwise.
They likely have not read your posts.

>>9572578
Axler has a book on precalculus, if i recall correctly.

>>9572578
Lang - Basic Mathematics, the canonical precalc textbook.
BTW, there's a cretin lurking here that keeps posting "Lang is a meme", don't listen to him.

>>9572756
>Lang - Basic Mathematics
Lang is a meme.

>>9572756
>BTW, there's a cretin lurking here that keeps posting "Lang is a meme", don't listen to him.
I'm not a "him".

How can I get better for euclidean geometry (as in, 5 Euclid's postulates+some equivalences)? For some reason the first 3 weeks of my Intro to Geometry course is about euclidean geometry.

Most books propose their own axiomatic system, but I want to practice with the one I mentioned earlier. Which book can help me solve some problems? My prof is autistic so there's no (useful) ref books

(pic related, I really struggled trying to prove that the sum of all angles in pic related is 180 degrees)

I visited my grandmother today after her appointment with a doctor. We discussed for hours, and the topics were war, the rotting effects of liberalism and globalism, and category theory.

It was interesting to hear her tell how she would have moved troops along the Eastern front. She then started asking me why the Rocket man is so aggressive, and I compared juche to sogun sasang explaining how that affects things. We then ended up discussing how all the LGBTQFT acceptance is nothing but mentally ill people normalizing mentally ill people, and how American rot is destroying the West. Using this perspective, I made her understand why I would never set my foot on the lost continent.

Then she told me to explain my master's thesis to her, and I did. I motivated Mitchell's embedding theorem by explaining what manifolds are, and then telling how a similar situation can be seen in abelian categories if one has sufficient imagination. I explained how the local concretization puts flesh on the bones of the abstract underlying skeleton. She understood it well enough to call it important stuff. Thanks granny 92 yo!

/blog <3

>>9572843
Anyone who calls math "important stuff" missed the point of it.

P.S. I am a research mathematician.

>>9572866
I don't remember asking for your opinion.

P.S. I am the backbone of these threads.

>>9572866
It's clearly important for anyone studying it.

>>9572881
This!

Neumann's Separation Lemma: Let [math]G[/math] be a permutation group acting on an infinite set, [math]\Omega[/math] with no finite orbits. Then for any finite subsets, [math]\Gamma[/math] and [math]\Delta[/math] of [math]\Omega[/math] ,there exists a permutation [math]g\in G[/math] for which [math]\Gamma^{g}\cap \Delta = \emptyset [/math]

can someone explain this

>>9573137
Write out what it means to take the Laplace transform of a function, and then T H I N K.

what does sgn(T) refer to, when T is a normal operator on a Hilbert space?

>>9573137
beautiful math incoming:
https://en.wikipedia.org/wiki/Linear_map

>>9572578
Pre-calculus: Stitz & Zeager (http://www.stitz-zeager.com/)), Axler (Precalculus: A Prelude to Calculus) or Stillwell (Numbers and Geometry)
All three are pretty rigorous and I would argue Stitz & Zeager is best one of them but is rather lengthy so you might be better off with Apostol. (Also you could unironically use Lang's Basic Mathematics... While not recommended it's still doable as a precalculus book)

Calculus:
Rigorous; Spivak, Lang or Apostol
Intuitive/Introductory; Stewart
Go with Stewart only if you plan on becoming an engineer or only do mathematics because it's mandatory

>>9573137
The laplacian is a linear application under holonome constraint

Is it wrong that I automatically dismiss a maths book if the author is a woman?

Change my view, lads. What maths books with female authors are worth reading?

>>9573604
>Is it wrong that I automatically dismiss a maths book if the author is a woman?
There are female authors? How did I not know this, spivak BTFO

>>9573604
The definitive work on computable structure theory was written Julia Knight. Also the article in the handbook of recursive mathematics on Pure and Computable model theory was written by Valentina Harizanov.

>>9572801
>I really struggled trying to prove that the sum of all angles in pic related is 180 degrees

Out of curiosity what was the correct way to prove it? I'd do something like drawing parallel lines (pic related) not sure if it's a valid proof though.

>>9573669
Wait? That Spivak guy is a woman?

>>9572801
My prof wrote a pretty good book on rigorous geometry. Check out Mark Solomonovich's Geometry.
He does everything as the Euclideans do but with good explanation and examples and drawings

>>9573604
In general, reading mathematics written by a human female is not worth it. There are some exceptions.
>What maths books with female authors are worth reading?
Topos annelés et schémas relatifs.

>>9573735
>rigorous geometry
what do you mean?

>>9573604
Anything by Claire Voisin, in particular "Hodge Theory and Complex Algebraic Geometry"

>>9572311
so your opinion of the ontological status of mathematical objects is neither that they are realized by computation, that they have independent, objective existence, nor that they are fundamentally mind-internal. What *do* you think, then?

I took real analysis and immediately switched to app math major

I have no idea how you guys do proofs. I just have no idea where to take them once I get started.

Ex prove sqrt(2) isnt rational. i know now you do contradiction but i have no idea how whoever came up with that chose proof by contradiction. and once you get to the part p^2 = 2 * p^2 idk how the fuck you knew that implies p/q is even (i know how, i just didnt think to look for it) which contradicts something earlier

you people are fuckin crazy

>>9573836
>they are fundamentally mind-internal
This does not uniquely determine "intuitionism" or "platonism".

>>9573604
No, it's not wrong since most of them are garbage. Forget the whole "maths" part, it applies for all books.

Not even a women hater, just being honest here.

>>9573846
it's entirely a matter of practice. i once felt exactly the way you do

>>9573855
So what's your position?

>>9573846
>I took real analysis and immediately switched to app math major
This makes no sense. Real analysis is a part of and is actually exclusively studied by "app math majors" and engineers.

>>9573861
i know
but i took it as an indicator that i would blow at further theory courses so i resigned myself to codemonkey

>>9573860
The thing I quoted would be the closest to my position. Although this discussion is hardly relevant to a mathematics thread.

>>9573861
are you trying to imply that R is not an extremely important object in massive swathes of mathematics

>>9573866
>theory courses
What the hell is a "theory course"?

>>9573869
>an extremely important object in massive swathes of mathematics
In what sense?

>>9573846
It takes practise like everything else, eventually you'll get the feel for it and you can often guess what kind of proof would probably be efficient for whatever you're trying to prove. Obviously most things can be proven in multiple different ways too, sometimes a certain approach is just easier and/or more elegant than the others. Also, coming up with a new proof for some new problem often takes long.

>tfw when you see everyone that struggles with probability

>>9573884
>tfw struggled with probability but still aced that shit after ramping up the effort

>>9573884
Can't relate to meeting people who study probability (aka engineers) on a regular basis.

>>9573879
are you fucking serious
- almost anything topological is gonna involve R at some point or another
- C is built on R and is pretty fucking important in algebra
- I hope I don't have to tell you that the zeta function, which is C -> C, is extremely significant in number theory

>>9573894
>not going balls deep in probability theory
Do you hate fun and comfy

>>9573899
What kind of demented notion of fun and comfy do you have?

>>9573894
>not majoring in mathematical engineering
Do you hate money?

>>9573903
The only comfier area/course I have studied is complex analysis desu
t. too brainlet for abstract algebra

>>9573904
>not majoring in mathematical statistics
Do you hate money?

>>9573909
low-level abstract algebra is not harder than complex analysis

>>9573912
>not majoring in applied mathematical actuarial science
Do you hate money?

>>9573914
>low-level abstract algebra
What do you mean specifically?

>>9573914
Didnt stop me from being too stupid to really understand sylows theorems while also almost acing complex analysis
>>9573918
>tfw actually taking a course in insurance mathematics
300k starting

>>9573922
stuff like elementary group theory

>>9573923
what do you mean by "really understand"

>>9573928
Reliably solving questions on tests where you need to use sylows theorems is my definition of "really understand", but it probably had to do more with a shaky foundation of abstract algebra to begin with

>>9572871
you do realize this is a thread on 4chan, nothing worth putting on a resume, bub

>>9573937
I care little for such petty things.

rate my proof

>>9573956
better:
if (p/q)^2 is an integer, then the prime factors of q^2 are subsumed in p^2; but since squaring only doubles the multiplicity of each factor, this means that the prime factors of q are subsumed in p, in which case p/q is an integer. therefore, rational square roots of integers are always integral, but no integer is a square root of 2.

>>9573956
>that retarded [math]\times[/math] symbol instead of [math]\blacksquare[/math]
It's trash.

>>9573956
You need to state that p and q are integers. and that K is an integer. Other than that, it's fine if a bit clunky.

>>9572843
Nobody cares bitch
><3
Fuck off

>>9573956
That's not a proof.

>>9573975
>You need to state that p and q are integers.
This is clear from the definition of [math]\mathbb{Q}[/math].

>>9573996
Well he let q^2=K which works for proving rad2 is irrational. But if he had to prove rad3 is irrational, he wouldve had to let q^2 = 2k/3 which wouldve violated q being an integer.

So I guess I more said that to get him to think about that.

>>9573684
Exactly. I'm almost sure that using an equivalence of the 5th postulate you can draw the parallels, and using an equivalence of the 4th postulate the angles are equal

>>9573735
THANKS

If anyone else ITT has something I'd be very grateful, my grades depend on this

How would you formulate equivalence classes under a fuzzy logic system?

>>9573956
Define p and q as integers with q not 0. Also state that p and q have no common divisors except 1, or you could say their gcd is 1 instead. You should include an argument why 2 divides p^2 implies 2 divides p. It's because if a prime k divides a product ab, then it must divide a or b. I wouldn't set K and J, it makes it harder to read and it's obvious that if p and q are integers then so are p^2 and q^2.
>an even number divided by an even number is even
This is not true, consider 2 divided by 2, giving 1 which is not even. It's true for 4q^2 though since any even number divided by a smaller even number is even and q^2 must be greater than or equal to 1. This is also why it is valid to say that 2q^2/2 is even thus q^2 is even, since q^2 is greater than or equal to 1, so 2q^2 is greater than or equal to 2.
A cleaner argument for q being even is that since 2 divides p, 4 divides p^2, thus p^2=4k=2q^2 thus 2k=q^2 and 2 divides q^2. Thus by the same argument 2 divides q.

>>9572935
>you can get away from any set if you translate it enough
Wow amazing.
>>9573197
What are its properties? I've never seen it defined even in Von Neumann's book on QM.
>>9573914
Neither is any level of abstract algebra.
>>9573956
Sorry but you won't be able to get into our topology club with that trash.

>>9573778
Everything is proven from the ground up, starting with undefined notions (axioms we believe to be true but cannot prove, such as the existence of planes, points, and lines), the existence of isometries, then proving things one step at a time and using old proofs to prove new ones and so on. Nothing is taken for granted and everything must have solid logic and come from the given/built theories. It's the same as most math courses with proofs, but many geometry books/classes take certain things for granted and use wrong notions.

>>9573956
>>9574231
Actually the proof isn't correct since an even number divided by an even isn't guaranteed to be even. Any number with a single factor of 2 in its prime factorization is odd when divided by 2. So you need to use the argument that 2|p implies 4|p^2 then use that to get 2|q^2.

>normies get out of my group

>>9574391
Refer to >>>/toy/physics/, that's where your kind belongs.

>>9574103
Forget it, that book isn't really helpful to me. Fuck.

The whole idea of linear systems is that I can find a basis spanning the set of solutions under addition, since if [math]g[/math] is a solution and [math]f[/math] is a solution, [math]f+g[/math]

I've wondered if there are non-linear systems where you can form a basis under a different operation.

For example, if [math]f[/math] is a solution, and [math]g[/math] is a solution [math]O(f,g)[/math] is a solution where [math]O[/math] is some operator. In the case of linear systems it would just be [math]O(f,g)=f+g[/math].

You could do something sort of like Fourier series for non-linear systems except it wouldn't be a series, it'd be iteration of the operator [math]O[/math]

Is this the right order of math? If not fix it.

Counting to 100
Addition
Addition of Large Numbers
Subtraction
Subtraction of Large Numbers
Multiplication
Division
Probability
Geometry
Pre-algebra
Algebra 1
Algebra 2
Trigonometry
Statistics
Pre-calculus
Calculus I
Calculus II
Calculus III

whats after calc 3?

my uni offers a phd in engineering math
is it a meme? what kind of job would it be useful for?

>>9575750
Linear algebra
Ordinary differential equations
Partial differential equations
Real analysis
Abstract algebra
Complex analysis

>>9575782
>>>/sci/sqt/

>>9572801

>>9573684
>>9572801
>>9575923
If you don't understand what I did here: >>9575923, I just transported the alpha line to the intersection of the beta line and L1, then the alpha+beta line to the intersection of the gamma line and L1, etc

>>9573846
Well, the first thing you'd realise that it would be extremely hard to prove it in any other way, considering the definition of irrational - ie: a number that is NOT rational.

I've never touched group theory or lie algebras before. I just want a cursory understanding so I can try and understand what this one paper is saying when they bring them up in a proof, whats a fairly easy and quick resource for this? I don't need it to be especially rigorous.

Be honest: will you ever lose your virginity?

In Atiyah's K-theory page 6 (http://www.cimat.mx/~luis/seminarios/Teoria-K/Atiyah_K_theory_Advanced.pdf)), he defines a covariant functor of one variable [math]T[/math] from finite dimensional vector spaces to finite dimensional vector spaces to be continuous if the map [math]T:\hom(V,W)\to \hom(T(V),T(W))[/math] is continuous (with the usual topology of hom being that of [math]\mathbb R^n[/math]). Then he develops some theory and claims this works too for functors of more than one variable, although he doesn't give an explicit definition of continuiity in this case. What I think a possible definition could be is (eg, 2 variables):

[math]T[/math] is continuous if the map [math]T:(\hom(V_1,W_1),\hom(V_2,W_2))\to\hom(T(V_1,W_1),T(V_2,W_2))[/math]

Does this look right?

>>9576232
Actually I think a better definition is continuity of the map [eqn]T:(\hom(V_1,W_1),\hom(V_2,W_2))\to\hom(T(V_1),T(W_1)\times\hom(T(V_2),T(W_2))[/eqn]

>>9576320
Try the tensor product.

>>9576329
How? Continuity of
[eqn]T:\hom(V_1,W_1)\times\hom(V_2,W_2)\to\hom(T(V_1),T(W_1))\otimes\hom(T(V_2),T(W_2))[/eqn]
?

>>9576333
Yes.

>>9576336
why are you so sure?

>>9576340
I'm not. Tensor products just seem more natural to me.

>>9576351
You're pretty dumb, huh?

>>9576402
>You're pretty dumb, huh?
Yes.

>>9576232
>functor of one variable
What is a "functor of one variable"?

>>9576402
Sure.

>>9576417
think

rate my latex retardation

took me an hour to type this

>>9576419
The only thing I can think of isn't well-defined.

>>9576422
It should be [eqn]\frac{\partial f}{\partial u}(u)[/eqn] otherwise its a type error unless f maps to functions.

>>9576426
A functor of one or many variables is a functor, just that the former takes a single object to a single object, and the latter takes several objects to a single object

>>9576433
>takes a single object to a single object
>takes several objects to a single object
This makes no sense, it's not even well-defined.

@9576436
you got your yous, fine

>>9576436
>This makes no sense
Please refrain from commenting on topics which you do not have the required mathematical maturity to understand.

>>9576438
What's confusing you?
>>9576441
I wholeheartedly agree. Typing in ill-defined garbage which is not invariant under equivalence shouldn't be tolerated around here.

>>9576447
le hurr durr being a retard

Take normal functor from a category whose objects are n-tuples of objects of some other category

>>9576450
Every category is equivalent to a category you just described.

>>9576422
\left({\Big shit}\right)

>>9576422
one of the ugliest things I've seen
probably would even look better in microsoft word

>>9573197
There is a notion of positivity for self-dual operators, it would probably be defined as 1 if T is positive and -1 otherwise.

>>9576562
actually, it would probably be defined using the spectral theorem (an operator with eigenvalues [math]sgn(\alpha_i)[/math] where [math]\alpha_i[/math] is an eigenvalue of T)

I'll take a power nap and then do some math! Good night <3

Hey fellas. I'm doing a PDEs course.

I don't feel smart at all right now.

Anyone want to give me the BRAINLET run down on method of characteristics?

>>9576668
Good morning!

>>9576575
this makes sense, thank you

>>9576840
You find solutions along lines that come out of the boundary curve. This is on occasion easier because you instead solve ODEs. The first time these lines intersect is when the solution stops being valid. A method to fix this is to have a weaker notion of solution that allows for "shocks" between certain lines.

What's a good book for geometry? i'm someone who can just calculate the area of a triangle

i had a dream this morning about something math related

i took an orientable closed surface and identified all points with the same tangent vector up to a scalar multiple

in my dream, i somehow knew that this operation is independent of parameterization, and was even able to work out that the resulting object was an orbifold, but i don't remember how i knew, or if it's even true

as a simple example, take the sphere: all points are identified with their antipodes, giving something like the real projective plane in 2 dimensions (i think?)

is this worth exploring when i get home or is it just my brain pranking me while i sleep

>>9577418
actually now that i think about it this will either give you a point or a projective plane

if you strengthen the definition to only identify points with the same tangent vector up to positive scalar multiple, do you always get a sphere?

also, can this be extended to a more general class of surfaces somehow?
i know the idea of tangent vector doesnt generalize well and i can't seem to work it out

>>9577342
Hartshorne's Algebraic geometry

>>9577462
Seems kind of difficult

>>9577467
brainlet

>>9577468
Seems so, nothing I can do about that. Suggest an easier book

>>9577470
Coxeter

>>9577468
t. retard Grothendieck-Serre fanboy

Let [math]V_i,W_i[/math] be finite dimensional vector spaces over [math]\mathbb R[/math]. How do I show that the map [math]\hom(V_1,W_1)\times \hom(V_2,W_2)\to\hom(V_1\oplus V_2,W_1\oplus W_2)[/math] is continuous?

The topology of the homs are that of the set of matrices and hence than of some power of [math]\mathbb R[/math]

>>9578032
The map is itself linear and linear maps between finite dimensional normed vector spaces are always continuous.

>>9578077
The first space isn't even a vector space though

Yo I applied to maths graduate school in canada (specifically waterloo and toronto)

Any idea when I will hear from them? I dunno how the north american system works.

I've been offered a phd in europe (rank around 100) and need to give them my decision soon. Not sure if its worth waiting for canadians.

>>9578080
>>9578077
>>9578032
Actually, is this right?

[math]\hom(V_1\oplus V_2,W_1\oplus W_2)\cong \hom(V_1,W_1)\oplus \hom (V_1,W_2)\oplus\hom(V_2,W_1)\oplus \hom (V_2,W_2)[/math] so any open set in the codomain is necessarily open in the preimage as a simple restriction.

>>9578080
A cartesian product of two vector spaces is always a vector space.

>>9578104
it is quite possible that I am retarded - i thought such thing was not true

>differential geometry

>>9578091
>canada
See >>9572843

>>9577342
Start with Grothendieck's EGA I. Be sure to download the revised Springer edition.
>>9577462
I wouldn't recommend something which can't even correctly define a presheaf.

>>9578390
>I wouldn't recommend something which can't even correctly define a presheaf.
And what is wrong with Hartshorne's definition?

>>9578091
>Not sure if its worth waiting for canadians.
Why would you ever voluntarily set foot on that shithole?

I want to switch from EE to Math because I never cared for this major and just pursued it to appease my father. How competitive is the graduate school process? Should I be thinking about that now as I consider switching? (I am a Sophmore but will probably be a second semester freshman after I switch)What are the career options for someone in Pure Math besides things related to academia?

I can't find much dates for PhD applications, and some places have stuff like
>choose your starting date and have it accepted by some person in some obscure office of ours
so am I supposed to just send my application and not care about such social constructs as dates, unless I can find some deadline or time interval on the page? And I mean unis in the civilized world, not shithole countries on the lost continent.

>>9576422
stick to word next time

>>9578437
Constant presheaves are not presheaves according to his definition. It doesn't match the definition of presheaves on an arbitrary category. The category of "presheaves" isn't equivalent to the usual one.

Is there a non algebraic proof that the torus is not homeomorphic to the sphere?

>>9578638
>non algebraic proof
No such thing.

>>9578458
You won't make it anyway whore

I wanna paper my walls in algebraic topology figures. Also
>>9574983
>Tits (1960)

>>9578880
That figure is not interesting, why?

>>9575155
That sounds a lot like a group with some generating set, although I don't know what kind of solution spaces it would work for.

>>9572801
https://www.euclidea.xyz/

its pretty fun

How are you supposed to pronounce this symbol

>>9578891
That's not the prettiest one, it's just what I was looking at. I think the relationships between spaces are really cool and they can sometimes be represented in a clean, striking way.

>>9571802
>slides for math classes

I don't get this part
why does [math]\frac{\partial}{\partial t}\frac{\partial z}{\partial x}=\frac{\partial ^2z}{\partial x^2}\frac{\partial x}{\partial t}+\frac{\partial ^2z}{\partial x\partial y}\frac{\partial y}{\partial t}[/math]

>>9579077
forgot image

>>9578929
Depends on context. If it's being used for the partial derivative a of function, you use the word partial, so for example [math]\frac{\partial f}{\partial x}[/math] reads as "the partial derivative of f with respect to x". But this symbol is also often used for the boundary of a region, so for example, [math]\partial S[/math] is read as "the boundary of S".

>>9579077
>>9579079
It's multivariable chain rule: http://tutorial.math.lamar.edu/Classes/CalcIII/ChainRule.aspx

>>9578638
I don't know any Morse theory, but from what I've heard about it, it might be relevant?

>>9579150
The part I don't understand is why [math]\frac{\partial}{\partial t}[/math] is expanded to [math]\frac{\partial z}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial z}{\partial y}\frac{\partial y}{\partial t}[/math] here as if it was [math]\frac{\partial z}{\partial t}[/math]

>>9579003
It was one of these things and he would hand-write everything in sharpie.

I hate every single one of you faggots

>>9579655
nice dubs

how do u guys feel about combinatorics?

Why do you care about fake math so much?

>>9579684
You can do some pretty cool stuff with enumeration in computer code.

>>9578880
Fomenko mathematical impressions

>>9578929
The symbol itself is called nabla, but it's usually better to refer to its usage as in >>9579145

What are some of your fondly remembered test problems, /mg/?

I remember proving that algebraic polynomials preserve algebraic/transcendental-hood with extension degrees, that one I found fun at the time.

>>9579781
No, nabla is [math]\nabla[/math].

>>9578848
This is probably what is going to happen, but could I get an actual reply?

Is performing well in and enjoying your Linear Algebra course a good indicator that you would be able to get by as a app math major? I don't want to switch and find out I'm a brainlet after it's too late.

>>9580014
Applied "math" is for brainlets anyway, so since you're not even doing math it would be perfect for you.

>>9580085
Perfect. Thanks anon.

>>9579684
it's the best
when you're young and shit you're attracted by sheaves and manifolds and whatevers but once you grow old and mature combinatorics is where it's at

>>9580132
Are you saying that old and mature mathematicians quit mathematics and go into combinatorics? Doesn't seem to be the case.

>>9580432
I wouldn't take zûr posts too seriously, considering zûr inability to use capital letters and periods.

reposting from sqt

I don't understand this proof. How does the expression above the two points circled imply the RREF of A is either the identity matrix or has a final row of zeroes? It feels like they made an unjustified leap with the part circled. Or they're redefining the proof to only encompass certain n x n matrices A and not all.

>>9579939
Oh yeah, whoops.
That's what I get for not doing vector calc for 3 years.

>>9580510
>ERO

>>9580510
If the RREF of A is not the identity, then A is singular so the RREF must have a zero row at the bottom. This is just a general observation, not following from the equation above.

>>9578929
https://en.wikipedia.org/wiki/%E2%88%82

>>9579684
>not posting the guy who wrote an actual song with combinatorics

>>9580696
>dabba dabba doo

>>9580438
I'm not a "zûr".

>>9580802
I misgendered xëm again...

>>9573846
lol I had to do that proof as in 5th year (junior year in America)

>>9578895

Yeah, I don't know if this is a thing or not.

I think just figured out how to generally solve PDE's of the form:

[math] Df=\beta f^n [/math]

Where [math]D[/math] is an linear first order differential operator but can possibly be of multiple variables( [math] D=g(x,y){\del}_x+h(x,y){\del}_y+... [/math] ). It seems pretty consistent so far.

>>9580812
Wrong angle. Here is the proper way to do it.

>>9579500
Try naively cancelling out the partial infinitesimal elements and it might help you see where some of the elements are coming from. Keep in mind its not valid to do this but you can get a dimensional understanding at least.

>>9581482
Looks sorta like a Bernoulli's Equation

>>9581723
Here is link: https://en.m.wikipedia.org/wiki/Bernoulli_differential_equation

>>9581700
>infinitesimal elements

>>9581723
>>9581733

This looks only like an ODE. I'm talking about multiple variables, a PDE.

Is there a version for this?

what is the vector of the arrow point away from the origin? pls halp im doing EM

>>9581781
Yeah I was just referring to their similar form, I wasn't saying they were identical. I haven't heard of a name for the PDE counterpart. You can check out techniques for solving the ODE and see if there is any connection to your method for the PDEs, though, which is why I posted.

>>9581782
What do you mean? What properties should the vector have? Also you've used a different coordinate system in your drawing than in your definitions for k.

>>9581782
>>9581807
The physishit threads are over at >>>/sci/phg/ and >>>/toy/.

>>9581807
im using xyz to show the orientation of the space. I have a wire set up as follows.
I want to find what is the magnetic field, B at the origin, O. The wire lie in the xy-plane.
I need to use Biot-Savart Law to solve this.


why am i such a fucking brainlet i want to die now

>>9581824
the pic.

>>9581803

It's kinda related.

The PDE part let's me set up initial value problems or boundary conditions. Then if you take the Fourier series not of the function, but of [math] f^{1-n} [/math], and then take the inverse transform with time evolution all under the root of 1-n you get something that kinda works.

Also there's some powers of n in the oscillating exponentials floating around.

Pretty dope being an integral equation that explicitly solves non-linear initial boundary problems, though I'm sure it's broken somehow.

Does anyone have a good reference for information on regularization of Eisenstein sums?
In particular, I want to know a good way regularize

[eqn]
\sum_{\substack{(m,n)\neq (0,0)\\ (m,n)\neq(m_0,n_0)}} {1 \over m + n \tau}
[/eqn]
with [math](m,n)[/math] taking values on an integer lattice and [math]\tau [/math] the complex modular parameter (not very important here).

Stokes-Cartan: If [math]\omega[/math] is a smooth [math](n-1)[/math]-form with compact support on a smooth [math]n[/math]-dimensional manifold with boundary [math]\Omega[/math], [math]\partial \Omega[/math] denotes the boundary of [math]\Omega[/math] given the induced orientation, and [math]i : \partial\Omega \hookrightarrow \Omega[/math] is the inclusion map, then [eqn] \int_{\Omega}d\omega = \int_{\partial \Omega}i^{*}\omega[/eqn]

>>9582599
stokes' formula is one of the few equations I find legitimately satisfying to look at
it's like how I'm supposed to be reacting to euler's meme equation

How would I go about getting the real and complex solutions of [math]x^{2}+y^{2}-1 = x^{3}+y^{3}-3xy[/math] (folium of Descartes with a unit cirlce)? Bezout's theorem says I should expect 6 in total, right?

>>9582694
actually at most 6, in the affine plane. regardless, how would I solve that algebraically?

How does one usually find a bijection between sets without using an actual function?

I had to use a super messy function divided into several cases by input for proof today and proving surjection was a pain in the ass

>>9581679
Thanks for the help!

>>9582781
Cantor–Bernstein–Schröder

>>9582781
>Find an injection and a separate surjection (in the same direction)
>Find bijections from both sets to a third set, or vice versa
>Find injections both ways
>Find surjections both ways
The list goes on...

>>9582852
very smart doggo. 10 marks for u

>>9571696
Who is this meme?

>>9582852
>Find surjections both ways

Only with AC.

>>9571696
What is (co)homology and why should I care about it?

>>9580666
Oh right I get it now. I haven't gotten the RREF of a matrix in months so I didn't picture in my head why this would be.

>>9582979
It's a way to measure how a (co)chain complex fails to be exact. You can use it for example when you consider topological spaces, and its usefulness comes from the way it simplifies certain problems. A babby's first example would be Brouwer's fixed point theorem. You can use (co)homology to show that spheres are not retracts of the balls they surround, and then use this fact to derive a contradiction after assuming the claim of the theorem is false.

Why is it called the Fredholm "alternative", what's it an alternative to?

>>9581826
What that vector is completely depends on the coordinate system. Where did you define [math]\theta[/math] to be zero at? If you need help with the actual EM, ask in the physics thread.

>>9583009
Because either
R( I - T ) = E
or
dim N ( I - T) > 0

There are only those two alternatives.

I remember there being a list of links to professor websites that had a repo for learning linear algebra. Can some kind anon repost it if they have it?

help a brainlet pls

>>9583580
is there an i within the sum, brainlet?

>>9583584
no. what does that mean

>>9582979
>why should I care about it
You shouldn't. We don't need your kind in math.

How to prove that every point of the interior of a d-dimensional cube can be expressed as convex combination of the corner points of the cube?

can someone give me a quick rundown on this guy?
https://www.youtube.com/watch?v=T04ONm6gT6Q
is he the jacob barnett of our times?

>>9583580
the average of any amount of u^2s is u^2

>>9583761
Use barycentric coordinates.

>>9583779
>can someone give me a quick rundown on this guy?
Not white, and measure theory is only borderline mathematics. Please don't post his videos again.

>>9583819
>measure theory is only borderline mathematics
Perhaps that's true if you mean it's on the other side of the border to mathematics.

>>9583853
Exterior, naturally. But it is closer than some engineering fields, and thus borderline.

>>9583819
>>9583859
>The only real math is related to algebra because it's personally important to me that what I study be incomprehensible even if you've done lots of calculus.

>>9583901
And who might you be quoting?

>>9583901
What exactly does "calculus" have to do with math?

>>9583901
How the hell were you brought up if you expect mathematics to be comprehensible to you if you've only done some light engineering?

>>9583906
>>9583908
You guys know that if the human race exists long enough, there's going to be a day when engineers have to learn the subjects you care most about as badly as engineers learn things relating to analysis today. That's not going to make those subjects any less mathematics (though it will certainly be sad to see people use them as tools without understanding or appreciating the underlying beauty).

>>9583919
How is this related to the sourceless quote?

>>9583921
You dismissed the guy for doing "borderline-mathematics" (+ racism). Plenty of posters on this board seem to revel in having as much abstraction as possible so that those who don't study what they study have no hope of understanding what they're talking about. This is silly and you should feel silly.

>>9583919
>there's going to be a day when engineers have to learn the subjects you care most about as badly as engineers learn things relating to analysis today
There is no known case of an engineer having to learn mathematics. And you're assuming the subjects people care about don't change with time. I hope the subjects I care about today are in retrospect essentially trivial cases of some other subject developed in the future.
>That's not going to make those subjects any less mathematics
In what way is this relevant to the discussion? Are you implying that "calculus" was at one point mathematics? That's not the case.

>>9583933
Incorrect. I did not dismiss myself. On the contrary, my post made me so proud I walked to my mirror and admired my good looks. That abstraction is somehow undecipherable is a false claim as well. Please, do try a bit more with your baits next time.

>>9583933
>You dismissed the guy for doing "borderline-mathematics"
This is a mathematical thread and posts about engineering topics should be discouraged.
>having as much abstraction as possible
This is not well defined.
>those who don't study what they study have no hope of understanding what they're talking about
That's always the case with any discipline. You have no hope of understanding something if you don't study things related to it.

>>9583940
Oops I misread the post. Time to sleep soon. The video was dismissable due to being 56% and an engineering topic. Nevertheless, I am hot.

If dx is an infinitesimal, then [math] (1+dx) = e^{dx} [/math]

What I'm wondering is if this works for matrices, basically if
[math] (I+dM) = e^{dM} [/math]
and
[math] log(I + dM ) = dM [/math]
are true. dM is taken to be a matrix with infinitesimal components, and I is the identity matrix.

>>9584563
>If dx is an infinitesimal
What do you mean?

>>9573820
seconding this

>>9573137
Expand both sides, then try to find a middle
Tip: homo ass bitch

>>9583761
Literally just write it down: if -1 <= x <= 1 then x is a convex combination of -1 and 1. Then you generalize.

>>9571696
my favorite math professor ever: Jordan Ellenberg
www.math.wisc.edu/~ellenber/

greatest teacher I've had

Help. I'm trying to retrace some of the big trigonometry projects like the India survey, but I'm stuck at this point.

[math]
\log\frac{206,264.8''}{4\cdot(5,280\cdot3,955.36)^{2}}
[/math]

supposedly has a Log of

[math]
\overline{10}.0727253
[/math]

How?

It's so windy I got blown away on my way to uni!

>>9583933
I still wonder what the author of this post meant by calling abstract things stuff people don't understand. Besides, it's not racism to avoid watching videos with non-white guys. It's all about requiring they look good.

just failed multivariable calculus, hold me

What is the combinatorical meaning of [math]{a}\choose{b}[/math] where [math]-b\notin\mathbb{N}[/math]?

>>9584831
[math] dx = lim (x+h) - x [/math]
Or
[math] dx(y) = lim x(y+h) - x(y) [/math]

>>9587793
I did pretty well in calc3, it was 2 that from fucked me over. Was there something fundamental you didn't understand, or did you just try to float through

>>9587804
you could have just asked when b is negative you nigger, and now you got it wrong

>>9588020
>nigger
Why the racism?

>>9587897
Unless you're using some type of nonstandard analysis (and you should specify which one, in that case) the first limit is 0 and the second one is 0 if x is continuous in y. Even if x is not continuous, if the limit exists it will be a real number (i.e. not an infinitesimal).

[eqn]\frac{1}{x}\sin(\frac{1}{x^{3}})[/eqn]
*blocks your integral*

>>9588020
no
I know gamma functions has 0 at every negative integers and I specifically asked for when b is a negative non-integer

>>9587660
>I still wonder what the author of this post meant by calling abstract things stuff people don't understand.
It's funny how his kind never seems to give "concrete examples" about their background and the specific topic that is supposedly "incomprehensibly abstract" for them.

>>9590808
My assumption is projecting insecurities, and then coming to a conclusion that any example would be incomprehensibly concrete for people committed to abstract wankery.

Math major here. Is a minor in comp sci worth it?

>>9591224
Ask in the >>>/g/hetto/. This is a thread about mathematics as can be clearly seen by reading the OP.

>do fine in analysis, linear algebra, abstract algebra
>still need to put in effort to do babby euclidean geometry
i don't understand this feel

>>9591276

Math isn't as cumulative as people say it is.
There are disjoint skill sets.

t. PhD student who forgot how to do long division

who here category theory?

>>9571981
absolutely. You can make a graph of possible positions in space time and search through that. Some robots do this to avoid hitting you. The real question though is how to come up with an algorithm that comes up with score maximizing trajectories in the configuration space of a bullet hell game.

This is actually a very interesting problem because some bullet trajectories are random or dependent on player position. Now that I think about it, I really want to plot the three-dimensional configuration space of some of these spell cards.

>>9581679
did you know if you get both of the guns perfectly lined up, you only make two holes in the head instead of four!

>>9591476
>t. PhD student who forgot how to do long division

You are either a PhD Student or someone who forgot how to do long division, you can't be both

>>9591654
This. Anyone studying mathematics wouldn't know or care about long division in the first place.

What applications does group theory have

>>9591975
It can be used to study group theory.

Where my analysissies at?

>>9591975
http://4chan-science.wikia.com/wiki/Mathematics#Survey_of_Abstract_Algebra_Applications

>>9587983
My course was scheduled to last for 20 weeks, I tried to take the test halfway through. I'll try again in 10 weeks.

How many of you fantasize about working in finance? Do you look at quant job ads with a huge salary and try to convince yourself that you could get a job like that?

>>9592108
I probably will get a job in finance as an actuary or something, though I can't say I fantasize about it. If I could get a comfortable salary in academia I'd probably choose that instead.

>>9592108
jobs in finance have been open to plebs for a long time now, so doing finance for the money is stupid. and now that proprietary trading is killed, then there is no point to even try.

>>9592147
Yeah I've heard stuff like that but there's still plenty of job ads for a lot of different stuff. They put big numbers for the salary in the ads too.

>>9592108
>>9592121
>>9592147
>>9592192
See >>>/biz/ and >>>/b/

>>9592213
The conversation is about mathematicians, isn't that on topic?

>>9592218
>The conversation is about mathematicians
It's about "jobs in finance". Refer to >>>/biz/ and/or >>>/b/ for a proper place to discuss these subjects.

>>9592227
Maybe I should have phrased it differently but it was supposed to be implied that it was jobs for mathematicians in finance.

>>9592258
It's still not related to mathematics since "finance" and mathematics are completely disjoint. Proceed to >>>/biz/ and/or >>>/adv/ if you are looking to switch to "finance".

>>9592264
I meant the stuff you would use a math degree to be able to get. It's not any more disjoint from mathematics than any job (except academia) where they want mathematicians.
Is it not on topic to discuss thing that we can do with the mathematics?

>>9592258
It's a shitposter, stop giving it attention.

being a quant is not fun. being prop trader was the most interesting job. now traders are from the middle class and some pathetic university.

if you want to do math, stick to financial research at the university, like a M2 of quantitative finance with El Karoui then a phd then a postdoc

I'm not sure if this is a greedy goy or a real rotting judenagent, but zůs posts will surely corrupt weak minded lurkers of this thread, those who desire money. Please take your Judeo-Christian filth out of my Tengrian Juche thread.

>anime and avatarfagging

>>9592380
Who are you quoting?

>>9592336
see >>9592213
>>9592332
How is redirecting people to proper discussion boards somehow "shitposting"?
>>9592336
Cool. Refer to >>>/biz/ and >>>/b/ though. Wanna move there so we can discuss "finance" together?

>>9592328
>(except academia)
So except mathematics? I'm glad you understand that non-mathematical activities such as "finance" and "day trading at Wall Street" are completely disjoint from mathematics. Now please refer to the boards mentioned above.
>Is it not on topic to discuss thing that we can do with the mathematics?
Not unless that thing is mathematics itself. Make a separate thread for so-called "applied math" if you wish to discuss it.

>>9592424
Die finwhore

>>9592264
>"finance" and mathematics are completely disjoint
You're entitled to your objectively wrong opinion

>>9592433
Scream in futile terror. I'm neither a finn nor a whore.
>>9592441
No knowledge of mathematics is needed to be a "stock trader". No knowledge of "finance" is needed to do mathematics. Proceed to >>>/biz/ to discuss this further with your fellow stock traders if you think otherwise.

>>9592449
Make me

>>9592336
trading is fun, but it's not a reliable source of income. you can't really live on it. it's more like something you can do on the side

>>9591654
>>9591662

??

How am I meant to go about this? I was given the hint to notice that V+iV is also a vector space over the reals, but I really have little idea what to do here.

I'm pretty bad when it comes to representation theory, and I'm guessing the determining factor here is wheter iV is isomorphic to V, but I'm not sure how to show this

>>9592449
>No knowledge of mathematics is needed to be a "stock trader"
This was about the parts of finance where you do need mathematics. Quantitative researchers, algo traders and such where you need a mathematics degree to get hired.

>>9591535
*raises paw*

>>9590340
>I know gamma functions has 0 at every negative integers
This is false.

>>9592773
suppose V+iV is not irreducible... then it is a sum of irreducible representations. Clearly V and iV are subrepresentations. But by assumption, they are irreducible...............

>>9592433
Consider getting help.

>>9592774
>This was about the parts of finance where you do need mathematics.
But such parts don't exist.
>where you need a mathematics degree to get hired
I don't recall talking about mathematics degrees.

>>9593243
what did I miss?

>>9593243
was he really that wrong?

>>9594168
think about the factorials in the binomial coefficients outside their normal range. what happens if you plug in -3 let's say to make the coefficient 0?

>>9594169
That's true though?

>>9594168
>what did I miss?
The truth

>>9594169
>was he really that wrong?
Yes.

>>9591535

>>9591535
Anyone who studies mathematics.

Just got an offer for a good uni PhD without any funding - I could apply next year but meh. Also my adviser looks like a pretty young associate professor and they're giving me until September to accept the offer. Is this a good idea?

I was thinking, since this is my first offer, could I start using it as leverage to make other unis start accepting/rejecting me a bit faster? Cos i havent heard anything from any other