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

[Anonymous No.11213806]

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 No.11213866]

[Anonymous No.11213897]

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

[Anonymous No.11214194]

[Anonymous No.11214226]

motion to abandon thread

[Anonymous No.11214230]

Threadly reminder to work with physicists.

[Anonymous No.11214648]

>>11214226
Motion denied.

[Anonymous No.11214859]

>>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 No.11214915]

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

[Anonymous No.11215327]

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

[Anonymous No.11215602]

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

[Anonymous No.11215631]

>>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 No.11215662]

>>11215631
these things fail.

[Anonymous No.11215734]

>>11215662
then you can try doing various things in [math]\mathbb{Q}(\sqrt{223})[/math] or in [math]\mathbb{Z}(\sqrt{223})[/math], 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 [math](x - y\sqrt{223})(x + y\sqrt{223}) = 1[/math]
- suppose that [math](a - b\sqrt{223})(a + b \sqrt{223}) = -3[/math]
- then you can obtain other solutions by taking [math](a - b\sqrt{223})(x - y\sqrt{223})^k[/math] for any [math]k \in \mathbb{Z}[/math]
- this way you can prove that if solution exists, then there exists a solution wit [math]|a|, |b| < C[/math] 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 No.11215773]

so subtraction doesn't exist

[Anonymous No.11215776]

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

[Anonymous No.11215850]

>>11213897
We must produce more.

[Anonymous No.11215869]

>>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 No.11215885]

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

[Anonymous No.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? 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 No.11216061]

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

[Anonymous No.11216176]

>>11216115

[Anonymous No.11216326]

Which books explains why iteration method works?

[Anonymous No.11216354]

>>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 No.11216355]

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 No.11216373]

>>11216355
Both.

[Anonymous No.11216375]

>>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 No.11216402]

>>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 No.11216476]

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 No.11216488]

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

[Anonymous No.11216510]

>>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 No.11216535]

>>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 No.11216540]

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

[Anonymous No.11216697]

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

[Anonymous No.11216720]

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

[Anonymous No.11216723]

>>11216720
meant for >>11216697

[Anonymous No.11216730]

>>11216697
Found it lol

[Anonymous No.11216796]

>>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 No.11216821]

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

[Anonymous No.11216920]

>>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 No.11216970]

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 No.11216998]

>>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 No.11217023]

>>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 No.11217268]

>>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 No.11217609]

>>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 No.11217684]

>>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 No.11217696]

>>11216821
Karatzas and Shreve
Durrett
Rogers and Williams

[Anonymous No.11217704]

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

[Anonymous No.11217708]

>>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 No.11217728]

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

[Anonymous No.11217734]

>>11217728
you too:
>>11217268

[Anonymous No.11217745]

>>11215327

Anabelian geometry

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

[Anonymous No.11217753]

>>11213806
oh look, a scientist with honor

[Anonymous No.11217757]

>>11216796
learn to LaTeX or lurk moar

[Anonymous No.11217790]

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

[Anonymous No.11217807]

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

[Anonymous No.11217810]

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

[Anonymous No.11217941]

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

[Anonymous No.11218129]

>>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 No.11218162]

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

[Anonymous No.11218169]

>>11218129
Same person, say I have
[math]
\begin{bmatrix}
1 & 3 & -5
\end{bmatrix}
\begin{bmatrix}
4 \\ -2 \\ -1
\end{bmatrix} = 3
[/math]
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 No.11218234]

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

[Anonymous No.11218269]

>>11218234

row * column vector is scalar

column * row vector is a matrix

[Anonymous No.11218276]

>>11218234

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

[Anonymous No.11218289]

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

[Anonymous No.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?
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 No.11218453]

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

[Anonymous No.11218458]

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

[Anonymous No.11218463]

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

[Anonymous No.11218469]

is math more fun than being a retard?

[Anonymous No.11218472]

>>11218453

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

[Anonymous No.11218474]

>>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 No.11218478]

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

[Anonymous No.11218481]

>>11218474
wait, is science fun?

[Anonymous No.11218549]

>>11217023
Someone help a brainlet out pls

[Anonymous No.11218552]

>>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 No.11218553]

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

[Anonymous No.11218557]

>>11213806
>Acknowledgements

[Anonymous No.11218576]

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

[Anonymous No.11218586]

>>11218576

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

[Anonymous No.11218612]

>>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 No.11218792]

>>11216697
>persistent homology
nice meme

[Anonymous No.11218798]

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

[Anonymous No.11218815]

whatever came of this

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

[Anonymous No.11218854]

>>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 No.11219009]

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 No.11219019]

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

[Anonymous No.11219117]

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 No.11219169]

>>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 No.11219218]

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

[Anonymous No.11219288]

>>11219218
assume [math]x_{n-1} > x_{n-2}[/math], show [math]x_{n} > x_{n-1}[/math]
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 [math] (x_{n-1}+2)/3 > (x_{n-2}+2)/3 [/math] , which you can substitute [math]x_{n}[/math] and [math]x_{n-1}[/math] in for

[Anonymous No.11219289]

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

[Anonymous No.11219313]

>>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 No.11219315]

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

[Anonymous No.11219324]

>>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 No.11219337]

>>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 No.11219351]

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

[Anonymous No.11219382]

>>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 No.11219492]

>>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 No.11219498]

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

[Anonymous No.11219520]

>>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 No.11219538]

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

[Anonymous No.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.
Looking mostly for OCW recommendations. Yes, there is the sticky, but I like active recommendations more.

[Anonymous No.11219577]

>>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 No.11219588]

>>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 No.11219596]

>>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 No.11219597]

>>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 No.11219792]

>>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 No.11219963]

>>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 No.11219969]

>>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 No.11219970]

>>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 No.11219972]

>>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 No.11219974]

>>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" - P(...) No.11220274]

>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 No.11220286]

>>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 No.11220301]

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

[Anonymous No.11220302]

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

[Anonymous No.11220308]

>>11220301

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

[Anonymous No.11220311]

>>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 [math]x_{n}\geq x_{n-1}[/math] holds, I seek to prove that [math]x_{n+1}\geq x_n[/math]. I expand the left side using the recurrence relation to get [math]\frac{x_{n+t}^2+2}{3}\geq x_n[/math]. Rearranging this, I can get the polynomial expression [math](x_n - 1)(x_n - 2)\geq 0[/math]. This holds if [math]x_n\geq 2[/math] or [math]x_n\leq 1[/math]. Since x0 and x1 are both <= 1, the relation holds.

Is this enough?

[Anonymous No.11220355]

>>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 No.11220365]

>>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 No.11220376]

>>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 No.11220463]

>>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 No.11220537]

>>11220311
No, not rigorous enough

[Anonymous No.11220555]

>>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 No.11220897]

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

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

[Anonymous No.11220900]

>>11220897
4th semester

[Anonymous No.11220991]

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

[Anonymous No.11221097]

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

[Anonymous No.11221104]

>>11218798
Shut the fuck up faggot

[Anonymous No.11221111]

>>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 No.11221157]

>>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 No.11221160]

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

[Anonymous No.11221164]

>>11220897
When I dropped out

[Anonymous No.11221169]

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

[Anonymous No.11221172]

>>11213806
What field is Japan especially good at?

[Anonymous No.11221183]

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

[Anonymous No.11221196]

>>11221160
it's trivial

[Anonymous No.11221199]

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

[Anonymous No.11221202]

>>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 No.11221233]

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

[Anonymous No.11221243]

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

[Anonymous No.11221419]

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

[Anonymous No.11221436]

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

[Anonymous No.11221443]

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

[Anonymous No.11221456]

>>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 No.11221468]

>>11217268
this is bait

[Anonymous No.11221472]

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

feels good

[Anonymous No.11221491]

>>11217268

[Anonymous No.11221900]

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

[Anonymous No.11221917]

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 No.11221989]

>>11218557
thank you based zuki

[Anonymous No.11221992]

>>11220274
slick proofs, Rudin

[Anonymous No.11222193]

>>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 No.11222208]

>>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 No.11222369]

>>11221900
...what?

[Anonymous No.11222427]

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

[Anonymous No.11222664]

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

[Anonymous No.11222672]

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

[Anonymous No.11222750]

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

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 No.11222757]

>>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 No.11222786]

>>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 No.11222838]

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

I actually like Trudeau intro to graph theory.

[Anonymous No.11222928]

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

[Anonymous No.11222965]

Is category theory worth learning for someone into discrete mathematics?

[Anonymous No.11223011]

>>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 No.11223017]

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

[Anonymous No.11223028]

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

[Anonymous No.11223040]

>>11222965
No

[Anonymous No.11223042]

>>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 No.11223048]

>>11220302
lmfao, great image. Keep em coming

[Anonymous No.11223049]

>>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 No.11223060]

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

[Anonymous No.11223064]

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

[Anonymous No.11223069]

>>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 No.11223070]

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

[Anonymous No.11223090]

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

[Anonymous No.11223095]

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

[Anonymous No.11223118]

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

[Anonymous No.11223149]

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 No.11223159]

>>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 No.11223164]

How many IQ points do I need to into Topology?

[Anonymous No.11223184]

>>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 No.11223186]

>>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 No.11223195]

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

[Anonymous No.11223196]

>>11223184
Looks like fun ngl

[Anonymous No.11223199]

>>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 No.11223215]

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 No.11223227]

>>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 No.11223242]

>>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 No.11223244]

What do you guys think of mathgreforums.com?

[Anonymous No.11223245]

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

[Anonymous No.11223256]

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 No.11223259]

>>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 No.11223265]

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

[Anonymous No.11223268]

>>11223227
>>11223242

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

[Anonymous No.11223273]

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

[Anonymous No.11223286]

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

[Anonymous No.11223321]

>>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 [math] { \mathbb Q } \to \{ 0, 1 \} [/math] defining a cut. E.g.

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

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 [math] f : { \mathbb Q } \to \{ 0, 1 \} [/math] 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 No.11223325]

>>11223321
the function [math] f [/math] ought to correspond to the real [math] \sqrt{7} [/math] btw.

[Anonymous No.11223333]

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

[Anonymous No.11223337]

>>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 No.11223344]

>>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 No.11223346]

>>11223344
nice get

[Anonymous No.11223350]

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

[Anonymous No.11223353]

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

[Anonymous No.11223363]

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

[Anonymous No.11223400]

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

So is this your way of saying no?

[Anonymous No.11223515]

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

[Anonymous No.11223518]

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

[Anonymous No.11223523]

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

[Anonymous No.11223540]

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

[Anonymous No.11223541]

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 No.11223552]

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 No.11223560]

>>11223540
Sqrt(x) has two solutions.

[Anonymous No.11223566]

>>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 No.11223580]

>>11223560
Not a function

[Anonymous No.11223606]

>>11223560
true and completely irrelevant

[Anonymous No.11223662]

>>11223560
not simultaneously

[Anonymous No.11223687]

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

[Anonymous No.11223690]

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

[Anonymous No.11223697]

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

[Anonymous No.11223700]

>>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 No.11223706]

easy to tell when highschool gets out.

[Anonymous No.11223710]

>>11223518
No.
>>11223515
Based

[Anonymous No.11223797]

>>11223697
Yes.

[Anonymous No.11223798]

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

[Anonymous No.11223806]

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

[Anonymous No.11223821]

>>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 No.11223832]

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

[Anonymous No.11223854]

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 No.11224088]

>>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 No.11224368]

This thread is shit. Post true/false questions.

[Anonymous No.11224369]

>>11213806

[Solivagus/ECHS No.11224379]

>>11213806
はい、望月。 言語、ストローク、放射状を忘れません。 私は、幾何学的な揺りかごをもう一度たたかないように、あなたが認めるべきだったことです。

成長し、移植片、ゆっくりクラフト、切断棒

>これらのロバ馬は私が無限無数の瞬間を侮辱することができます

[Anonymous No.11224689]

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

[Anonymous No.11224754]

>>11219576
Read up school textbooks by Gelfand

[Anonymous No.11224761]

>>11224379
>これらのロバ馬は私が無限無数の瞬間を侮辱することができます

>I can offend these mules for infinite countless instants

Wft is this guy a bot or not?

[Solivagus/ECHS No.11224764]

>>11224761
私は底ではない、私はケンカゴマコマです

[Anonymous No.11224837]

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

[Solivagus/ECHS No.11224843]

>>11224837
ユーザー推定。 従事紅葉季節嗜好

[Anonymous No.11225481]

Woah broah

[Anonymous No.11225525]

>>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 No.11225867]

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 No.11225882]

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

[Anonymous No.11226100]

How much of this image is a meme?

[Anonymous No.11226164]

>>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 No.11226261]

>>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 No.11226335]

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

[Anonymous No.11226381]

>>11215773
which book is this?

[Anonymous No.11226412]

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 No.11226415]

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

[Anonymous No.11226541]

>>11226412
Yes.
Read this

[Anonymous No.11226555]

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 No.11226658]

Please help.

[Anonymous No.11227158]

SOMEBODY HELP

[Anonymous No.11227199]

>>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 No.11227209]

>>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 No.11227302]

>>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 No.11227329]

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

[Anonymous No.11227642]

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 No.11227724]

>>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 No.11227737]

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

[Anonymous No.11227955]

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

[Anonymous No.11227968]

>>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 No.11227980]

>>11227968
thank you

[Anonymous No.11227997]

>>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 No.11228008]

>>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 No.11228055]

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 No.11228110]

>>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 No.11228111]

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 No.11228120]

>>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 No.11228209]

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

[Anonymous No.11228228]

We start out with an affine variety [math]A^n[/math] 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 [math]\tau = \{ a \in R ~ such ~ that I(V(f))=I(V(f+ a L_f)) \} [/math] as f goes through all polynomials in [math]R[x_1, ..., x_n[/math], and [math]L_f[/math] is the leading term or some appropriately chosen polynomial.
Does a construction like this show up anywhere in ring theory or algebraic geometry?

[Anonymous No.11228261]

>>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 No.11228274]

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

[Anonymous No.11228316]

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

[Anonymous No.11228323]

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 No.11228404]

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

[Anonymous No.11228504]

where the fuck did "a" come from?

[Anonymous No.11228529]

>>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 No.11228543]

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

[Anonymous No.11228544]

>>11227642
You betcha!

[Anonymous No.11228547]

>>11228543
this is freshman highschool math in America

[Anonymous No.11228579]

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

[Anonymous No.11228597]

>>11227199
>>11227209
>>11227302
Thanks

[Anonymous No.11228645]

>>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 No.11229178]

>>11223344
checked

[Anonymous No.11229368]

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 No.11229575]

>>11221436

a sequence is a sequence of constant functions, undergrad

[Anonymous No.11229745]

>>11228504
bump

[Anonymous No.11229760]

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 No.11229807]

>>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 No.11230175]

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

[Anonymous No.11230275]

tfw too smoothbrained for proofs

[Anonymous No.11230533]

> 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 No.11230609]

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

[Anonymous No.11230625]

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

[Anonymous No.11230639]

>>11230625
This

[Anonymous No.11230794]

>>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 No.11230947]

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 No.11231088]

>>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 No.11231099]

>>11226381
Apostol calculus book 1

[Anonymous No.11231115]

>>11221160
By recapping your highschool knowledge?

[Anonymous No.11231287]

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

[Anonymous No.11231464]

[Anonymous No.11231497]

>>11216697
Are you interested in TDA?

[Anonymous No.11231508]

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

[Anonymous No.11231510]

>>11231464
peak coom meme fren

[Anonymous No.11231527]

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

[Anonymous No.11231576]

>>11231464
Honestly lad.

[Anonymous No.11231745]

Is there a quick way to solve these without factoring?

[Anonymous No.11231753]

>>11231745
>>>/sci/sqt/

[Anonymous No.11231765]

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 No.11232534]

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

[Anonymous No.11232559]

>>11231745
Yes. Combine them.

[Anonymous No.11233099]

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 No.11233146]

>>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 No.11233380]

>>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 No.11234618]

>>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.