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# /sci/ - Science & Math

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File: 100 KB, 801x1200, langlands.jpg [View same] [iqdb] [saucenao] [google] [report]

Talk maths

The Work of Robert Langlands:
http://publications.ias.edu/rpl/

https://ncatlab.org/nlab/show/Langlands+program

 >> Anonymous Fri Dec 29 15:14:47 2017 No.9401535 File: 47 KB, 1143x647, Capture.png [View same] [iqdb] [saucenao] [google] [report] What's the worst mathematical Wikipedia page?https://en.wikipedia.org/wiki/Analytization_trick
 >> Anonymous Fri Dec 29 18:19:16 2017 No.9401926 sup piggots
 >> Anonymous Fri Dec 29 18:22:06 2017 No.9401930 File: 416 KB, 1214x1140, 1513605348878.png [View same] [iqdb] [saucenao] [google] [report] why exactly is a linear transformation defined with these two properties in mind (over real vector spaces):$T(\mathbf{u}+\mathbf{v}) = T(\mathbf{u})+T(\mathbf{v})$$T(c\mathbf{u}) = cT(\mathbf{u})$
 >> Anonymous Fri Dec 29 18:27:12 2017 No.9401943 >>9401930How else would you define it?
 >> Anonymous Fri Dec 29 18:27:33 2017 No.9401944 >>9401930>why exactly is a linear transformation defined with these two properties in mind (over real vector spaces):That's how it's defined for all vector spaces, not just real ones.The only things you can do in a vector space are add vectors or scale vectors, so linear transformations are defined to "preserve" that structure.This structure-preserving property is very useful when considering functions between two algebraic structures of the same type:https://en.wikipedia.org/wiki/Homomorphism
 >> Anonymous Fri Dec 29 18:30:47 2017 No.9401957 File: 28 KB, 417x480, 1502136283960.jpg [View same] [iqdb] [saucenao] [google] [report] >>9401944thanks
 >> Anonymous Fri Dec 29 19:01:00 2017 No.9402008 >>9401930like >>9401944 said, whenever you have some kind of structure, you should investigate maps which preserve this structure in some sensein this case, it follows that every linear map can be represented by a matrix and composition of maps becomes matrix multiplication. this makes linear maps extremely easy to analyze. linear maps also have very clear geometric meaning: they are rotations, reflections, shears and scalings (i.e. the things you can do at photoshop).
 >> Anonymous Fri Dec 29 19:05:20 2017 No.9402021 >>9402008>every linear map can be represented by a matrixWrong.
 >> Anonymous Fri Dec 29 19:08:38 2017 No.9402031 >>9402008>thinks you can describe translations by a linear map.
 >> Anonymous Fri Dec 29 19:11:55 2017 No.9402044 >>9402031Where was that implied?
 >> Anonymous Fri Dec 29 19:13:29 2017 No.9402050 >>9402044>(i.e. the things you can do at photoshop).
 >> Anonymous Fri Dec 29 19:28:53 2017 No.9402075 File: 210 KB, 581x581, 1496608646492.png [View same] [iqdb] [saucenao] [google] [report] 'bout to blow my FUCKING brains out . FUCK LINEAR ALGEBRA. FUCK IT. FUCK IT. FUUUUCCCCK IT ALLLLLLLLLLLLLLL
 >> Anonymous Fri Dec 29 19:29:59 2017 No.9402078 >>9402075>LINEAR ALGEBRAliterally the easiest maths
 >> Anonymous Fri Dec 29 19:31:52 2017 No.9402079 >>9402075Linear algebra is one of the simplest mathematical topics. Just because you can't handle taking an ordered basis doesn't mean you should insult La-chan.
 >> Anonymous Fri Dec 29 19:32:24 2017 No.9402080 >>9402078i have no idea how to change coordinates.
 >> Anonymous Fri Dec 29 19:32:48 2017 No.9402082 >>9402075Why are you even at college if you can't even understand linear algebra? Why waste your money like that?
 >> Anonymous Fri Dec 29 19:32:52 2017 No.9402083 >>9401530To the anon here >>9401135 I answered your question here >>9402063.
 >> Anonymous Fri Dec 29 19:54:47 2017 No.9402107 >>9402080if you have a basis $\{v_i\}_{i\leq n}$ and want to change it to a basis $\{w_k\}_{k\leq n}$, then in particular you can write any vector $w_k$ in terms of sums of the $v_i$. But then you have a system $w_k = a_{1,k}v_1 + a_{2,k}v_2+...+a_{n,k}v_n$ for every$k$. So you can write the matrix of the transformation in terms of the $a_{i,j}$, and this is your transformation matrix to change any coordinate in terms of the $v_i$ to coordinates in the basis $w_k$.
 >> Anonymous Fri Dec 29 20:00:29 2017 No.9402111 File: 18 KB, 833x76, wtff.png [View same] [iqdb] [saucenao] [google] [report] >>9402075linear algebra depends on the teacheryou can have either an autist that wants all proofs or someone that plugs and chugs into systems of linear equations for u engi majorspic is a problem on the final that fucked pretty much everyone so he dropped it rofl
 >> Anonymous Fri Dec 29 20:12:02 2017 No.9402139 Why is/are there no linear transform(s) to get the transpose?
 >> Anonymous Fri Dec 29 20:13:24 2017 No.9402143 >>9402139>Why is/are there no linear transform(s) to get the transpose?What do you mean? The transpose is a linear transformation.
 >> Anonymous Fri Dec 29 20:14:42 2017 No.9402145   >>9402143Aporogees for poor Engrish..Why is there no way to find B such that$A*B = A^T[math]  >> Anonymous Fri Dec 29 20:15:13 2017 No.9402146 >>9402143Aporogees for poor Engrish..Why is there no way to find B such that[math]A*B = A^T$
 >> Anonymous Fri Dec 29 20:16:28 2017 No.9402148 >>9402111Really? Did he not cover basic matrix factorizations in class, then?(Though he should have put some quantifier on "n". As, "for any positive integer n".)
 >> Anonymous Fri Dec 29 20:18:47 2017 No.9402152 >>9402111Is diagonalizing a matrix considered hard on Amerifatland?
 >> Anonymous Fri Dec 29 20:21:23 2017 No.9402158 Given square matrices $A,B$ and an inverse $M$ for $1-AB$, show that there is an inverse for $1-BA$ expressed in terms of $A,B,M$.
 >> Anonymous Fri Dec 29 20:22:02 2017 No.9402160 File: 354 KB, 760x965, 1484696561045.jpg [View same] [iqdb] [saucenao] [google] [report] I want to start learning more about discrete stuff / combinatorics. I have a strong background in differential geometry and functional analysis / PDE. Is it possible to use this knowledge to my advantage? Are there scenarios in combinatorics where methods / intuition from the aforementioned fields can be applied?
 >> Anonymous Fri Dec 29 20:22:43 2017 No.9402161 >>9402158What have you tried?
 >> Anonymous Fri Dec 29 20:24:00 2017 No.9402162 >>9402161I know how to solve it. This is a nice exercise for you guys. You can try convincing yourself that 1-AB is invertible if and only if 1-BA is invertible; that can be done abstractly without expressing the inverse for one in terms of A,B and the inverse for the other.
 >> Anonymous Fri Dec 29 20:24:51 2017 No.9402163 >>9402162I'm not a "guy".
 >> Anonymous Fri Dec 29 20:25:09 2017 No.9402164 >>9402152its more of wtf is the question asking
 >> Anonymous Fri Dec 29 20:26:13 2017 No.9402167 >>9402111That's a very simple problem, once you know that every self-adjoint matrix is diagonalizable.
 >> Anonymous Fri Dec 29 20:26:19 2017 No.9402169 >>9402163faggot mentally ill nigger bitch ass
 >> Anonymous Fri Dec 29 20:27:27 2017 No.9402170 >>9402158>Given square matrices A,B and an inverse M for 1−AB, show that there is an inverse for 1−BA expressed in terms of A,B,M.Please no homework in this thread
 >> Anonymous Fri Dec 29 20:27:58 2017 No.9402171 >>9402111>pic is a problem on the final that fucked pretty much everyone so he dropped it roflWhich school for brainlets do you go to?
 >> Anonymous Fri Dec 29 20:28:29 2017 No.9402173 >>94021581-BA trivially has inverse BA-1, no need for M.
 >> Anonymous Fri Dec 29 20:29:08 2017 No.9402174 >>9402170This is apparently an interview question from Microsoft.
 >> Anonymous Fri Dec 29 20:30:11 2017 No.9402178 >>9402173Multiplicative inverse is what's asked for, not additive.
 >> Anonymous Fri Dec 29 20:30:45 2017 No.9402179 >>9402169>faggot mentally ill nigger bitch assAre you okay?
 >> Anonymous Fri Dec 29 20:36:22 2017 No.9402182 >>9402171saint louis university in stl
 >> Anonymous Fri Dec 29 20:52:16 2017 No.9402209 >>9402160The closest interactions with combinatorics those fields have is ergodic theory. Mainly the representation theory of discrete amenable groups has some nice connections with geometric group theory and ergodic theory both of which are connected to combinatorics. There is some more abstract work that is connected with combinatorics under the guise of operads, specifically through Stasheff polytopes.
 >> Anonymous Fri Dec 29 20:52:35 2017 No.9402210 >>9402169How old are you?
 >> Anonymous Fri Dec 29 21:59:44 2017 No.9402310 File: 439 KB, 732x708, Screen Shot 2017-12-28 at 9.24.24 AM.png [View same] [iqdb] [saucenao] [google] [report] >>9402146pls
 >> Anonymous Fri Dec 29 22:09:00 2017 No.9402322 >>9402146If * is matrix product then it definitely is possible sometimes, like when A is invertible. Can you be more specific? Maybe you mean *when* is there no way?
 >> Anonymous Fri Dec 29 22:47:56 2017 No.9402365 >>9402075This is why brainlets should stay away from universities.
 >> Anonymous Fri Dec 29 23:12:45 2017 No.9402396 File: 114 KB, 900x900, 554554554.jpg [View same] [iqdb] [saucenao] [google] [report] >>9401535Thanks for the laugh
 >> Anonymous Fri Dec 29 23:12:57 2017 No.9402397 File: 38 KB, 661x661, 1496536016446.jpg [View same] [iqdb] [saucenao] [google] [report] I've seen the light. After journeying to hell and back, and mustering every last IQ point I have, I now understand where I went wrong. Forgive me, linear algebra. Take me back into your embrace.
 >> Anonymous Fri Dec 29 23:25:21 2017 No.9402421 >>9402397If you're that brainlet who was struggling with LA, check this playlist out for a nice intuition based introduction to LA.It's pretty good and not too long either. https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
 >> Anonymous Fri Dec 29 23:32:54 2017 No.9402433 File: 1023 KB, 1269x362, Capture.png [View same] [iqdb] [saucenao] [google] [report] >>9401530Are these the most challenging maths textbooks of all time?
 >> Anonymous Fri Dec 29 23:46:37 2017 No.9402449 >>9402433Are those TAOCPs even worth the time?
 >> Anonymous Sat Dec 30 01:29:01 2017 No.9402576 >>9402158Cayley-Hamilton.
 >> Anonymous Sat Dec 30 02:51:43 2017 No.9402672 >>9401535Why are physishits so retarded?
 >> Anonymous Sat Dec 30 02:54:00 2017 No.9402674 >>9402083>solving other people's homework for freeFag.
 >> Anonymous Sat Dec 30 02:58:25 2017 No.9402681 >>9402433lel gb2 >>>/g/
 >> Anonymous Sat Dec 30 03:03:04 2017 No.9402686 >>9402674>Fag.Why the homophobia?
 >> Anonymous Sat Dec 30 06:40:16 2017 No.9402855 >>9402433No, IUT is
 >> Anonymous Sat Dec 30 06:45:02 2017 No.9402858 >>9401535Good lord it's actually real
 >> Anonymous Sat Dec 30 07:52:52 2017 No.9402904 >>9402686>homophobiaFag.
 >> Anonymous Sat Dec 30 08:04:43 2017 No.9402918 >>9402158For small real numbers a and b1/(1-ba)=1+b(1+ab+(ab)^2+...)a=1+bma Be inspired therefrom.
 >> Anonymous Sat Dec 30 08:04:54 2017 No.9402919 >>9402163I'm not your guy, buddy.
 >> Anonymous Sat Dec 30 08:05:22 2017 No.9402920 >>9401930Everyone else who answered this is educated stupid; I'll tell you the real reason because this is a good question not left to undergrads who just memorized this 2 years ago or whatever. Linear transformations are defined this way because it is just the precise way of saying "Knowing how the basis vectors transform tells you how ALL vectors in your space transform."
 >> Anonymous Sat Dec 30 08:08:10 2017 No.9402925 >>9402031>>thinks you can describe translations by a linear map.you can tho
 >> Anonymous Sat Dec 30 08:10:49 2017 No.9402928 >>9402031[eqn]\begin{bmatrix}a & b & r \\ c & d & s \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix}x \\ y \\ 1\end{bmatrix} = \begin{bmatrix} ax+by+r \\ cx+dy+s \\ 1\end{bmatrix} [/eqn]not that other guy but you can represent translations with matrix multiplication, this is called homogeneous coordinates where you look at translations as being rotations restricted to a surface.
 >> Anonymous Sat Dec 30 08:14:19 2017 No.9402934   >>9402925No, you need an affine map. Brainlet.
 >> Anonymous Sat Dec 30 08:27:54 2017 No.9402959 >>9402158$(1-BA)B = B(1-AB)$, hence $(1-BA)B(1-AB)^{-1} = B$ and $(1-BA)B(1-AB)^{-1}A = BA$.Finally, $1-BA + (1-BA)B(1-AB)^{-1}A = (1-AB)(1+B(1-AB)^{-1}A) = 1$.It's easy to check that $1+B(1-AB)^{-1}A$ is also a left inverse.
 >> Anonymous Sat Dec 30 08:36:56 2017 No.9402978 >>9401930So that it is a homomorphism for the operations of vector spaces.Generally a homorphism is a map between algebraic structures A and B (f:A-->B) with which:computing in A and then sending in Bis the same assending in B and computing in BWhy study homomorphisms?Because with them you can study part of B from the point of view of A, and vice versa.How?Partition A in cells where in each cell you have elements that are sent to the same element of B. i.e. a1,a2 are in the same cell whenever f(a1)=f(a2).It is possible define "new" operations on these cells: (Cell where a1 is) * (Cell where a2 is) = (Cell where a1*a2 is) and this operation is independent of which elements of the cell you picked.The cells along with those operations form a structure which is the same (except in names) as the image of A under f ( f(A) ).This is called "First Isomorphism theorem".
 >> Anonymous Sat Dec 30 08:41:11 2017 No.9402990 Does anyone have the wolframalpha android app?Is there a point buying it or is it the same as using the browser version?
 >> Anonymous Sat Dec 30 08:47:21 2017 No.9402998 >>9402928Still not technically a linear map, since you always need the last component to be 1. They're elements of the projective general linear group on R^n, which is the quotient group of GL(R^n+1) by scalar multiplication (isomorphic to R*).
 >> Anonymous Sat Dec 30 08:56:30 2017 No.9403012 >>9402998Of course it is a linear map, but it is not a translation in all of R^3. Still, it restricts to a translation on the plane {z=1}
 >> Anonymous Sat Dec 30 09:01:21 2017 No.9403015 >>9402158In the same vein, but easier: Let A and B be square matrices such that $A+B=AB$. Prove that A and B commute
 >> Anonymous Sat Dec 30 09:17:00 2017 No.9403035 >>9402146Oh...you mean a B that works for all A.If you set A = I then you get B = I so obviously that won't work.
 >> Anonymous Sat Dec 30 09:47:59 2017 No.9403087 >>9402164it's asking you to prove that n-th root of a matrix exists if the matrix is hermitian and positive semidefinite.
 >> Anonymous Sat Dec 30 10:07:20 2017 No.9403123 >>9402111This is a REALLY simple problem. It's there to test if you know the real spectral theorem.Your class is retarded / you professor did a terrible job at teaching.
 >> Anonymous Sat Dec 30 10:23:11 2017 No.9403159 File: 75 KB, 501x504, happy wolfram.jpg [View same] [iqdb] [saucenao] [google] [report] >>9402990no point, he has enough shekels already
 >> Anonymous Sat Dec 30 10:42:30 2017 No.9403203 >>9402998Linear maps are defined on vector spaces, which {z=1} is not. It's the restriction of a linear map on an affine subset.
 >> Anonymous Sat Dec 30 10:44:58 2017 No.9403209 >>9402855>No, IUT isIUT is a series of papers, not a textbook.
 >> Anonymous Sat Dec 30 10:48:18 2017 No.9403217 >>9402920>Linear transformations are defined this way because it is just the precise way of saying "Knowing how the basis vectors transform tells you how ALL vectors in your space transform."But that's not true at all, linear transformations are still defined that way even for vector spaces that don't have a basis.
 >> Anonymous Sat Dec 30 11:36:07 2017 No.9403321 >>9403203meant to reply to >>9403012
 >> Anonymous Sat Dec 30 11:37:20 2017 No.9403323 File: 819 KB, 1000x1494, 1512422470624.jpg [View same] [iqdb] [saucenao] [google] [report] >>9403217>vector spaces that don't have a basisI sense a rain of pro-AC posts incoming.
 >> Anonymous Sat Dec 30 11:51:59 2017 No.9403347 File: 65 KB, 641x581, 1498774316181.jpg [View same] [iqdb] [saucenao] [google] [report] >>9403217>vector spaces that don't have a basisIn non-retarded circles "vector space" means "free module over a field". Perhaps you meant to say that they were defined the same way for all homomorphisms of modules?
 >> Anonymous Sat Dec 30 11:54:25 2017 No.9403350 >>9403217>vector spaces that don't have a basisautism or ignorance
 >> Anonymous Sat Dec 30 11:56:29 2017 No.9403354 >>9403347>>9403323he means that defining linear transformations in infinite dimension is independent of AC, clearly
 >> Anonymous Sat Dec 30 11:57:42 2017 No.9403356 >>9403354>heI'm not a "he".
 >> Anonymous Sat Dec 30 11:58:13 2017 No.9403359 >>9403350>autism or ignoranceSpeak for yourself.
 >> Anonymous Sat Dec 30 12:00:56 2017 No.9403364 >>9403356shut the fuck up, faggot
 >> Anonymous Sat Dec 30 12:01:25 2017 No.9403367 >>9403347>In non-retarded circles "vector space" means "free module over a field".You meant "module over a field".
 >> Anonymous Sat Dec 30 12:02:32 2017 No.9403369 >>9403354>independent of ACYes, "every free module over a field is free" is independent of AC. Your point?>>9403367No, I meant "free module over a field".
 >> Anonymous Sat Dec 30 12:08:13 2017 No.9403381 >>9403369>No, I meant "free module over a field".Then your statement is not true. Find one (1) source that defines a vector spaces as such.
 >> Anonymous Sat Dec 30 12:11:17 2017 No.9403386 >>9403364>faggotWhy the homophobia?
 >> Anonymous Sat Dec 30 12:20:38 2017 No.9403401 >>9403381>Find one (1) source that defines a vector spaces as such.The book I'm currently writing.
 >> Anonymous Sat Dec 30 12:36:48 2017 No.9403439 >>9403386I'm not a "homophobe".
 >> Anonymous Sat Dec 30 12:43:41 2017 No.9403456 >>9403386Because faggots are not human.
 >> Anonymous Sat Dec 30 12:54:54 2017 No.9403481 File: 20 KB, 348x342, 1483742309590.jpg [View same] [iqdb] [saucenao] [google] [report] >>9403354But with AC comes a basis, and so that wording is there to tell xį does not require choice to be axiomatically true. Your interpretation of žůr post is incorrect.
 >> Anonymous Sat Dec 30 12:59:55 2017 No.9403490 >>9403481What are your preferred axioms?
 >> Anonymous Sat Dec 30 13:04:36 2017 No.9403501 File: 177 KB, 1412x1175, 109.jpg [View same] [iqdb] [saucenao] [google] [report] >>9403490Axiom of Equality: every human is to be treated the same way.Axiom of Infinity: there is an infinite amount of genders.Axiom of Racial Purity: only white people (at least 57%) are to be considered human.
 >> Anonymous Sat Dec 30 13:13:31 2017 No.9403519 File: 146 KB, 1920x1080, 1478220275649.jpg [View same] [iqdb] [saucenao] [google] [report] >>9403490Ps. I'm not a "you". Please refer to me as "thou" from now on.
 >> Anonymous Sat Dec 30 13:17:00 2017 No.9403529 >>9403501The second two can be derived from the axiom of faggotry
 >> Anonymous Sat Dec 30 13:22:13 2017 No.9403543 File: 137 KB, 594x530, cf57d8c2.png [View same] [iqdb] [saucenao] [google] [report] >>9403529Why the homophobia? You should try homotopia instead. Just imagine you were sitting on the lap of some nice guy explaining him Quillen's model categories work, and he would then reward you with an intense kiss. So much more fun!
 >> Anonymous Sat Dec 30 13:33:37 2017 No.9403573   File: 6 KB, 617x133, 72f15a.png [View same] [iqdb] [saucenao] [google] [report] i know i'm retarded but i can't for the life of me get this same answer for the lcm
 >> Anonymous Sat Dec 30 13:40:29 2017 No.9403583 >>9403573>i know i'm retarded but i can't for the life of me get this same answer for the lcmWhat do you get?
 >> Anonymous Sat Dec 30 13:42:26 2017 No.9403586   >>9403583408/25pi
 >> Anonymous Sat Dec 30 13:45:00 2017 No.9403590 >>9403586>>9403583oh fuck me i'm so stupid i realized what i've done. i blame the calculator interface it confused me. nevermind i'll delete my posts now
 >> Anonymous Sat Dec 30 13:46:49 2017 No.9403591 >>9403590>>9403583I don't understand. What's the point of studying LCD's in the real numbers? The real numbers have no non-trivial divisibility structure. Everything divides everything. What the fuck?
 >> Anonymous Sat Dec 30 13:49:04 2017 No.9403597 >>9403591it's a trick question. The answer is $\forall\epsilon>0:\epsilon$
 >> Anonymous Sat Dec 30 13:50:18 2017 No.9403600 >>9403597Is it really? Because it looked like a high school problem. I just thought it was shitty math education teaching retarded bullshit as usual.
 >> Anonymous Sat Dec 30 13:50:20 2017 No.9403601 >log in>no new yous>log out
 >> Anonymous Sat Dec 30 14:22:08 2017 No.9403657 File: 11 KB, 934x80, Screenshot from 2017-12-30 14-02-46.png [View same] [iqdb] [saucenao] [google] [report] I'm not sure what this question wants exactly. Is it something like, e.g. for (1, 1)-tensors [eqn]\mathbf{T} = \left\{\begin{align}& \mathbf{x} \in V_n \mapsto (\mathbf{\omega} \in V_n^* \mapsto T_j^i\ \mathbf{e}_i \otimes \mathbf{\theta}^j (\mathbf{\omega}, \mathbf{x}) \in \text{Hom}_\text{Vect}(V^*_n, \mathbb{R}) = V^{**}_n = V_n) \in \text{Hom}_\text{Vect}(V_n, V_n) \\& \mathbf{\omega} \in V^*_n \mapsto (\mathbf{x} \in V_n \mapsto T_j^i\ \mathbf{e}_i \otimes \mathbf{\theta}^j (\mathbf{\omega}, \mathbf{x}) \in \text{Hom}_\text{Vect}(V_n, \mathbb{R}) = V^{*}_n) \in \text{Hom}_\text{Vect}(V^*_n, V^*_n) \\\end{align}\right. \\\therefore \mathbf{T} \in \text{Hom}_\text{Vect}(V_n, V_n) \cup \text{Hom}_\text{Vect}(V^*_n, V^*_n)[/eqn] and then I do something like that for all the other (r, s)?
 >> Anonymous Sat Dec 30 15:20:12 2017 No.9403763 >>9403657yes
 >> Anonymous Sat Dec 30 15:26:29 2017 No.9403776 >Another difference from elementary geometry is the way in which parallel lines can be said to meet in a point at infinity, once the concept is translated into projective geometry's terms. What the fuck. How is this possible?
 >> Anonymous Sat Dec 30 15:30:53 2017 No.9403787 >>9403776>What the fuck.Do you need to swear?
 >> Anonymous Sat Dec 30 15:31:50 2017 No.9403789 >>9403787yes. how can two lines that are parallel "meet", especially "at" """"""infinity"""""""""? that makes no sense.
 >> Anonymous Sat Dec 30 15:36:10 2017 No.9403801 is there an extension of linear algebra to "non" linear transformations?
 >> Anonymous Sat Dec 30 15:37:07 2017 No.9403805 >>9403801>is there an extension of linear algebra to "non" linear transformations?https://en.wikipedia.org/wiki/Linear_algebra#Generalizations_and_related_topics
 >> Anonymous Sat Dec 30 15:50:46 2017 No.9403829 >>9403801Pretty much algebraic geometry.
 >> Anonymous Sat Dec 30 15:59:06 2017 No.9403838 What do I need to approach Langlands program?
 >> Anonymous Sat Dec 30 16:06:04 2017 No.9403846 >>9403838algebraic number theory, algebraic geometry, functional analysis, representation theory
 >> Anonymous Sat Dec 30 16:11:01 2017 No.9403852 What is calculus and why do we need it?
 >> Anonymous Sat Dec 30 16:13:21 2017 No.9403857 File: 61 KB, 1321x319, 1512199292978.png [View same] [iqdb] [saucenao] [google] [report] >>9403852see pic
 >> Anonymous Sat Dec 30 16:47:01 2017 No.9403941 >>9403846>functional analysiswhy?
 >> Anonymous Sat Dec 30 16:48:39 2017 No.9403946 >>9403941>why?Infinite dimensional representations of Lie groups come into play
 >> Anonymous Sat Dec 30 16:59:11 2017 No.9403984 I'd just like to interject for a moment. What you're referring to as calculus, is in fact, real analysis, or as I've recently taken to calling it,$\Bigg(\mathbf{R},+,\times, \leq, |\cdot|,\tau = \{ A\subset \mathbf{R}\hspace{0.1cm} | \hspace{0.1cm}\forall x \in A, \exists \epsilon > 0 ,\hspace{0.1cm} ]x-\epsilon,x+\epsilon[\hspace{0.1cm} \subset A \},\hspace{0.1cm} \displaystyle \bigcap_{\substack{\text{A} \hspace{0.1cm}\sigma-\text{algebra of}\hspace{0.1cm}\mathbf{R}\\ \tau \subset A}}A , \hspace{0.1cm}\mathscr{L}\Bigg)$ -analysis. Calculus is not a branch of mathematics unto itself, but rather another application of a fully functioning analysis made useful by topology, measure theory and vital $\mathbf{R}$-related properties comprising a full number field as defined by pure mathematics.Many mathematics students and professors use applications of real analysis every day, without realizing it. Through a peculiar turn of events, the application of real analysis which is widely used today is often called "Calculus", and many of its users are not aware that it is merely a part of real analysis, developed by the Nicolas Bourbaki group. There is really a calculus, and these people are using it, but it is just a part of the filed they use. Calculus is the computation process: the set of rules and formulae that allow the mathematical mind to derive numerical formulae from other numerical formulae. The computation process is an essential part of a branch of mathematics, but useless by itself; it can only function in the context of a complete number field. Calculus is normally used in combination with the real number field, its topology and its measured space: the whole system is basically real numbers with analytical methods and properties added, or real analysis.All the so called calculus problems are really problems of real analysis.
 >> Anonymous Sat Dec 30 17:05:24 2017 No.9404009 >>9403984This is overcomplicating things.Those are a finite amount of finite tools trying to separate the inseparable in various ways.
 >> Anonymous Sat Dec 30 17:07:26 2017 No.9404012 >>9404009it's a meme you dip
 >> Anonymous Sat Dec 30 19:49:52 2017 No.9404397 >>9403789If you stand on a railroad and look straight ahead, you will see that the rails "meet" a long distance away in the horizon. Projective geometry deals with this notion
 >> Anonymous Sat Dec 30 19:53:07 2017 No.9404404 >>9403801Yes, simply consider all functions instead of just linear transformations.
 >> Anonymous Sat Dec 30 19:53:22 2017 No.9404405 File: 154 KB, 441x662, 5a5669a3aca58521d7bed492074275e4.jpg [View same] [iqdb] [saucenao] [google] [report] >>9404397i see.
 >> Anonymous Sat Dec 30 20:10:47 2017 No.9404424 >>9404405Please refrain from posting black people here.
 >> Anonymous Sat Dec 30 20:12:22 2017 No.9404427 File: 67 KB, 624x351, p03696p7.jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Sat Dec 30 20:14:26 2017 No.9404429 >>9403984IMO calculus is much more about linear transformations than real analysis.Equations like:[eqn]\int^b_a f(x) g(x) dx + \int^b_a k(x, y) h(x) dx = 0[/eqn]are basically similar to tensor equations like:[eqn]A_{\alpha} B_{\alpha} + C_{\alpha\beta} D_{\alpha}[/eqn]
 >> Anonymous Sat Dec 30 20:19:03 2017 No.9404437 >>9402021But it's always true for finitely dimensional spaces
 >> Anonymous Sat Dec 30 20:19:58 2017 No.9404439 Are functions of the form:[eqn] \sum^{\infty}_{k = 0} c_k \frac{\Gamma(x + k - a)}{\Gamma(x - a)} [/eqn]real analytic?Is there a formula for converting between this form and a polynomial series?
 >> Anonymous Sat Dec 30 20:21:17 2017 No.9404443 >>9404437The Schwartz kernel theorem also shows the same thing for integral transforms.
 >> Anonymous Sat Dec 30 20:34:56 2017 No.9404462 >>9404405watch n j wildberger math history projective geometry very helpful and intuitive
 >> Anonymous Sat Dec 30 21:13:40 2017 No.9404526 >>9401930invariance under action>>9401943stoopid>>9401944handwavy>>9402008finite-dimensional>>9402920estupido, this is one of many consequences>>9403217low iq
 >> Anonymous Sat Dec 30 22:07:11 2017 No.9404591 >>9404526all me
 >> Anonymous Sat Dec 30 22:24:11 2017 No.9404620 File: 24 KB, 558x614, 123123.png [View same] [iqdb] [saucenao] [google] [report] >tfw really struggling with the theory of L^p spaces.Should I just end it all? I get physically sick when doing relevant exercises and it's anything more advanced than some super simple Hölder application.
 >> Anonymous Sat Dec 30 22:31:21 2017 No.9404632 >>9404591samefag
 >> Anonymous Sun Dec 31 00:43:42 2017 No.9404781 >>9404591wew
 >> Anonymous Sun Dec 31 01:03:28 2017 No.9404805 File: 189 KB, 394x373, wot.png [View same] [iqdb] [saucenao] [google] [report] I'm in highschool, which math topics should i focus on other than Calculus? Geometry?Discrete math?
 >> Anonymous Sun Dec 31 01:04:39 2017 No.9404806 >>9404805Introduction to mathematical proofs and reasoning
 >> Anonymous Sun Dec 31 01:06:19 2017 No.9404809 >>9404805What's discrete math?I would say trigonometry or algebra in general. Trying linear algebra will put you ahead, it's really easy.
 >> Anonymous Sun Dec 31 01:18:57 2017 No.9404814
 >> Anonymous Sun Dec 31 01:28:04 2017 No.9404818 >>9404806>>9404814You don't need proofs unless you're gonna major in math.
 >> Anonymous Sun Dec 31 02:26:52 2017 No.9404866 redpill me on topos
 >> Anonymous Sun Dec 31 02:51:53 2017 No.9404891 File: 139 KB, 607x1024, gorillas and niggers.jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Sun Dec 31 02:56:49 2017 No.9404895 >>9404620Just keep practicing, that stuff gets easy. Just remember Holder, Egorov, Jensen, convolutions, things like $|g| = |g|^{1/p} |g|^{1/q}$, and that if you want to show that a sequence goes to zero a.e., you can show that the integral of its infinite sum is finite. Among other things.
 >> Anonymous Sun Dec 31 02:59:44 2017 No.9404898 What are the simplest examples of $\infty$-groupoids?
 >> Anonymous Sun Dec 31 03:20:57 2017 No.9404908 >>9404805underage b&Start with some linear algebra and basic proofs
 >> Anonymous Sun Dec 31 03:47:35 2017 No.9404918 File: 266 KB, 384x288, arigato.gif [View same] [iqdb] [saucenao] [google] [report] >>9404814>>9404806Thanks!>>9404809Discrete math is topics like introductory Logic, Set Theory, Combinatorics and so on>>9404818I plan on majoring in math, but I'm not 100% sure, might go for compsci or physics>>9404908Isn't linear algebra very hard?
 >> Anonymous Sun Dec 31 04:23:55 2017 No.9404935 >>9404429That's some nice point of view - actually, linear ODEs behave like systems of linear equations.. But dealing with integral and differential equations also relies heavily on topological (resp. "analytical") arguments for many finite-dimensional arguments don't work any more...
 >> Anonymous Sun Dec 31 06:16:01 2017 No.9405007 >>9404918>Discrete "math"It's not a field of math strictly speaking, much like "combinatorics". It's best to ignore it entirely and study logic and set theory in their own right.>Isn't linear algebra very hard?No. You'll have to learn it anyway since it's used everywhere even outside of mathematics.
 >> Anonymous Sun Dec 31 06:21:09 2017 No.9405008 >>9402978>cellWhat?
 >> Anonymous Sun Dec 31 09:27:14 2017 No.9405202 >>9404805Linear Algebra for sure.
 >> Anonymous Sun Dec 31 09:29:18 2017 No.9405206 >>9405008Is blocks the correct term? I don't remember. I am not anglo.
 >> Anonymous Sun Dec 31 11:00:57 2017 No.9405309 >>9405007>study logic and set theory Why?
 >> Anonymous Sun Dec 31 11:06:14 2017 No.9405317 >>9405206'Coset' is the word you're looking for.
 >> Anonymous Sun Dec 31 12:00:26 2017 No.9405394 >>9405317But, isn't coset a term for groups only?
 >> Anonymous Sun Dec 31 12:11:49 2017 No.9405418 >>9404866A topos is the natural model for intuitionist higher-order logic.
 >> Anonymous Sun Dec 31 12:12:51 2017 No.9405420 >>9404898The fundamental infinity-groupoid.
 >> Anonymous Sun Dec 31 12:14:38 2017 No.9405426 >>9405394Vector spaces are groups under addition.If you just have a set, then the word should be "partition".
 >> Anonymous Sun Dec 31 12:26:03 2017 No.9405446 >>9405426Not exactly. The partition is the set of all equivalence classesYou can call them equivalence classes/classes/blocks. But cosets are a special case.
 >> Anonymous Sun Dec 31 12:57:23 2017 No.9405497 >>9402433Nop, whole books just use linear algebra,few calculus and some easy combinatorics.As textbook algebraic geometry hartshorne will be more hard book for students.
 >> Anonymous Sun Dec 31 14:06:58 2017 No.9405599 File: 1.09 MB, 1366x768, are you not entertained.png [View same] [iqdb] [saucenao] [google] [report] >>9403657>$V_n^{**} = V_n$Only if $V_n$ is finite dimensional. Also replace $n$ by $x$ to denote tangent vector spaces $T_xM$ at the point ${\bf x}$, on which this $(r,s)$-tensor business makes sense.>${\bf e}_i$What space is this basis for? $T$ should act on the basis for $V_n$ and the basis for $V_n^*$ at the same time, not separately. You need to put what you've written down together.>${\bf T} \in \operatorname{End}(V_n) \cup \operatorname{End}(V_n^*)$No. You need the exterior algebra.>>9403776>How is this possible?Have you never looked at a photograph in your life before?>>9404429General Volterra equations of the first kind can't be cast into an ODE tho. One way to construct solutions is via the resolvent map, which exists depending on the topology of your function space. >>9404439Expand $\frac{1}{\Gamma}$ in its Laurent series and you'll see that at specific points $x \in \mathbb{R}$ it acquires infinitely many negative powers.>Is there a formula for converting between this form and a polynomial series?You mean formal Laurent series? Use the Cauchy integral formula.
 >> Anonymous Sun Dec 31 14:09:00 2017 No.9405604 File: 1.08 MB, 947x941, unknown.png [View same] [iqdb] [saucenao] [google] [report] >>9405599>>${\bf T} \in \operatorname{End}(V_n)>\cup \operatorname{End}(V_n^*)$Meant ${\bf T} \in \operatorname{End}(V_n)\cup \operatorname{End}(V_n^*)$.
 >> Anonymous Sun Dec 31 14:26:12 2017 No.9405620 >>9405420Every infinity groupoid is equivalent to a fundamental infinity groupoid.
 >> Anonymous Sun Dec 31 14:52:33 2017 No.9405666 >>9405426True, but I was talking about a general algebraic structure.Here:https://en.wikipedia.org/wiki/Isomorphism_theorems#General
 >> Anonymous Sun Dec 31 15:06:27 2017 No.9405693 File: 32 KB, 600x600, quantum-systems-channels-information.jpg [View same] [iqdb] [saucenao] [google] [report] I'm studying quantum information theory using pic related. Anyone ever study this before? Not sure where to go. Would like to perhaps study more general C*Algebras as I have covered a lot of that topic. I've also heard of quantum information having ties to geometry.
 >> Anonymous Sun Dec 31 15:08:07 2017 No.9405698 >>9405604this picture is funny because it's true
 >> Anonymous Sun Dec 31 15:45:15 2017 No.9405757 >>9405604You are comparing notation for abstract theory and notation for computation.Topologists are as messy when it comes to computation (i.e. spectral sequences)
 >> Anonymous Sun Dec 31 17:21:08 2017 No.9405924 >>9405620Proof?
 >> Anonymous Sun Dec 31 17:26:54 2017 No.9405932 >>9402928but that's affine and not linear transformation
 >> Anonymous Sun Dec 31 17:27:27 2017 No.9405933 >>9405924$$\left| - \right|:\operatorname{Kan} \rightleftarrows \operatorname{Top} :\operatorname{Sing}$$ is a Quillen equivalence in the standard model structures of the two categories.
 >> Anonymous Sun Dec 31 17:28:29 2017 No.9405935 >>9405933*$\left| - \right|:\operatorname{Kan} \rightleftarrows \operatorname{Top} :\operatorname{Sing}$
 >> Anonymous Sun Dec 31 17:42:22 2017 No.9405951 >>9403217norman pls go
 >> Anonymous Sun Dec 31 17:43:42 2017 No.9405952 >>9403381It's not untrue, it's just redundant since module over a field is always free
 >> Anonymous Sun Dec 31 17:50:10 2017 No.9405955 >>9405952>it's just redundantNo, it's simply incorrect.
 >> Anonymous Sun Dec 31 17:55:59 2017 No.9405961 >>9405952It's actually not a bad definition. It allows you to do linear algebra without globally assuming the axiom of choice. He's still being an ass about it though.
 >> Anonymous Sun Dec 31 17:59:36 2017 No.9405965 >>9405961>It's actually not a bad definition. It allows you to do linear algebra without globally assuming the axiom of choice.But he/she did assume the axiom of choice.
 >> Anonymous Sun Dec 31 18:09:18 2017 No.9405977 >>9405961>It's actually not a bad definition.It's bad because now it becomes extremely difficult to tell whether certain modules over a field are vector spaces or not.
 >> Anonymous Sun Dec 31 18:12:46 2017 No.9405982 File: 79 KB, 700x700, nomizi.jpg [View same] [iqdb] [saucenao] [google] [report] There's countably many finite cardinalities (0,1,...).Are there countable many infinite cardinalities? (ordered by power sets?)
 >> Anonymous Sun Dec 31 18:16:49 2017 No.9405988 File: 84 KB, 378x252, contradict.png [View same] [iqdb] [saucenao] [google] [report] >>9405982There are countable many countable infinite cardinalities but uncountably many infinite cardinalities in general.Uhh I mean>infinite cardinalityNo such thing exists xDdxXDd
 >> Anonymous Sun Dec 31 18:18:46 2017 No.9405992 >>9405988>There are countable many countable infinite cardinalitiesIsn't there only one countable infinity?
 >> Anonymous Sun Dec 31 18:23:00 2017 No.9405996 >>9405992$\omega + 1,\omega + 2 ,\dots$
 >> Anonymous Sun Dec 31 18:29:19 2017 No.9406004 File: 27 KB, 1280x720, maxresdefault.jpg [View same] [iqdb] [saucenao] [google] [report] >>9405996>ω+1,ω+2Do those not have the same cardinality?
 >> Anonymous Sun Dec 31 18:31:23 2017 No.9406012 File: 98 KB, 250x312, file.png [View same] [iqdb] [saucenao] [google] [report] >>9406004Cardinals, ordinals, what's tha differenece???
 >> Anonymous Sun Dec 31 18:32:00 2017 No.9406015 >>9406004they have
 >> Anonymous Sun Dec 31 21:38:22 2017 No.9406235 >>9405992Finite sets are countable, little one.
 >> Anonymous Mon Jan 1 05:08:48 2018 No.9406834 File: 42 KB, 645x729, tfw no brain.png [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Mon Jan 1 08:10:43 2018 No.9406989 >>9405977Just don't use arbitrary modules over a field, that should be fine for you and your kind since you have already decided to lose generality by working over a field in the first place.
 >> Anonymous Mon Jan 1 08:11:55 2018 No.9406991 >>9405965>But he/she did assume the axiom of choice.I didn't though. You could even assume its negation and that would still be the correct definition of "vector space".
 >> Anonymous Mon Jan 1 09:22:26 2018 No.9407061 >>9405977>it becomes extremely difficult to tell whether certain modules over a field are vector spaces or notYes, which is something you would need to prove explicitly in a constructive universe. This is the point of constructivism, it forces you to prove things in a constructive/more informative way.
 >> Anonymous Mon Jan 1 12:37:13 2018 No.9407347 >>9401530So I just learned about $Li(x)$ from my number theory book. It's applications to number theory are fun, but what I want to know now is what new integrals can I find antiderivatives for using this beast?
 >> Anonymous Mon Jan 1 14:14:00 2018 No.9407485 How can I get into relation theory? Something better than Halmo's pls
 >> Anonymous Mon Jan 1 15:08:48 2018 No.9407594 File: 87 KB, 1200x692, 1514477693529.jpg [View same] [iqdb] [saucenao] [google] [report] >>9405599H-how do you know so much of so many different fields of maths? Or am I just retarded?
 >> Anonymous Mon Jan 1 15:36:11 2018 No.9407638 >>9407594Finishing college
 >> Anonymous Mon Jan 1 15:36:46 2018 No.9407640 >>9407594Not him but that's pretty standard info for undergrads and first year grad students in math. Basic facts about manifolds and dual vector spaces are encountered at the undergrad and grad level, so is complex analysis, the only one that isn't standard is the ODE stuff, unless you're doing applied math
 >> Anonymous Mon Jan 1 15:38:48 2018 No.9407647 >>9407640>him
 >> Anonymous Mon Jan 1 16:22:46 2018 No.9407715 How much maths should I know to stop hating myself for being retarded?
 >> Anonymous Mon Jan 1 16:32:35 2018 No.9407729 >>9407647Jesus fucking Christ
 >> Anonymous Mon Jan 1 16:34:48 2018 No.9407731 >>9407729>Jesus fucking ChristAre you okay?
 >> Anonymous Mon Jan 1 16:39:32 2018 No.9407739 >>9407731No. I want this meme to stop. We know you are just pretending to not be male. I bet you aren't even actually trans in real life.
 >> Anonymous Mon Jan 1 16:40:54 2018 No.9407741 >>9407739>No. I want this meme to stop. We know you are just pretending to not be male. I bet you aren't even actually trans in real life.But this isn't about me, it's about her.
 >> Anonymous Mon Jan 1 16:43:02 2018 No.9407747 >>9407741>her
 >> Anonymous Mon Jan 1 16:43:26 2018 No.9407748 >>9407747Yes?
 >> Anonymous Mon Jan 1 16:45:28 2018 No.9407753 >>9407739>I bet you aren't even actually trans in real life.He is pretty pathetic, so I wouldn't be surprised at him being "tr*ns".
 >> Anonymous Mon Jan 1 16:46:17 2018 No.9407757 >>9407753>He
 >> Anonymous Mon Jan 1 16:48:48 2018 No.9407763 >>9407757That's a bit of a bizarre question.
 >> Anonymous Mon Jan 1 16:51:39 2018 No.9407768 Here's a problem that I'm struggling with:find absolutely integrable function f: R->R, such that f is zero outside the interval [-1, 1], and the convolution of f with itself is constant on interval [-1, 1].Is there any such function except for zero?
 >> Anonymous Mon Jan 1 17:05:15 2018 No.9407796 File: 22 KB, 600x450, azu64.jpg [View same] [iqdb] [saucenao] [google] [report] >>9407715No amount will suffice. It is not related to anything mathematical.>>9407729>Jesus fucking ChristWhy the blasphemy?
 >> Anonymous Mon Jan 1 17:19:15 2018 No.9407827 >>9407796>No amount will suffice. It is not related to anything mathematical.How about the amount of maths I need to know so that I don't fear people considering me a fucking retard?
 >> Anonymous Mon Jan 1 17:29:54 2018 No.9407849 File: 330 KB, 719x512, haha.png [View same] [iqdb] [saucenao] [google] [report] >>9407827That amount is obviously related to the population you surround yourself with. On the other hand, the fact that you are even asking a question like this makes me think you will most likely be permanently percieved as a retard.
 >> Anonymous Mon Jan 1 17:30:05 2018 No.9407851 >>9407827>fuckingWhy the vulgarity?
 >> Anonymous Mon Jan 1 17:30:37 2018 No.9407853 File: 15 KB, 662x69, vice corrects pronouns.jpg [View same] [iqdb] [saucenao] [google] [report] >>9407741>herWhen did you ask for my pronouns shitlord?
 >> Anonymous Mon Jan 1 17:33:28 2018 No.9407859 File: 245 KB, 512x512, weird toy.png [View same] [iqdb] [saucenao] [google] [report] >>9407715A finished course in Algebraic Geometry, then you're slightly less retarded.IUT if you want the hate to stop.
 >> Anonymous Mon Jan 1 17:53:33 2018 No.9407904 >>9407849>On the other hand, the fact that you are even asking a question like this makes me think you will most likely be permanently percieved as a retard.How so?
 >> Anonymous Mon Jan 1 17:58:35 2018 No.9407917 File: 50 KB, 540x720, f316d662.jpg [View same] [iqdb] [saucenao] [google] [report] >>9407904Because the question was ill-formulated. The reason was given in my post. Btw look at this cat inside this sock. It is cute.
 >> Anonymous Mon Jan 1 18:01:55 2018 No.9407925 >>9407917I don't understand why people will perceive me as a retard.
 >> Anonymous Mon Jan 1 18:04:08 2018 No.9407930 File: 25 KB, 377x364, 1512344500765.jpg [View same] [iqdb] [saucenao] [google] [report] >>9407925Teehehee~
 >> Anonymous Mon Jan 1 18:34:54 2018 No.9407981 >>9407768Fourier transform
 >> Anonymous Mon Jan 1 18:41:46 2018 No.9407989 What would be a good math textbook for an of age highschooler taking AP Calc BC? The one I use for my class is very problem heavy- and while that's great and all, I feel like my understanding of the topic is pretty shit.
 >> Anonymous Mon Jan 1 19:23:05 2018 No.9408048
 >> Anonymous Mon Jan 1 19:29:51 2018 No.9408058 >>9408048>amazon.com>not libgen.io
 >> Anonymous Mon Jan 1 19:30:38 2018 No.9408062 >>9408058But piracy is I L L E G A L!!!
 >> Anonymous Mon Jan 1 19:31:10 2018 No.9408064 >>9408062>But piracy is I L L E G A L!!!Which memecountry do you live in?
 >> Anonymous Mon Jan 1 19:33:53 2018 No.9408071 >>9408064Oh, I live in the memiest of them all. In which there are no restrictions placed on libgen either. I was just helping that person justify linking books on sale insteadd of ones free for everyone to take.
 >> Anonymous Mon Jan 1 19:54:54 2018 No.9408106
 >> Anonymous Mon Jan 1 20:04:02 2018 No.9408123 File: 256 KB, 516x604, 1503523267785.jpg [View same] [iqdb] [saucenao] [google] [report] confidence is low ladslong story short: i'm 30 years old and going to college in a few weeks. my placement test is in about a week and depending on how i score i'll be placed in either pre-college(non-credit) courses or college level courses. there's a lot of pressure the goal is to graduate with a STEM degree so knowing maths is a must. it's been 12 years since i've been in an academic setting and my math skills are as bad as you can imagine. i've been studying with khan academy for three weeks and i'm up to algebra(factoring quadratics, polynomials, nested fractions and the like). to get to my point, i'm struggling, and i'm beginning to doubt i'm smart enough for STEM. getting every problem is really wearing me out. i'm learning but it's going very slowly. word problems are what i'm struggling with the most(write an equation to solve x word problem). i fucking hate word problems. i feel a lot dumber than i used to be, and the hopes of placing into college level courses are non-existent. i've accepted that i'll have to spend a semester learning the basics. i just hope that i'm smart enough to get into a proper physics/mathematics course by the fall semester. i do enjoy doing math which is surprising. i thought i'd hate it. solving a hard problem is very satisfying. i'd like to make a career out of it; astrophysics or something along that vein, but i realize that's a long ways down the road. i'll probably be close to 40 by the time i graduate but i honestly don't care anymore. anyway, i guess i'm posting here to see if anyone else is in a similar situation, and if being in a classroom setting with a proper teacher will make it easier to learn, and if my intellect will ever return
 >> Anonymous Mon Jan 1 20:05:07 2018 No.9408124 >>9408106>tfw no manga guide to IUT
 >> Anonymous Mon Jan 1 20:42:03 2018 No.9408181 File: 1.05 MB, 1362x762, back2work.png [View same] [iqdb] [saucenao] [google] [report] >>9407594Read.
 >> Anonymous Mon Jan 1 21:19:47 2018 No.9408244 >>9407917>Btw look at this cat inside this sock. It is cute.Does me finding the cat cute require the axiom of choice, categories can get a little hairy like that.>>9408123Depending on the degree the workload can get pretty heavy, I'd say have a back up to a stem degree that you have confidence in getting.
 >> Anonymous Mon Jan 1 21:24:17 2018 No.9408250 File: 31 KB, 1381x661, karvinen abstraktio.png [View same] [iqdb] [saucenao] [google] [report] >>9408244No. It only requires a little spark of animal love.
 >> Anonymous Mon Jan 1 21:27:20 2018 No.9408255 >>9408244>Does me finding the cat cute require the axiom of choiceNo, the category of cats having enough projectives suffices.
 >> Anonymous Mon Jan 1 22:59:39 2018 No.9408403 The wiki suggests A Transition to Advanced Mathematics by Smith, Eggen, and St. Andre in the computer science for intro to proofs, but it doesn't include number theory which is something that I'm interested in.Is there another comparable book that touches on number theory?
 >> Anonymous Mon Jan 1 23:34:45 2018 No.9408465 >>9408255So, what do we call the category of cats...$CAT$?>>9408403>Is there another comparable book that touches on number theory?Are you specifically interested in number theory as related to compsci? Knuth's art of programming has the relevant number theory
 >> Anonymous Mon Jan 1 23:52:28 2018 No.9408496 >>9408123Wtf? What took you so long to go to college?Sorry, I know that's not helpful. I don't know what to tell you, because you're not really being specific. Word problems are typically pretty easy to translate into equations, but I don't think I've had to do such problems since I was in elementary school or something.Do you have a decent grasp of algebra? Trigonometry?
 >> Anonymous Tue Jan 2 01:49:12 2018 No.9408685 >>9408181"no"
 >> Anonymous Tue Jan 2 03:53:19 2018 No.9408841 File: 51 KB, 736x736, cute.jpg [View same] [iqdb] [saucenao] [google] [report] >>9408123Unless you have a good plan, try my experimental study guide :31: Finish Khan Academy math subjects up to Algebra 2 and have done the tests2. Pick up Serge Lang's "Basic Mathematics" and do everything except Trigonometry chapter. Now you will have clear and rigorous grasp on College Algebra and able to prove few things and learn bonus things like Binomial Theorem3. Go back to Khan Academy and only do Trigonometry chapter. Because trig is fairly easy and at college level it's nothing but memorizing identities and formulas, you can learn more about trig later in calculus. ALSO, Khan Academy exercises are very intuitive so I recommend going back to Lang's book to do the trigonometry exercises there.4. Now you are well prepaired to do Calculus. Depending on which letter you choose to major in STEM, you can choose a Calculus book on appropriet difficulty. So you can pick up a soft Calculus book for E like Stewart's Early Transcendentals or if you choose to go for a better major like M you can pick up Spivak's Calculus which is rigorous.4.5. At this point you're doing well so you should do another book to help you through problem-solving and proving things to ease your mind during difficult exercises and heavy texts like Spivak's. I recommend "How to prove it" by Velleman and/or "How to Solve it" by Polya. Polya's is important if you need help solving things in general, while Velleman's is great foundation for later studies in university like Analysis and Linear Algebra.
 >> Anonymous Tue Jan 2 03:54:52 2018 No.9408844 File: 28 KB, 532x565, cuter.jpg [View same] [iqdb] [saucenao] [google] [report] >>94088415. At this point you should be very familiar with Calculus and easily get into university if you do entrance exam applications. Now you can go find your major, and do some headstart studies by checking the curriculum of your class. Or alternatively you could do things like:Re-visit and skim through some other calculus books to get a better and clear grasp on things and be polished.Try more rigorous books and topics like Linear Algebra, Number Theory and Multivariable Calculus.Master problem-solving by doing things like archived Olympiad problems and some difficult ones on Brilliant.orgWhatever you choose to do is up to you and about how much you like mathematics or if you need to get better understanding of things. The point is that it's important to keep doing math and not take too long breaks.6. Make your own study guide and plan ahead :3
 >> Anonymous Tue Jan 2 05:46:18 2018 No.9408923 >>9407981Please elaborate, i thought about fourier transform but it didnt help.
 >> Anonymous Tue Jan 2 06:05:19 2018 No.9408934   >>9408923Yeah actually after thinking about it, I realized that it didn't actually solve the problem. You could have deduced what you want under the stronger assumption that f*f is constant everywhere (because then the fourier transform of f is continuous, and its square is a multiple of the dirac mass at 0, hence zero)I'm not sure what to do about this
 >> Anonymous Tue Jan 2 06:11:44 2018 No.9408936 >>9408403The only "number theory" in a discrete math courses is Fermat's Little Theorem / Euler's Theorem and Euclid's Algorithm.Just read one of the three intro books here:http://4chan-science.wikia.com/wiki/Mathematics#Number_Theory
 >> Anonymous Tue Jan 2 07:46:00 2018 No.9408979 >>9408923What is the Fourier transform of a function constant on [-1,1] and zero everywhere else?
 >> Anonymous Tue Jan 2 08:57:30 2018 No.9409013 >>9408923It was actually more complicated than I thought, I'll have to keep thinking about it>>9408979It's not assumed to be zero outside of [-1,1]
 >> Anonymous Tue Jan 2 10:43:15 2018 No.9409148 >>9409013Assume f(x) is zero inside [-1,1]. Then rect(x)*f(x) = 0 everywhere, so sinc(w) convolve F(w) = 0 everywhere, i.e. the integral of sinc(w) F(a-w) is 0 for all a. Perhaps differentiate the integral wrt a?
 >> Anonymous Tue Jan 2 11:53:47 2018 No.9409253 File: 34 KB, 1024x576, w.jpg [View same] [iqdb] [saucenao] [google] [report] >>9405604>picNice OC. Saved.
 >> Anonymous Tue Jan 2 12:04:13 2018 No.9409278 What is a binary operation? Is it a function from the set AxB to C? Any other properties/definitions?
 >> Anonymous Tue Jan 2 12:07:45 2018 No.9409290 >>9409278like when youdo operations on digits in base 20*0=00*1=01*0=01*1=1AND
 >> Anonymous Tue Jan 2 12:08:13 2018 No.9409292 >>9409278A binary operation $\rho$ on a set S is a subset of $S \cross S \cross S$ such that $(x,y, *) \in \rho \ \forall x,y \in S$. Generalisations to binary operations on multiple (distinct) sets are left as an exercise to the reader.
 >> Anonymous Tue Jan 2 12:09:18 2018 No.9409296 >>9409292Errata: $\rho \subseteq S \times S \times S$.
 >> Anonymous Tue Jan 2 12:14:01 2018 No.9409309 >>9409292Oh, and * is uniquely associated to the pair (x,y).
 >> Anonymous Tue Jan 2 12:15:52 2018 No.9409313 >>9409309Errata: $\forall x,y \in S \exists ! * \in S, \ (x,y,*) \in \rho$.
 >> Anonymous Tue Jan 2 12:24:14 2018 No.9409331 >>9401530Where can I learn about topics related to p-adic 'density'? What I mean is, imagine you have a p-adic rational with infinitely many non-zero digits. You now multiply it by another p-adic rational. How many non-zero digits will the resulting number have?E.g. in binary, 11111111111..... = -1 in the 2-adics. If you multiply this by 1111111111... you get 1. So you got a very 'sparse' number (1) from multiplying two very dense numbers. What I'm interested in is a theory for when the numbers aren't necessarily algebraic or rational. Will two 'dense' numbers generally speaking multiply to form a sparse number? Will a sparse number and a dense number tend to form another sparse number?
 >> Anonymous Tue Jan 2 12:29:59 2018 No.9409354   >>9401530Why do topologists write $\mathbb{C}{\mathbb{P}^n}$ but geometers write $\mathbb{P}_\mathbb{C}^n$ ?
 >> Anonymous Tue Jan 2 12:48:48 2018 No.9409413 Why do topologists write $\mathbb{C}{\mathbb{P}^n}$ but geometers write $\mathbb{P}_\mathbb{C}^n$ ?
 >> Anonymous Tue Jan 2 15:44:27 2018 No.9409809 File: 51 KB, 899x544, .png [View same] [iqdb] [saucenao] [google] [report] Man why math teacher is a literal retard.
 >> Anonymous Tue Jan 2 15:45:53 2018 No.9409817 >>9409809Can you re-post it but not in Arabic this time?
 >> Anonymous Tue Jan 2 15:54:08 2018 No.9409840 File: 1.54 MB, 230x230, 1511935228934.gif [View same] [iqdb] [saucenao] [google] [report] >>9409413Because it's called the $\mathbb{C}$omplex $\mathbb{P}$rojective space and not the other way around.
 >> Anonymous Tue Jan 2 15:54:20 2018 No.9409841 File: 127 KB, 480x270, 1511608881745.gif [View same] [iqdb] [saucenao] [google] [report] >>9409817>xyeet doesn't know german
 >> Anonymous Tue Jan 2 15:55:48 2018 No.9409845 >>9409841Most of the people currently living in Germany don't either.
 >> Anonymous Tue Jan 2 15:57:24 2018 No.9409851 File: 427 KB, 1920x1080, 1512363672240.jpg [View same] [iqdb] [saucenao] [google] [report] >>9409845So we must help our Germanic brethren by preserving their language. Thank you for providing a good reason to know it.
 >> Anonymous Tue Jan 2 15:58:04 2018 No.9409852 >>9409817Oh sorry, it's just a find the maximum/minimum exercise with ${ x }_{ i } \ge 0$ and the formula to minimize being $5{ x }_{ 1 }-{ x }_{ 2 }+{ x }_{ 3 }+2{ x }_{ 4 }$. I have no idea why he is fucking around with the stuff in the brackets when he already has 1s everywhere. Seems like a dumbass thing to do but what do I know.
 >> Anonymous Tue Jan 2 16:08:14 2018 No.9409880 >>9409840or l'espace $\mathbb P$rojectif $\mathbb C$omplexe
 >> Anonymous Tue Jan 2 16:09:53 2018 No.9409887 >>9409840Or, you know, projective space over C
 >> Anonymous Tue Jan 2 16:24:13 2018 No.9409910 File: 271 KB, 560x560, 1.jpg [View same] [iqdb] [saucenao] [google] [report] >>9409880> l'espace $\mathbb P$rojectif $\mathbb C$omplexeHow about no.
 >> Anonymous Tue Jan 2 16:40:17 2018 No.9409944 >>9409413Because $\mathbb{P}_\mathbb{C}^n = \operatorname{Proj} \mathbb{C}\left[ {{x_0},...,{x_n}} \right]$ and $\mathbb{C}{\mathbb{P}^n} = \left( {{\mathbb{C}^{n + 1}}\backslash \left\{ 0 \right\}} \right)/ \sim$ .Both spaces are interesting to a geometer, but only the latter to a topologist (because the Zariski topology is boring from a topological perspective).
 >> Anonymous Tue Jan 2 19:10:47 2018 No.9410302 File: 560 KB, 1366x768, chiaki_self_energy.png [View same] [iqdb] [saucenao] [google] [report] >>9408685Then enjoy being treated like a brainlet for the rest of your life.
 >> Anonymous Wed Jan 3 02:53:17 2018 No.9411197 >>9409331Your usage of "dense" and "sparse" is non-standard. As to your particular question, I have no idea.
 >> Anonymous Wed Jan 3 03:55:31 2018 No.9411261 File: 2.00 MB, 4032x3024, 760EE043-1D62-493B-AFFD-F7623157D532.jpg [View same] [iqdb] [saucenao] [google] [report] >>9401535https://en.m.wikipedia.org/wiki/Analytization_trick#/issues>This article does not cite any sourcesHmmm...
 >> Anonymous Wed Jan 3 04:27:58 2018 No.9411289 File: 323 KB, 1080x1080, gns88jf4no701.jpg [View same] [iqdb] [saucenao] [google] [report] >>9408123Most likely you're going to get placed at the level you need to be at in order to have a fair shot at progressing it's not really worth stressing too much about just keep chugging through problems. I wouldn't isolate myself to khan academy either sometimes it is bit unhelpful. Studying math on your own is hard compared to with a class with an experienced professor to guide you I wouldn't get too down about the frustration you might be feeling now.People like to be all up their own ass on this board about math but at least for where you are skill is a byproduct of work. The more time you spend with a pencil to a page working problems or taking notes the more your skills will improve.
 >> Anonymous Wed Jan 3 08:12:32 2018 No.9411485 >>9411261Samuel has a nice amerimutt face.
 >> Anonymous Wed Jan 3 08:20:50 2018 No.9411494 >>9408124be the change you want to see in the world, anon
 >> Anonymous Wed Jan 3 10:03:56 2018 No.9411659 File: 20 KB, 347x334, elliptic.png [View same] [iqdb] [saucenao] [google] [report] i think /sci/ is a hellhole but langlands is my guywhat are you all up to? i left for software last year and i have this silly hope that in my spare time i can toy with the conjectures i was too cowardly to chase while in academiai'm a few years out of date on bsd and that's the project for january
 >> Anonymous Wed Jan 3 10:05:34 2018 No.9411667 >>9411659>i have this silly hope that in my spare time i can toy with the conjectures i was too cowardly to chase while in academiaGo for it!What kind of software are you doing?
 >> Anonymous Wed Jan 3 10:20:00 2018 No.9411693 >>9411667"mobility" for an automaker. it's not as exciting as one might think but my only relevant experience was as a hobbyist, so i'm quite grateful
 >> Anonymous Wed Jan 3 15:46:53 2018 No.9412193 How do I visualize an Euclidean 4D space
 >> Anonymous Wed Jan 3 16:02:55 2018 No.9412228 File: 254 KB, 2048x1536, este.jpg [View same] [iqdb] [saucenao] [google] [report] why is this wrong?
 >> Anonymous Wed Jan 3 16:05:00 2018 No.9412235 File: 161 KB, 223x309, complacency.png [View same] [iqdb] [saucenao] [google] [report] >>9412193Visualize an n-space and set n = 4.
 >> Anonymous Wed Jan 3 16:15:49 2018 No.9412256 >>9412228Can you Latex it? Your disgusting handwriting is illegible.
 >> Anonymous Wed Jan 3 16:17:59 2018 No.9412258 >>9412228ups basic mistake sorry for the brainletism
 >> Anonymous Wed Jan 3 16:32:01 2018 No.9412296 >>9412256apart from the arctg (which is merely different) it's not bad
 >> Anonymous Wed Jan 3 20:20:01 2018 No.9412670   Is there a Stable Hurewicz Theorem?i.e. Given an (n-1)-connected spectrum $E$ , is ${\pi _k}\left( E \right) \to {\pi _k}\left( {H\mathbb{Z} \wedge E} \right)$ an isomorphism for k<=n ?I can't find a reference.
 >> Anonymous Wed Jan 3 21:34:38 2018 No.9412815 >>9405007>look at how retarded I am
 >> Anonymous Wed Jan 3 21:35:13 2018 No.9412818 >>9412815>>look at how retarded I amWho are you quoting?
 >> Anonymous Thu Jan 4 00:20:37 2018 No.9413023 >>9412193Are you assuming choice?
 >> Anonymous Thu Jan 4 00:37:17 2018 No.9413041 >>9412193So you know how in microsoft paint or adobe photo shop you have the color scale, let's say from red to blue, well consider this, you know how to visualize 3d space, then at each point imagine being able to assign this red-blue color scale. In effect what you've created is a 4d space where the fourth dimension is represented by color (since you can associated a color to a numerical quantity based on it's placement on the scale, you could say the edges of the scale are assigned to plus and minus infinity so that you never actually reach the edges of the scale). From there it's easy to gain some intuition about the properties of objects in 4d space.
 >> Anonymous Thu Jan 4 00:39:02 2018 No.9413045 >>9413041>you know how to visualize 3d spaceI don't...
 >> Anonymous Thu Jan 4 02:02:06 2018 No.9413130 >>9405309Pretty much all of modern mathematics uses sets as mathematical objects; its pretty useful to know their properties.Logic is the formalism by which all proofs are written. Understanding logic makes prof writing/reading much easier.
 >> Anonymous Thu Jan 4 02:04:09 2018 No.9413133 >>9413130Depends, formal logic can cease to be useful to most areas of mathematics. Once you go down the set theorist or logician path you will never come back.
 >> Anonymous Thu Jan 4 02:10:05 2018 No.9413139 >>9413130>Pretty much all of modern mathematics uses sets as mathematical objects; its pretty useful to know their properties.>Logic is the formalism by which all proofs are written. Understanding logic makes prof writing/reading much easier.The post that was replying to said to study them "in their own right". Anything beyond the most elementary of properties of set theory and logic is irrelevant to most mathematics
 >> Anonymous Thu Jan 4 04:43:15 2018 No.9413252 File: 104 KB, 320x425, Hypersphere_coord.png [View same] [iqdb] [saucenao] [google] [report] >>9413041Tried your method but still can't visualize a 3-sphere in my head
 >> Anonymous Thu Jan 4 07:04:09 2018 No.9413318 >>9412193you don't, only through methods in R-3 can we approximate what manifolds might look like in higher dimensions.
 >> Anonymous Thu Jan 4 07:37:28 2018 No.9413335 >>9413318>manifoldsTheir existence is only a conjecture at this point.
 >> Anonymous Thu Jan 4 09:30:07 2018 No.9413406 >>9413252That doof forgot to mention that a single point could have a line extending from red to blue, which still may give you some intuition about 4d, but is not so easy to visualize.
 >> Anonymous Thu Jan 4 11:12:50 2018 No.9413513 >>9413252If you want, here's a playlist that tries to explain how to visualize higher dimensions through various methods, for the 3-sphere in particular they employ the hopf fibration. They form a nice little series (a couple of hours long but it's fun so who cares).https://www.youtube.com/playlist?list=PLelIK3uylPMGj__g3PeO9yg1QTCiKhwgF
 >> Anonymous Thu Jan 4 11:51:35 2018 No.9413579 >>9413335pls go away
 >> Anonymous Thu Jan 4 14:05:25 2018 No.9413891 >>9413579What are you trying to say?
 >> Anonymous Thu Jan 4 14:06:56 2018 No.9413896 >>9413891fuck you and fuck off
 >> Anonymous Thu Jan 4 14:23:50 2018 No.9413928 File: 1.04 MB, 1366x768, 1448724538618.png [View same] [iqdb] [saucenao] [google] [report] >>9413896You are very rude.
 >> Anonymous Thu Jan 4 14:25:48 2018 No.9413931 >>9413896>fuckWhy the vulgarity?
 >> Anonymous Thu Jan 4 14:59:43 2018 No.9413986 Calculus is shit desu
 >> Anonymous Thu Jan 4 15:03:39 2018 No.9413996 >>9408123I'm doing an HNC in Electronics Engineering, hadn't done maths since GCSEs and was rubbish at it then, got a C and struggled and now my course is pretty much all maths.It's a cunt but I'm getting through it with help. I found Khan Academy takes too long, I think once you get back into maths some of the stuff comes back to you.You might be slow though, it takes me longer to memorise things and actually understand them. So far I've got the top grade on both my assignments so far though so I'm getting through it.
 >> Anonymous Thu Jan 4 16:54:32 2018 No.9414318 >>9413928>>9413931expect he's 100% right, so fuck off.
 >> Anonymous Thu Jan 4 16:55:59 2018 No.9414323 >>9414318>expect he's 100% right, so fuck off.Do you need to swear?
 >> Anonymous Thu Jan 4 17:01:21 2018 No.9414332 >>9414323yes
 >> Anonymous Thu Jan 4 17:04:54 2018 No.9414339 >>9413986agreed
 >> Anonymous Thu Jan 4 17:07:13 2018 No.9414345 >>9413986why?
 >> Anonymous Thu Jan 4 17:21:40 2018 No.9414378 File: 559 KB, 1024x595, 1506967902611.png [View same] [iqdb] [saucenao] [google] [report] >tfw will NEVER be as smart as my proffsAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
 >> Anonymous Thu Jan 4 18:21:38 2018 No.9414473 >>9414407new
 >> Anonymous Fri Jan 5 00:33:42 2018 No.9415071 Can someone give me a quick rundown on the current state of math ? I'm curious as to what are the important fields of mathematics today, and what problem they're trying to solve.
 >> Anonymous Fri Jan 5 00:40:37 2018 No.9415089 >>9415071>Can someone give me a quick rundown on the current state of math ?Too broad of a question, but if you look at https://arxiv.org/ a lot of research falls under the headings of:Algebraic Geometry; Algebraic Topology; Analysis of PDEs; Category Theory; Classical Analysis and ODEs; Combinatorics; Commutative Algebra; Complex Variables; Differential Geometry; Dynamical Systems; Functional Analysis; General Mathematics; General Topology; Geometric Topology; Group Theory; History and Overview; Information Theory; K-Theory and Homology; Logic; Mathematical Physics; Metric Geometry; Number Theory; Numerical Analysis; Operator Algebras; Optimization and Control; Probability; Quantum Algebra; Representation Theory; Rings and Algebras; Spectral Theory; Statistics Theory; Symplectic Geometry
 >> Anonymous Fri Jan 5 02:07:21 2018 No.9415248 >>9415089Thanks, do people just specialize themselves or is it possible to, for example, learn every branch of Algebra.
 >> Anonymous Fri Jan 5 02:32:25 2018 No.9415287 >>9415248Depends on what you mean by learning. Whatever you do, you should finish your undergraduate with some knowledge in as many of the areas listed above as possible and, if you can, take a wide range of graduate classes. The reason for this is that your interests might change and that you never know where a problem could take you.That being said, people do specialize, but algebraists usually have (at least) some working knowledge of most other parts of algebra.
 >> Anonymous Fri Jan 5 14:47:29 2018 No.9416336 should proof of academic enrollment in as a math/physics/chemistry major be requirement for browsing /sci/
 >> Anonymous Fri Jan 5 15:01:17 2018 No.9416360 bump
 >> Anonymous Fri Jan 5 15:02:19 2018 No.9416362 why was hilbert a brainlet
 >> Anonymous Fri Jan 5 15:04:57 2018 No.9416368 killing this thread with no survivors
 >> Anonymous Fri Jan 5 15:05:59 2018 No.9416373
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