/sci/ - Science & Math » Thread #11213806

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/mg/ maths general: Mochi's doing fine edition

Anonymous Tue 10 Dec 01:35:34 2019 No.11213806 View Reply Original Report

Quoted By: >>11214859 >>11215327 >>11216697 >>11217753 >>11218453 >>11218478 >>11218557 >>11219315 >>11219596 >>11220286 >>11221157 >>11221172 >>11224369 >>11224379

talk maths, formerly >>11198243

http://www.kurims.kyoto-u.ac.jp/~motizuki/news-english.html
>2019-12-10
>(Papers) Revised version (list of revisions):
>The Mathematics of Mutually Alien Copies: from Gaussian Integrals to Inter-universal Teichmuller Theory.
http://www.kurims.kyoto-u.ac.jp/~motizuki/Alien%20Copies,%20Gaussians,%20and%20Inter-universal%20Teichmuller%20Theory.pdf
>Reformatted the manuscript using the style file for the Bessatsu series
>Slightly reworded Step 8 of \S 1.6
>Added references to \S 3.10, (ii); \S 3.11, (iv), (v), to the Introduction
>Updated the Acknowledgements
>In \S 3.7, (ii), 10^{est}, 11^{est}, added references to [IUTchIII], Remark 3.9.5
>In \S 3.10, (ii), added a reference to [IUTchII], Definition 4.8, (viii)
>Slightly modified the final portion of \S 3.10, (vi)
>Added items "(iv)", "(v)" to \S 3.11
>Slightly reworded the statement at the end of the Bibliography concerning preprints

LMC !!6bFXHDKL67m

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LMC !!6bFXHDKL67m Tue 10 Dec 2019 01:52:04 No.11213866 Report

Quoted By:

Anonymous

Anonymous Tue 10 Dec 2019 02:04:47 No.11213897 Report

Quoted By: >>11215850 >>11215885

Are there not enough asspies to give a final veredict on Mochizuki's paper.

Anonymous

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Anonymous Tue 10 Dec 2019 04:30:45 No.11214194 Report

Quoted By:

Anonymous

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Anonymous Tue 10 Dec 2019 04:45:49 No.11214226 Report

Quoted By: >>11214648

motion to abandon thread

Anonymous

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Anonymous Tue 10 Dec 2019 04:46:58 No.11214230 Report

Quoted By:

Threadly reminder to work with physicists.

Anonymous

Anonymous Tue 10 Dec 2019 10:07:18 No.11214648 Report

Quoted By:

>>11214226
Motion denied.

Anonymous

Anonymous Tue 10 Dec 2019 14:01:16 No.11214859 Report

Quoted By: >>11214915

>>11213806
y = x! * 2^x. Given that y >0, solve for x.

I can do this for low integer values of y. For example, if y=8, then x=2. However I can't come up with a generic formula, and I don't think I could do it at all when y gets big.

Anonymous

Anonymous Tue 10 Dec 2019 14:47:09 No.11214915 Report

Quoted By:

>>11214859
Fiddle around with approximations of n!.
Not like you can't afford to approximate.

Anonymous

Anonymous Tue 10 Dec 2019 19:02:17 No.11215327 Report

Quoted By: >>11217745

>>11213806
Calling yourself an "Inter-universal Geometer".
Mochizuki is truly the greatest mind of all time.

Anonymous

Anonymous Tue 10 Dec 2019 20:50:40 No.11215602 Report

Quoted By: >>11215631 >>11215776

How to prove a^2 - 223b^2 = -3 has no integer solutions? Wolfram alpha says there aren't but doesn't explain why.

Anonymous

Anonymous Tue 10 Dec 2019 21:02:02 No.11215631 Report

Quoted By: >>11215662

>>11215602
it's a generalized kind of pell equation, you should be able to google this
first, you should test the equation modulo various numbers, for example it might be that -3 is not a square residue mod 223, and then you're done, otherwise you can still try small moduli like 3, 8, 9
if this fails things get more complicated

Anonymous

Anonymous Tue 10 Dec 2019 21:17:09 No.11215662 Report

Quoted By: >>11215734

>>11215631
these things fail.

Anonymous

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Anonymous Tue 10 Dec 2019 21:54:53 No.11215734 Report

Quoted By:

>>11215662
then you can try doing various things in $\mathbb{Q}(\sqrt{223})$ or in $\mathbb{Z}(\sqrt{223})$ , but it might be just not doable by hand
here's an idea that reduces the problem to a finite number of cases:
- by knowledge of the standard pell equation, you can compute the fundamental solution to $(x - y\sqrt{223})(x + y\sqrt{223}) = 1$
- suppose that $(a - b\sqrt{223})(a + b \sqrt{223}) = -3$
- then you can obtain other solutions by taking $(a - b\sqrt{223})(x - y\sqrt{223})^k$ for any $k \in \mathbb{Z}$
- this way you can prove that if solution exists, then there exists a solution wit $|a|, |b| < C$ where C is some constant which depents on x, y, and d
you can read more here https://kconrad.math.uconn.edu/blurbs/ugradnumthy/pelleqn2.pdf

Anonymous

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Anonymous Tue 10 Dec 2019 22:17:05 No.11215773 Report

Quoted By: >>11215869 >>11226381

so subtraction doesn't exist

Anonymous

Anonymous Tue 10 Dec 2019 22:18:18 No.11215776 Report

Quoted By:

>>11215602
Did you try doing modulo computations for random small modulos?

Anonymous

Anonymous Tue 10 Dec 2019 22:52:55 No.11215850 Report

Quoted By:

>>11213897
We must produce more.

Anonymous

Anonymous Tue 10 Dec 2019 22:58:19 No.11215869 Report

Quoted By:

>>11215773
> so subtraction doesn't exist
It's defined right there in 1.12. It isn't a primitive operation because it doesn't need to be; a-b=a+(-1)*b.

Anonymous

Anonymous Tue 10 Dec 2019 23:07:40 No.11215885 Report

Quoted By:

>>11213897
scholze and stix gave their verdict, now probably no one will bother to study mochi's papers

Anonymous

Anonymous Wed 11 Dec 2019 00:17:42 No.11216027 Report

Quoted By: >>11216061 >>11216354 >>11216796 >>11216920 >>11217708

What is the point of matrices? I get that it's a nice way to tabulate data... but why is multiplication defined in the way that it is? The multiplication in particular seems like it should just be for two matrices that have the same number of rows and columns, and each element is multiplied by the corresponding matrice's element, like for addition

Anonymous

Anonymous Wed 11 Dec 2019 00:37:27 No.11216061 Report

Quoted By:

>>11216027
im a noob but I'm pretty sure it let's you algebra a space

Anonymous

Anonymous Wed 11 Dec 2019 01:49:41 No.11216176 Report

Quoted By:

>>11216115

Anonymous

Anonymous Wed 11 Dec 2019 02:48:52 No.11216326 Report

Quoted By:

Which books explains why iteration method works?

Anonymous

Anonymous Wed 11 Dec 2019 03:06:01 No.11216354 Report

Quoted By: >>11216796 >>11218129

>>11216027
a matrix is a way to specify a linear mapping from one vector space to another. matrix multiplication is defined so that multiplying matrices corresponds to composing the two corresponding linear maps

Anonymous

Anonymous Wed 11 Dec 2019 03:06:18 No.11216355 Report

Quoted By: >>11216373 >>11216375 >>11216510

Brainlet here, R cross R is an R-algebra, being a cross product of (trivial) R algebras. It's clearly two dimensional. but this:

https://math.stackexchange.com/questions/2217906/what-are-the-three-non-isomorphic-2-dimensional-algebras-over-mathbbr

shows that all 2d R algebras are either the complex numbers, the set A = {x + jy} where j^2 = 1 or B = {x + ey} where e^2 = 0. Which one of these is RxR then?

Anonymous

Anonymous Wed 11 Dec 2019 03:16:50 No.11216373 Report

Quoted By: >>11216402

>>11216355
Both.

Anonymous

Anonymous Wed 11 Dec 2019 03:18:27 No.11216375 Report

Quoted By: >>11216402

>>11216355
>>11216355
The set A has a complex part set b doesn't though set B is a subset of set a, not a proper one either.

Anonymous

Anonymous Wed 11 Dec 2019 03:27:06 No.11216402 Report

Quoted By: >>11216510

>>11216373
Well it can't be both because those three algebras are non-isomorphic. So it's either isomorphic to one or none at all and I've misunderstood what exactly was proved in the linked post.

>>11216375
What does that have to do with RxR?

Anonymous

Anonymous Wed 11 Dec 2019 03:57:00 No.11216476 Report

Quoted By: >>11216488

is there a way to just open /mg/, and not have to go to /sci/ catalogue, then cntrl+f “/mg/“? this would also be great for when threads die, as it would lead me to the new one.

Anonymous

Anonymous Wed 11 Dec 2019 04:00:32 No.11216488 Report

Quoted By: >>11216535

>>11216476
type 4chan.org/sci/mg into the address bar

Anonymous

Anonymous Wed 11 Dec 2019 04:06:58 No.11216510 Report

Quoted By:

>>11216355
>>11216402
Ok, I have found that it's isomorphic to A (which are called the "split complex" numbers). You can see the isomorphism by considering the basis (1 +/- j) / 2.

Anonymous

Anonymous Wed 11 Dec 2019 04:16:49 No.11216535 Report

Quoted By: >>11216540

>>11216488
so this just puts /mg/ at the top of the catalogue. better, and thanks!, but not perfect. i’ll probably just write a script for it if nothing is built in

Anonymous

Anonymous Wed 11 Dec 2019 04:17:51 No.11216540 Report

Quoted By:

>>11216535
>puts at top
ok i see now it searches for threads with “/mg/“

Anonymous

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Anonymous Wed 11 Dec 2019 05:54:17 No.11216697 Report

Quoted By: >>11216723 >>11216730 >>11218792 >>11231497

>>11213806
What does it mean here by homology of the inclusions? I understand standard homology (of a topological space).

Anonymous

Anonymous Wed 11 Dec 2019 06:07:55 No.11216720 Report

Quoted By: >>11216723

Is $H_*$ supposed to be the homology group(s)? If so is it saying iterated inclusion gives boundary maps?

Anonymous

Anonymous Wed 11 Dec 2019 06:09:26 No.11216723 Report

Quoted By:

>>11216720
meant for >>11216697

Anonymous

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Anonymous Wed 11 Dec 2019 06:14:30 No.11216730 Report

Quoted By:

>>11216697
Found it lol

Anonymous

Anonymous Wed 11 Dec 2019 06:59:33 No.11216796 Report

Quoted By: >>11217757 >>11218129

>>11216027
> What is the point of matrices? I get that it's a nice way to tabulate data... but why is multiplication defined in the way that it is?
A matrix isn't *just* a 2D array. It's a 2D array containing the coefficients of a linear map. E.g. the matrix
[a b]
[c d]
represents the map
y1 = a*x1 + b*x2
y2 = c*x1 + d*x2
Matrix multiplication is composition. So if you have a second matrix
[e f]
[g h]
representing the map
z1 = e*y1 + f*y2
z2 = g*y1 + h*y2
their composition is
z1 = e*(a*x1 + b*x2) + f*(c*x1 + d*x2) = (e*a+f*c)*x1 + (e*b+f*d)*x2
z2 = g*(a*x1 + b*x2) + h*(c*x1 + d*x2) = (g*a+h*c)*x1 + (g*b+h*d)*x2
which is represented by the matrix
[e*a+f*c e*b+f*d]
[g*a+h*c g*b+h*d]
Which is what you get from matrix multiplication as defined.

The above is basically a more detailed explanation of what >>11216354 said.

It's also why the matrices don't need to have the same size; instead, the number of columns in the left-hand matrix must match the number of rows in the right-hand matrix. An m×n real matrix represents a map R^n->R^m while a k×m matrix represents a map R^m->R^k and their composition R^n->R^k. The output from the first function (right-hand matrix) must have the same dimensionality as the input to the second.

Anonymous

Anonymous Wed 11 Dec 2019 07:16:04 No.11216821 Report

Quoted By: >>11217696

any good references for Stochastic Processes? i’m fairly comfortable with measure theory-level Probability

Anonymous

Anonymous Wed 11 Dec 2019 09:08:13 No.11216920 Report

Quoted By: >>11217268 >>11218129

>>11216027
>I get that it's a nice way to tabulate data
No, it isn't. It's not about tabulating data.

A matrix is a complete description of a linear mapping, if you want to understand what a matrix is and why operations on it are defined the way they are you first have to understand the concepts of:
Vector space
Linear mapping
basis
After that it will immediately all make total sense.

Anonymous

Anonymous Wed 11 Dec 2019 09:49:22 No.11216970 Report

Quoted By: >>11216998

Why is the group (x,x) where x is an integer generated by two elements? I mean (1,1) generates the entire group but isn’t that just one element?

Anonymous

Anonymous Wed 11 Dec 2019 10:12:23 No.11216998 Report

Quoted By: >>11217023

>>11216970
Are you sure you aren't talking about Z x Z?
When the integers can be different, then you need at least 2 elements to generate, but (x,x) is just isomorphic to Z

Anonymous

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Anonymous Wed 11 Dec 2019 10:31:52 No.11217023 Report

Quoted By: >>11218549 >>11219337

>>11216998
Yeah that’s what I thought but pic related question got me confused.
The answer turns out to be <a,b,c | [b,c], a^2=bc> but I thought that h:x->(x,x) forces b and c to have the same value so all elements in ZxZ would be of the form (x,x), so b=c. Turns out my reasoning is wrong but I don’t really get why so hence my previous question

Anonymous

Anonymous Wed 11 Dec 2019 14:03:50 No.11217268 Report

Quoted By: >>11217609 >>11217684 >>11217704 >>11217734 >>11221468 >>11221491

>>11216920
You're a big brainlet. Math is fucking easy. Matrix multiplication is nothing but a LIST of dot products . You are doing nothing with matrix multiplication but taking the dot product of rows of the first matrix with columns of the second. It's nothing more than a list of dot products (matrix multiplication).

I hate people like you that try to make math algebraic and non intuitive. Don't state the obvious huh?

Anonymous

Anonymous Wed 11 Dec 2019 17:26:54 No.11217609 Report

Quoted By:

>>11217268
Hate to say it but you're the brainlet my dude. When someone asks why an "abstract" algebraic object is important, you tell them what it represents, not how you multiply it. So it's a list a of dot products, cool. What does that mean? What's the underlying meaning of that? Why would that be important

Anonymous

Anonymous Wed 11 Dec 2019 17:59:37 No.11217684 Report

Quoted By: >>11217728

>>11217268
>Matrix multiplication is nothing but a LIST of dot products .
That is a true, but VERY bad and unintuitive view. I think it is safe to say that you do not understand linear algebra.

It is much better to interpret a matrix as the change of basis vectors, which is much more intuitive and generalizes better and the "dot product" view hides this most important fact from you.

>non intuitive
Your explanation is non intuitive and bad. It hides the important properties.

Anonymous

Anonymous Wed 11 Dec 2019 18:05:39 No.11217696 Report

Quoted By:

>>11216821
Karatzas and Shreve
Durrett
Rogers and Williams

Anonymous

Anonymous Wed 11 Dec 2019 18:08:24 No.11217704 Report

Quoted By:

>>11217268
hands down, this is one of the most retarded posts I have ever seen on this board

Anonymous

Anonymous Wed 11 Dec 2019 18:10:45 No.11217708 Report

Quoted By:

>>11216027
in photoshop you can do the following operations: scaling, rotation, shearing, reflection. all of these (and some more) can be encoded it matrices. matrix multiplication is composition of these operations (i.e. first you rotate, then you resize)

Anonymous

Anonymous Wed 11 Dec 2019 18:22:24 No.11217728 Report

Quoted By: >>11217734 >>11218162

>>11217684
you are comparing matrix multiplication meaning with matrix multiplication computation. Why would you do that?

Anonymous

Anonymous Wed 11 Dec 2019 18:24:59 No.11217734 Report

Quoted By:

>>11217728
you too:
>>11217268

Anonymous

Anonymous Wed 11 Dec 2019 18:32:24 No.11217745 Report

Quoted By:

>>11215327

Anabelian geometry

https://en.wikipedia.org/wiki/Anabelian_geometry

Anonymous

Anonymous Wed 11 Dec 2019 18:35:42 No.11217753 Report

Quoted By:

>>11213806
oh look, a scientist with honor

Anonymous

Anonymous Wed 11 Dec 2019 18:38:14 No.11217757 Report

Quoted By:

>>11216796
learn to LaTeX or lurk moar

Anonymous

Anonymous Wed 11 Dec 2019 18:48:24 No.11217790 Report

Quoted By: >>11217807 >>11217941

what is the algebraic operation on vectors that is the product of all sums of a_i and b_i for all i ?

Anonymous

Anonymous Wed 11 Dec 2019 18:52:00 No.11217807 Report

Quoted By: >>11217810

>>11217790
you mean (a1+b1)(a2+b2)... ?

Anonymous

Anonymous Wed 11 Dec 2019 18:53:21 No.11217810 Report

Quoted By: >>11217941

>>11217807
yes. Is that useful in vector algebra? I dont remember learning it

Anonymous

Anonymous Wed 11 Dec 2019 19:55:54 No.11217941 Report

Quoted By:

>>11217790
>>11217810
no one talks about such an operation, it sounds worthless

Anonymous

Anonymous Wed 11 Dec 2019 21:03:48 No.11218129 Report

Quoted By: >>11218169

>>11216354
>>11216796
>>11216920
Okay, I vaguely know what a vector space is. I was never very good at systems of (linear?) equations in school, but I'll refresh myself on the subject. My hobbyist "speciality" is number theory. What are some entry level applications of linear algebra to (algebraic?) number theory?

Anonymous

Anonymous Wed 11 Dec 2019 21:19:32 No.11218162 Report

Quoted By:

>>11217728
>Why would you do that?
Why not? You need to be able to understand the why and the how.

Anonymous

Anonymous Wed 11 Dec 2019 21:21:45 No.11218169 Report

Quoted By: >>11218234

>>11218129
Same person, say I have
$ \begin{bmatrix} 1 & 3 & -5 \end{bmatrix} \begin{bmatrix} 4 \\ -2 \\ -1 \end{bmatrix} = 3 $
Is matrix multiplication commutative? My guess is no. And what happens when I have more than one row and more than one column, do I get a matrix as a result?

Anonymous

Anonymous Wed 11 Dec 2019 21:47:30 No.11218234 Report

Quoted By: >>11218269 >>11218276

>>11218169
$ \begin{bmatrix} 4 \\ -2 \\ -1 \end{bmatrix} \begin{bmatrix} 1 & 3 & -5 \end{bmatrix} = ? $
i recommend you just read a standard textbook

Anonymous

Anonymous Wed 11 Dec 2019 21:57:08 No.11218269 Report

Quoted By: >>11218289

>>11218234

row * column vector is scalar

column * row vector is a matrix

Anonymous

Anonymous Wed 11 Dec 2019 21:58:20 No.11218276 Report

Quoted By: >>11218289

>>11218234

if n is a vector
transpose(n)*n is a singular matrix

Anonymous

Anonymous Wed 11 Dec 2019 22:02:05 No.11218289 Report

Quoted By:

>>11218269
>>11218276
>inb4 tensor product hits you hard and fast

Anonymous

Anonymous Wed 11 Dec 2019 23:13:25 No.11218441 Report

Quoted By: >>11218552 >>11218854

If I have topological spaces X, Y a subset A of X and
f: A -> Y continous,
then does there exist an extension
g:X -> Y continuous with g|A = f?
In the generam case this is not true right? Does it work for metric spaces? or R^d?
If I pick x1,...,xn and y1,...,yn points in a metric space, does there exist a continuous function on the whole space mapping all xi to yi?

Anonymous

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Anonymous Wed 11 Dec 2019 23:18:25 No.11218453 Report

Quoted By: >>11218458 >>11218463 >>11218472 >>11218553 >>11223195

>>11213806
How the fuck do I into proofs?
Where do I start?

Anonymous

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Anonymous Wed 11 Dec 2019 23:20:06 No.11218458 Report

Quoted By: >>11219520

>>11218453
Munkres Topology first chapter is a great intro to proofs and logic.

Anonymous

Anonymous Wed 11 Dec 2019 23:23:37 No.11218463 Report

Quoted By: >>11218798 >>11219520

>>11218453
Lang’s Basic Mathematics, Apostol’s Calculus, Axler’s Lin Alg book

Anonymous

Anonymous Wed 11 Dec 2019 23:26:19 No.11218469 Report

Quoted By: >>11218474

is math more fun than being a retard?

Anonymous

Anonymous Wed 11 Dec 2019 23:27:16 No.11218472 Report

Quoted By:

>>11218453

just write "the trivial proof is left to the reader"

Anonymous

Anonymous Wed 11 Dec 2019 23:28:06 No.11218474 Report

Quoted By: >>11218481

>>11218469
no math sucks, science is just more enjoyable with pretty maths employed sparingly and effectively. mathfags are as degenerate as wallstreet sociopaths and /lit/tards preying upon homely undergrad trannies

Anonymous

Anonymous Wed 11 Dec 2019 23:30:03 No.11218478 Report

Quoted By:

>>11213806
do i get a badge as an independent researcher

Anonymous

Anonymous Wed 11 Dec 2019 23:30:26 No.11218481 Report

Quoted By:

>>11218474
wait, is science fun?

Anonymous

Anonymous Wed 11 Dec 2019 23:56:17 No.11218549 Report

Quoted By:

>>11217023
Someone help a brainlet out pls

Anonymous

Anonymous Wed 11 Dec 2019 23:56:52 No.11218552 Report

Quoted By: >>11218612

>>11218441
>If I have topological spaces X, Y a subset A of X and
>f: A -> Y continous,
>then does there exist an extension
>g:X -> Y continuous with g|A = f?
>In the generam case this is not true right? Does it work for metric spaces? or R^d?
not at all. extension of continuous map is a very hard and deep problem, because a lot of problems in (algebraic) topology can be formulated as an extension problem. i.e. a map S^n -> X represents a trivial element in the homotopy group if and only if it can be extended to the whole disc D^n+1. it gets easier when the codomain is contractible, because then basically all of algebraic topology disappears and it's just general topology. for example Y = R. then it's still not true, try to find a counter example for f : R->R. it is true though when A is closed and X is normal, this is Tietze extension theorem.

Anonymous

Anonymous Wed 11 Dec 2019 23:57:51 No.11218553 Report

Quoted By:

>>11218453
A proof book maybe? Like How to prove it by velleman

Anonymous

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Anonymous Wed 11 Dec 2019 23:59:49 No.11218557 Report

Quoted By: >>11218576 >>11221989 >>11223821

>>11213806
>Acknowledgements

Anonymous

Anonymous Thu 12 Dec 2019 00:09:38 No.11218576 Report

Quoted By: >>11218586

>>11218557
zuki needs to go abroad to explain what he's doing

Anonymous

Anonymous Thu 12 Dec 2019 00:13:06 No.11218586 Report

Quoted By:

>>11218576

>mfw he is actually just a Schizophrenic and is writing gibberish and nobody notices

Anonymous

Anonymous Thu 12 Dec 2019 00:22:51 No.11218612 Report

Quoted By:

>>11218552
>>11218552
Thanks, intetesting.
I'm trying to do something like this:
Define A* = {x in A: A is not dense in x}
Then D(A) := (A_closure\)*
D(A) gives us all the most directly "new" points when considering the closure of A.
we can look at D(D(...(A)) and for most A this sill become empty after finitely many steps, but for some it will be nonempty forever.
If there exists an f:X -> X that maps
A to B then it must also map D(A) to D(B).
So a necessary condition for the existence of gwould be that |D^n(A)| >= |D(B)| for all n.
Is this also sufficient? Of course mot in the general case but in more special cases I think it is.

Anonymous

Anonymous Thu 12 Dec 2019 01:19:15 No.11218792 Report

Quoted By:

>>11216697
>persistent homology
nice meme

Anonymous

Anonymous Thu 12 Dec 2019 01:20:51 No.11218798 Report

Quoted By: >>11221104

>>11218463
>Lang’s Basic Mathematics, Apostol’s Calculus, Axler’s Lin Alg book
The holy trinity of meme books.

Anonymous

Anonymous Thu 12 Dec 2019 01:27:40 No.11218815 Report

Quoted By:

whatever came of this

https://thehighergeometer.wordpress.com/2019/01/18/taylor-dupuy-on-mochizukis-iutt-infamous-corollary-3-12/

Anonymous

Anonymous Thu 12 Dec 2019 01:44:30 No.11218854 Report

Quoted By:

>>11218441
Nope. For instance, the function f(x) = 1 for x>0, f(x) = 0 for x<0 is certainly continuous on R\{0}, but has no continuous extension to R.
The best thing you can get afaik is Tietze Extension, a standard topology result. It says that a continuous function on a CLOSED subset of a NORMAL topological space can be extended to the whole space. All metric spaces are normal, and all compact hausdorff spaces.

Anonymous

Anonymous Thu 12 Dec 2019 02:38:56 No.11219009 Report

Quoted By: >>11219019 >>11219351

Trying to prove that f(x)=exp(-x) and g(x)=x intersect using RA techniques. Would I be right to show that since f(x) and g(x) are continuous on [0,1], and that f(0)>f(1) and g(1)>g(0), they have to intersect on that range?

Anonymous

Anonymous Thu 12 Dec 2019 02:41:08 No.11219019 Report

Quoted By:

>>11219009
Scratch that, I guess I'd need to show that f(0)>g(0) and g(1)>f(0)

Anonymous

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Anonymous Thu 12 Dec 2019 03:23:12 No.11219117 Report

Quoted By: >>11219169 >>11219382 >>11219492 >>11219970 >>11219974

Bros my frenchie professor made a long ass Linear algebra/Vectorial espaces final where only half of it were Vectorial espaces/Bases and change of base matrices. The first half was shit we had already seen and was "TOO fucking long to finish". 70% of my class stayed until the end of the 3hrs.
I want to call on her bullshit exam but dunno where.
Is it worth it?
Yeah I pass this class for sure. (A+ B4 this final)

Anonymous

Anonymous Thu 12 Dec 2019 03:40:26 No.11219169 Report

Quoted By:

>>11219117
>I want to call on her bullshit exam but dunno where.
>Is it worth it?
>Yeah I pass this class for sure. (A+ B4 this final)
Look at it like this:
Case 1: You complain, likely nothing happens and you get on her shit list, but at least you still have your A, but if you ever need to, you're locked out of a letter of recommendation
Case 2: Don't complain, either let her continue or let someone else fall into the deathtrap that is complaining about their professor to administration, you still get your A and you still have access to an at least neutral letter of recommendation

Anonymous

Anonymous Thu 12 Dec 2019 04:08:20 No.11219218 Report

Quoted By: >>11219288 >>11219313

I'm in a basic Real Analysis class, and I'm struggling to understand induction.
I've been asked to prove that
$x_n=\frac{x_{n-1}^2+2}{3}$ is monotonically increasing if $x_0=0$ . I know that $x_1=\frac{2}{3}$ , so x1>x0. I then find that $\{x_n\}$ is monotonically increasing if $x_{n+1}>x_n$ . What am I missing to make this proof come together?

Anonymous

Anonymous Thu 12 Dec 2019 04:40:24 No.11219288 Report

Quoted By: >>11219289 >>11219324

>>11219218
assume $x_{n-1} > x_{n-2}$ , show $x_{n} > x_{n-1}$
you can square both sides of the first inequality and it still holds because all xn are positive, and the same for adding 2 and dividing by 3. then you have $(x_{n-1}+2)/3 > (x_{n-2}+2)/3$ , which you can substitute $x_{n}$ and $x_{n-1}$ in for

Anonymous

Anonymous Thu 12 Dec 2019 04:41:30 No.11219289 Report

Quoted By: >>11219324

>>11219288
i forgot to square the xn-1 and xn-2 but you get the idea

Anonymous

Anonymous Thu 12 Dec 2019 04:50:32 No.11219313 Report

Quoted By:

>>11219218
this is a boring example because it's monotonically increasing for all real numbers besides 1 and -1, but it is an ok exercise for induction.

Anonymous

Anonymous Thu 12 Dec 2019 04:52:22 No.11219315 Report

Quoted By:

>>11213806
How do you say “slant eyed fraud” in your language?

Anonymous

Anonymous Thu 12 Dec 2019 04:55:58 No.11219324 Report

Quoted By: >>11219577

>>11219288
>>11219289
I guess I'm just failing to see how that proves anything, (not a knock against you I just feel I'm missing something)

Anonymous

Anonymous Thu 12 Dec 2019 05:03:16 No.11219337 Report

Quoted By:

>>11217023
I don't understand the notation you are using for your "answer", but (1,1) doesn't generate ZxZ, you only get the "diagonal" elements of ZxZ, a subset isomorphic to Z (because cyclic group generated by one elem of inf order).
I don't see why (Z, (x, x) to 2x, x to x) doesn't work as an answer though, but maybe I'm misreading the problem. The compositions all work as required. Seems like a very strange problem, like its just testing your reading ability.

Anonymous

Anonymous Thu 12 Dec 2019 05:08:28 No.11219351 Report

Quoted By:

>>11219009
f(0) is 1
g(0) is 0
f(1) is 1/e
g(1) is 1
do you see now?

Anonymous

Anonymous Thu 12 Dec 2019 05:21:14 No.11219382 Report

Quoted By: >>11219498

>>11219117
>I want to call on her bullshit exam
?
I never had a single exam where I (or anybody else) had enough time.
That seems normal.

Anonymous

Anonymous Thu 12 Dec 2019 06:18:30 No.11219492 Report

Quoted By: >>11219963

>>11219117
Are your grades not scaled? At my uni when a lecturer fucks up and makes an exam to hard your marks are scaled accordingly.

Anonymous

Anonymous Thu 12 Dec 2019 06:20:33 No.11219498 Report

Quoted By: >>11219963

>>11219382
I walk out of most of my exams early.
An ideal exam shouldn't rely on time pressure to be hard.

Anonymous

Anonymous Thu 12 Dec 2019 06:43:50 No.11219520 Report

Quoted By: >>11221111 >>11222838

>>11218463
>>11218458
Not him, but is Spivak as a first introduction to proof based maths too masochistic? I'm not doing too hot right now. I hope I'm not a brainlet.

Anonymous

Anonymous Thu 12 Dec 2019 06:56:18 No.11219538 Report

Quoted By:

There's a reason grade inflation exists you retards. The point is that only exceptional students get A+

Anonymous

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Anonymous Thu 12 Dec 2019 07:25:02 No.11219576 Report

Quoted By: >>11219588 >>11224754 >>11225525

Assuming I'm a college flunkie that spent more time chewing on the barrel of a gun than studying, what would be the best way to get back into the swing of math from the pre-calc level also assuming just going back to college is impossible.
Looking mostly for OCW recommendations. Yes, there is the sticky, but I like active recommendations more.

Anonymous

Anonymous Thu 12 Dec 2019 07:26:29 No.11219577 Report

Quoted By: >>11220311

>>11219324
Basic mathematical induction requires first proving a base case and second an inductive step. If you're unfamiliar with these terms, or how these concepts are used to prove statements on the natural numbers, I'd recommend checking out wikipedia.org/wiki/Mathematical_induction#Description and also working through the provided examples.

If you feel comfortable with the mechanics of induction, but aren't able to apply them to this exercise, try explicitly writing out your base case, induction hypothesis, and what you need to prove for the inductive step.

Anonymous

Anonymous Thu 12 Dec 2019 07:32:27 No.11219588 Report

Quoted By: >>11219597

>>11219576
Try choosing a book for your topic of interest and then search google for syllabus and the book's title. This will provide a list of public class websites which cover your topic and typically include homework sets, practice exams, related resources, and a reasonable timeline to follow along with.

Anonymous

Anonymous Thu 12 Dec 2019 07:37:23 No.11219596 Report

Quoted By: >>11219792 >>11219969 >>11219972

>>11213806
What's the best way to start learning how to do proofs? I'm a freshman, and next semester I'm taking a discrete math/algorithms class that's notoriously brutal for those without proof-writing experience. I'd like to get a head start during the month we have for winter break. The textbook the class uses is Discrete Mathematics and Its Applications.

Anonymous

Anonymous Thu 12 Dec 2019 07:37:43 No.11219597 Report

Quoted By:

>>11219588
I have zero focus so topics that interest me can be anything from programming trig to math theory for shits and giggles. Gotta build those aspie good boy points.

Anonymous

Anonymous Thu 12 Dec 2019 10:28:23 No.11219792 Report

Quoted By: >>11219969 >>11219972

>>11219596

This book in combinatorics, problem, lemma and proof style like Math book, but very informal proof, a lot problems!.
https://doc.lagout.org/science/0_Computer%20Science/3_Theory/Mathematics/Discrete%20Mathematics/A%20Walk%20Through%20Combinatorics%20-%20An%20Introduction%20to%20Enumeration%20and%20Graph%20Theory%2C%202nd%20Ed.pdf

More formal style but lack meanful mathematics
https://www.people.vcu.edu/~rhammack/BookOfProof/BookOfProof.pdf

Use both, usually C.S text are too weak or informal in both.

Anonymous

Anonymous Thu 12 Dec 2019 12:47:45 No.11219963 Report

Quoted By:

>>11219498
>An ideal exam shouldn't rely on time pressure to be hard.
I mean, most my exams are oral anyway, since that is just a better way to test people.

>>11219492
Only scam universities here do that. Here it is unheard of, since courses are *supposed* to filter people.

Anonymous

Anonymous Thu 12 Dec 2019 12:58:03 No.11219969 Report

Quoted By:

>>11219596
>The textbook the class uses is Discrete Mathematics and Its Applications.
Just start reading the book and the first chapter, there is literally a chapter on introduction to proofs.
You can also read https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf already posted by >>11219792
but it's the last version of the book with more stuff.

Anonymous

Anonymous Thu 12 Dec 2019 12:58:42 No.11219970 Report

Quoted By:

>>11219117
There are two ways this can go.
Either the prof will grant more points than the maximum (ie. grade out of 25 instead of 20) and then somehow scale down to 20 (truncating or applying a more complicated transformation) depending on the distribution they want. This is the uni system.
Another way is to grade downwards from the best paper: if the best student is worth a full mark, then give them a full mark, and then grade the other students with respect to that. This is the usual prepa type exam.
If you are to stay in the French system, I suggest you stop worrying about finishing your tests and focus on doing what your best, ie. first and foremost focusing on the logic and the phrasing, then trying to do that as succinctly adn quickly as possible (but only after you know how to write properly). The length is probably only going to get worse as you progress.

Anonymous

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Anonymous Thu 12 Dec 2019 13:00:35 No.11219972 Report

Quoted By: >>11234618

Anonymous

Anonymous Thu 12 Dec 2019 13:01:24 No.11219974 Report

Quoted By: >>11220555

>>11219117
There are two ways this can go.
Either the prof will grant more points than the maximum (ie. grade out of 25 instead of 20) and then somehow scale down to 20 (truncating or applying a more complicated transformation) depending on the distribution they want. This is the uni system.
Another way is to grade downwards from the best paper: if the best student is worth a full mark, then give them a full mark, and then grade the other students with respect to that. This is the usual prepa type exam.
If you are to stay in the French system, I suggest you stop worrying about finishing your tests and focus on doing your best, ie. first and foremost focusing on the logic and phrasing, then trying to do that as succinctly and quickly as possible (but only after you know how to write properly). The length is probably only going to get worse as you progress.

What do we mean by "equal" - Pierre Deligne

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What do we mean by "equal" - Pierre Deligne Thu 12 Dec 2019 16:05:43 No.11220274 Report

Quoted By: >>11221992

>Abstract: In the univalent foundation formalism, equality makes sense only between objects of the same type, and is itself a type. We will explain that this is closer to mathematical practice than the Zermelo-Fraenkel notion of equality is.
https://www.youtube.com/watch?v=WfDcrN5_1wA

Anonymous

Anonymous Thu 12 Dec 2019 16:12:37 No.11220286 Report

Quoted By: >>11220301 >>11220302 >>11220376

>>11213806

I am trying to understand the concept of a geometric realization of an abstract simplicial complex.

In order to understand that, I need to understand what a direct limit is.

Is there any way this can be done without category theory?

Anonymous

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Anonymous Thu 12 Dec 2019 16:20:40 No.11220301 Report

Quoted By: >>11220308

>>11220286
>made it all the way to simplicial sets without learning what a colimit is
How

Anonymous

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Anonymous Thu 12 Dec 2019 16:21:19 No.11220302 Report

Quoted By: >>11223048

>>11220286
>can category theory be done without category theory?

Anonymous

Anonymous Thu 12 Dec 2019 16:25:08 No.11220308 Report

Quoted By: >>11220355

>>11220301

I am studying algebraic combinatorics (stanley reisner rings) not topology

Anonymous

Anonymous Thu 12 Dec 2019 16:27:48 No.11220311 Report

Quoted By: >>11220463 >>11220537

>>11219577
Okay, I did more brainstorming, and I think I got it.
I know that x1>x0, as x0=0 and x1=2/3. That's my base case. Assuming I have some n for which $x_{n}\geq x_{n-1}$ holds, I seek to prove that $x_{n+1}\geq x_n$ . I expand the left side using the recurrence relation to get $\frac{x_{n+t}^2+2}{3}\geq x_n$ . Rearranging this, I can get the polynomial expression $(x_n - 1)(x_n - 2)\geq 0$ . This holds if $x_n\geq 2$ or $x_n\leq 1$ . Since x0 and x1 are both <= 1, the relation holds.

Is this enough?

Anonymous

Anonymous Thu 12 Dec 2019 16:48:18 No.11220355 Report

Quoted By: >>11220365

>>11220308
Geometric realization can be given an explicit description if you unpack the colimit definition in the category of topological spaces. See the alternate definition on Wikipedia.

https://en.wikipedia.org/wiki/Abstract_simplicial_complex

Anonymous

Anonymous Thu 12 Dec 2019 16:53:59 No.11220365 Report

Quoted By: >>11221097

>>11220355

That definition still uses the concept of a direct limit

You try to learn what a direct limit is and you end up in category theory

Anonymous

Anonymous Thu 12 Dec 2019 16:59:17 No.11220376 Report

Quoted By:

>>11220286
Listen anon, I don't like category theory either.
But just go pick it up, you can figure out limits and colimits in ~2 hours.

Anonymous

Anonymous Thu 12 Dec 2019 17:43:14 No.11220463 Report

Quoted By:

>>11220311
Nice, your base case and inductive hypothesis look great.

It can be difficult to prove statements in which you are given very little to work with. Similar to proofs by contradiction, inductive proofs give you an additional assumption to work with for free. This free assumption is the inductive hypothesis.

Make use of your inductive hypothesis, x_n > x_{n-1} for some n>1, to close out your proof. You may have to abandon the polynomial argument for another, unrelated approach.

Anonymous

Anonymous Thu 12 Dec 2019 18:18:11 No.11220537 Report

Quoted By:

>>11220311
No, not rigorous enough

Anonymous

Anonymous Thu 12 Dec 2019 18:23:31 No.11220555 Report

Quoted By: >>11222193 >>11222208

>>11219974
>This is the uni system.
Really? What a fucking joke.
If here half the class fails, than so bad for them. I have never seen an exam get retroactively scaled that seems ridiculously idiotic.

Anonymous

Anonymous Thu 12 Dec 2019 21:20:34 No.11220897 Report

Quoted By: >>11220900 >>11221164

When did you stop keeping track of what grade you're in?

For me it was after I did a postdoc (27th grade)

Anonymous

Anonymous Thu 12 Dec 2019 21:22:08 No.11220900 Report

Quoted By:

>>11220897
4th semester

Anonymous

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Anonymous Thu 12 Dec 2019 22:01:51 No.11220991 Report

Quoted By:

I'm on an Euler Project binge. It is so frustrating when you can not find the pattern.

Anonymous

Anonymous Thu 12 Dec 2019 22:53:47 No.11221097 Report

Quoted By:

>>11220365
You only need to understand how colimits work in Top, and the page even tells you exactly how to form the space.

Anonymous

Anonymous Thu 12 Dec 2019 22:56:12 No.11221104 Report

Quoted By:

>>11218798
Shut the fuck up faggot

Anonymous

Anonymous Thu 12 Dec 2019 22:59:07 No.11221111 Report

Quoted By:

>>11219520
I didn’t say Spivak first, I said Lang’s basic Mathematics, then Spivak and then Axler. You don’t need to read all 3 you could use Apostol and H&K or Courant, many other alternatives exist. There’s no such thing as masochism when learning basic calculus the proofs are not even remotely as difficult as what you would see later on.

Anonymous

Anonymous Thu 12 Dec 2019 23:25:29 No.11221157 Report

Quoted By:

>>11213806
I want to retrain myself in math. What is the best way to do this? I had a shitty upbringing and didn't pay attention in class, especially not in math. I have grown to appreciate math on a superficial level with it's patterns, but I want to know it on a deeper level. Yet I barely know high school math.
Also note that one of the biggest gripes I had with math was being forced to rote memorize formulas without knowing how the formula actually came about or why it needed to be found in the first place; would be reading math history be a good idea to solve this issue?

Anonymous

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Anonymous Thu 12 Dec 2019 23:29:29 No.11221160 Report

Quoted By: >>11221169 >>11221183 >>11221196 >>11221202 >>11221900 >>11228543 >>11228645 >>11231115

how is anybody expected to memorize all this in
39 hours (13 week semester, 3 hours/week)?

Anonymous

Anonymous Thu 12 Dec 2019 23:30:44 No.11221164 Report

Quoted By:

>>11220897
When I dropped out

Anonymous

Anonymous Thu 12 Dec 2019 23:33:59 No.11221169 Report

Quoted By:

>>11221160
You're supposed to understand it, not memorize it, moron. It's all elementary.

Anonymous

Anonymous Thu 12 Dec 2019 23:38:11 No.11221172 Report

Quoted By: >>11221233

>>11213806
What field is Japan especially good at?

Anonymous

Anonymous Thu 12 Dec 2019 23:44:19 No.11221183 Report

Quoted By: >>11221199

>>11221160
you know you're allowed to study more than three hours per week right?

Anonymous

Anonymous Thu 12 Dec 2019 23:48:29 No.11221196 Report

Quoted By:

>>11221160
it's trivial

Anonymous

Anonymous Thu 12 Dec 2019 23:49:13 No.11221199 Report

Quoted By:

>>11221183
I think the point is that the courses are designed to be n-credit hours = n hours a week

Anonymous

Anonymous Thu 12 Dec 2019 23:49:46 No.11221202 Report

Quoted By:

>>11221160
what the fuck is this for? precalculus? they don’t teach all of these topics usually, just what’s necessary so people don’t fail out of calc

Anonymous

Anonymous Fri 13 Dec 2019 00:04:52 No.11221233 Report

Quoted By: >>11221243

>>11221172
Algebraic geometry, Information geometry, Stochastic Methods.

Anonymous

Anonymous Fri 13 Dec 2019 00:07:21 No.11221243 Report

Quoted By:

>>11221233
2/3 based, that’s not too bad

Anonymous

Anonymous Fri 13 Dec 2019 01:07:17 No.11221419 Report

Quoted By: >>11221436 >>11221443 >>11221472

woopsie didn't study for real analysis final tomorrow haha. Guess my grade is uniformly convergent to 0 hahaaaaaaaaaaaaaaaaaa

Anonymous

Anonymous Fri 13 Dec 2019 01:11:53 No.11221436 Report

Quoted By: >>11221456 >>11229575

>>11221419
>finite sequence of numbers
>uniformly convergent
yep, you didn't study

Anonymous

Anonymous Fri 13 Dec 2019 01:13:23 No.11221443 Report

Quoted By: >>11221456

>>11221419
just know when things are close, it's all good; and you'll be okay.

Anonymous

Anonymous Fri 13 Dec 2019 01:17:53 No.11221456 Report

Quoted By:

>>11221436
What if my grade is given by a sequence over each day after starting the course?
>>11221443
Thanks, I'll try my best

Anonymous

Anonymous Fri 13 Dec 2019 01:20:29 No.11221468 Report

Quoted By:

>>11217268
this is bait

Anonymous

Anonymous Fri 13 Dec 2019 01:21:41 No.11221472 Report

Quoted By:

>>11221419
Just got my RA grade back today. A

feels good

Anonymous

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Anonymous Fri 13 Dec 2019 01:29:33 No.11221491 Report

Quoted By:

>>11217268

Anonymous

Anonymous Fri 13 Dec 2019 05:07:10 No.11221900 Report

Quoted By: >>11222369

>>11221160
>39 hours (13 week semester, 3 hours/week)?
You DO realize that you are supposed to self study, right?

Anonymous

Anonymous Fri 13 Dec 2019 05:13:24 No.11221917 Report

Quoted By:

Hey guys, you should watch Gromov's lectures, they're funny and insightful. Turns out all that work by Donaldson on 4-manifolds is just a consequence of 2+2=4

Anonymous

Anonymous Fri 13 Dec 2019 05:53:35 No.11221989 Report

Quoted By:

>>11218557
thank you based zuki

Anonymous

Anonymous Fri 13 Dec 2019 05:55:16 No.11221992 Report

Quoted By:

>>11220274
slick proofs, Rudin

Anonymous

Anonymous Fri 13 Dec 2019 08:25:32 No.11222193 Report

Quoted By:

>>11220555
Well overall, many people do get weeded out. (50% passing rate in 1st year I think)
I'm thinking that if professors really wanted to grade drastically, then only a handful of people would pass each year, which would be very impractical. The goal is not to weed out people.
I don't know what happened in your life to give you this punitive view of math education but it is just not how it should be.
Here, math is mainly a weed-out tool and, as a result, most people who don't work in science actively hate math instead of being merely uninterested as is usually the case.

Anonymous

Anonymous Fri 13 Dec 2019 08:36:07 No.11222208 Report

Quoted By:

>>11220555
I don't know if you have ever seen some actual french exams but, usually, the tests are far too long to finish.
There are several reasons for this. Some profs want to make tests that will be hard enough to keep the best students busy for however long the exam is. Some just want to make something interesting and give a proof of an actual theorem as a problem (cut into many pieces).
The result is usually a problem set that is unreasonably long, and therefore they usually decide on how they grade it after they see how students performed.
Still, overall, many people do get weeded out. (50% passing rate in 1st year I think)
I'm thinking that if professors really wanted to grade drastically, then only a handful of people would pass each year, which would be very impractical. The goal is not to weed out people.
I don't know what happened in your life to give you this punitive view of math education but it is just not how it should be.
Here, in the early years of education (elementary, high school), math is mainly used as a weed-out tool and, as a result, most people who don't work in science actively hate math instead of being merely uninterested as seems the case elsewhere.

Anonymous

Anonymous Fri 13 Dec 2019 10:55:44 No.11222369 Report

Quoted By:

>>11221900
...what?

Anonymous

Anonymous Fri 13 Dec 2019 11:39:40 No.11222427 Report

Quoted By: >>11222664 >>11222786

Is statistics really a good field or am I being memed?

Anonymous

Anonymous Fri 13 Dec 2019 14:10:48 No.11222664 Report

Quoted By:

>>11222427
Statistics is an absolute dogshit tier field, would recommend studying literally anything else.

Anonymous

Anonymous Fri 13 Dec 2019 14:17:05 No.11222672 Report

Quoted By:

Math exams have gotten like 30% harder since I took them. (Bongland here)

Anonymous

Anonymous Fri 13 Dec 2019 15:09:30 No.11222750 Report

Quoted By: >>11222757 >>11222786 >>11223042

Let $f,g: \mathbb R \to \mathbb R$ be continuous and compactly supported, and assume also $g$ is $C^1$ . How do I show that the convolution $f*g = \int_{\mathbb R} f(t)g(x-t)dt$ is differentiable and satisfies $(f*g)' = f*g'$ ?

I've tried several approaches. Essentially I get to this point where I'd like to show that I may push this limit inside some integral, but I don't know how to justify it.

I've seen some papers/SE threads address this issue but they all rely on the DCT and measure theoretic concepts in general, which I'm unfamiliar with. Any hints are appreciated, /sci/.

Anonymous

Anonymous Fri 13 Dec 2019 15:14:20 No.11222757 Report

Quoted By:

>>11222750
I'm sure if you Google "Feynman trick differentiating under the integral sign,x you inevitably end up with a discussion of the proper requirements

Anonymous

Anonymous Fri 13 Dec 2019 15:37:33 No.11222786 Report

Quoted By:

>>11222427
One of the easiest fields to get a job in (statistical physics, biostats, finance, administration)
However not much research and intellectual activity going on, except perhaps on their relationship with Baysian probabilities or Stochastic processes, but that's very "down to Earth" mathematics. Don't expect to handle ultra-abstract and ultra-elaborate object with elegant proofs.
depends on what you like, really

>>11222750
>I may push this limit inside some integral, but I don't know how to justify it.
Not sure if you've seen it, but you just need to how that the integral of the limit converges "uniformally", in other words, that it converges at all

f is is continuous in a compact, so it's bounded and actually reaches its boundaries, work from that and inequalities to show convergence
then you can play with differentials and integrals as much as you want

Anonymous

Anonymous Fri 13 Dec 2019 16:14:26 No.11222838 Report

Quoted By:

>>11219520
Yeah. make spivak the 2nd book.

I actually like Trudeau intro to graph theory.

Anonymous

Anonymous Fri 13 Dec 2019 16:56:46 No.11222928 Report

Quoted By:

Does anyone know if you can graph polynomials in $\mathbb{Z}_n [x, y]$ with Sage?

Anonymous

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Anonymous Fri 13 Dec 2019 17:16:46 No.11222965 Report

Quoted By: >>11223011 >>11223017 >>11223028 >>11223040 >>11223049 >>11223095

Is category theory worth learning for someone into discrete mathematics?

Anonymous

Anonymous Fri 13 Dec 2019 17:37:40 No.11223011 Report

Quoted By: >>11223049

>>11222965
No, don't bother learning this. It really adds no substance, it literally leeches off of real math (i.e. algebraic topology, algebra). Instead, study something like Algebraic Topology from, say, Hatcher or study Differential Topology from Lee's Smooth Manifolds book. I have friends who study category theory and they are not the best math majors.

Anonymous

Anonymous Fri 13 Dec 2019 17:40:50 No.11223017 Report

Quoted By:

>>11222965
CT is fun, honestly.
would recommend that you get a good grasp of the "whole" of math first though.

Anonymous

Anonymous Fri 13 Dec 2019 17:48:03 No.11223028 Report

Quoted By:

>>11222965
finish your undergrad, then learn categories. please

Anonymous

Anonymous Fri 13 Dec 2019 18:01:38 No.11223040 Report

Quoted By:

>>11222965
No

Anonymous

Anonymous Fri 13 Dec 2019 18:02:32 No.11223042 Report

Quoted By:

>>11222750
honestly, just learn measure theory. one of the reasons why the Lebesgue integral is superior to the Riemann integral is that it's much more compatible with the interchange of limits. I'm no analyst, but I skimmed through the Folland's book a while ago, I definitely remember theorems like that.

Anonymous

Anonymous Fri 13 Dec 2019 18:05:12 No.11223048 Report

Quoted By:

>>11220302
lmfao, great image. Keep em coming

Anonymous

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Anonymous Fri 13 Dec 2019 18:05:31 No.11223049 Report

Quoted By: >>11223060 >>11223064 >>11223070 >>11223245

>>11223011
It's just a language, bre. There's literally nothing wrong with pointing out universal properties where they exist.
Hating on category theory is just reactionary

>>11222965
https://en.m.wikipedia.org/wiki/Combinatorial_species

Anonymous

Anonymous Fri 13 Dec 2019 18:12:49 No.11223060 Report

Quoted By: >>11223069

>>11223049
>Outsideness avi
>Muh category theory
>reactionary
Tranny detected.

Anonymous

Anonymous Fri 13 Dec 2019 18:14:53 No.11223064 Report

Quoted By: >>11223069

>>11223049
>It's just a language, bre.
actual category theorists wouldn't agree with you, bre

Anonymous

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Anonymous Fri 13 Dec 2019 18:17:58 No.11223069 Report

Quoted By:

>>11223060
Land is a bit too right for that but points taken, twitter is at fault for a lot

>>11223064
I don't think it's a good foundation in itself, but as I said, not having a theory of math that systematically studies/collects/points out adjoint Hom-classes would be a grand missed opportunity

Anonymous

Anonymous Fri 13 Dec 2019 18:18:06 No.11223070 Report

Quoted By:

>>11223049
you are not a mathematician, nor are you cute, nor will you ever pass.

Anonymous

Anonymous Fri 13 Dec 2019 18:25:34 No.11223090 Report

Quoted By: >>11223118

https://motls.blogspot.com/2018/11/scholze-stix-dont-have-magic-power-to.html

Anonymous

Anonymous Fri 13 Dec 2019 18:27:20 No.11223095 Report

Quoted By:

>>11222965
Category theory isn't really useful or meaningful unless you already have plenty of baggage and experience.

Anonymous

Anonymous Fri 13 Dec 2019 18:33:52 No.11223118 Report

Quoted By:

>>11223090
first blog by motl I've read where he's not autistically insulting someone who has another opinion, what gives

Anonymous

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Anonymous Fri 13 Dec 2019 18:49:33 No.11223149 Report

Quoted By: >>11223159 >>11223186 >>11223199

what on EARTH does Norman Wildbeger mean when he says the reals dont exist? Is he right? w-we can construct t-the reals, right?

Anonymous

Anonymous Fri 13 Dec 2019 18:53:01 No.11223159 Report

Quoted By:

>>11223149
the world is finite, therefore everything in math should also be finite. it's not mathematics, it's just a matter of opinion, and this is his opinion.

Anonymous

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Anonymous Fri 13 Dec 2019 18:54:56 No.11223164 Report

Quoted By: >>11223184

How many IQ points do I need to into Topology?

Anonymous

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Anonymous Fri 13 Dec 2019 19:08:11 No.11223184 Report

Quoted By: >>11223196

>>11223164
enough to expect and understand that once you get past the honeymoon period with mugs, doughnuts and klein bottles, it's absolute hell.
pic related. it's what actually doing topology looks like.

Anonymous

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Anonymous Fri 13 Dec 2019 19:10:11 No.11223186 Report

Quoted By: >>11223215 >>11223321

>>11223149
Incompleteness hits set theory in some inconvenient ways. For example, standard theories of sets (such as ZFC) can't decide statements such as
>If you have a set X and another set Y with more elements than X, then the bigger set Y also has more subsets than X does. (I.e., the claim that bigger cardinality, |Y|>|X|, implies the same for the power sets, |PY|>|PX|)

That there are some of those rather natural sounding but unprovable statements was already noted by Cantor in the 19th century. Then 60 years later in the late 30's, Gödel set out to find stronger axioms that would make those things true but weren't the statements themselves ("more natural axioms for set theory"), but now another 90 years later we're arguably still not smarter.

Effectively, the issue is that the axioms aren't suited to control the size of the power set. If N denote the smallest countable infinite set, i.e. the natural numbers, then the "available" subsets of N, which we may write as PN, aren't actually a set that can be compared or classified in the "natural" sequence of cardinal numbers given by the cardinalities of the ordinal (the totally directed/linear) numbers. That is to say, PN or 2^N isn't limited from above, in size, by any reasonable cardinal number.

A more hands-on way in which this shows in the real numbers (which have PN) is that the bulk of reals are not accessible on an individual level: You can enumerate the finite texts describing numbers, so you can describe only a countable quantity of number (such as 2, 5, 3225.233523, pi as given by some of its integral, e given by its power series).
The size of 2^N isn't controlled by any of its semantic definitions. The notion of the set of reals can be described, but it arguably fails to capture the intuitive notion of sets well.

Regarding Wildberger, the inaccessibility of the standard definition of the reals (e.g. each real number is a equivalence-class set of sequences), let him into finitism. He's a bit cranky.

Anonymous

Anonymous Fri 13 Dec 2019 19:15:26 No.11223195 Report

Quoted By:

>>11218453
Utm Mat102 course notes
Common proofs: Contradiction, Induction (especially in comsci), Contrapositive, direct reasoning
Important distinction: => as opposed to <=>

Anonymous

Anonymous Fri 13 Dec 2019 19:16:01 No.11223196 Report

Quoted By:

>>11223184
Looks like fun ngl

Anonymous

Anonymous Fri 13 Dec 2019 19:18:11 No.11223199 Report

Quoted By:

>>11223149
Wait a minute

>infinity is not a number
>infinity cannot be a real number by virtue of the fact it isn’t a number of any kind
>Reals BTFO??!!??

Anonymous

Anonymous Fri 13 Dec 2019 19:30:52 No.11223215 Report

Quoted By: >>11223227 >>11223242

interesting, good post
>>11223186
>the inaccessibility of the standard definition of the reals (e.g. each real number is a equivalence-class set of sequences)
How do current mathematicians conceive of the reals? Ive simply always thought of them as isomorphic to some uncountable set.

Also, Does he not buy diagnolization arguments?

Anonymous

Anonymous Fri 13 Dec 2019 19:38:37 No.11223227 Report

Quoted By: >>11223268

>>11223215
>Also, Does he not buy diagnolization arguments?
he does not need to concern himself with diagonalization arguments, because he rejects any structure where the argument could be used to begin with. IIRC he even thinks that there should be an upper bound for natural numbers A (I guess something like the number of all possible permutations of all elementary particles in the universe) and the symbol A+1 is meaningless to him, just like 1/0.

Anonymous

Anonymous Fri 13 Dec 2019 19:45:36 No.11223242 Report

Quoted By: >>11223268

>>11223215
>How do current mathematicians conceive of the reals?
You can construct them just fine if you believe in ZFC. You have a few standard approaches to them, all of which basically amount to the same thing.
Most mathematicians (and probably nearly all analysts) see the reals as the fundamental number system and the best representation of the continuum.

>Also, Does he not buy diagnolization arguments?
He doesn't even buy the natural numbers.
Diagnolization is irrelevant to him, since he doesn't even accept the premises to which the argument could be applied.

Anonymous

Anonymous Fri 13 Dec 2019 19:46:23 No.11223244 Report

Quoted By:

What do you guys think of mathgreforums.com?

Anonymous

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Anonymous Fri 13 Dec 2019 19:46:54 No.11223245 Report

Quoted By:

>>11223049
>Hating on category theory is just reactionary
Yes.

Anonymous

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Anonymous Fri 13 Dec 2019 19:53:41 No.11223256 Report

Quoted By: >>11223259 >>11223273

Is it true that going into pure maths or pure physics is as bad as majoring in liberal arts? Or is that just more bucket-crab nonsense characteristic of this site?

Anonymous

Anonymous Fri 13 Dec 2019 19:55:10 No.11223259 Report

Quoted By: >>11223265

>>11223256
the intelligence needed to pursue pure maths carries over into most anything one wishes to pursue. the same can not be said for liberal arts.

Anonymous

Anonymous Fri 13 Dec 2019 19:56:55 No.11223265 Report

Quoted By:

>>11223259
In theory sure, but does the job market really acknowledge this simple logic?

Anonymous

Anonymous Fri 13 Dec 2019 19:57:48 No.11223268 Report

Quoted By: >>11223337

>>11223227
>>11223242

he rejects infinite sets altogether? lmao
no wonder hes /ourguy/, hes a windbag

Anonymous

Anonymous Fri 13 Dec 2019 19:58:55 No.11223273 Report

Quoted By: >>11223286 >>11223333 >>11223344 >>11223400

>>11223256
just do engineering and learn math/physics along the way its easier and less stressful

Anonymous

Anonymous Fri 13 Dec 2019 20:02:53 No.11223286 Report

Quoted By: >>11223333

>>11223273
How could it be easier learning on your own, let alone with a course-load of irrelevant subjects.

Anonymous

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Anonymous Fri 13 Dec 2019 20:15:58 No.11223321 Report

Quoted By: >>11223325

>>11223186
Probably the simplest approach (w.r.t. size characterization) to wrap your hands around is to identify the set of reals with the set of functions ${ \mathbb Q } \to \{ 0, 1 \}$ defining a cut. E.g.

$f : { \mathbb Q } \to \{ 0, 1 \}$
$f(x) := 1\, {\mathrm { if }}\, (x^2 < 7 ) \ {\mathrm { else }}\, 0$

The cardinality of this set is quite explicitly that of the power set of the rational numbers. As noted above, how many such functions exist is not captured by a hierarchy of ordinals in ZFC.

Dedekind cuts are a variant of the above, except you use predicates instead of functions, which in set theory are an available language apriori (because you use logic to write down the axioms), unlike in type theory.

For curiosity sake, note that there's "small reals" way out by restricting yourself to constructive logic and its weak ZFC equivalences. Effectively, you take the $f : { \mathbb Q } \to \{ 0, 1 \}$ Dedekind'esk view on the reals, but make more concrete (and thus restrict) what sort of functions you allow. You may end up with a set of such reals that is subcountable
https://en.wikipedia.org/wiki/Subcountability
But note that in those weak frameworks, you lose the theorems that an infinite subset of N is in bijection to N. So I'm not sure if this "making the reals nicer" is a worthy candidate.

Anonymous

Anonymous Fri 13 Dec 2019 20:17:18 No.11223325 Report

Quoted By:

>>11223321
the function $f$ ought to correspond to the real $\sqrt{7}$ btw.

Anonymous

Anonymous Fri 13 Dec 2019 20:21:00 No.11223333 Report

Quoted By:

>>11223273
>>11223286
if anything, doing math/physics and learning engineering along the way is the better choice

Anonymous

Anonymous Fri 13 Dec 2019 20:21:43 No.11223337 Report

Quoted By:

>>11223268
>he rejects infinite sets altogether?
Yes, he believes in a largest number.

>lmao no wonder hes /ourguy/, hes a windbag
I think it is a *reasonable* position, but I simply do not see it as a true or helpful position.

What I grant him is that his ideas are lending themselves very well to a totally computerized mathematics.

Anonymous

Anonymous Fri 13 Dec 2019 20:23:02 No.11223344 Report

Quoted By: >>11223346 >>11223350 >>11229178

>>11223273
>just do engineering and learn math/physics along the way
LMAO, as if you could gain any reasonable insight into mathematics while studying engineering.

Anonymous

Anonymous Fri 13 Dec 2019 20:23:19 No.11223346 Report

Quoted By:

>>11223344
nice get

Anonymous

Anonymous Fri 13 Dec 2019 20:25:20 No.11223350 Report

Quoted By:

>>11223344
Depends what type of engineering you do anon. If you just do a flat "engineering" course then obviously not.

Anonymous

Anonymous Fri 13 Dec 2019 20:25:57 No.11223353 Report

Quoted By: >>11223363

Any of you guys have a BS in applied math? What do you do for a living?

Anonymous

Anonymous Fri 13 Dec 2019 20:27:49 No.11223363 Report

Quoted By:

>>11223353
>Doing a course for the money
Never going to make it

Anonymous

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Anonymous Fri 13 Dec 2019 20:38:46 No.11223400 Report

Quoted By:

>>11223273
>can I learn thing I like and get job?
>Just do boring thing instead

So is this your way of saying no?

Anonymous

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Anonymous Fri 13 Dec 2019 21:36:31 No.11223515 Report

Quoted By: >>11223710

>he/she/xhe/zem adheres to the normalcy of getting a "job"
lol, y i k e s

Anonymous

Anonymous Fri 13 Dec 2019 21:37:22 No.11223518 Report

Quoted By: >>11223710 >>11224088

Can a book like "G. Polya, How to Solve It" help me improve my poor executive function? My solutions are a fucking mess.

Anonymous

Anonymous Fri 13 Dec 2019 21:38:28 No.11223523 Report

Quoted By: >>11223540

The graph of a function can take any shape or form.

Anonymous

Anonymous Fri 13 Dec 2019 21:46:53 No.11223540 Report

Quoted By: >>11223560

>>11223523
False. Functions cannot have multiple Y values for a given X value. You learn that in grade 7 ffs

Anonymous

Anonymous Fri 13 Dec 2019 21:46:56 No.11223541 Report

Quoted By:

Not really math but I told my prof I'd finish my master thesis in the next 1-2 months. This was at the beginning of October. And I haven't written a single word since then

Anonymous

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Anonymous Fri 13 Dec 2019 21:50:50 No.11223552 Report

Quoted By:

Can you figure out what kind of a "sine" function this is? Its spectrum is on the right. Note that this is a logarithmic scale and the graph still looks curvy! Fascinating, eh?

Anonymous

Anonymous Fri 13 Dec 2019 21:54:32 No.11223560 Report

Quoted By: >>11223566 >>11223580 >>11223606 >>11223662 >>11223690 >>11224689

>>11223540
Sqrt(x) has two solutions.

Anonymous

Anonymous Fri 13 Dec 2019 21:56:56 No.11223566 Report

Quoted By:

>>11223560
If you define sqrt(x) in a way such that it can have 2 solutions depending on the x, then it is not a function.

Anonymous

Anonymous Fri 13 Dec 2019 22:00:44 No.11223580 Report

Quoted By:

>>11223560
Not a function

Anonymous

Anonymous Fri 13 Dec 2019 22:10:41 No.11223606 Report

Quoted By:

>>11223560
true and completely irrelevant

Anonymous

Anonymous Fri 13 Dec 2019 22:34:10 No.11223662 Report

Quoted By: >>11223798

>>11223560
not simultaneously

Anonymous

Anonymous Fri 13 Dec 2019 22:47:01 No.11223687 Report

Quoted By: >>11223700

https://www.youtube.com/watch?v=SYWaQe0qmNI

Anonymous

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Anonymous Fri 13 Dec 2019 22:48:54 No.11223690 Report

Quoted By: >>11223697

>>11223560
>why yes, whenever I'm working over the reals I just read $y= \sqrt{x}$ as the inverse function of $y=x|x|$ , isn't that obvious?

Anonymous

Anonymous Fri 13 Dec 2019 22:54:21 No.11223697 Report

Quoted By: >>11223797

>>11223690
so sqrt(-1) = -1?

Anonymous

Anonymous Fri 13 Dec 2019 22:55:18 No.11223700 Report

Quoted By:

>>11223687
Does anyone have the link to the anime song about how they're about to die but they just proved some important theorem or something. I think it was vocaloid.

Anonymous

Anonymous Fri 13 Dec 2019 22:58:40 No.11223706 Report

Quoted By:

easy to tell when highschool gets out.

Anonymous

Anonymous Fri 13 Dec 2019 23:02:39 No.11223710 Report

Quoted By:

>>11223518
No.
>>11223515
Based

Anonymous

Anonymous Fri 13 Dec 2019 23:35:06 No.11223797 Report

Quoted By:

>>11223697
Yes.

Anonymous

Anonymous Fri 13 Dec 2019 23:35:19 No.11223798 Report

Quoted By: >>11223806

>>11223662
there are no simultaneous things in nature, we live in a discrete and sequential world.

Anonymous

Anonymous Fri 13 Dec 2019 23:36:24 No.11223806 Report

Quoted By:

>>11223798
No we don’t. Nature is continuous, local, and deterministic.

Anonymous

Anonymous Fri 13 Dec 2019 23:44:09 No.11223821 Report

Quoted By: >>11223832

>>11218557

"thank you based zuki"
thank you based zuki
"thank you based 'zuki" in this thread
"thank you based 'zuki"
"(red) thank you based 'zuki" in this thread
"(red) thank you based 'zuki"

Anonymous

Anonymous Fri 13 Dec 2019 23:52:02 No.11223832 Report

Quoted By:

>>11223821
>(red)
>not making the text red with LateX
Oh no no no...

Anonymous

Anonymous Sat 14 Dec 2019 00:06:54 No.11223854 Report

Quoted By:

I decided to stop being stupid after being many years out of university. I started doing statistics problems out of a large math for engineers textbook. I'm getting the answers but I don't feel like I'm gaining a lot of understanding. Do you have anything to recommend, like some sort of intro to pure maths book that will allow me to start understanding in a deeper way?

Anonymous

Anonymous Sat 14 Dec 2019 01:57:25 No.11224088 Report

Quoted By:

>>11223518
>Can a book like "G. Polya, How to Solve It" help me improve my poor executive function?
Why don't you try it and find out?

Anonymous

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Anonymous Sat 14 Dec 2019 04:30:36 No.11224368 Report

Quoted By:

This thread is shit. Post true/false questions.

Anonymous

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Anonymous Sat 14 Dec 2019 04:31:06 No.11224369 Report

Quoted By:

>>11213806

Solivagus/ECHS

View Same Google iqdb SauceNAO main-qimg-cf57eb30c121ded62c1dd0 (...).jpg, 27KiB, 360x360

Solivagus/ECHS Sat 14 Dec 2019 04:36:55 No.11224379 Report

Quoted By: >>11224761

>>11213806
?????? ??????????????????? ???????????????????????????????????????????

????????????????????

>?????????????????????????????

Anonymous

Anonymous Sat 14 Dec 2019 07:21:22 No.11224689 Report

Quoted By:

>>11223560
Yes and it is a function from R to RxR.
For each input there is a UNIQUE output.

Anonymous

Anonymous Sat 14 Dec 2019 07:59:37 No.11224754 Report

Quoted By:

>>11219576
Read up school textbooks by Gelfand

Anonymous

Anonymous Sat 14 Dec 2019 08:12:08 No.11224761 Report

Quoted By: >>11224764 >>11224837

>>11224379
>?????????????????????????????

>I can offend these mules for infinite countless instants

Wft is this guy a bot or not?

Solivagus/ECHS

View Same Google iqdb SauceNAO koma-1_275_206.jpg, 6KiB, 275x206

Solivagus/ECHS Sat 14 Dec 2019 08:16:06 No.11224764 Report

Quoted By:

>>11224761
???????????????????

Anonymous

Anonymous Sat 14 Dec 2019 09:17:27 No.11224837 Report

Quoted By: >>11224843

>>11224761
He google translated some bullshit into Japanese, when you try to translate stuff like that back it gets mangled

Solivagus/ECHS

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Solivagus/ECHS Sat 14 Dec 2019 09:21:45 No.11224843 Report

Quoted By:

>>11224837
??????? ????????

Anonymous

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Anonymous Sat 14 Dec 2019 16:52:26 No.11225481 Report

Quoted By:

Woah broah

Anonymous

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Anonymous Sat 14 Dec 2019 17:13:32 No.11225525 Report

Quoted By:

>>11219576
>Assuming I'm a college flunkie that spent more time chewing on the barrel of a gun than studying, what would be the best way to get back into the swing of math from the pre-calc level also assuming just going back to college is impossible.

Anonymous

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Anonymous Sat 14 Dec 2019 19:38:25 No.11225867 Report

Quoted By: >>11225882 >>11227329

I really want to be a mathematician and go all the way to a PHD but I really need to know if i'm smart enough to do it. My verbal/reasoning IQ is 133-139 so I should be smart enough but my working memory is a nigger tier 84.

Is there any book or course I should try that's a perfect shit test to see if i'm smart enough?

Anonymous

Anonymous Sat 14 Dec 2019 19:44:46 No.11225882 Report

Quoted By:

>>11225867
>believes in IQ shit
never gonna make it
also racism is a clear indication of low intelligence

Anonymous

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Anonymous Sat 14 Dec 2019 21:38:40 No.11226100 Report

Quoted By: >>11226164 >>11226261 >>11226335

How much of this image is a meme?

Anonymous

Anonymous Sat 14 Dec 2019 21:59:54 No.11226164 Report

Quoted By:

>>11226100
>logic, proof books
Memes, waste of time. If you have any aptitude for math you will pick it all up as you go along studying real math.
>set theory book
Useless for a beginner. Pick an actual beginner maths book (be it algebra or analysis) and it will teach you all the set theory you need to know.
>calculus, basic mathematics
Better just use khanacademy. It's interactive, made specifically for these topics and you will learn much quicker.

This whole list is a meme aimed at demotivating you and making you give up. The person who made this, assuming this is not a troll image, which is likely) was never gonna make it in the first place.

Anonymous

Anonymous Sat 14 Dec 2019 22:30:58 No.11226261 Report

Quoted By:

>>11226100
if you need to learn maths for classes then you're better off asking your teacher and classmates
starting with a book on logic is a terrible idea
old books by famous people (halmos, landau, lang, polya) tend to be harder than other books

if you're studying for your own sake, then everything depends on your background and interests
what do you find interesting? my first experience with mathematics was competitions in school, from simple stuff in 2nd grade up to high school olympiads. I feel like this gives you a natural progression because you start out just thinking about simple problems about numbers, plane geometry, combinatorics, all you want to do is to be able to solve problems. Then any kind of "theory" is learned only if it has purpose reflected in what you want to solve
there must be something specific that you want to learn, otherwise what's the point? if you have this, then you see set theory, basic analysis, as merely "tools", which you develop, but only as long as the development is useful
people who don't have those feelings become undergrad category theorists

Anonymous

Anonymous Sat 14 Dec 2019 22:58:50 No.11226335 Report

Quoted By:

>>11226100
this is a total shit guide. I'm not even gonna elaborate, just delete this image please.

Anonymous

Anonymous Sat 14 Dec 2019 23:17:34 No.11226381 Report

Quoted By: >>11231099

>>11215773
which book is this?

Anonymous

Anonymous Sat 14 Dec 2019 23:31:21 No.11226412 Report

Quoted By: >>11226415 >>11226541

i spent the past years being a depressed neet and jerking off to anime
my brain is now rotten but i want to get back into mathematics
will textbooks and practice unrot my brain or is hope lost

Anonymous

Anonymous Sat 14 Dec 2019 23:32:29 No.11226415 Report

Quoted By:

>>11226412
All is lost. You a cumbrian now.

Anonymous

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Anonymous Sun 15 Dec 2019 00:18:13 No.11226541 Report

Quoted By:

>>11226412
Yes.
Read this

Anonymous

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Anonymous Sun 15 Dec 2019 00:22:16 No.11226555 Report

Quoted By: >>11227199 >>11227209 >>11227302

I'm doing Spivak's Calculus and I'm already struggling a bit in the first 3 exercises of chapter 1, I've never been asked to prove things like this, with a complete focus on algebraic properties. While I do want to learn this a lot, it's starting to get frustrating and I'm asking myself if I'm simply not ready for this or if I should do whatever I can, check the solutions when necessary(they're not available for all questions anyway) and go on, only worrying about really doing 100% of it on a future occasion. What do you think?

Anonymous

Anonymous Sun 15 Dec 2019 01:08:15 No.11226658 Report

Quoted By:

Please help.

Anonymous

Anonymous Sun 15 Dec 2019 05:04:02 No.11227158 Report

Quoted By:

SOMEBODY HELP

Anonymous

Anonymous Sun 15 Dec 2019 05:25:07 No.11227199 Report

Quoted By: >>11228597

>>11226555
>giving up after 3 exercises
you need to try harder and for a sustained period of time, give it at least a month with daily effort paid towards solving more exercises with less reliance on solution manuals. This habit of people bitching after a few days of a few hours daily effort is ridiculous. You probably aren’t a mathematical genius, were you expecting to find out that you were?

Anonymous

Anonymous Sun 15 Dec 2019 05:28:25 No.11227209 Report

Quoted By: >>11228597

>>11226555
If Spivak is too difficult try Courant or Apostol, they’re significantly easier, but this will rob you of the intuition you would have developed in preparation for Analysis. The expectation should be that you are untrained, ignorant, and largely clueless until you have demonstrated consistent proficiency at abstract mathematics. You will get curb stomped in any seriously demanding class or with any higher level book if you can’t ask more of yourself than you’re accustomed to for a long period of time while you still qualify as clueless, ignorant and untrained.

Anonymous

Anonymous Sun 15 Dec 2019 06:24:07 No.11227302 Report

Quoted By: >>11228597

>>11226555
if you're not struggling you're doing it wrong
the frustration and struggle will go away as you get your sealegs. it won't be long before you can feel how to start and approach a proof. but it takes time and practice to get there.

Anonymous

Anonymous Sun 15 Dec 2019 06:43:37 No.11227329 Report

Quoted By:

>>11225867
You just need to give it a try. Read some math books.

Anonymous

Anonymous Sun 15 Dec 2019 10:46:19 No.11227642 Report

Quoted By: >>11227724 >>11227737 >>11228544

Ax = b has a solution for every b iff A has a full row rank?
I checked but I need someone to confirm it.

Anonymous

Anonymous Sun 15 Dec 2019 12:01:35 No.11227724 Report

Quoted By:

>>11227642
it may not have a *unique* solution if rank A = min { #of rows, #of columns }, but if it's a square matrix then the solution will be unique and the matrix invertible

Anonymous

Anonymous Sun 15 Dec 2019 12:10:27 No.11227737 Report

Quoted By:

>>11227642
yes, full row rank means that A (as a map between vector spaces) is surjective

Anonymous

Anonymous Sun 15 Dec 2019 13:56:30 No.11227955 Report

Quoted By: >>11227968 >>11227997 >>11228008 >>11228110

Is average phd math guy can clearly understands perelman's explanation of poincare conjecture? Or it's only professor tier?

Anonymous

Anonymous Sun 15 Dec 2019 14:09:51 No.11227968 Report

Quoted By: >>11227980

>>11227955
The proof is not too difficult for a PhD student to understand, but very few PhD students actually bother to learn it.
Students in geometric analysis or related areas understand it (source: I have friends doing geometric analysis who know it), but for anyone else it's too much work for no benefit. It's way too hard with too many specialized prerequisites to learn just for of mild curiosity.

Anonymous

Anonymous Sun 15 Dec 2019 14:17:59 No.11227980 Report

Quoted By:

>>11227968
thank you

Anonymous

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Anonymous Sun 15 Dec 2019 14:26:35 No.11227997 Report

Quoted By:

>>11227955
Morgan and Tian have literally written a five hundred page exposition of it, where they give the entire proof from basic Riemannian Geometry.
Not only can 90% of PhD students who aren't autistic hyper-specialized combinatorialists read it, but a good number of master's students and undergrads can, with the appropriate patience.

Anonymous

Anonymous Sun 15 Dec 2019 14:31:51 No.11228008 Report

Quoted By:

>>11227955
only if the student's specialization is such that he has a substantial knowledge of differential and algebraic topology, differential geometry and geometric analysis.
I mean there are working mathematicians who don't know what a Riemannian manifold is.

Anonymous

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Anonymous Sun 15 Dec 2019 14:55:01 No.11228055 Report

Quoted By: >>11228261

I have been playing online slots. I want to create an excel table listing how many times each symbol appeared in each reel. I have about 4000 screenshots. Is there a way to do this without manually inputting what I see?

Anonymous

Anonymous Sun 15 Dec 2019 15:30:37 No.11228110 Report

Quoted By: >>11228209 >>11228404 >>11228529

>>11227955
Claim: There's nothing that a Prof can know that a dedicated 18 year old can't. It's just a matter of time effort one puts into it. 100 years ago, most PhD's were handed out to people around 25 or so... people don't get naturally smarter with age, they just have had more time to dedicate time to something

Anonymous

Anonymous Sun 15 Dec 2019 15:30:47 No.11228111 Report

Quoted By: >>11228120

Computer science is the superclass over mathematics.
All mathematics is a computation, and the laws of computation are innate to reality.
Mathematics is, therefor, discovered and not invented.

Anonymous

Anonymous Sun 15 Dec 2019 15:34:02 No.11228120 Report

Quoted By:

>>11228111
>All mathematics is a computation
You have never been to an actual math course.

>the laws of computation are innate to reality.
You have never listened to a CS course.

Anonymous

Anonymous Sun 15 Dec 2019 16:26:49 No.11228209 Report

Quoted By: >>11228316

>>11228110
i'm almost 25, seems like i'm only going to get more retarded from math from here on out

Anonymous

Anonymous Sun 15 Dec 2019 16:40:44 No.11228228 Report

Quoted By: >>11228529

We start out with an affine variety $A^n$ constructed on a ring R, and a function I that sends it's subvarieties to some set. In practical terms, I would be some sort of invariant of the subvariety, i.e. number of singularities.
We induce a topology on R by considering small perturbations (usually on the leading coefficient or on all of them) that preserves the invariant. So the sets in the base would be $\tau = \{ a \in R ~ such ~ that I(V(f))=I(V(f+ a L_f)) \}$ as f goes through all polynomials in $R[x_1, ..., x_n$ , and $L_f$ is the leading term or some appropriately chosen polynomial.
Does a construction like this show up anywhere in ring theory or algebraic geometry?

Anonymous

Anonymous Sun 15 Dec 2019 16:59:13 No.11228261 Report

Quoted By: >>11228274

>>11228055
under the assumption that all the images are perfectly aligned - you can write a rather simple script to crop the symbols from the reels and work from there by possibly hashing/comparing hashes and going from there.
unfortunately I don't see how would you do it directly in excel

Anonymous

Anonymous Sun 15 Dec 2019 17:07:16 No.11228274 Report

Quoted By:

>>11228261
He could have a team of slaves from Yimbatswana do it for him

Anonymous

Anonymous Sun 15 Dec 2019 17:28:06 No.11228316 Report

Quoted By:

>>11228209
What do you study? What are you good at?

Anonymous

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Anonymous Sun 15 Dec 2019 17:34:02 No.11228323 Report

Quoted By:

The nLab decided to stop giving out personal websites as subspaces of the lab.
Too many people stopped to quickly using them, leaving behind just clutter.

Anonymous

Anonymous Sun 15 Dec 2019 18:13:26 No.11228404 Report

Quoted By:

>>11228110
interesting point of view, thank you for this

Anonymous

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Anonymous Sun 15 Dec 2019 19:01:43 No.11228504 Report

Quoted By: >>11229745 >>11229807

where the fuck did "a" come from?

Anonymous

Anonymous Sun 15 Dec 2019 19:14:41 No.11228529 Report

Quoted By:

>>11228110
>>11228228

Total bullshit.

That reminds me of anarchists who think having a government isn't really necessary or flat earthers who believe that scientists like to just make shit up.

Anonymous

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Anonymous Sun 15 Dec 2019 19:20:37 No.11228543 Report

Quoted By: >>11228547

>>11221160
that's pretty much easy high school stuff in Europe

Anonymous

Anonymous Sun 15 Dec 2019 19:21:41 No.11228544 Report

Quoted By:

>>11227642
You betcha!

Anonymous

Anonymous Sun 15 Dec 2019 19:22:43 No.11228547 Report

Quoted By: >>11228579

>>11228543
this is freshman highschool math in America

Anonymous

Anonymous Sun 15 Dec 2019 19:36:43 No.11228579 Report

Quoted By:

>>11228547
this is womb stuff when I was still a a swimming sperm

Anonymous

Anonymous Sun 15 Dec 2019 19:46:49 No.11228597 Report

Quoted By:

>>11227199
>>11227209
>>11227302
Thanks

Anonymous

Anonymous Sun 15 Dec 2019 20:03:54 No.11228645 Report

Quoted By:

>>11221160
You aren't. You're supposed to print out all the past exam papers, and use the material as a reference while practicing how to solve the questions.

Anonymous

Anonymous Mon 16 Dec 2019 00:42:11 No.11229178 Report

Quoted By:

>>11223344
checked

Anonymous

Anonymous Mon 16 Dec 2019 02:18:36 No.11229368 Report

Quoted By:

To anyone who is familiar with subject:
Is it worth it to actually get into derived differential geometry? Does it strike you as something interesting or with a future?

Anonymous

Anonymous Mon 16 Dec 2019 04:23:47 No.11229575 Report

Quoted By: >>11230175

>>11221436

a sequence is a sequence of constant functions, undergrad

Anonymous

Anonymous Mon 16 Dec 2019 06:09:20 No.11229745 Report

Quoted By:

>>11228504
bump

Anonymous

Anonymous Mon 16 Dec 2019 06:21:57 No.11229760 Report

Quoted By:

anyone have a good resource for discrete mathematics? I want to study it before i go through knuths book for computing.
propositional logic, trees, graph theory, set theory, basic counting, proofs

Anonymous

Anonymous Mon 16 Dec 2019 06:53:14 No.11229807 Report

Quoted By:

>>11228504
You are finding a fourth degree polynomail. So the coefficient of x^4 can be any number; hence 'a' (not equal to zero) is that arbitrary coefficient.

Anonymous

Anonymous Mon 16 Dec 2019 12:38:50 No.11230175 Report

Quoted By:

>>11229575
yep, that's exactly what that anon was trying to say. my bad mr. senpai desu san

Anonymous

Anonymous Mon 16 Dec 2019 13:52:09 No.11230275 Report

Quoted By:

tfw too smoothbrained for proofs

Anonymous

Anonymous Mon 16 Dec 2019 16:39:18 No.11230533 Report

Quoted By: >>11230609 >>11230794 >>11232534

> group project for university
> go to the library with the group, many cool idea for the project, subject is graph theory (max-flow min-cut).
> they don't understand the proof even if they did more research than me
> we start planning how to organize tasks
> "guys, we could use git to share our work"
> they don't even know what is git...
> I set up an overleaf project for them with the basic structure of the document and share them the link
> they start adding random shit, useless commands, very big font, exclamation points and color everywhere
I hate normies

Anonymous

Anonymous Mon 16 Dec 2019 17:31:01 No.11230609 Report

Quoted By:

>>11230533
>using fucking git for a class presentation
It's not the normies anon, you're just a smug autist

Anonymous

Anonymous Mon 16 Dec 2019 17:42:46 No.11230625 Report

Quoted By: >>11230639

>the Riemann surface of $z^{1/2}$ has a physical and unphysical sheet
We must protect mathematics from physicists and their bullshit.

Anonymous

Anonymous Mon 16 Dec 2019 17:51:12 No.11230639 Report

Quoted By:

>>11230625
This

Anonymous

Anonymous Mon 16 Dec 2019 19:04:58 No.11230794 Report

Quoted By:

>>11230533
And that is why you always make sure to NEVER do a group project with normies.
This is absolutely vital.

Also, don't let them near typesetting. Do the document on your own, let them send you what they did and NEVER let them get in the position where they might edit your work, git is a very bad idea, just as overleaf.

Anonymous

Anonymous Mon 16 Dec 2019 20:13:04 No.11230947 Report

Quoted By: >>11231088

Can someone who isnt dumb as shit tell me how I can get an A in low level maths? I've suffered full on depression brainrot for like 4 years, I can't even get into B territory right now.

Anonymous

Anonymous Mon 16 Dec 2019 21:03:18 No.11231088 Report

Quoted By:

>>11230947
Everyone will tell you the same shit: study everyday, sleep well, exercise twice a week, wake up everyday at the same time, reduce masturbation to maximum 3 times a week (without porn), some meditation (10 min a day is a good start), get natural light if possible (walk outside for 15min and work near a window), space repetition (use Anki), do many exercises, choose good resources (just search the web for the best books on a subject), stop screens 1h before sleeping, good nutrition (more veggies, eggs and nuts), take small breaks when you study (it's stupid to study 6 hours without pause), try to be really interested in the subjects you study (it comes with time eventually), read the wikipedia page for a global view and the history of the subject, connect what you are learning with what you already know, take coffee or tea (one or two cups a day), reduce room temperature at night (better for sleep)...
I could continue this unordered list forever, just apply theses tips and it will help.

Anonymous

Anonymous Mon 16 Dec 2019 21:10:57 No.11231099 Report

Quoted By:

>>11226381
Apostol calculus book 1

Anonymous

Anonymous Mon 16 Dec 2019 21:17:21 No.11231115 Report

Quoted By:

>>11221160
By recapping your highschool knowledge?

Anonymous

Anonymous Mon 16 Dec 2019 22:16:33 No.11231287 Report

Quoted By:

Do conjugates of functions have the same derivatives?
I'm doing QM shit and I have int Psi dPsi*

Anonymous

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Anonymous Mon 16 Dec 2019 23:46:33 No.11231464 Report

Quoted By: >>11231508 >>11231510 >>11231576

Anonymous

Anonymous Mon 16 Dec 2019 23:59:03 No.11231497 Report

Quoted By:

>>11216697
Are you interested in TDA?

Anonymous

Anonymous Tue 17 Dec 2019 00:07:41 No.11231508 Report

Quoted By:

>>11231464
I actually chuckled at a wojak, kill me

Anonymous

Anonymous Tue 17 Dec 2019 00:08:45 No.11231510 Report

Quoted By:

>>11231464
peak coom meme fren

Anonymous

Anonymous Tue 17 Dec 2019 00:14:05 No.11231527 Report

Quoted By:

Where can I find solutions to Jiri Lebl's Basic Analysis?

Anonymous

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Anonymous Tue 17 Dec 2019 00:26:02 No.11231576 Report

Quoted By:

>>11231464
Honestly lad.

Anonymous

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Anonymous Tue 17 Dec 2019 01:43:51 No.11231745 Report

Quoted By: >>11231753 >>11232559

Is there a quick way to solve these without factoring?

Anonymous

Anonymous Tue 17 Dec 2019 01:47:37 No.11231753 Report

Quoted By:

>>11231745
>>>/sci/sqt/

Anonymous

Anonymous Tue 17 Dec 2019 01:54:55 No.11231765 Report

Quoted By:

I'm reading my QM book during the break to prepare for next semester, and I'm having some trouble with transforming probablity distributions.
The problem involves a needle on a spedometer that can freely move between 0 and pi radians. The angle is uniformly distributed, so P(theta)=1/pi between 0 and pi.
That part I get. However, the problem then asks me to find the probability distribution of the length of the shadow of the needle as if there was a light above it. I know that the length r=cos(theta). How would I get P(r) from P(theta)?

Anonymous

Anonymous Tue 17 Dec 2019 07:41:02 No.11232534 Report

Quoted By:

>>11230533
max-flow min-cut is trivial. what is there to present on?

Anonymous

Anonymous Tue 17 Dec 2019 07:51:05 No.11232559 Report

Quoted By:

>>11231745
Yes. Combine them.

Anonymous

Anonymous Tue 17 Dec 2019 13:41:40 No.11233099 Report

Quoted By: >>11233146 >>11233380

I'm pretty much a Math brainlet, but I've decided to apply myself. I've already looked at the guide in the sticky, but I want to gain a deep and solid understandig of the matter to the point of it becoming intuitive, so I feel like I should start even pre-undergrad and put in the work instead of jumping off of shitty, half-assed education.
Any recommendations for this in terms of books or courses?

Anonymous

Anonymous Tue 17 Dec 2019 14:08:44 No.11233146 Report

Quoted By:

>>11233099
i am also a math brainlet tradesman. even forgot some arithmetic lmao. basically just read /mg/ threads and you will absorb more knowledge than a petty "book" can teach you

Anonymous

Anonymous Tue 17 Dec 2019 16:53:40 No.11233380 Report

Quoted By:

>>11233099
You will not get a "deep and solid intuitive understanding" of something until you move past it and do something harder.

If your shit education is enough so that it's _possible_ for you to read a calculus book, you're only wasting your time re-doing high school. This idea that you have to do everything "properly" and be algebra Jesus before you start calculus and calculus Jesus before you start analysis... is impossible; it's just an excuse your brain uses to paralyze you into doing nothing.

Anonymous

Anonymous Wed 18 Dec 2019 02:23:15 No.11234618 Report

Quoted By:

>>11219972
i had that book for a discrete math class and desu i wouldn’t recommend it. It is extremely long winded and explained many concepts in a weird and unintuitive way, making them seem way more confusing than they actually were. I’d recommend just seeing what topics you need to understand and using another book instead. I used Book of Proof and How to Prove it and both are more concise and the explanations are more clear in my opinion.

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