/sci/ - Science & Math

Is mathematics worthwhile?

What's the best intro to Number Theory?

>>11556333
>What's the best intro to Number Theory?

How much time would it take in general for someone to read and do the exercises of the following books:
>Set Theory, Jech
>Categories for the Working Mathematician, Mac lane
>A Mathematical Introduction to Logic, Enderton
>Linear Algebra Done Right, Axler
>Real Mathematical Analysis, Pugh
>Complex Analysis, Kodaira
>Differential Geometry of Curves and Surfaces, Do Carmo
>Differential Geometry, Tu
>An Introduction to Manifolds, Tu
>Smooth Manifolds, Lee
>Topological Manifolds, Lee
>Introduction to Riemannian Manifolds, Lee
>Homotopical Topology, Fuchs-Fomenko
>Algebra: Chapter 0, Aluffi
>Commutative Algebra, Eisenbud
>Basic Algebraic Geometry I and II, Shafarevich
>Complex Algebraic Geometry, Kollár
>Lie Groups, Lie Algebras and Representations, Hall
>Quantum Theory for Mathematicians, Hall
>Quantum Mechanics, Gottfried
>The Quantum Theory of Fields, Weinberg
>Several Complex Variables, Grauert

?

>>11556354
>How much time would it take in general for someone to read and do the exercises of the following books:
>>Set Theory, Jech
>>Categories for the Working Mathematician, Mac lane
>>A Mathematical Introduction to Logic, Enderton
>>Linear Algebra Done Right, Axler
>>Real Mathematical Analysis, Pugh
>>Complex Analysis, Kodaira
>>Differential Geometry of Curves and Surfaces, Do Carmo
>>Differential Geometry, Tu
>>An Introduction to Manifolds, Tu
>>Smooth Manifolds, Lee
>>Topological Manifolds, Lee
>>Introduction to Riemannian Manifolds, Lee
>>Homotopical Topology, Fuchs-Fomenko
>>Algebra: Chapter 0, Aluffi
>>Commutative Algebra, Eisenbud
>>Basic Algebraic Geometry I and II, Shafarevich
>>Complex Algebraic Geometry, Kollár
>>Lie Groups, Lie Algebras and Representations, Hall
>>Quantum Theory for Mathematicians, Hall
>>Quantum Mechanics, Gottfried
>>The Quantum Theory of Fields, Weinberg
>>Several Complex Variables, Grauert
>?
Why don't you try it and find out?

>>11556354
Hundreds of thousands of years.

>>11556354
Forgot:
>Special Relativity, Woodhouse
>General Relativity, Woodhouse
>Riemann Surfaces, Donaldson

>>11556287
Apostol or Kline? Which do you recommend /mg/? A guy in the EE thread told me that I should quit wasting my time with Apostol and just use Kline. I took a look at it but it seems a lot lengthier and verbose. I already took a course in calculus so I am not completely unfamiliar with the methods, but I want to git gud. What should I do?

>>11556361
Apostol is the jack of all trades, Courant is the best calculus book ever made if you have the time to work through it. Spivak is overrated. All others are mediocre at best.

>>11556354
you could have read one or two of them in the time you spend making this giant-ass list you're never going to read

>>11556403
25 books is a gigantic list? Some books have 100+ others as references...

My main objective is to go through all those in 4~5 years, I just wanted to know if others believe it's doable.

>>11556422
Should take hundreds of thousands of years.

>>11556403
> gigantic list
found the undergraduate student

>>11556354
>read and do the all exercises in Jech
It won't happen, most, if not all researchers in set theory specialize way before they work through it. Jech is a reference text, each chapter in most of the second and third section even has their own textbook on the topic.

Are there any [math]\omega[/math]-ranked von Neumann sets that have a finite cardinality? In particular, does something like the following exist in ZFC: [math]\{\phi, \{\phi, \{\phi, ..., \{\phi\}\}\}\}[/math] (basically a version of [math]\omega[/math] where the zero is [math]\{\phi\}[/math] and the successor function is [math]S(x) = \{\phi, x\}[/math]), which would have a cardinality of 2 but a rank of [math]\omega[/math].

>>11556354
3-4 years?
Seems somewhat equivalent to a focused Bachelor degree...

>>11556370
>he hasn't read either Granville or Piskunov

>>11556568
I see, I thought Jech was an intro to set theory, would you recommend me a good book for the subject then?

>>11556287
How many sheets have you written today doing folding@home?

>>11557397
None. Should I? This is the first time I heard of the whole thing.

The best boards:

/sci/>/lit/>/g/>/a/>/out/

An anon in the stupid question thread said there's no good book on relativity. Is that true? That makes me sad. Why is there no good book that just walks through the theory, explains the concepts with pictures and the mathematics, and has exercises at the end of each chapter in order to instill the concepts? There is nothing about relativity that renders this impossible.

>>11557457
There are two excellent books on relativity:
Special Relativity by Woodhouse
General Relativity by Woodhouse

>>11557450
Surely you mean /lit/ > /sci/ > /fa/ > /a/ > /s4s/.

Extreme brainlet question, but why do averages exist? Like, why is it that if you roll a six sided dice, you tend to come up with 3-4 more often than other numbers? If input is randomized, why does output skew towards the middle?

>>11557518
The expected value is not the same as the most probable one. Suppose you had an ideal dice with six sides. After six million rolls the most probable distribution of the sides is that each side has faced up roughly one million times. However, the average outcome in this case will seem like just rolling 3 roughly half of the times and 4 in the case it's not 3.

>>11557457
there are a lot of books that do exactly that.

spacetime and geometry by carrol, for instance, is a very easy and gentle introduction to the topic.

>>11557450
>>11557512
>browsing boards
>not browsing selected generals

>>11556644
I don't see how you'd think this doesn't work. Take and two set, then their pair exists.

>>11557518
You can motivate "best guess" estimators (e.g. the average) in any finite combinatorical case by going through all possible outcomes and seeing what would have been the best guess.

Consider a (weakly) closed set [math]X[/math] in a Hilbert space, and define [math]\overline{\mathrm{co}}(X)[/math] to be the weak closure of its convex hull, with
[math]\mathrm{co}(X) = \{ \sum_{i=1}^n a_i x_i : a_i \geq 0,\, \sum_{i=1}^n a_i = 1,\, x_i \in X \}[/math].

Can any element [math]y \in \overline{\mathrm{co}}(X)[/math] be written as [math]y = \sum_{i=1}^{\infty} a_i x_i[/math] for some choice of [math]x_i \in X[/math] and nonnegative [math]a_i[/math] with [math]\sum_{i=1}^{\infty} a_i = 1[/math]?

I remember reading somewhere that this is not possible in a general Banach space, i.e. there will not always exist a countable decomposition of any [math]y \in \overline{\mathrm{co}}(X)[/math] into elements of [math]X[/math], but one needs to consider more general (continuous) measures. Not sure if this can be done in a Hilbert space?

>>11556644
Stop doing Jewish math. You're wasting your time

>>11557770

Yes, but can you do it an infinite number of times? The Axiom of Infinity only postulates (inductive) sets of infinite sizes, not sets with an infinite depth. [math]\omega[/math] has an infinite depth because of its infinite size (its members have all possible finite depths).

What is the most comprehensive mathematics dictionary/reference book/encyclopedia?

>>11558099
Princeton companion to mathematics

>>11557362
>I thought Jech was an intro to set theory
lmao what the fuck
why even spend all that time making a list if you have literally no clue what you're putting on it?

>>11557828
All maths is ours now, goy. What are you gonna do about it?

>>11558099
https://www.encyclopediaofmath.org/index.php/Main_Page

>>11558109
Making a booklist is the beginnning of every study plan.

>>11558134
no, opening a book and solving a problem is

>>11557518
What your saying isn’t true, in case that wasn’t clear.

>>11558134
Yes it is. And if your goal is to use that study plan to actually learn something, your booklist is exactly one book long.
That example illustrates the (second) biggest problem with trying to make "book lists", after the obvious fact that you spend that time not reading math. He's selecting books he's so massively underqualified to read he can't even tell the difference between an introduction and a reference for experts.

>>11558099
my diary desu

Just stop browsing for books and solve a Putnam problem instead.

>>11558194
>P*tnamfags

Can someone learn all the high school level math in 2 months or so? differential and integral calculus included.
I went to Med school for a year just because my family wanted but it bored me so I want to change career paths.

>>11558160
No, a good organization and research is the start of any decent study plan, spending a few minutes searching for good books to read in undergraduation and graduation is not at all a waste of time, you're mistaking it for procrastination which is indeed a big problem in modern society but it doesn't stem from creating lists. There's also nothing wrong in coming here asking for advices on which of those books are worthy, which is what that post was all about.

>>11558232
fuck off

Also, Jech does have an introductory book on set theory https://www.amazon.com/dp/0824779150

>>11558243
based

Terre used to be a website about simple finite groups. Anyone knows what happened to it? Is it archived anywherre?

>>11558232
Why did you have to post that webm? Now I'm sad and lonely and don't know what to do to cope besides rotting my brain further with a coom.

>>11558243
y u mad son? I'm only asking a simple question. I know Biology, not maths.
>>11558285
To get attention in the /fit/ fashion, sorry brah

>>11558292
>To get attention in the /fit/ fashion, sorry brah
Easy to be sorry after the fact, much harder to be considerate and not commit the transgression in the first place. But anyways, if you're smart and diligent (you probably are if you got to med school), then it shouldn't be too much of an issue a priori, but maybe my perspective is very skewed from studying mathematics for too long now.

Ugh... Is it me or has /mg/ become very trashy these days?

>>11558237
>No, a good organization and research is the start of any decent study plan
You cannot have good organization and research 10,000 pages ahead of yourself. It's impossible. You are not capable of deciding whether or not you even want to read a representation theory book, let alone which representation theory book you want, if you haven't studied linear algebra yet. There is a reason you don't select all 40 courses you're going to take in uni during your first semester.
>There's also nothing wrong in coming here asking for advices on which of those books are worthy, which is what that post was all about.
That's not what the post was about at all. The only text contained there was "how long would it take me to read all these and do the exercises?" He was not asking for book recommendations, he just wants to impress people with his big-ass list of hard books he's totally going to get more than 20 pages into.

>>11558318
Was it ever not trashy or what? Besides, what are you doing to make it better besides posting retarded shit that begins with "Ugh..." like you're some passive-aggressive femoid.

>>11556354
>>Set Theory, Jech
Good
>>Categories for the Working Mathematician, Mac lane
Good, but I personally prefer Kawashiwa/Schapira 's book on category theory
>>Linear Algebra Done Right, Axler
It's okay for a book in English about linear algebra, but really not that great tbqh
>>Real Mathematical Analysis, Pugh
>>Complex Analysis, Kodaira
Read Rudin.
>>Differential Geometry of Curves and Surfaces, Do Carmo
Good book
>>Homotopical Topology, Fuchs-Fomenko
Good book
>>Algebra: Chapter 0, Aluffi
Never heard of this book, read Lang.
>>Commutative Algebra, Eisenbud
>>Basic Algebraic Geometry I and II, Shafarevich
>>Complex Algebraic Geometry, Kollár
Books in English about algebraic geometry are utter shit for the most part
>>Lie Groups, Lie Algebras and Representations, Hall
Don't know this book, but I would recommend Barry Simon's book.
>>Quantum Theory for Mathematicians, Hall
Good book
>>The Quantum Theory of Fields, Weinberg
Read Deligne's book instead

>>11558306
Thank for not getting butthurt like the clown that first replied to me.
>>11558325
Bet he talked about my Webm.

>>11558335
>It's okay for a book in English about linear algebra, but really not that great tbqh
What would a great LA book be?
>Books in English about algebraic geometry are utter shit for the most part
I can read in french and german as well, are there any better options in those languages?

>>11558323
You mad brainlet?

>>11558335
>Read Rudin.
Rudin is a meme.

>>11558364
Not a meme, just hard as fuck

>>11558254
ATLAS of Finite Group Representations? http://brauer.maths.qmul.ac.uk/Atlas/v3/
>>Read Rudin.
In my country we read Fichtenholz.

Dumb question, but what are some conditions to get [math] \| \nabla f_n\|_p \rightarrow \| \nabla f\|_p[/math] for Sobolev functions? For example what if [math] f_n \rightarrow f [/math] strongly in Lp and the sequence is bounded in the Sobolev norm. Could that be enough?

>>11558357
>What would a great LA book be?
If you're French, monier and griffone are good introductory books, and mansuy's book on reduction or gourdon's books are great as a follow up. Otherwise, Lang is good.
>I can read in french and german as well, are there any better options in those languages?
As an introductory book, Daniel perrin is good. Then, read Grothendieck.
I forgot Qing Liu's book, it's in English and quite good.
But if you don't even know linear algebra, why do you even want to learn algebraic geometry? It's like wanting to build a rocket but not knowing what a resistance is.

>>11558318
Some people are on lockdown and goin' crazy (OK, crazier).
Some people are on Easter break.

>>11558400
I know LA, I just want to further develop my abilities in it with a more advanced book.

>>11558400
Perrin's book is translated into English, isn't it? Or has he written multiple of them?

>>11558417
This book is gold

>>11558417
Oh, I didn't know. I just don't like translated books, I try to avoid them unless they're in a language I don't know like japanese

>>11558318
All the fucking attention whore weebs.

>>11558335
Lang is a meme.

>>11558463
No it's not. If you're reading it as your first algebra book, you might find it hard. But you aren't a stupid undergrad, are you?

>>11557786
It doesn't get any better in a Hilbert space.
Consider the Hilbert space [math]H = L^2[0, 1][/math], and define the functions [math]f_t := 1_{[0, t]}[/math], for [math]0 \leq t \leq 1[/math]. Let [math]X := \{f_t : 0 \leq t \leq 1 \}[/math].
[math]X[/math] is weakly closed, because if [math]f_{t_i} \rightarrow g[/math] weakly, then [math]t_i = \langle f_{t_i}, 1_{[0,1]} \rangle \rightarrow \langle g, 1_{[0, 1]} \rangle[/math].
Now,roughly speaking because formally the elements of H are defined up to measure zero, [math]\overline{co}(X)[/math] = functions f which are nonincreasing and [math]0 \leq f(0) \leq 1 [/math].
For example, [math]f(x) = 1 - x[/math] is in the [math]\overline{co}(X)[/math], but it's clearly not a countable sum of [math]f_x[/math]'s.

>>11558470
I'm an undergrad and my crazy professor is using Lang as the main text for the course, this shit shouldn't be allowed

>>11558486
My condolences. Also fuck off.

>>11558490
Tu est un merde

>>11558497
Moi je préfère le terme de bourbakiste.

>>11558392
It is enough for [math]f[/math] to saturate the Poincare inequality [math]|f|_p \leq |\nabla f|_p[/math]. These functions are discussed briefly here https://arxiv.org/abs/1202.2071.. This might be stronger than what you need however.

>>11558745
Prove that [math](A,+,\cdot)[/math] is a ring

What is the name of distribution with cumulative distribution function [math]a^{b^x},x\in\Re, 0<a,b<1[/math]

>>11559119
Definitely Hans or Jürgen. You can feel the Teutonic vibes.

>>11559119
If you toy with coefficents, you may turn it into Gumbel distribution, I guess (its 1:30 AM. I'm not thinking too clearly) https://en.wikipedia.org/wiki/Gumbel_distribution

>>11559130
Common, this is clearly a Lewdinsky-Assner type of name that you are expecting here. Maybe Fickey F.

>Be bong
>Go to school
>Fucked
After studying (read: rote-learning ad nauseum) medicine during the day, I want to study maths in the evening. And I mean real maths-maths, not garbage sixth-form maths. What's a good place or group of textbooks to start with learning university level maths after completion of old syllabus A-level maths with statistics (C1, C2, C3, C4, S1, and S2 edexcel)?
I don't want to waste money on books full of shit I already know or be completely stuck because I picked something too hard. End goal is pure maths for the sake of understanding the universe.

>>11559175
>What's a good place or group of textbooks to start with learning university level maths after completion of old syllabus A-level maths with statistics (C1, C2, C3, C4, S1, and S2 edexcel)?

>>11558318
Dilate.

>>11559275
Based.

which class should i take next semester?
>pde
>intro probability
>gr
>numerical analysis

>>11559324
pdes are based, but go with numerical analysis

>>11559324
>pde
Trash
>probability
Trash
>gr
Great
>numerical analysis
You can't go lower than that

>>11559346
>t. physishit
Remember to work with them anon

>>11559346
based this

>>11559175
Don't waste money on textbooks, most maths books are made freely available by their authors and those that aren't can be pirated really easily.

Start with linear algebra and real analysis. For linear algebra I like Linear Algebra Done Right (Axler) but some people here hate it. I didn't use a textbook for real analysis so I can't help you there.

From there learn some group/ring theory with Algebra (Artin) and analysis for metric spaces (again I don't have a textbook).

After this where you go depends on what you've been enjoying. If you've been enjoying algebra check out Galois theory, algebraic number theory, or algebraic geometry. If you've been enjoying analysis check out differential geometry,measure theory, or functional analysis.

Pointset topology is a waste of time beyond the basics, just learn it as you need it. Algebraic topology is a area which Hatcher is a good intro to.

>>11559362
>He doesn't feel pleasure by owning and collecting lots of academic books
Damn, your life must be pretty fucking boring

>>11556287
You can probably what is what by looking all the isomorphic but separately labeled neighborhoods of numbers that are X% of the way down the real number line.

>Fractional Distance: The Topology of the Real Number Line with Applications to the Riemann Hypothesis
>https://vixra.org/abs/1906.0237

>You can probably TELL what is what by looking AT all the isomorphic but separately labeled neighborhoods of numbers that are X% of the way down the real number line.

>>11559347
>physicist
>doesn't even know that solving EFE/optimizing EH action requires solving a bunch of tensor PDEs
>calls PDE trash while GR great
Yeah, not convinced.

>>11559447
Who says I don't know that, arrogant prick? I recognize the importance of PDEs for physics, but that doesn't make it any less trash and boring.

Also, you better keep in mind that when it comes to physics I'm far above you, so sit down and be humble, pal.

>>11559477
>harmonic maps, flatness of projective connections, HYM vortices etc are trash and boring
Haha ok kid, don't get uppity.

>>11559496
>Throwing a bunch of concepts to show off to brainlets here
Ara, how cute, can you even solve a simple GR problem like pic related? I'll give you 15 minutes, if you can't then that means I've won this discussion.

>>11559524
Hey Shitface, while gr is better than pde's, you're making me regret calling you based. This is /mg/, stop talking about physics, stop arguing with Yukari, and stop shitting up the thread with petty bullshit

leave the e-drama to Scholze's OnlyFans, people

Hi there, mathriends, I'm currently im the quest of learning french, but I need to read things in french in order to practice, do you guys know any french site about math or science that I could use? Much appreciated.

>>11559617
download a copy of EGA and get to work

>>11559628
>EGA
Which edition, Springer one or the original 1000+ pages one?

>>11558364
>>11558463
Why do people keep shit talking Rudin and Lang? Both are pretty good.
>>11559617
If you aren't learning via the natural method then you might as well quit now.

>>11559324
PDEs or numerical analysis, at least that is where I had the most fun.

Brainlet here, how the fuck do I prove this, either constructively or non-constructively?

If p,q are rational numbers with p<q, then there exists a rational number x such that p<x<q.

>>11558745
Good fucking lord. Why do you bother replying if you are clearly out of your wits?
You give some useless commentary and link to a TOTALLY unrelated paper about some physics stuff, I mean it doesn't even give a rigorous statement of the Poincare inequality, the wiki article is more helpful then that...

Aside from that I fail to see how a bound for the function by it's derivative would help you? But that is probably just me being retarded.

Seriously, what is wrong with you?

>>11560068
(p + q)/2

>>11559346
Just a garbage post. Fucking end yourself geometer scum.

>>11558392
I think you can get (for p not 0 or inf), at the very least, a sub sequence such that the derivatives converge weakly, that would be mainly Rellich's theorem and the weak compactness of the spaces.
But I am retarded, there might just be a very elementary way to deduce this.

>>11560070
This seems like a post that was written by a second-year undergraduate.

>>11560108
Why?

What makes me a "second year undergrad" by pointing out that it is stupid to answer a question you clearly have no clue about and appending a random physics paper which doesn't even *engage* with the question asked?

Also please show me how you would use Poincare inequalities to show the asked convergence, genuinely curious.

>>11559324
Out of those four, probabilities would probably be easiest but GR would be generally the least boring choice.

>>11559524
But can you even pronounce "Nordström"?

>>11560068
Non-constructively: suppose there is no [math]x\in \mathbb{Q}[/math] such that [math]p < x < q[/math]. There is then (see >>11560071) an irrational number [math]y[/math] between [math]p, q[/math], so we may define [math]r := \min \{ y-p, q-y\}[/math], and consider the neighbourhood [math]U := (y-r, y+r)[/math] of [math]y[/math], It follows that [math]U\cap \mathbb{Q} = \emptyset[/math], which contradicts the fact that [math]\overline{ \mathbb{Q}} = \mathbb{R}[/math]. Thus, there must be a rational number [math]x\in (p, q)[/math]. Please don't do it like this, though.

>>11559617
http://www.les-mathematiques.net/phorum/
I must warn you beforehand though, people there are actual mathematicians, unlike /mg/'s undergraduates

>>11558392
Ok so I kinda figured out what I wanted, or anyone intetested:
[math] \int |\nabla f|^p dx[/math] is weakly lower semicontinuous so weak convergence in [math] W^{1,p}[/math] gives me at least
[math]\| \nabla f\|_p \leq liminf \|f_n\|_p [/math] which is good enough for my purposes.

Okay, so on an informal level all possible mathematical theorems could be arranged in a directed graph, or they could be given a partial order, which indicates dependence.
If someone wants to research mathematics he has to first start high up in the graph and work himself down to deeper and deeper theorems: You have to start with learning sequences, series and babby analysis before you can do research in PDE for example.
Now with every year this graph grows both deeper and wider. But of the graph gets deeper then for any particularily "deep" strand one has tp study longer before being able to add new theorems.
By this heuristic it seems like the depth of mathematics known by humanity is fundamentally limited: If it takes 30 years of study to understand cutting edge mathematics at some point then progress will stagnate.
If this is accurate then only increasing the breadth is possible (new fields).

Do you think this view is accurate?

Oh my god why is [math]LaTeX[/math] so fucking sexy, every time I write something I can't stop looking at it.

>>11560425
one could say "proofs and concepts get simplified over time and a 100-page proof from 100 years ago can be now expressed on 2 pages"
but I think that your point still stands and it's already happening. The size and necessary background knowledge discourages a lot of people from going into, for example, algebraic geometry.

Why is this faggot so dramatic? He's not remotely connected to the field in question

>>11560425
>Do you think this view is accurate?
Not neccesarrily. Because historically it is totally invalid, it would be ridiculous to assume that Riemann, or anybody else at that time, did mathematics on "easy mode" since most of the complexity revealed to today's mathematicians was hidden from him.

What happens in actuality is that long and complex theories are over time getting simplified, which allows for new mathematicians to pick them up easily.
Just IMAGINE what an analysis textbook would look like if it tried to order things in a historically, it would be an insane mess and learning anything from it would be extremely hard.

That said, there is certainly *some* effect, but that usually causes specialization, which is exactly what we are seeing.

>>11560629
I also cringed reading this

>>11560629
Stop. Please stop. STOP

S T O P
T
O
P

Why are wh*tes so weak in math? It looks like all relevant math was invented by asians, middle easterns and blacks.

>>11560761
>It looks like all relevant math was invented by asians, middle easterns and blacks.
Where are you looking?

>>11560630
it's just hard to believe that this simplification process could continue indefinetly... I think most mathematicians would agree that any theory has some core of necessary understanding that can't be elegantly swept away.

>>11560770
Yes and certainly the fact that mathematics becomes more and more specialized is evidence of that, I just wanted to point out that there is also a reverse trend, which might of course be weaker.

>>11560762
I'm counting the years when all of the world was equally poor, after wh*tes got into the other continents they made sure to destroy them, therefore they monopolized almost all areas. But when the world was equally capable, wh*tes got destroyed by others races.

>>11560778
Fuck those wh*toid scum, they couldn't even ethnically cleanse the planet of niggers, bugmen and and sandniggers...
Truly the weakest race.

>>11560784
How does it feel like when the biggest wh*te university got completely destroyed by ramanujan?

>>11560793
>got completely destroyed by ramanujan?
Totally indifferent.

>>11560118
>For f that saturate the Poincare inequalities
>HOW DO U USE LE POINCARE INEQUALITIES LOSER?!
You don't. You use the fact that the functions SATURATE the inequalities, in which case it is PLAINLY OBVIOUS how to get your result.
I haven't clicked on the paper, but I can only imagine that it's perfectly relevant and that you're just indignantly misreading something.

>>11560815
>in which case it is PLAINLY OBVIOUS how to get your result.
Please be more specific.

>I haven't clicked on the paper
Do it and tell me how relevant it is PLEASE.

>>11560629
He's correct.
>>11560633
You make me cringe. You are cringy.
>>11560730
Stop.

>>11560823
yikes

>>11560118
>>11560819
What makes you look like a "second year undergrad" is that you haven't yet understood the anime avatar faggot just spams random nonsense in the hope that some brainlet will see a bunch of words and think he's smart. By even opening the paper you fucked up.

>>11560824
Seething

>>11560825
>What makes you look like a "second year undergrad" is that you haven't yet understood the anime avatar faggot just spams random nonsense in the hope that some brainlet will see a bunch of words and think he's smart. By even opening the paper you fucked up.
More likely that is my mild autism...

>>11560825
>he

>>11560819
Oh dear. You are right. That paper seems to be completely irrelevant. At best it gives one or two extremely specific conditions under which the Poincare inequality is saturated, and not even in a way that can prove your convergence.
Why do I bother trying to defend Yukari?
>>11560825
This is false. Yukari typically knows what he's talking about with respect to operator theory and differential geometry. I've found his discussions to be enlightening.
What have you contributed to this board?

>>11560840
Which Poincare inequality would be enough for ""my"" convergence?

Should I study mathematics?

Algebra makes me feel dumb. :(

>>11560849
Not Poincare inequality. Reverse poincare inequality with a constant. That's what saturating means.
It's bounding the norm of nabla f_n.

>>11560884
That picture is shockingly relevant, had a similar situation saturday night.
I don't know if it quite gave me a boner though.

>>11560888
>Reverse poincare inequality with a constant.
Ah, sure.

>That's what saturating means.
never heard that term to be honest, but I am not a native english speaker either...

>>11560900
No worries, as I mentioned you were right to be angry. The paper doesn't even state the condition explicitly, just in terms of typical energies for Burgers.
I appreciate that you're working on such subjects. Many seem to dislike them, even in this thread.

>>11560871
yes

>>11560409
Could you expand on it a little bit? What do you mean by weak lower semicontinuity of that integral, isn't it a constant? Or you mean the functional given by integration against the gradient of f?

>>11560990
Yea I mean the functional [math]f \mapsto \int |\nabla f|^p dx [/math]. We call [math] J[/math]sequentially weak lower semicontinuous when [math] f_n \rightharpoonup f \Rightarrow J(f) \leq \liminf J(f_n)[/math].
Why IS this functional weak lower semincontunuous? We had a theorem in our FA class that showed if we have a functional [math] \int F(x,u(x),\nabla u(x)) [/math] where F is nice enough and convex, then it is sequentially weak lower semicontinuous

>>11560512
What made algebraic geometry so "hardcore" anyways?

>>11561068
Ok, thank you!

Hey /sci/
I'm having a little difficulty identifying an expression concerning a cyclotomic field algebraically. Perhaps someone more algebraic minded than me can help.
Let's say we are looking at the field generated over Q by a primitive 30th root of unity.
Then we have the minimal polynomial f(x)x^8 + x^7 - x^5 - x^4 - x^3 + x + 1
The real part of any element is given by a field with minimal polynomial g(x)=x^4 + x^3 - 4*x^2 - 4*x + 1
You can see this because f(x)=x^4g(x+1/x)
But how do I pass from the first representation to the second? Let's say z is a root of f and r is a root of g. I can obviously say that Re(z)=r, and so deduce things like Re(z^29+1)=r+1, but how do I find something like Re(z^2) in terms of r?

>>11561068
Btw, could you provide the name of the book that you were using for your FA course, where I can find theorems like that?

>>11561075
I'm not sure if it's "hardcore" in any way. Fields where it's hopeless to find any good theory or structure can probably be said to be "harder."
In any case, algebraic geometry deals a lot with "modern" (post 1850, say) topology

>>11561114
ufile [dot] io/56vjebpl
you didn't get it here

>>11561183
Do you think this is a good first course in functional analysis?

>>11559324
What's gr?

>>11561191
Read rudin

>>11561191
no idea desu, it covers the most important stuff I suppose. Mostly stuff about Banach and Hilbert spaces and Sobolev spaces, Linear functionals. Calculus of Variations and Operators only appear very briefly at the very very end, so if you're looking for that it's maybe not the best course

>>11561194
Groups and rings

>>11561194
Gromov-Witten theory

>>11561196
>>11561199
Also should I care about FA if I only care about pure maths, especially number theory and topology?

>>11561194
GRaph theory

>>11561194
general relativity

>>11561217
Ih, what the fuck? You think FA is for applied mathematicians? It's very fucking important in algebraic topology

>>11561217
>Also should I care about FA if I only care about pure maths, especially number theory and topology?
No.

>>11561245
>Ih, what the fuck? You think FA is for applied mathematicians?
My impression that it was primarily used for quantum mechanics.
>It's very fucking important in algebraic topology
How so?

>>11561114
>where I can find theorems like that?
You don't *really* want to look into FA books for that, the main field which deals with questions *exactly* like this is Calculus of Variations, which obviously uses a lot FA.
But this theorem is one significant part in the existence theory for minimizes of first order functionals, which is almost certainly the reason you can find it even in an FA book.

>>11561245
>You think FA is for applied mathematicians?
If you consider people doing PDE theory "applied" then it DEFINITELY is.

>>11561258
>primarily used for quantum mechanics.
It is all over analysis. From PDEs to CoV, it finds it's place everywhere...

>>11561258
>>11561254
>>11561245
I think FA is a field of pure math on its own, although its popularity has been fading over time.
Things worth knowing in my opinion: what's a Banach/Hilbert space, all kinds of topology you can have there, notion of dual space, some basic results (riesz representation theorem, closed mapping theorem, inverse mapping theorem, banach-alaoglu).

>>11561183
Danke schön!
>>11561263
Any sugestions for a good book/good notes about Calculus of Variations?

>>11559324
It depends. If it's solving PDEs with the characteristic method and that stuff, then don't, it's fucking boring. If it's regularity theory, then sure. Numerical analysis is also a good choice. A lot of people don't like it, and I understand why, but it's still good to know. Intro to probability sounds ezpz, might be boring unless the prof is good, and GR done properly is hard as fuck, and otherwise it's a waste of time, just go watch PBS Space Time.
>>11559330
Based.
>>11559346
Cringe.
>>11559987
Based.
>>11560081
Gigabased, this coming from a geometer.

>>11559348
Oops, sorry, forgot to tell you you're cringe.
>>11559409
Completely and absolutely based. Reading them is optional, the point is to have shit on your shelves.

>>11559546
No, let him argue with Yukari. With any luck he'll fuck off and never return.

>>11559524
>Demonstrate that the Kerr-Newman solution contains closed timelike curves; are these accessible observers who are unwilling to traverse any event horizons?
They're not accessible, r-right?!? Also
>tfw no ara-ara onee-san who teaches you GR

>>11559972
*notices unorthodox learning method*
OwO what's this?

>>11561327
>Any sugestions for a good book/good notes about Calculus of Variations?
In my course my Professor provided Lecture notes, so I didn't really bother with reading into the literature.
Some of the books he seems to recommend are:
Calculus of Variations, Steffen
Direct Methods in the Calculus of Variations, Dacorogna

I would choose the first for a more general overview and the second for a more focused view on thing like the discussed problem (since the result used above is one of the main results of "the direct method").

>>11561361
Thank you!

>>11559972
>Why do people keep shit talking Rudin and Lang? Both are pretty good.
Lang was an AIDS denying retard

>>11560871
What do you want out of studying mathematics?

>>11561217
If you're doing analytical number theory, then yes. Otherwise, no.

>>11561392
reason to not kill myself and a gf

>>11561406
you will find neither of those

>>11561406
>reason to not kill myself and a gf
LOL

The first *maybe* the second *definitely* not.

>>11561406
LOL
The first *definitely not* the second *maybe*.

>>11561406
>reason to not kill myself
Stay away from symplectic stuff.

>>11561406
Mathematics may very well give you more reasons to kill yourself, and I honestly don't understand how you expect a gf out of the whole ordeal unless you do stuff that brings big shekels.

>>11561406
Can't guarantee the first thing will be obtained, but you will become the gf if you keep doing this stuff.

What are the programming languages that mathematicians should definitely learn?

Haskell?

>>11561075
More like who made it hardcore

>>11561492
Fortran, Cobol, Algol, B, and Python and R for the shekels.

>>11561492
python, [math] \LaTeX [/math]

>>11561494
which phenotype is that

>>11561497
>Fortran
Outdated
>Cobol
Uh, why would a mathematician learn Cobol?
>Algol
>B
Know nothing about those, why would a mathematician learn them?
>Python
That was obvious, like LaTeX, both of which I already know

>>11561492
Haskell/python/C

>>11561514
I can understand the first two, but why C?

>>11561512
>Outdated
Wrong.
>Uh, why would a mathematician learn Cobol?
Why wouldn't he?
>Know nothing about those, why would a mathematician learn them?
Yikes, and you consider yourself a mathematician?

>>11561492
Python
C++ if you care about applied stuff
R if you're interested in statistics

Haskellfags are the undergrad category theorists of programming

>>11561504
Hassidic/north Germanic Mix, apparently.

>>11561518
>but why C?
If you ever have to do something *really fast* you need to know how to use C or something similar to it.

>>11561504
Grothendieck was jomon

>>11561520
>Yikes, and you consider yourself a mathematician?
Nice reason.

>>11561512
that guy's obviously trolling--fortran is still used in some simulation software (eg in physics and some areas of medicine) and in some cases still has cutting-edge performance. cobol is not being written anymore but is still used in some major financial systems.

b and algol have been dead since at least the 70s.

>>11561492
> What are the programming languages that mathematicians should definitely learn?
imo this is kind of like a professional model asking what cameras and lenses they should learn how to use--it might be tenuously related to what you do but it's certainly not necessary. that said, if you want to learn how to do real things (not likely because you are a mathematician), learn python. if you want something more devoted to mathematics, learn how to use mathematica or take a look at a proof assistant (https://en.wikipedia.org/wiki/Proof_assistant)), especially Lean which has been getting a lot of hype recently. if you want a functional programming language with sophisticated types take a look at haskell or idris

>>11561548
>especially Lean which has been getting a lot of hype recently
Sadly it is guaranteed to turn into the most horrible pile of shit over next 5+ year.s

>>11561548
Yeah, I was memeing with the list. I did know that the first two had niche uses that could be profitable, especially the second, and the other two I mentioned because of their historical importance and the fact that they are dead. My actual list would be quite expected (Python, R, C/C++, etc...).

>>11561548
>mathematica
>not open source
Yikes, good luck with the government seeing everything you do

>>11561551
Why?

>>11561548
>that guy's obviously trolling--fortran is still used in some simulation software (eg in physics and some areas of medicine) and in some cases still has cutting-edge performance. cobol is not being written anymore but is still used in some major financial systems.
>b and algol have been dead since at least the 70s.

That's a nice rant, but if the question is
>What are the programming languages that mathematicians should definitely learn?
then how is defending those languages relevant?

>>11561612
Because that is the inevitable fate of everything Microsoft gets their hands upon.

Also, who of you reported me for racism. Seriously, that was obviously satire.
Yes, ban me again this is a mobile IP so you are literally wasting your time...

>>11561646
Were you the one posting some shit about 'becoming a nazi and killing jews' in one of the last few threads? If so, then it was me, not gonna let this general be destroyed by your kind, sorry.

which are some math fields that aren't dead?

>>11561688
Propositional logic

>>11561688
Dynamical systems
Symplectic geometry
Algebraic geometry
Algebraic topology
Complex geometry
Number theory
Category theory
Set theory
Logic

>>11561688
Complex Geometry
Algebraic Geometry
Symplectic Geometry
Algebraic Topology
Dynamical Systems
Foundations

What is /mg/'s opinion on Part 3 of the math tripos at Cambridge? It's supposed to be one of the best masyers programs in the world, if not the best. There's a course list online, and other than functional analysis it has a lot of stuff. Which courses are the most based? What should I do next year?
>>11561686
Anon, being a nazi and wanting to exterminate kikes is obviously based. You speak as if you're against this, which would make you a faggot. However, if you support this but don't want politics on /mg/ that's understandable. So which one is it?

>>11561686
No. I responded to >>11560778 with an equally obnoxious, but obviously over the top reply, because I was bored.

>'becoming a nazi and killing jews'
Not me. But did you know that *the* Teichmüller literally dropped his cushy office job to fight for Hitler?

>>11561688
International Mathematical Olympiad
Putnam Competition

>>11561704
Part 3 is beyond overrated.

>>11561704
>What is /mg/'s opinion on Part 3 of the math tripos at Cambridge?
Never heard about that, could you tell more about it?

>>11561708
How so? I know people who did their masters at Oxford and got flat out rejected for PhDs because they didn't do Part 3. I would imagine it's a pretty good program.

gram schmidt suck my balls

>>11561718
It gives you a lot of clout and that's it.

>>11561753
i think he's dead, can i suck your balls instead?

>>11561492
Haskell
A theorem prover (I like Lean)
Sage or Macaulay2
Something imperative (eg Python)

>he's never computed an groebner basis in his life

>>11561704
There's a Part IV

Looks pretty heavy to me, you must have a 130+IQ to be there from the looks of it

https://dec41.user.srcf.net/notes/

>>11561785
>Sage or Macaulay2
Why those?

>>11561785
>Sage or Macaulay2
>Something imperative (eg Python)
Sage IS Python

>>11561795
For computational algebraic geometry. Symbolic manipulation of polynomials, rings, etc.

There's a lot of stuff people learn non constructively in algebraic geometry that has constructive proofs and can be computed in practice.

>>11561811
Yeah, it's a glorified python library which makes it easier to learn. M2 syntax is disgusting (but I think M2 is more fully featured).

>>11561759
I'm sure it's still a good program though, right? Maybe not the best but there's still plenty of good courses to take.
>>11561792
>heavy
>130IQ
>thinking that Part 4 is anything more than a joke made by Dexter
Anon, I...

>>11561825
pic related

>>11561845

>>11561858
What's wrong anon? Never seen a polynomial before?

>>11557457
Because plenty of physicists aren't willing to use a modern an correct approach to tensors even if it's a really easy concept.

>>11561921
I still don't understand why my phisicist friends find tensors to be such a big deal.

>>11561844
Did you see the courses? That's not normal at all.

Let [math]C,D[/math] be two closed convex cones such that [math]C \cap D = \{0\}[/math]. Is [math]C + D = \{ c + d : c \in C, d \in D\}[/math] closed?

>>11561955
What have you tried?

What branch of mathematics is 'dynamical systems'?

prerequisites to HoTT?

>>11561967
homesexuality

>>11561967
Logic, set theory, category theory, algebraic topology

>>11561966
dynamical systems

>>11561966
It's its own field

>>11561984
hmm
that explains a lot, thanks.

R.I.P. John Conway https://en.wikipedia.org/wiki/John_Horton_Conway#Death

>>11561930
I find they require quotient space constructions that, on the set theoretical side, are horrendously blown up - not to say obstruse. Or, on the category theoretical side, require the notion of forgetful functor, that never really given a hands on definion. I don't know what it leads to if you let the latter merely be defined as any Set valued functor.

>>11562003
i wonder how many noteworthy people will be lost to the kung flu

>>11561949
Anon, they're graduate level courses. Of course they're gonna be very advanced. What I was making fun of was you implying that 130IQ was a high bar, which it definitely isn't.
Back to the topic, any recommendations for (pure maths) courses to take in part 3, or thoughts about the degree itself?

>>11562027
Kek, you've no idea hoe IQ works if you think 130 isn't high

>>11562003
I was thinking it was the John Conway who wrote 'functions of one complex variable', but it's just some random combinatoric guy, meh, but even then RIP.

>>11561966
It's the study of maps of the form [math]\phi: T\times M \to M[/math], where [math]T[/math] is an ordered monoid such as [math]\mathbb Z_{\geq 0}[/math], [math]\mathbb R_+[/math] or [math]\mathbb R[/math], and [math]M[/math] is a manifold (or more generally a non-empty set). Here [math]T[/math] is thought of as the "time" and [math]M[/math] as the "state space" of the system. This allows one to use analytical and geometric tools to study discrete systems such as
[eqn]f_{n+2} = f_{n+1} + f_n, ~~ f_1 = 1, ~~ f_0 = 0,[/eqn]
as well as continuous systems such as the ODE
[eqn]x' = f(t,x),[/eqn]
under an unified framework (even though discrete and continuous systems will have their own unique phenomena due to the fact that [math]\mathbb Z \neq \mathbb R[/math]).
https://en.wikipedia.org/wiki/Dynamical_system_(definition)

>>11562046
That's a very non-intuitive definition, someone outside the field won't understand anything. Basically Dynamical Systems is the study of the behavior of a model after a certain period of time. For instance, the growth of the population of some country is a dynamical system.

>>11562060
> /mg/
> a very non-intuitive definition
wew lad. More seriously, I agree.

Tell me about discrete mathematics.

>>11562033
Are you retarded? I'm over 130IQ tested and I'm still nowhere near as smart as the people at the top of my cohort. I'm fairly smart but they're genuinely scary.
132IQ is the entry level for Mensa, and a ton of these guys are pretty dumb.
Now back to the question on hand. Any opinions on Cambridge part 3 maths?

>>11562090
Telling you would be the opposite of discrete, no?

>>11562094
That just says you're not dedicated enough, you had the potential but it's probably all wasted. 130 IQ is fucking huge, but the growth if exponentially, so someone with 140IQ is not just a 'little' smarter than you, it's someone far smarter than you.

Even then, the average IQ here is probably 100, so you're still far above the average

>>11562060
>That's a very non-intuitive definition, someone outside the field won't understand anything
is it though? I think he gave a cool pitch. in fact, he made it out to be cooler than I think it is

>M is a manifold (or more generally a non-empty set)
lel

>>11562116
>me
>wasted potential
Nigger you don't know anything about me. I'm in a good spot academically with good achievements so far. Stop assuming shit.
130IQ is incomprehensibly tiny compared to the vast majority of PhD students at Cambridge or other top unis, so you saying "wow you need at least 130IQ to understand the material of these graduate courses" is not far off from saying "you need to not be clinically retarded". It's true but a stupid thing to point out, which is why I called you out on it.

>>11561704
It's good for a British university in math, which doesn't tell you much. I've seen some of the courses/exams and although this might apply to anglo-saxon universities as a whole, I feel like most of the questions in the exams are just memorization from the course, and the few that aren't don't really seem that difficult. Honestly my university which is considered average in my country had far better courses.

>tfw 150IQ in very good pre eng-school, decent grades in maths/physics, but absolutely no motivation to study from home
I just spent the last fucking month doing nothing because of quarantine, I don't get how people have motivation for anything other than wasting time playing some shit vidya that can run on my potato pc

>>11562147
Not him, but does you happen to know if your university has its courses uploaded somewhere?

>>11562139
I'm starting to doubt you're 130IQ, you're too far off reality to think that it's tiny, even in an institution like Cambridge, a 130IQ could easily graduate in any university, except maybe Harvard's honor class.

>>11562162
Only on a private platform available to the students.

>>11561690
Logic, in general but especially Algebraic and Categorical approach.

>>11561688
Also:

Applied shit like A.I modelling etc. But you know... not really math to me unless it is pure.

>>11562193
>not really math to me unless it is pure.
How old are you? Just curious...

>>11562116
This is retarded because while its true that the difference in probability density grows exponentially with a linear difference in IQ score from the mean, its not at all true that the difference in 'smartness' is exponential. Actually the IQ model basically assumes that a linear difference in IQ is a linear difference in intelligence. Thats the whole point.

>>11562164
I said it's tiny compared to PhD students, anon. For undergrads it's fairly good but still not amazing.
Being able to simply graduate from an institution is again a completely idiotic metric to use. You must be some 90IQ retard who dropped out from some really shitty third world college and thinks anyone who attends a half decent uni is a genius amd anyone with 120+ IQ is a literal god. You're the one who is really far off from reality.
>>11562147
>le epic butthurt Frenchfag still thinking their institutions are the only good ones in the world
Or maybe you're Russian or German, would make no difference. I've never seen anyone cope so hard before.
You're beyond delusional and completely mental if you think Cambridge is not top tier worldwide. The quality of students and inherent competition it fosters is unimaginable to people who attend average unis. Exams aren't the only relevant metric here, and even then they're graded completely against other students' scores. Look at example sheet questions instead of past exams, and also look at the actual material lectured. A lot of courses touch upon super recent research level stuff. Going off the top of my head I think at some point the course on Percolation covers a theorem only proven in 2016 or some shit like that.

>>11562224
>Complains about assuming stuff
>Assumes stuff he doesn't know anything about
>Passive-agressive language
>/pol/ slangs
>Xenophobia
>Can't understand that 130IQ is high anywhere in the world, even in Cambridge
>Can't into statistics
hum, yeah, not buying it... I estimate you to be around 95IQ.

>>11562266
>butthurt about my language
Where do you think we are?
>m-muh pol is bad!!1!
Kill yourself nigger.
>using the word xenophobia unironically
Pathetic soiboi cuck.
>repeatedly misreads my posts and twists my words to fit his argument
For the last time, I was talking about PHD STUDENTS ONLY when I said they're above 130IQ. You know, the roughly 20 of them accepted every year. I clearly stated this not to be the case for the roughly 250 undergrads each year.
>m-muh you're winning the argument and completely raping me so I'm gonna say you're a liar and low IQ
Think what you will. You are subhuman nigger trash beneath my existence. Kill yourself.

>>11562277
holy seetheoli

>>11562281
I got dubs so I won the argument. Cope harder faggot.

Who is the Griffith of mathematics?

For me it's Perelman
>Abandoned everything for the sake of proving the PC
>Has nothing left now

>>11562402
Richard Hamilton is Gatts

https://arxiv.org/abs/2004.05631

>>11556292
This man always makes a frightening amount of sense

>>11562813
So? Why are you posting this here? Trying to bait people here into being racist or some /pol/-shit? Get the fuck out retard.

>>11562830
its actually very interesting, just seems like an odd topic for a math thesis

Im an engineering major who's only done non-rigorous calc1-calc3 and differential equations. Im really fucking bored and figured I'd like to study some math the /mg/ way. Im pretty autistic about shapes/geometry and stuff so I was wondering if you guys had some learning path (resources and books, etc) for becoming very knowledgeable about geometry related topics. Bonus if it can help me figure out how to write my first proof or whatever. Thanks.

>>11562813
Just flipped through it a bit, it's actually very aesthetically pleasing, a lot of really good typesetting and diagrams, the layout is really nice too, same with most of the exposition. She could probably make some really good textbooks or mathematics books aimed at a broad audience that aren't shit tier.

>>11562954
Geometry is a big field, theres differential geometry, algebraic geometry, symplectic geometry, hyerbolic geometry, complex geometry and more. Which one do you want to get into?

>>11562955
Legit yeah, wow

>>11562954
Speaking of good books aimed at the broader public >>11562955 try Hilbert's geometry and the imagination. It'll give you a baby version of some more advance geometry if you pursue that path. Basically, you can go down the route of differential geometry, in which you'll see the tools of calculus generalized and abstracted, or you can do towards algebraic geometry, where things like projective and affine spaces will serve as a nice prelude (which you can learn about in Hilbert's book). I mean, technically there's also geometric measure theory, noncommutative geometry, complex geometry, stochastic/probabilistic geometry ala Schramm-Loewner and the Brownian map, combinatorial geometry, dynamical systems, tilings and number theory, and so on...but maybe stick with Hilbert's book for now and move onto those after you get a bit more math under your belt and you figure out what else you like.

>>11562954
Someone's gonna post the meme topics list with all the geometry garbage.

What do you do if you have to prove A so that your paper can publish but you have spent 4 months and your proof hasn't had any progress?
I feel so stressed out.

https://vocaroo.com/n4YqvKKTzw6

>>11562986
Either Leave it for a month or settle for a weaker result/paper. It's not the end of the world.

>>11562986
Depends, if I ever get stuck what I try doing is looking over papers that tackle similar topics and see if I can glean any ideas or techniques that may be useful. Other times, I try proving things in a limited context and then see if I can generalize the proof. Sometimes talking about the problem and what you're trying is super helpful, maybe you can type up the problem here and maybe that'll help just clear your mind. Worst comes to worst, if it isn't all that important to the paper, just leave it as a conjecture or something.

>>11562966
of the topics you listed, which would you say lies in the middle in terms of difficulty
>>11562970
Thanks I'll look into it
>>11562974
Im interested

>>11563021
>I'm interested
No, you're not.
I'm sure someone here has it saved.

>>11563021
Someone already fucking posted it this thread. Jesus.
>>11559275

>>11563091
>>11563021
It's in the thread already >>11559275

i wish i were so cool as you guys and knew so much maths

>>11563311
Start studying. No excuses.

>>11563319
im too stupid

>>11563330
That's an excuse. Wanna know something? I'm stupid too, but I can still study.

Do you guys use/though about using anki (or any other spaced repetition software/methods) for your math studies?

>>11562955
>very aesthetically pleasing, a lot of really good typesetting and diagrams, the layout is really nice too,
the typesetting and layout is just \usepackage{tufte-latex} and change link color to pink

>>11563344
here's an article about using Anki for maths http://cognitivemedium.com/srs-mathematics
there's more stuff by Michael Nielsen about Anki if you google, it's pretty thoughtful and well written

>>11563352
interesting, thank you

>>11563344
The only Anki I use is Lindqvist https://www.youtube.com/watch?v=UDUKBRDsOus

>>11563319
I'm gonna need a sauce on that img

>>11563352
Take that link outta here you fucking idiot, do you want every brainlet to become as capable as us? Fucks sake, you people never learn, somethings need to be hidden, you imbecile

>>11562046
>using the word monoid in the context of dynamical systems
I fucking hate mathematics.

>>11562224
>muh IQ
>even bothering to differentiate between 130 and 140
>muh Cambridge
>muh theorems from 2016 (lmao)
>muh quality of student
>muh competition (as if it were a good thing)
>muh exams (as if that system were only present in Cuntbridge)
>muh sheet questions
You're beyond fucking retarded, and any mathematician with a good sense of things would detest your attitude. I know because I know them. Holy shit and you didn't stop there.
>>11562277
>m-m-muh only 25 PPhDick diversity hires a year!!!

>>11563471
You could want to improve your ability to use the internet. Here you go, enjoy. https://mangadex.org/chapter/172355/37

>>11562407
Good meme, but actually Perelman tried to contact Hamilton about his project before he started it and got ignored.

>>11562820
That`s because he`s tremendously smart. That doesn't mean he's necessarily right, of course, and I do have my personal disagreements, but there's no denying he raises very poignant points about society and its future.

>>11562813
>The parallels are not coincidental, and a common blueprint is found in category theory.
THIS IS WHY I HATE WOMEN AND NIGGERS AND IN PARTICULAR NIGGRESSES IT SEEMED LIKE SUCH AN INTERESTING CONCEPT THAT WAS INPIRED BY QUANTUM PHYSICS WHICH IS ALWAYS A GOOD WAY TO DO MATHEMATICS AND SHE COMES WITH THIS SHIT REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE I JUST WANT PUSSY REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

>>11563494
You are braindead. All my points are valid and you should kill yourself.

>>11563333
Is not seeing the point of anything anymore also an excuse? What isn't an excuse, really?

>>11563513
>NOOO NOT THE HECKIN' CUNTBRIDGERINO
>NOT MY IQ NOOOO
>YOU CAN'T JUST POINT OUT HOW WRONG I AM IN SUCH A DERISIVE MANNER! I HAVE TO BE ABLE TO CONCEDE WHILE STILL SAVING FACE AND PRETENDING I WAS RIGHT ALL ALONG NOOOO!

>>11563516
>what isn't an excuse
That's irrelevant. What is relevant, though, is that no excuses were allowed. Study or give up, but don't cry about not knowing stuff if you don't even try.

(11563523)
Thanks for outing yourself as a plebbitor retard. You are now dismissed, and have been granted permission to terminate your pathetic, sad existence.

>>11563529
Oh wow, sorry Mr. Anonymous, I didn't I was talking with 4chan himself in all his 150 kilograms of glory. By the way, bringing Reddit up proves you yourself used to be one and now feel ashamed. It's okay Anonymous, you should forgive yourself. We understand.

(11563533)
Stop projecting and kill yourself.

>>11563526
>That's irrelevant. What is relevant, though, is that no excuses were allowed
You just contradicted yourself. If no excuses are allowed, then nothing is an excuse. And for how long do I have to try to be able to give up and lament my wretched life? Let me guess, it will never be long enough, right?

>>11563538
You just keep making up reasons why you shouldn't pick up a book. Maybe it's just better if you give up before even starting. Not allowing excuses isn't the same thing as saying there are no excuses. "i'm stupid :(((" is an excuse, but I don't allow it. However, in your case I can make an exception. I will tell you to not even try. You clearly don't even want to be good at this stuff. I'm asking you to prove me wrong. Show me how you will beat each and everyone of us in this game. I want you to write this in the foreword of your thesis:
>a dumb bitch on a kuala lumpurian bone carving forum said i don't have the willpower and now i proved her wrong
PLEASE

>>11563552
Anon, these kind of attempts only work on functional people who didn't need such advice in the first place. I've studied mathematics at uni, still am, I don't know what else do you want of me. Do you want me to finish my abortion of a Master's? Maybe also trudge through a PhD? And for what? So that some some anon in /mg/ can feel better for having "helped" someone? I've already started and gone a fair while, you want me to continue but give me no reason to beyond the vanity of having achieved something.
>You clearly don't even want to be good at this stuff.
Do you really and honestly think the world works this way? Most people are wastes, I'm trying to find a way to cope, but all you people do is tempt me with impossible possibilities of meaningless glory.

But whatever, maybe I'm just a melodramatic bitch and should take those meds that don't do fucking anything at all.

>>11563592
You are right. You are a crybaby beyond salvation. You have chosen to be one of those waste people of yours. Enjoy the rest of your life like that. Since I don't like animals suffering, I hope it will be a short life.

>>11562402
>Griffith
what did he do??

>>11562813
She seems to be related the "PBS Infinite series" youtube channe (e.g. this is her https://youtu.be/H4I2C3Ts7_w)) and seems to write on this blog
https://www.math3ma.com/blog/the-yoneda-embedding

I might look into the thesis. She's also got this 10 minute pitch of her work here.
https://youtu.be/wiadG3ywJIs

>>11562955
>She could probably make some really good textbooks or mathematics books aimed at a broad audience that aren't shit tier.
From glancing at the twitter, looks like she's writing a topology textbook

>>11563612
I love how easily you guys change your tune once you see it's going to take more than a pat on the back and some generic encouragement. All it took is a fucking post, not even a long one. Anything other than admitting that maybe some people's problems are too much for you, or that your advice is not some divine epiphany.

>>11563653
Nope. It's just because you are just making excuses. If a pat on the back isn't enough, go get a shot in your head.

>>11563677
I will remember this advice so I can give it back to you when life inevitably fucks you up.

>>11563721
Look who's butthurt. Well, at least you don't have to put any effort into studying if you just spend your time waiting for that.

>>11563728
I'm not feeling anything right now, I just wanted to make a point you keep ignoring.

>>11563734
L M A O
M
A
O

>>11563495
Is that good?

>>11563785
Yes, the book on algebras.

>>11563789
I meant the manga

>>11563797
No idea. I thought I would give it a try, though. Looks quite nice judging by the art.

>>11563808
>the manga is about the art

>>11563817
Who are you quoting?

>>11563808
Looks bretty gud, I wish there were mangas about math

>>11563827
Well, there is this https://en.wikipedia.org/wiki/Math_Girls

>>11563830
That manga is pretty bad though and the math in it is pretty basic stuff

>>11563863
Yep. That's the reason for the
>well

In which field of mathematics is it the most probable to make groundbeaking discoveries?

>>11564011
Category theory

>>11564031
Where did you take that from, retard? You even know what is category theory?

>>11564011
Serious answer, It would be probably algebraic topology or algebraic geometry