What's the point of functional programming?
Why would an undergrad be interested in algebraic geometry? Serious question
>>9348319Depends on your interests. Certain subjects pave natural paths to algebraic geometry, but they are different.
>>9348319>Why would an undergrad be interested in algebraic geometry?Presumably for the same reason to be interested in any other field, to research/solve problems using the theory from that field
>>9348319>Why would an undergrad be interested in algebraic geometry? Serious questionpolynomials are very common objects
>>9348319Either they're patrician or a major pleb
https://www.youtube.com/watch?v=PxMY4NQFrOQthis isn't algebraic topology...
What's the current state of the art on the category of all axioms?
Why are PDEs harder than ODEs?
>>9348785Because they have, in some sense, less restrictions.
>>9348319They fell for the abstraction meme.
Would the homotopy category be concretizable if we relax the restriction that Set must be wellfounded?
>>9349069the homotopy category of what
>>9348319it's a very beautiful subject. everyone already knows the most elementary connections between algebra and geometry (analytic geometry), which may inspire them.
>>9349191>Grothendieck used to draw shit on his notes just like me!
>>9349203he drew that because he thought the theorem was satanic
>>9348327>>9348330>>9349191I'm interested in algebra, geometry, and rigour. Which is why I'm not enjoying so much algebraic topology, and I am quite enjoying the small amount of plane algebraic geometry I've done (and algebraic number theory and Riemannian geometry for that matter). Also, how can I explain to a prof that I want to do a PhD in this subject without sounding (a) like a retard, and (b) like I am talking out of my league, given that I don't have that much experience in the subject
>>9349203>try to write out a theorem in algebraic geometry>accidentally create a primordial summoning symbol and your stationery becomes infested with demons
How important are anime girls to learning Math?
>>9348319memes
>>9349272You will never be able to convince a prof working in the area that you aren't talking out of your league (because you are), but unless that prof is a huge jackass, it shouldn't be a problem. The question is, how do you really know that you want to do a PhD in it ?
>>9348333I've never seen a polynomial in my life
how can i get over my hatred for all things set-theoretical or topologicali enjoy algebra but i am at the point where i need a good background in topology to continue and i just don't think i can push forward
>>9349376
>>9349357not at all, they lead you into falling for meme lists
>>9349272>interested in rigor
>>9349357They aren't important but they can increase your enjoyment of doing math. It's always nice to have company when you're engaged with something that pleases you, and anime girls are the most pleasant companions in the world.
>>9349272>>9349272Just get an algebraic geometry book and work through it. Since you have done Riemannian Geometry, start with a book on complex algebraic geometry. That way you can lean back on differential geometric techniques if you aren't comfortable with heavy algebra.
>>9348316so people can pretend to know category theory
>>9348316Some people find it easier to problem solve in that mode of thinking. I personally prefer it.
>>9349485can you teach me the art of mathematical anime grills?
>>9349793there is something relaxing in the algebraic approach(in contrast to complex analytical one), just take a commutative algebra book such as eisenbud, a theoretical algebraic geometry book such as shafarevich 1 and an enjoy a book such as harris
>>9349917You should start with classical complex algebraic geometry.
>>9349917Eisenbud is really long and may get boring if you want to do geometry. A-M is much shorter, the exercises are nice, and you can probably move through it quickly if you are comfortable with standard algebra.
>>9349917>>9349922>>9349952best tip for doing algebraic geometry is too read a classic or undergraduate level text where the geometry is more obvious. Post Grothendieck Algebraic geometry is awesome and patrician as you can get but without a solid understanding of the actual geometry its is abstract autism.
Shalom /sci/I was stuck on this problem for an embarassingly long time for some pretty stupid reasons.The problem is to find the surface area of the cone z^2 = 4(x^2+y^2) the answer is (sqrt5)*4piSome guy here http://mathhelpboards.com/calculus-10/surface-integral-2568.html got the right answer. Is this the right way to do it or just a fluke? If it's the right way, why is it R dr dtheta?
>>9350315this is how you calculate the area of a surface of revolutionjust take a differential surfaces book
i want to find square numbers of the form [math] n! + 1 = k^2 [/math] for integers kthere are only three known solutions for n: 4,5, and 7i would like to know exactly how many there arei have tried some simple number theory and analysis approaches, but nothingi found an interesting approach which treats the factorial as the order of a symmetric group, and then used some other basic group theory stuff, and it felt like i was getting close to something, but i am inexperienced and was unable to prove anything significant related to the original problemideas?
>>9350703https://en.wikipedia.org/wiki/Brocard%27s_problem
>>9350703Give up
>>9350703>>9350737>Overholt (1993) showed that there are only finitely many solutions provided that the abc conjecture is true.finitely many then
>>9350737god damnit every time i think i've found something cool ramanujan or terry tao have already published 9 papers and a movie about it>abc conjecture implies finitely many solutionsso what's the consensus on abc conjecture? has anyone been able to learn IUTT and confirm mochizuki's stuff yet?i suspected that there were only finitely many solutions after bruteforce searching for n up to about 10,000i also can't seem to find any bounds on the number of solutions, only that there's finitely manyi must know the number
>>9350947I'm currently interested in quasi-perfect numbers. Wanna join an effort?https://en.wikipedia.org/wiki/Quasiperfect_number
>>9348319if they like itif they want to look cool and impress professors/grad students
>>9349069The axiom of foundation is essentially unnecessary in the definition of Set ... it should remain a well-pointed topos with NNO even without foundation. So it's unlikely to make a difference. The real obstacle in the proof is "size", it's concretizable in proper classes / large sets IIRC.
>>9348316It's way easier to reason about and prove things about programs that don't have side effects or an environment to worry about. If you can prove things about a program you can optimize it better and make sure it doesn't break stuff - typed functional programming (especially dependent types) allows you to specify the behavior of a program much better than the bolted-on type systems like Java and C++ have.
>>9350947>so what's the consensus on abc conjecture?It's now Mochizuki's theorem>has anyone been able to learn IUTT and confirm mochizuki's stuff yet?Yes but not peer reviewed
>>9350947>so what's the consensus on abc conjecture? has anyone been able to learn IUTT and confirm mochizuki's stuff yet?It's still in limbo basically. Not much news since Conrad's summary. A few people are convinced but they're in the minority.
>>9351085>Not much news since Conrad's summary.http://www.kurims.kyoto-u.ac.jp/~gokun/DOCUMENTS/abc2017Nov20.pdf
>>9350970what kind of background do i need to try to work on stuff like thisi feel like this is one of those things where a proof is going to come from magical arithmetic geometry lala land and it's going to be way too complicated for me to understand
>>9351090>nationalist jap supports his fellow nationalist japHeh
check this out https://www.youtube.com/watch?v=_X1p7HhCzmA and tell me it isn't useless shit
>>9348316Functional programming is a lot more mathematically natural I think. Also code is usually very short in length.
>>9350947why don't you see for yourself :)http://www.kurims.kyoto-u.ac.jp/~gokun/DOCUMENTS/abc2017Oct.pdf
>>9351285You do realize thats not IUT Mochizuki right?
>>9351319what made you think I thought it has anything to do with inter-universal Tiechmemer theory?
Please help>>9351391
why are there four roots to z conjugate = z^2, z is a complex number? I only got two.
>>9351406i unironically went through the same part of the book 2 months ago and couldnt figure out why either
>>9351196But that's a good path to learn stuff, I'd argue. I don't know too much about number theory either.
>>9351529Kek. Pic related is one more I took a while to understand but it wasn't as bad as that one.
>>9351090I mean news for us non-experts. Consensus last I heard is that this guy is just as incomprehensible as Mochi.
>>9348316>>9349861>>9349901>>9351044>>9351288Fuck off to another thread with this garbage.
>>9351626>Fuck off to another thread with this garbage.But this is /mg/
>>9351629Which means programmer garbage is not welcome here.
>>9351631https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
>>9351631>Which means programmer garbage is not welcome here.math is a subset of computer science
>>9351635subcategory*
>>9351422>why are there four roots to z conjugate = z^2, z is a complex number? I only got two.http://www.wolframalpha.com/input/?i=conjugate(z)%3Dz%5E2
>>9351633Why did you feel the need to post this? Type theory is quite different from "programmer garbage".>>9351635>subset>>>/g/
>>9351633>https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondencehttps://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation
>>9351633>posting this instead of >>9351645Pr*grammer spotted.
>>9351645>>https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence>https://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretationhttps://ncatlab.org/nlab/show/computational+trinitarianism
>>9351635Exactly backwards.
>>9351650Thinking in terms of sets is pretty backwards indeed.
>>9351633So called "functional programming" is in no way related to this. Types in those languages usually fail to even form a category. Discuss "programming" in >>>/g/
>>9351650can't define logic without computation anon
>>9351684>logic is all of mathPr*grammer spotted.
>>9351620Who did you hear that from? A brainlet?I love when brainlet westerns don't give the credit Mochizuki deserves because they all see it as incomprehensible alien bullshit when in reality it's just on a way higher level than anything weak brain westerns have come across. The best facepalm moments is westerns who dive into IUT proof without reading the 10+ prerequisite papers required to even begin it and get shook like "woah this is impossible to understand". It's like bunch of highschoolers diving into Perelman proof for Poincaré-Conjecture expecting to understand it because numberphile talked about it. I look down on people with this ignorant-thickheaded behaviour because it contributes nothing to the community and just honestly makes them look retarded. By the way over 30+ European mathematicians and some more from North America have confirmed the proof
>>9351620>non-expertsNon-experts discussing this should kill themselves.
>>9351740>Non-experts discussing this should kill themselves.Why?
>>9351727>t. chink with an inferiority complex
>>9351746You're fine with buzzfeed journalists who's never taken a course in physics and not beyond highschool math should write articles on black holes and string theory? It's kind of like that.
>>9351771Not him, but I'm not fine with anyone writing articles on black holes and string theory because black holes don't exist and string theory is a bunch of unphysical bullshit mathematics.
>>9351786(you)
>>9351787The fact that you buy that shit is one more reason to distrust Mochizuki actually achieved anything. (Go back to China.)
>>9351746So they don't have to embarrass themselves by making retarded posts.
How does one obtain the physical intuitions needed for doing math?
>>9351824by doing math in the "right" order. real analysis gives you intuition for topology. linear algebra gives you intuition for algebra. complex geometry gives you intuition for algebraic geometry. none of those are actual prerequisites.
>>9351830>real analysisStopped reading right there, what a stupid suggestion.
NEW 3BLUE1BROWN VIDEOhttps://www.youtube.com/watch?v=OkmNXy7er84
>>9351830That's pretty good for wasting your time.
>>9351841>hurr hurrrrrif you have anything to say, go ahead
>>9351848it's faster than the other way around, so where do you waste time?
>>9351849>hurr hurrrrr>>>/r/eddit/
I shaved my head today but it's snowing outside and I own no caps. What do?
>>9351853>it's faster than the other way aroundHow much does it take?
>>9351877Die
can someone explain the determinate to me at three different levels?>fresh out of intro linear algebra level>graduate level>wizard levelI still don't really know what "it" is.
>>9351841>>9351848This board is a joke.
>>9352033more evident by the fact that I can not spell it>determinant *
>>9351841>Stopped reading right there, what a stupid suggestion.t. couldn't make it past chapter 2 in Rudin
>>9352033>intro levelthe determinant of a matrix is how much that matrix scales n-volumes>graduate levelthe determinant is a morphism of algebraic groups from the general linear group to the multiplicative group>wizard levelthe determinant is a symmetric monoidal functor from the category whose objects are bounded chain complexes of finite rank vector spaces and whose morphisms are quasi-isomorphisms, to the category whose objects are graded lines and whose morphisms are homogeneous isomorphisms
>>9351924to get where? for learning basic real analysis, basic topology, linear algebra and basic algebra, that's like a year
>>9352081>the determinant is a morphism of algebraic groups from the general linear group to the multiplicative groupthis does not define itit's just one property of it
>>9352099that's not just one property though, it's several properties neatly packed into one, which actually turns out to be sufficient to define the determinant
>>9352033Let [math] F [/math] be a field.Consider [math] F^n [/math] as a vector space over [math] F [/math]. (it has dimension [math] n [/math] )The determinant is a map [math] \underbrace{F^n \times \ldots \times F^n}_{n \text{ times}} \to F [/math] such that: 1) It is multilinear. (linear in each slot, if the other slots are fixed)2) It is alternating. (swapping two slots multiplies it by -1)3) It maps [math] (e_1, \ldots , e_n) [/math] to 1. Here [math] e_1=(1,0, \ldots ,0) , e_1=(0,1, \ldots ,0) [/math] etc. Such a map Exists and is Unique. The usual formulae follow: first the product one with the permutations, the the other one with the minors. See how you get them here: https://www.youtube.com/watch?v=23LLB9mNJvcFrom these properties if your field is [math] \mathbb{R} [/math] , you can see that the determinant is the (signed) volume of the input vectors.Also, if your field is [math] \mathbb{R} or \mathbb{C} [/math] then the deteminant of a matrix is equal to the product of the matrix's eigenvalues. (I guess it holds for other fields as well, if you extend to the closure, but not sure.)Definitely watch this as well for geometric intuition:https://www.youtube.com/watch?v=Ip3X9LOh2dk
>>9352198it's always the product of the eigenvalues. the eigenvalues always live in the algebraic closure.even in R, they can be strictly in C, consider (0 -1)(1 0)
>>9352206Yes, I know that eigenvalues exist in "the" algebraic closure of the F.But what if the algebraic closure of F is not of finite dimension over F?
>>9352217Wait nvm I guess this doesn't make it problematic.But, when you have R as the field, you can prove that the determinant is the product of the eigenvalues by complexifying the operator.How do you go on about doing a similar process for an arbitrary field?
>>9352067Yeah, you would have to at least start the book to make it past chapter 2.
>>9352217well, what then? an nxn matrix over the field K has n eigenvalues on an algebraic closure Fif the eigenvalues are x1,x2, ..., xn, then there is a finite (since the xi are algebraic) extension K(x1, x2, ..., xn) that contains them as well, the splitting field of the characteristic polynomial
>>9352081The third one doesn't uniquely define it.
>>9352239the determinant is the characteristic polynomial evaluated at 0. the eigenvalues are the roots of the characteristic polynomial.
>>9352082> basic topology, linear algebra and basic algebra>that's like a yearWhat exactly is basic topology and basic algebra?
>>9352250at the level of Weil's Basic Number Theory
>>9352250basic topology means a book like munkres, enough theory to prove things like tietze's extension theorem and the baire category theorem. basic algebra means part of a book like rotman's "introduction to abstract algebra", maybe groups and rings.
>>9352258>enough theory to prove things like tietze's extension theorem and the baire category theorem>basic algebra means part of a book like rotman's "introduction to abstract algebra", maybe groups and rings.>that's like a yearMaybe for someone severely handicapped.
>>9352250basic should be normal undergraduate = basic graduate
>>9352262read the whole post. the year also includes linear algebra (up the say the JNF) and real analysis (up to say implicit / inverse function theorems)
linear algebra is some crazy shit man it blew my mind when they figured out the moon's orbit with matrices
>>9352266>real analysisMight as well ignore it.
>>9352242>>9352247Oh right I am retarded.[math] p(x) = |A-xI| = \sum a_i x^i \implies a_0=p(0)= |A| \\ p(x)= \prod (x-\lambda_i) \implies a_0 = \prod \lambda_i [/math]
>>9352269learn it in a week to understand why basing a theory on inequalities is shit for your future
>>9352266Even that taking someone a whole year pretty much means mental retardation.
>>9352269hahahahah you're so funny anon, this joke cracks me up every time you make it hahahahaha
>>9352275>a weekWhat a waste of time.>>9352277That's not a joke though.
>>9352273nah mate sounds like you learned your material pretty well. keep it up. hmu if you need anything
>>9352246prove it
Alright bud, I'll take your shit bait. Explain to all of us why real analysis isn't worth the time of day.
>>9352279>>a week>What a waste of time.I don't expect a highschool student to take less time if he wants to go through any verificationand it's not really a waste of time for them
>>9352292It looks like you're new. Just ignore him. It's just one finitist crank. He doesn't believe infinite sets exist.
>>9352350Oh, I see.
>>9352291It doesn't define it and therefore doesn't uniquely define it.
>>9352350>finitistNot even close, I literally believe in large cardinal axioms.
>>9352350it's not the finitist crank. it's the "i only do useless non-mathematics" categorytard. he actually believes he's doing algebra or something.
>>9351877Another problem occurred guys. I went to do my groceries this evening and I ended up staring at the cashier's boobs because they were pretty plump, and she noticed and started to laugh at me. I fear I may never be able to do my shopping there again.
>>9352389I would laugh at someone who likes chest tumors too.
>>9352382>uselessEngineer spotted.
>>9352382I think it's the same guy. He only changed his tack.
>>9352402Foundational mathematics ARE useless.
>>9352402not the first time you call this algebraic geometry student an engineer, mr useless
>>9352406Yes, but set theory is pretty much the only thing which is described by this and it has been obsolete for quite some time now.
>>9352410>algebraic geometry studentDoesn't really matter. They can be engineer-like too, as you have just shown.
>>9352415>my work in foundations is not foundations because that's an ugly wordkekset theory is enough, your shit is literally useless
>>9352398Boobs are great. Are you perchance a homosexual? (I really liked that hypermarket too. Great prices and wide variety of produce. And it is very close to my apartment.)
>>9352420>your shit is literally uselessIt's used pretty often in mathematics, someone who enjoys "real analysis" obviously wouldn't know.
>>9352420>kekI hope being retarded works out for you, anon.
>>9351824>>9351830I somewhat agree. For group theory you can get intuition from either geometric (linear/affine) symmetries as in linear algebra, or finite set permutations. I'm not sure why you put complex geometry before alg geometry, it seems no more concrete to me.
>>9352422>hypermarket
>>9352542I take it you don't have hypermarkets in America?
>>9352425>w-weal anawisisssss!!!>REEEEEEEEEEEEL ANAAAAAAAAAL ISISS!!!!!WHEEEEELLLUHHHHHHHNAAHHHHHHHLISSSSSSSSISSSSSSS!!!!!!!!!
>>9352499with complex geometry I kinda also mean classical algebraic geometry in CP2 and so on, gives you good intuition for the general theory of schemes
>brainlets still falling for the troll's lame as fuck bait even after all these monthsIt's the Wildberber shitposter ffs. He's constantly bringing up the same talking points, except he's now changed his backstory a little. > I literally believe in large cardinal axioms.
>>9352081>category whose objects are bounded chain complexes of finite rank vector spaces and whose morphisms are quasi-isomorphismsThis would be the category of perfect complexes on a point, right?
>>9351824Do physics and math in parallel during your first years of uni, desu. Also, look for examples for each notion and try to see each new theorem in action on your examples
>>9352564Put a bullet through your head.>>>/r/eddit/
>>9352634>Do physicsNope. Not interested in engaging in subhuman activities.
>>9352499>get intuition for group theory>""concrete""Haven't heard of a more retarded waste of time in a while. Is this truly what the less fortunate ones do to learn mathematics?
>>9352404>I think it's the same guy.I'm not a "guy".
>>9352675>pretending to be another guy>>>/b/
>>9352650>subhuman activities.Way to be a freshman. I don't even like physics but I do regret not having applied myself when I had physics classes. I'm just saying that the intuition you gain there can be very beneficial when working in geometric/analytic areas (ie. differential geometry, ODE, PDE, dynamics etc.) and provide both intuition and a large stock of examples (and for good reason, since many problems in these areas arise from physical problems)
Threadly reminder to work with physicists.
>>9352675>>9352720>>>/r/taiwan/
>>9352717>working in geometric/analytic areasI genuinely feel sorry for you.
>>9352766Go on
>>9352663Is it the same retard posting this same reply to everything in this thread?
>>9352720dude, so many details in this image i really love it, i hope i'll someday be good enough in physics/math to understand that book
>>9348310how long are string-theoretic strings?
>>9352919[eqn]\mathbb{B}[/eqn] [eqn]\mathbb{A}[/eqn] [eqn]\mathbb{B}[/eqn]
>>9352919String length is not a fixed parameter.
>>9352930>String length is not a fixed parameter.alright what kind of ranges of lengths are we talking about then (theoretically)
>>9352919>>9352922>>9352930>>9352934Please keep it contained to >>>/x/
>>9352942Witten is the absolute Chad of /sci/, sorry you can't handle the PHENOTYPE
>>9352934String length is has an inverse square proportionality with string tension. String tension of course measuring the energy per unit in the string.
>>9352919We need an image exactly like this but with Mochizuki holding Hartshorne's AG
[eqn]\int \text{erf}(\csc(x))\ \text{d}x[/eqn]
>>9352675What are you?
>>9348310Why are (co)ends denoted by integral signs? I don't see the relation.
>>9353328>What are you?Not a "guy".
>>9353331I think end/product coend/coproduct(sum)been years since I looked at that, and I never needed it, but maybe the category of elements construction helpshttps://ncatlab.org/nlab/show/category+of+elementswhere you get a disjoint union of things out.Also has a short Wikipedia page. And btw. the so called Grothendieck construction is related.----What are relevant stochastic processes, where the variance does NOT take the form proportional to t^a, for some a? (E.g. a=1/2)
>>9353331>I don't see the relation.The relation to what? Does something else in math use an integral sign?
>>9353375>integral
>>9353378Yes, the integral sign. Usually it is written as [math]\displaystyle \int[/math]
>>9349369You've never worked with rings then
>>9350970>>9353371There are special websites for avatar users.
>>9353383Ok that doesn't help me make sense of [math]\operatorname{hocolim} \left( F \right) = \int_{}^{c \in \mathcal{C}} {N\left( {{}^{c/}\mathcal{C}} \right)} \odot F\left( c \right)[/math]
>>9353375
>>9348310>Lurie won't win a fields everWhy are we here? Just to suffer?
taking projective geometry next semester, can anyone drop me some red pills on it?
>>9353449coordinates are for plebs, axioms are for patricians
>>9353449projective geometry <---> graded commutative algebraaffine geometry <---> commutative algebra
>>9353454>>9353455will it make women wet?
>>9353475I don't see why not. And if it doesn't, are those really the kind of women you need in your life?
>>9353480very valid point
do i need a [math]\mathbb{BAB}[/math] to understand gauge theory?
how many cliques are there on a complete graph K_n?
What's a quick redpill book of Galois theory?
>>9354084>redpill>>>/pol/
>>9353455explain a bit pls
>>9353475Whispering how Proj construction is done in a girls ear is the only time I've made a girl multiple orgasm
>>9354091Projective space is the space of lines, and lines are invariant under scaling. The algebraic manifestation of invariant under scaling is homogenous polynomials and graded algebras.
>>9353840[math] \binom{n}{1} + \binom{n}{2} + \cdots + \binom{n}{n} = 2^n-1 [/math]
>>9354086What does /pol/ have to do with movies?
>>9354084johnstone for polynomials
>>9351529>unironicallyare you retarded?
godel proved logicians were fagat least model theory is somehow useful
>>9354388>godel provedstopped reading your pop-sci garbage right there.
>>9353574What the hell is a bab?
>>9354407Big Ashkenazi Brain
>>9354416He talks like a girl.
>>9354419That's because his vocal chords are 11 dimensional d branes
>>9354115Thanks this is what I was suspecting with K_5 but it was a slog looking at every case like a peasant because my brain hasn't been math for years
>>9354278i am unironically retarded
>>9354115>>9354594Oh one more thing, Choose(n,k) for the clique on k vertices, right? So if I want only cliques of 3 vertices and higher, it'ssum_k=3^n choose(n,k)orwhat you've said, minus n, minus the count of pairwise edges
>>9354607>Oh one more thing, Choose(n,k) for the clique on k vertices, right?Yes> So if I want only cliques of 3 vertices and higher, it's sum_k=3^n choose(n,k)Yes> or what you've said, minus n, minus the count of pairwise edgesYes to that as well, it is the same thing as the previous one.
>>9354607>ChooseWhat if I don't accept the axiom of choice?
>>9354106What about the affine part?
I've been stuck on the second half of this problem. I'm completely lost on how to do it.I did the first part just fine and got 96 pi, but I can't figure out how to do the double integral.
>>9354901And as soon as I posted I think I came up with a solution.
>>9354901S is a sphere centered at O of radius 2, you can integrate it in spherical coordinates (no shit), the normal vector to S at (x,y,z) is [math]\vec n = \frac{(x,y,z)}/2[/math] and the surface element is [math]dS = 2\sin(\theta)d\theta d\phi[/math]
>>9354918Thanks.How did you find the normal vector and dS? I kept fucking up when I tried to do it in spherical coordinates.
need advice about gre, posting here instead of /adv/ because I figure I might get more grad students to read thisapplying to (applied) math programs. first time I took general test, got 170 math, 161 verb, and 3.5 writing. I retook it to fix my writing score, and got 163/163/5.0 the second time. so in the quant section, I dropped from 97 percentile to 84. however, my math subject test score is decent— 790 (77 percentile). with this in mind, would you send the first or second general scores, or both?
>>9353449You can think of the projective line in two different ways: as the space of lines through a point, or as the real line plus a point at infinity.You can see these as homeomorphic by taking the lines through the point (0, 1), so each line corresponds with the point on the x axis it intersects, except the horizontal line which "is" the point at infinity.
>>9353422He'll win the Abel prize though, so that's pretty good.
>>9354992Send the second, your math gre score will count for a hell of a lot more than just the quant section alone, plus your verbal is higher than before and your writing score went from shit to pretty good. The second all around is stronger even if the quant is slightly lower.
>>9354920well for the dS I don't know what to tell you (also, my bad, it was 4*sin... instead of 2*sin...), I can give you a handwavy explanation for it: If you're at a point with spherical coordinates [math](2, \theta, \phi)[/math] and move to [math](2, \theta+d\theta, \phi+d\phi[/math], then you move along [math]e_{\theta}[/math] by [math]2\sin(\theta)d\theta[/math], since you're moving on a circle of radius [math]2\sin(\theta)[/math] by an angle of [math]d\theta[/math] (draw it), and you move along [math]e_{\phi}[/math] by [math]2d\phi[/math] because you're moving on a circle of radius 2 by [math]d\phi[/math], spanning a surface of [math]4\sin(\theta)d\theta d\phi[/math].For the normal vector, again, draw it and you'll understand why it works, but by definition the normal vector to a surface defined by an equation f(x,y,z) = 0 at a point p is the normalized gradient [math]\dfrac{\nabla f(p)}{||\nabla f(p)||}[/math], which here turns out to be exactly what I said. But I think it would be much more enlightening to just doodle it and see that it works.
>>9355011Thanks for explaining, I really appreciate it.I went back over my notes and it turns out that I was confusing the del operator with gradient which is why I kept fucking up the normal vector.I bet you can never guess what I'm majoring in.
>>9355010thanks chief
>>9354388Löwenheim-Skolem theorems are cooler
>>9355191>Löwenheim-Skolem theoremsnot science or math
>>9355197how ?
>>9355202>how ?What do you mean?
>>9355262>What do you mean?why do you ask ?
>>9355265>why do you ask ?Because I don't know what you mean.
>>9355267huh ?
>>9355271>huh ?What are you confused by?
>>9355272Hello?
>>9355262how is lowenheim-skolem not math ?
>>9355296>how is lowenheim-skolem not math ?That's a bit of a bizzare question. It's the same reason Occam's razor isn't math, simply because there's nothing mathematical about it.
>>9355191yes, with compactness, quantifier elimination and the theory derived from considering arrows that 'preserve truth' is the only thing I can appreciate from logic>>9355197>>9355318that's because you are thinking about Skolem paradox and not lowenheim-skolem theorem (up/downward)? Skolem paradox is just a historical misunderstanding, not that interesting yes
What's the intuition behind conferences for female mathematicians?http://www3.mathematik.tu-darmstadt.de/index.php?id=3312
>>9354847You can understand a space by understanding functions on it. So polynomial rings.
>>9353343not a guy.So a boy? you must be at least 18 to post on /sci/
>>9354403>pop-scikeked at you internally right there
>>9354992a lesson for all you kids don't take the quant high/drunk
>>9349861Why not use Hoare triples instead?
>>9348310Hi. Quick question.P(n,k) is the number of permutations of k-sized subsets of an n-sizedset. C(n,r) is the same but when order doesn't matter.This can be calculated as: P(|A|, k) = |{x | x ⊂ A ∧ |x| = k}|And is the permutation or combination depending on whether you areworking with ordered sets or unordered sets.But this need not use the counting measure.For the counting measure one counts all the possible subsets B that solve: Σ [x ∈ B] = k; B ⊂ AThis seems "obviously" generalizable to me as: ∫^{∞}_{-∞} B(x) dx = k; ∀x. 0 ≤ B(x) ≤ A(x)or maybe even for quantum mechanics something like (where B gives a complex result): ∫^{∞}_{-∞} B(x)2 dx = kBut how do I "count" the amount of possible solutions for B?
>>9355619really all it was is I made a silly mistake and spent too much time on one question, so I had to rush throught the last few questions.
>>9355640if A is big enough, with integral (or square integral in the second case) bigger than k, then too many Bs will satisfy the condition to be usefulthe point about combinatorics is that you can count finite things.
>>9355691But couldn't you count degrees of freedom for example?
>>9355640>>9355702Interesting question. It's only a linear space when k = 0, otherwise it's an affine space so you can measure it via affine dimension. But it will probably be infinite dimensional in general.
>>9355777*convex, not affine (because of the 0 ≤ B(x) ≤ A(x) condition)
>>9355377Women suck at mathematics, so they have to build a safe space for themselves so that they won't feel too bad about it.
I'm not going to post this in /sci/ general because that place is a shit hole, but do you guys think that IQ corresponds to math performance because one can do math at a very superficial level just via symbolic manipulation without actually learning the material? This advanced symbolic manipulation ability would be good in passing exams and perhaps even solving some research problems; however, it seems like that "age" of math is coming to an end. This is why I think Grothendieck is a greater genius than Von Neumann, because Von Neumann was gifted with very high processing speed and was thus able to state space search the solution to various problems, but he was never able to come up with a discovery like Grothendeick was . We all know by this point that Grothendeick was not known for his processing speed nor his technical mastery( Grothendieck prime). People who can do state space searches will be replaced by advanced neural networks who will out class them in every way possible, but can we make a machine that will encompass Grothendieck's level of insight and inner wisdom? Perhaps that's why he went insane later in his life.
>>9348310I am trying to grasp existence and uniqueness theoremhttps://en.wikipedia.org/wiki/Picard%E2%80%93Lindel%C3%B6f_theoremI do not understand why do they say without any justification that [math]f(s, y(s))ds[/math] is integrable?
>>9355377They want to motivate you to improve your life and immigrate somewhere without this shit.
>>9356110That is why there are still people doing category theory and such feminine things. When proper mathematics like real and complex analysis are too hard for them, they tend to avoid such matters and do the more "artistic" stuff.
>>9356357e.g. infinite groups instead of finite ones
>>9356116You could make an argument out of that line of thought, but stating Neumann wasn't innovative is just silly. He worked in set theory and invented game theory and classes of automata, etc.>>9356176I can't find where they say that.If you're stating it's equal to y' at that point, then it is.
>>9356176>I do not understand why do they say without any justification that >f(s,y(s))dsf(s,y(s))ds is integrable?It says that f(t,y(t)) is Lipschitz continuous, which implies uniform continuity, which implies continuity, which implies integrability.
>>9356475Only in the second variable, not in both, but in the integral both are changing.
>>9356412Is any derivative integrable?
>>9356597Which derivative? Doubeault? Frechet? Fractional? Which integral? Riemann? Stieltjes? Lebesgue?
>>9356600Lebesgue obviously
>>9356600Riemann>>9356601Fuck off shill
>>9356601I don't think so
>>9356613>>9356616
>>9356623you think every derivative is integrable ?
>>9356613This isn't the engineering general anon
>>9356412> If you're stating it's equal to y' at that point, then it is.It is true for the solution y. But to prove its existence we consider convergent sequence of continuous functions [math]\varphi_n[/math], and we need [math]f(t, \varphi_n(t))[/math] to be integrable as a funnction of t for all functions [math]\varphi_n[/math].
