/sci/ - Science & Math

>0 posts
>page 5
wew

>>9890434
thank you for saving the day bro, your a real hero

[eqn]\sf\color{red}{Gook}\; \color{orange{moot}\; \color{yellow}{\bb STILL}\; \color{green}{hasn't}\; \color{cyan}{fixed}\; \color{blue}{the}\; \color{indigo}\TeX\; \color{violet}{tags}[/eqn]

most comfy threads up right now:

>>>/r9k/47025017
>>>/r8k/47030029

>>9890446
>>>/r9k/47030029

oh yeah, I too am in a psych ward after my suicide attempt failed
such is life but good news is they have a lot of math books in the library and I get a notebook to write in
and i get to keep my smartphone, cool.

>>9890073
Serious question

is probability theory math?

is statistics?

>>9890471
Yes, but contrary to what statisticucks will tell you, doing only that for 4 years will not make you more employable than a CS major who specialized in machine learning.

>>9890471
Yes and no. Probability theory is (since Kolmogorov integrated it via measure theory) a purely mathematical field, and so it the simpler descriptive statistics. However, the decision theory part has a completely different flavor. While the object in the theory are always expressed in a formal fashion, e.g. the enterprise of coming up with loss functions to compute best estimates is always grounded in one soft philosophy or another (the Bayesian approach, say) and so in practice missors more what doing physics feels like

>>9890471
Why wouldn't it be? Because some cucks complain about formalism? Kolmogorovs axiomatisation is beautiful, but it's hardly what you would call "probability".

>>9890471
probability theory yes
statistics no

>>9890442
apparently u gotta turn adblock off completely for the page

however your tex is still badly formatted

>>9890509
>sure, I'll just let 4chan mine Bitcoins using my machine

I am beginning to forget most of the shit I used to know.

soon

http://www.icm2018.org/portal/en/program-at-a-glance

anyone here going to rio?

>>9892005
>Anyone want to get their wallets stolen in Rio?
No

>>9892160
Really? You can't take care of your own belongings?

>>9890495
>>9890498
Probability theory is just a measure theory for mentally challenged

What are some examples of applications of math that could not be solved geometrically whatsoever, or even related to geometry? I know some problems would be too difficult to solve by hand, but I’m asking for problems that could not possibly be solved using geometric principles.

>>9892661
Your question is overly strict and too general at the same time. Proving that something is undecidable is a pretty tall order. We do know that no such problems exist in elementary euclidean geometry (see Tarski), but any sufficiently advanced geometric model will admit undecidable theorems. How to find them? Write your PhD on this problem, and collect your Fields medal on the way.

>>9890440
>>9891099
Will you faggots ever leave?

>>9892678
>faggots
Why the homophobia?

How do I determine what the cutting edge is in a very specific part of mathematics? Lots of times I get ideas on some nice theory I could try to develop that might have something to say in my undergrad research, but a lot of the time it has already been done 20 years ago. It is hard to see where I can try to contribute even if I

>>9893399
>How do I determine what the cutting edge is in a very specific part of mathematics?
Read recent papers: http://arxiv.org/

>>9892638
Lol no. That's like saying topology is set theory for mentally challenged.v

Undergrad doing a grad-level course this semester. For this course I need to write a report on an open problem in graph theory. Suggestions?

>>9893741
The Riemann Hypothesis

>>9893743
>graph theory

Also this course is for first year grad students. Are people expected to write really formally at that level?

>>9893748
>>graph theory
connect graph theory to the riemann hypothesis. if you can't, then just be a gay engineer.

>>9893741

TSP.

>prove that there is exactly one xi that solves this equation and find it to an accuracy of 1/4.
>tip: you may assume that e^-x is strictly monotonically decreasing

I know that I have to prove that the Banach Fixed point theorem can be applied, so I solve the equation for xi which gives me either xi = (e^-xi)^(1/3) or xi = -log(xi^3).
Then I need to prove that d(f(x),f(y)) = q d(x, y) with q element of [0, 1[ to show that f is a contraction, which means that Banach Fixed Point theorem can be applied, but I have no idea how.
I know that it has something to do with the monotony, so I tried to bring down the interval where xi can be from R to [0, 1] since all other points are impossible due to the monotony of both sides of the original equation.
Also I have absolutely no clue how to actually apply the theorem to find xi and I cant find anything either in my lecture script or online.

anyone pure maths here find any satisfaction in taking a course on applied PDEs or would it just be a huge waste of time?

Which mathematician make you go “Damn, he’s hot”?

>>9893876

Using IVT on g(t)=e^(t)t^(3) for existance and noting that g is strictly increasing on R+ for uniqueness should be easier.

Fuck yeah boyz

>>9894439
What's the catch?

>>9894452

It's only 2nd edition probably

Why are there 3 points to a line in PG(3,2)?

What even is a line in PG(3,2)?

>>9894511
Why don't you read your textbook?

>>9894459
>probably
It says so right there on the cover.

a little bird told me the fields medalists this year are peter scholze, sophie morel, wei zhang, and geordie williamson.

i would appreciate it if this information stayed between us.

I am actually kinda sad that Manolescu and Figalli aren't getting medals. Also a little annoyed since something tells me they were passed over to make room for under-represented mathematicians (Morel and Zhang).

>>9894805(you)

Because i dont have one you ninny. I'm reading wikipedia

>>9894856(you)

But that's probably the reason. It may also be damaged

>>9892005
I live in Rio and not even I am going there. It's fucking expensive for any Brazilian. Mathematics is, after all, a hobby for the rich, it seems.

>>9895279
You're joking right?

>>9895282
The first part? No.
The rich part? Yes.

>>9895039

I have absolutely no confidence in academia anymore

>>9894990
You're full of shit. Both Sophie Morel and Wei Zhang are number theorists. There's no way two number theorists will get the Fields in the same year. The committee kinda fucked itself over by giving the medal to Mirzakhani in 2014 now that a woman that actually did something impressive is finally on the scene, namely Maryna Viazovska, so they won't repeat the same mistake and give the medal to a mediocrity just because she has an extra hole in her body.

The 2014 ICM was a huge fucking mistake even ignoring the fact that Maryam Mirzakhani was awarded a Fields medal. If the committee doubles down on their retardation, then the prize is pretty much worthless from hereon out.

I blame Timothy fucking Gowers. Fuck that piece of shit. Brits ruin everything.

You here G*wers? Fuck you.

>>9890460
Are you autistic?

>>9894193
Me.

>>9895811
I've more than once read that Maryam Mirzakhani didn't deserve the Fields Medal (only read it here, though), but why is that the case? Why is Maryna Viazovska, on the other hand, worthy of it? Also, I think we have to keep in mind that Maryam had cancer, and died not too long after being awarded the Fields. How much of a factor could that have been?

>>9896392
Because Mirzakhani did not make any significant breakthrough. She was pushed to the forefront by the clique that is very into mathematical physics and other kinds of "applied math" shit, which made her popular with non-mathematicians. Her output was consistent but "mediocre". Nothing remarkably original. She was a worker bee, not a mathematical genius.

> How much of a factor could that have been?
I think the fact that she was both Iranian (so ex-muslim) and a woman played a bigger role in her getting chosen (other than the fact that her work had a lot of intersections with physics).

>Why is Maryna Viazovska, on the other hand, worthy of it?
She solved a hard problem in a very original and elegant way.

Mind you, Mirzakhani wasn't the only uninspired choice for a Fields in 2014. Hairer getting a Fields medal was also fucking bizarre, and he was even less deserving than Mirzakhani.

Artur Avila was the only one that undoubtedly deserved to get the Fields in 2014. The committee that year was a lot more political than usual.

>>9896446

Mathematicians seem to think of the fields medal as not meant to be taken seriously for some reason.

It's like a cute science fair award ceremony for zoomers

>>9896476

I think that was the original intention or something, but obviously the influence this has on it today is totally poisonous

>>9896441
Mirzakhani wasn't even the most deserving woman(!) if we were to judge by mathematical output alone, but since it had been decided well in advance that one slot would be for an affirmative action recipient, she won on diversity points (Ursula Hamenstädt was too white for example, while Sophie Morel was French to boot, and "too many" frenchmen have been awarded the medal already).

But in the end it can't be helped. Such is life in the current year.

>>9896441
>>9896446
How do you judge this, though?

Sucks to be mediocre. But, let's admit -- genetics are essential.

>>9896548
For example, one of Mirzakhani's main achievements was to give a new proof of Witten's conjecture about intersection numbers of tautological classes on moduli spaces. That's what got her noticed (the mathematical physics clique has had a very pernicious influence on the field in the last couple decades). Here's the thing though: she was the [math] 3^{\text{rd}} [/math] person to give a proof of that conjecture! And her proof wasn't even particularly insightful compared to the previous ones.

Most of her career has been shades of this. She was a very typical, competent academic. Nothing much out of the ordinary with her, other than her life story.

>>9896392
>only read it here, though
Because this is one of the few public spaces where you can be frank about things. Most mathematicians are damn cowards (and I am throwing stones while living in a glass house when I say this), too afraid to discuss something so tendentious in public openly, but trust me when I say that the issue has created a lot of dissatisfaction in private spaces.

Has any one here ever read the Springer Soviet Mathematics series? Is it any good?

Also, pls post soviet math textbook recommendations

Last math class I took was undergrad calc 7 years ago. Now I'm 26 and want to get serious about math. Mathematical maturity is the goal.

R8 my stack pls. I've been through Hurley twice, just starting with Spivak and Apostol.

>>9896694
Never seen that series before (it seems old, small, and doesn't have much in the way of big names other than a calculus book by Pontryagin) but I hunt down Russian books on stuff deliberately.
The style of writing of the Moscow school seems to consistently be that the writers just want to show you a bunch of cool shit without worrying about difficulty or comprehensiveness. They're fun to read.

Kostrikin/Manin's linear algebra text (the one from the undergrad curriculum meme) is unironically an excellent book even (or especially) if you already know linear algebra. Anything by Shafarevich is nice too.

Also about half the Translations of Mathematical Monographs series from the AMS is Russian (the other half is Japanese) and the quality of the few I've checked out is pretty good. There's a neat functional analysis book by Helemskii in there that opens up with a discussion of category theory and uses it throughout. Kind of weird but it's pretty cool.

>>9896776
Halmos and especially Dedekind in that pile are probably a waste of time for you to read unless you're that special kind of weirdo who jerks off to foundational issues. Contrary to popular belief you don't actually develop any "maturity" by forcing yourself to slog through dry texts about the autistic nitpickers of math.
3 calculus books is a good idea provided you don't actually try to read all 3 straight through. It's good to have alternative explanations when you get stuck though. Good habit to have if you keep studying further.

>>9896833
>special kind of weirdo who jerks off to foundational issues

Yeah actually. The prof in the logic course had a hard-on for rigour so when I started checking proofs in apostol/spivak their solutions were too hand-wavey for me to accept. It was always "BUT WHY CAN NUMBERS DO THAT AND NOT THIS?"

Anyway, pls recommend. I think i need algebra

>>9896853
>Apostol
>handwavy
u wot

Assuming you mean high school algebra and not abstract the best sources for anything from high school math are the AoPS books.

>>9896853
I was asked to teach abstract algebra from the text by Niels Lauritzen, Concrete Abstract Algebra, Cambridge University Press 2003. It looks like something you might like. It's seems to be a real book though, not easily gotten online.

>>9896776
>secrets of mental math
for vvhat pvrpose?

>halmos naive set theory
You should have read this as a freshman. It's a cute little book, but there are better ways to waste your time.

>Kolmogorov functional analysis
Very good but outdated.
>Kolmogorov foundations of probability
This one is 100% worth reading.
>Apostol
Complete waste of time. Too verbose, and his proofs and constructions are very inelegant (too "calculatorial").

>>9893407
This. If you want money, prestige, follow the current trends. If there is a mathematical equivalent of climate change hysteria, jump on the bandwagon.

>>9896906
>If there is a mathematical equivalent of climate change hysteria, jump on the bandwagon.
ouch

>>9893927
I would look into the professor teaching it/ syllabus. It is certainly rich enough to contain lots of interesting theoretical problems within it but if it's an intro class they might just teach you basic bitch numerical techniques and not dig too deep.

>>9896872
>Lauritzen, Concrete Abstract Algebra
> It's seems to be a real book though, not easily gotten online.
You can find the pdf on libgen.

>>9895039
I can envision in the future (2050,2060) an evil White Male solving the Riemann Hypothesis or whatever and being denied the Fields medal because ''muh colonialism'' or what not, despite White people being a minority in Europe/America/Australia, etc and less than 5% of the global population.

>>9896936
yikes

Are the animeniggers finally gone?

>>9896868
Is linear algebra 'high school' algebra? I always heard there was some distinction between 'high school' and 'college algebra', even within the umbrella of linear algebra.

And maybe it was Spivak that was handwavy but I just remember checking one of my proofs and the solution relied on some properties of exponents/manipulating expressions without connecting to the stated 10 axioms or consequent theorems.

>>9896904
>mental math
My arithmetic is TRASH

>better ways to waste your time
pls suggest

Apostol was suggested to me to complement Spivak, as I was having some trouble there.

>>9896872
>>9896929
Thanks

Also, any classic texts on combinatorics?

>>9896973
Matrices and matrix multiplication are highschool topics. The concept of vectors and coordinates are also highschool level.

Undergrad level linear algebra includes discussion of foundational construction of vector spaces (axiomatically or via mappings on tuples), linear maps and linear operators, bases, dimension, determinant and multilinear forms, and inner product spaces. Optional topics include quotient spaces and the tensor product.

>>9896990
Thanks! I've only covered very basic matrix operations.

>>9896938
Sorry for the /pol/ post but bypassing meritocracy in favor of muh feels pisses me off. If they deserve it, then fine.

>>9896918
yeah, well this is basically what my advisor told me last week. You know, anon: I've read a lot of papers about Fractional PDE's recently. You can research that and we can get some money.

>>9896938
Come on, you know the Riemann Hypothesis will be proven either by a white guy or an asian guy. And I think we can all agree that the former is likelier than the latter.

Hmmm: https://golem.ph.utexas.edu/category/2018/07/the_duties_of_a_mathematician.html#more

>>9897140
>you are MORALLY OBLIGATED to read 3000 pages of my pet meme theory because you are a number theorist
never change memesenko

>>9897222 witnessed

Vis-a-vis from my apartment there is an apartment block that is under construction and someone is there on the 8th floor right now praying really loudly (some evangelical woman I assume). It echoes so much (since there are no exterior walls on the side that's facing my apartment) that it's kinda creepy, like some spooky Mass in the middle of the night.

I wanted to record the event but I'm not sure if that's ethical.

>>9896936
>>9897131
It's going to be proven by a (((white))) guy and you know it.

>>9897433
((()))s are going extinct. Their intellectual output has dropped vertiginously in recent years.

How do people find or even think of open problems? I've already finished my Bachelor's but I still feel I don't know or have done any maths.
>>9897449
How do you know? A friend of mine went to a conference recently and a lot of people chose the kosher food option kek.

>>9897459
>a lot of people chose the kosher food option kek.
I'm willing to bet most of them weren't jewish, just hipsters "concerned" with their body health. You'd be surprised to find how easy it is to find kosher servings in areas with literally no jews.

>How do you know?
They have very low fertility rates outside Israel. The Orthodox types are really, really dumb, so there's little chance of any great intellectual achievement coming out of that particular (((pool))).
They also intermarry at very high rates.
Lastly, they've stopped pursuing intellectual fields at the same rate as in the past. Call this one the curse of having high status. You'd be surprised to find how many jews now pursue worthless degrees entirely for signalling purposes. Why work hard when you have it made?

>>9897480
A very big reason why jews were overrepresented by a pretty wide margin in fields like math starting in the 20th century is because they had just entered polite society a couple generations prior and were looking for ways to gain prestige. Being on top makes you lose your drive to succeed. (This is independent of the fact that they've been diluting their smarts genes by intermarrying.)

Now the asians are the strivers. Which is kinda tragic because they just don't have what it takes.

>>9897517
>Which is kinda tragic because they just don't have what it takes.
One could say they weren't the (((chosen))) ones.

>>9897535
>One could say they weren't the (((chosen))) ones.
L-lame. I totally did not chuckle at this.

>>9897535
>tfw (((chosen)))
Jews never loose
;^)

>>9897459
>How do people find or even think of open problems?
If you're not creative enough you simply won't produce a novel problem on your own. The best way to do it is to start skimming through new work and see if you can spot any gaps that you can fill. Many authors specifically point out new avenues or make remarks on what deserves further investigation in their articles.
Lists for known open problems usually feature problems that are pretty hard. That's how they ended up on a list in the first place, otherwise someone would have solved them by now.

>>9897459

You have to actually be motivated to work through your ideas outside of class. It takes a lot of trial and error.

> tfw math majors are just as bad as CS majors

>>9897691
I recommend that you use some journal aggregator to look for articles that might interest you and have already passed review. Preprints often have mistakes, many of which are subtle, and that can trip you up really hard if you don't have a good working knowledge of the subject.

>>9897710
The few times I have ideas, I just don't know what to do with them. For example, I once wondered whether the algebraic closure of a field could be related with a topological closure (under whatever the appropriate topology might be). I asked my professor if that was the case, and though he usually had an answer for any question, he wasn't able to answer me.
He didn't know, and I have no fucking idea where to even begin with the idea, so at the end I might as well not have thought of anything. And while someone might be able to answer me in this thread, the point is that I don't know how to answer the question myself.

>>9897762
>For example, I once wondered whether the algebraic closure of a field could be related with a topological closure (under whatever the appropriate topology might be). I asked my professor if that was the case, and though he usually had an answer for any question, he wasn't able to answer me.
Because your question is over-general. The start of your inquiry was probably nothing but a simile (and the word "closure" in particular). You can't think mathematics like you would poetry.

>>9897794
>The start of your inquiry was probably nothing but a simile (and the word "closure" in particular)
Yes it was, he himself told me that when I asked him. Though he did explain to me that topology does intersect with fields (if I remember correctly, via a generalization of the correspondence theorem that's taught in a standard Galois theory course).
But the same has happened to me with more concrete questions; sadly, I can't think of any right now, and I'm more interested in my problem in general and not so much with this instance in particular, I just wanted to illustrate what I meant.
>>9897710
>You have to actually be motivated to work through your ideas outside of class. It takes a lot of trial and error.

>tfw defeatist attitude
>tfw brainlet
>tfw lazy
>tfw i'm as bad as a CS major

>>9890471
Is anything not mathematics?

>>9895812
can i get a quick rundown?

>>9897902
yes

>>9896621
>Here's the thing though: she was the 3rd person to give a proof of that conjecture!
Witten won the award for his new proof of the positive energy theorem and Fefferman was awarded his partly for his new proof of the Carleson's theorem. She also seemed to prove a hard conjecture and get some really nice results.
>>9896446
>Hairer getting a Fields medal was also fucking bizarre
This is closer to my wheelhouse and I have to disagree. Hairer's results are some of the best in the study of stochastic integrals in a really long time. Sure, they don't have a lot of umpf, but that's because no one has made results like his in while.
>>9894990
>>9895039
There's no way Manolescu won't be getting a fields medal. I can see Figalli not getting one though. Now Simon Brendle is the guy you should really be feeling sorry about.

>>9897902
no

>>9897900
>Is anything not mathematics?
English, logic, there are parts of computer science that aren't mathematics, psychology, economics, etc.

>>9897978
You picked very bad examples.

Going into college for civil engineering. Brushing up on my math skills this summer. What do I expect my course load to be like? Is it advanced math? Should I be going beyond basic algebra?

>>9897997
You wont need more than calculus 2 or 3 and linear algebra. Study materials science.
I'm not an civil engineer but I have many in the family.

>>9898010
In my freshman year is that the coursework I should be expected to be given?!? I haven't even studied precalc yet! Oh no.

>>9898014
Precalc is just the first chapter of any calculus book. Download the Stewart book read the first chapter and do all the exercises and you will be hella fine. You can do that in one afternoon. Always think of the domain of the functions.

Calculus and linear algebra are not hard. I think they get the fame because all stem majors have them so they get exposed to a lot of brainlets. For a civil engineer there are more important topics to be good at such as structures and materials resistance.

>>9898014
Not calc 2 and 3 in the first year, but there's probably going to be a calc 1 course, and a linear algebra course. You're gonna need a lot of trig, a lot of linear algebra and a lot of physics (which takes all of the above and some calculus).

>>9898029
>>9898030
I'll get studying right away.

>>9898035
Good luck!

>>9894439
>Proofs from THE BOOK
Is this an Erdos reference?

>>9898057
>Is this an Erdos reference?
Yes it is.

>>9898076
cool

>>9897762

The problem with that is it's not a concrete idea. Especially because It involves topology.

The concept of "experimental mathematics" is the bread and butter of a based mathematician.

Develop any idea you have by yourself. Don't talk until you've done the math.

Techniques to develop ideas:
> write a program
> state your observations in prose on paper
> read a book about the subject

>>9898127
Techniques to write better posts:
> Know what you're talking about
> Stop posting on /sci/
> Kill yourself

>>9898154

> t. Topology monkey

It happens that I do know what I'm talking about

>>9897991
pretty sure there was a whole controversy with principia mathematica where they tried to prove logic was math and it wound up conclusive that it absolutely is not.

>>9898127
>>9898154
>>9898165
Who am I to believe?

>>9898662
Nobody.

Ok boys, time to finalise your predictions on who will win the Fields medal next week.

>>9897925
So you're betting on Peter Scholze, Geordie Williamson, Ciprian Manolescu, and Simon Brendle (with him potentially replaced by a woman)?

2 * 4 + 4 is the same as (2 + 1) * 3

Can someone explain how?

>>9898726
The fuck? No it isn't.

>>9898705
I think Scholze is absolutely gonna win, to a lesser degree I think Manolescu is gonna win, I know that they're both presenting at the IMU. I would like either Figalli or Brendle to win, but both of them do geometry and PDEs so it's doubtful they'll both win in the same year. Figalli can still win one in 2022 so here's hoping he gets it next time. Brendle really deserves to win one, but then again so did Lurie. Hugo Copin is also an invited speaker but he's a bit on the younger side so they may pass him up for 2022 or even 2026. All I know about Williamson is that he's won some pretty big awards and it's the last time he can be nominated so maybe he'll win. If someone was gonna be passed up this year it'd be Brendle unfortunately, probably for Morel. Viazovska still has 2022 and will probably make more progress on sphere pack by them. I wouldn't be surprised if she won this time around though, even if she only solved 2 cases of sphere packing it is a really tough open problem. I don't think Zhang will win. So Scholze, Manolescu, Williamson, Brendle but more likely that Brendle will be replaced by replaced Morel or Viazovska

>>9898726
Base 7?

>>9898726
define *

>>9898798
[math] 2*4 + 4 =_{\text{base-7}} 15 [/math]
[math] (2+1)*3 =_{\text{base-7}} 6 [/math]

Can't you just feel the moonshine?

https://www.youtube.com/watch?v=Jliw4bpefGU

Is there a pure geometry solution for IMO 2018 p6 without using inversion?

>>9898929
Yes. Read this thread: https://artofproblemsolving.com/community/c6h1671293p10632360

Who exactly is in the wrong here?

>>9899075
Who's the Chad samurai there?

Can someone explain eigenvectors in a clear, for dummies way?
Beginning to study chemistry and I stumble on this term a lot (orbitals and stuff)

>>9899135
If an operator operates on a vector without changing its direction, then the vector is an eigenvector of that operator. In chemistry, this usually means that the operator has the effect of multiplying the eigenvector (electron state) by a scalar

>>9899124
his name is peter scholze

>>9899143
Did you really think of him when I wrote "Chad samurai"?

>>9899124
>Who's the Chad samurai there?
Go Yamashita

>>9899075
high quality OC right here

>>9899075
this juxtaposition is really... man, I think my brain short-circuited.

>scholze and stix both have long hair
>scholze has the face of a 10 year old boy
>stix doesn't even have an supraorbital ridge = literally the forehead of a woman
>timid, unthreatening facial expressions
>stix is smiling like a dork
>scholze is looking up at the camera all puppy eyed

meanwhile

>mochizuki looks like he's about to shoot lasers through his glasses
>dresses like a granny, but doesn't give a fuck
>oozes confidence
>go yamashita looks like a fucking caveman that could snap your neck with one hand
>suspicious, piercing gaze
>[kid who's name I don't know but I assume he's mochizuki's student]: total fratboy, smug
>fasenko is also hiding a smug smirk
>slightly frowning but calm, like he's anticipating something big
>literally looking down on you

scholze about to get dunked isn't he?

Why is it so difficult to create good quality difficult algebra problems for IMO? The last good quality difficult algebra is IMO 2010 Q6. Since 2010 there are no more algebra for P3 and P6. (IMO 2011 P3 doesn't count because it's too easy) Is there any hope for algebra, is it done to death already?

I hope Peter Scholze can create a good quality difficult algebra P3/P6 for IMO.

>>9899254
>kid who's name I don't know but I assume he's mochizuki's student
Fucheng Tan

>>9899254
That cute femboi better prepare his boipucci to Samurai Chad.

>>9899339
I hope someone will write a doujin based on the encounter.

>>9899384
Apart from mindbreak, what other tags should it have?

>>9898431
No. Principia tried to build all mathematics on a single solid foundation that would then be used for anything else in the future. Then Gödel proved with his incompleteness theorem that that no axiomatic system can be complete and consistent at the same time. That is, if Russell's system did not contain a paradox it would some time. But nevertheless we still have set theory as the main foundation of mathematics.

>>9893927
Depends, I echo the suggestion to look at the syllabus/prof closely in order to make this decision. If the course takes a real rigorous functional analytic or semigroup approach to the topic, I bet you'll enjoy it. If not, you might find it less stimulating and will probably just "solve" a lot of boring BVPs numerically without ever having anything explained.

>>9899426
Humiliation, rape, moral degeneration, drugs, lactation.

>>9899505
>lactation
I see that you're a scholarly man who has made abject degeneracy his topic of erudition.

>>9899523
The way this runs in my head, Mochizuki would force Scholze to go through HRT, so he'd start to develop tits, and after several torture sessions where he'd call him a brainlet and laugh at him for not being able to understand the mysteries of interuniversality, little Peter would start to lactate from stress.

>>9899555
Those trips are very promising. Hoping to see what Scholze looks like in a maid dress.

>>9899075
>tfw you will never have Fucheng's jaw

>>9899444
It really isn't that big of a deal, just "this sentence is false" self-referential kind of statements that you'll have with any language strong enough for self referencing. Any language strong enough for arithmetic of natural numbers is strong enough for self referencing through Godel numbering.

You can work around this with object / meta-object / meta-meta-object languages or trinary truth values but a lot of people don't bother because it is just some irrelevant true statements about the language you can't prove within the language for obvious reasons.

In fact, the lair's paradox has been around for thousands of years before Godel and he just formalized it.

>>9899254
At least the others maintain eye contact, wouldn't mind them as professors. Michozuki looks like he's about to leave twin primes conjecture as exercise before ascending to a higher plane of existence.

>>9899569
>Hoping to see what Scholze looks like in a maid dress.
So do I. One that looks something like this pic >>9891099

>>9890442
[math]\mathrm{\color{red}{am}\;\color{yellow}{I}\;\color{blue}{retarded?}}[/math]

did the gays leave?

>>9901492
Nah, they're probably just American, or are roleplaying on Discord.

>spend two semesters doing combinatorics
>still fail at basic enumerative problems

kill me

>>9899339
>>9899384
>>9899426
>>9899505
>>9899523
>>9899555
>>9899569
>>9900030

>>9901606
don't be too hard on yourself. combinatorics is a bitch.

>>9897914
see above

>>9898010
>>9898014
Civil and math major here. In practice, you literally need nothing more than geometry. In school, up to calc 2 should suffice.

>>9901718
huh?

Am I missing something here? My proof:

If a is a unit, take c any element, q=0 and r=a
If a=0, take c any element, q=0 and r=0
If a is irreducible, take c=a, q=1, r =0
If a is not irreducible, unit or 0 then (since EDs are UFDs) look at its unique factorization into irreducibles and take c to be any irreducible, q the rest of the factorization and r=0.

This covers all the cases and I haven't used at all that R is an ED other than the fact that its also a UFD.

>>9901895
>Am I missing something here?
It needs to be the same c for every a.

>>9901897
oh right lmao

>>9901897
>>9901895
ok having a second brainlet moment

assuming the negation of the statement, then for all c there is an a such that for all q,r with a =qc+r, then r is neither 0 not a unit.

But taking c=a and q=1 with r=0 is a contradiction of this statement?
idk is up with my brain rn

>>9901944
oh fuck the last part of the negation should be r=0 or r a unit nvm

>>9901895
A little hint, try to construct said element for the integers and the ring of polynomials with coefficients in a field.

>>9901956
>>9901944
>>9901914
>>9901897
>>9901895
>>9902001

fuck it's way easier than i thought

choose a non-unit, nonzero c in R (which exists since R not a field) to have minimal value in the Euclidean valuation v. Then we can write any a in R as a =qc +r with r=0 or v(r)<v(c). But since v(c) is minimal then it forces r to be a unit or 0.

What are the best books about Goedel and his interest in Platonism/mysticism?

>>9902497
>>>/x/

>>9902512
There's nothing paranormal about philiosophy mate.

>>9897762
>topological closure related to algebraic closure

Topological closure and algebraic closure are both instances of this concept

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

2 more days until we find out who got shafted by the International Mathematical Union.

>>9902588
>2 more days until we find out who got shafted by the International Mathematical Union.
what's that about?

The ICM this year is in my country and better yet, in my city, but I have no friends to go with and I'm not going alone... feelsbad

>>9902602
dumb animeposter

>>9902605
That's not an anime, it's an image.

>>9902602
We will go with you anon. Go attend the public lectures and gives us the scoop on all the cutting edge shit the cool people are working on.

Be adorkable. Start networking. For the glory of mathematics and the honour of our general!

What is the best intro book to Differential Topology that does not require prior knowledge of Calculus?

>>9902754
? niger wtf go get a fucking calculos book and then you can do diff topology

>>9902778
It is not that I don't know Calculus, but since any laymen can pick up Munkres' Topology book and start doing math. I feel like a good Differential Topology book would require only knowledge of Topology.

How do I ask a professor if I can explain what I've been working on to them?

I'm 100% confident it's interesting and wouldn't be a waste of time. I go to a big 10 state school and I'm an undergrad math major.

> inb4 "stfu undergrad hack"

>>9902822

Also is it bad to email a professor who isnt my professor because their area of expertise is more relevant

I hate doing this type of shit

>>9902814
Maybe Milnor's topology book is what you're looking for
>>9902602
Try going and making friends. You may meet some cool mathematicians. If Villani is going you can talk about Black jack with him.

Can someone tell me why?

>>9902822
>>9902831
Even if the guy isn't you prof if they have relevant experience you might as well email them. Doing work on your own shows initiative that most undergrads don't have, I think at the very least they'll appreciate that. Most profs I know are fairly chill guys, so just go for it. If you still feel awkward, try attending a seminar that that guy goes to and feel the waters. If you're patient you'll get the chance to talk to him in a natural setting and be able to bring up your work at some point in the conversation. You also might learn something from the seminars

>>9902844

Lol is this bait

[Anything]^0 = 1 because:
> it's considered to be an "empty product," or
> the recurrance that defines exponents has an initial condition of x^0 = 1 and x^(n+1)=x*(x^n)

https://terrytao.wordpress.com/2018/07/28/gamifying-propositional-logic-qed-an-interactive-textbook/
>About six years ago on this blog, I started thinking about trying to make a web-based game based around high-school algebra, and ended up using Scratch to write a short but playable puzzle game in which one solves linear equations for an unknown {x} using a restricted set of moves...

>It took a while for me to come up with a workable game-like graphical interface for all of this, but I finally managed to set one up, now using Javascript instead of Scratch (which would be hopelessly inadequate for this task); indeed, part of the motivation of this project was to finally learn how to program in Javascript, which turned out to be not as formidable as I had feared (certainly having experience with other C-like languages like C++, Java, or lua, as well as some prior knowledge of HTML, was very helpful). The main code for this project is available here. Using this code, I have created an interactive textbook in the style of a computer game, which I have titled “QED”.

>http://www.math.ucla.edu/~tao/QED/QED.html

>This text contains thirty-odd exercises arranged in twelve sections that function as game “levels”, in which one has to use a given set of rules of inference, together with a given set of hypotheses, to reach a desired conclusion. The set of available rules increases as one advances through the text; in particular, each new section gives one or more rules, and additionally each exercise one solves automatically becomes a new deduction rule one can exploit in later levels, much as lemmas and propositions are used in actual mathematics to prove more difficult theorems. The text automatically tries to match available deduction rules to the sentences one clicks on or drags, to try to minimise the amount of manual input one needs to actually make a deduction.

>>9903153

Should we tell him about Coq?

is it just me or are there fewer anime posters nowadays?

>>9903802
reporting in

>>9903810
fuck...

>>9897535
So much this.

Go to a school and asians all do STEM, but they just rest on their ability to do spatial roations super well, so they are all chemists/physicists/engineers. Never do anything original that isn't spoonfed to them by an employer or professor.

Jews are worse though. (((verbal intelligence))) can be applied to pure math, sure, but I think there is some intuition lacking that is necessary for breakthroughs. Prove me wrong?

>>9902844
a^0 = a^(1-1) = a^1 * a^-1 = a * 1/a = 1

>>9903153
Brainlet here, stuck on exercise 8-something.

Given A IMPLIES (B IMPLIES C) : deduce (A AND B) IMPLIES C

>>9904022
[math] A \rightarrow (B \rightarrow C) = \neg A \vee (\neg B \vee C) = (\neg A \vee \neg B) \vee C = \neg (A \wedge B) \vee C = (A \wedge B) \rightarrow C [/math]

>>9904092
>>9903153
>The objective of this "game" is to prove statements in propositional logic from the given hypotheses by clicking and dragging on statements that one has already deduced.
How the fuck do you play this game? I completed the task but it won't give me the next exercise. I already deduced [math] A \wedge B [/math]!

>>9904151
Oh shit, I should have scrolled up. Apparently, I also needed to deduce [math] B \wedge A [/math]. The interface sucks major ass, and this exercise is retarded. Conjunction is commutative.

>>9904092
Appreciate it, but in this game there's no negation my dude.

>>9904196
Replace negation with whatever derivation of it you have available then. I gave up at exercise 5 ("A, assuming B, A"). I find this interface extremely annoying. Going through trial and error to figure out how the damn thing works is boring because the exercises are too simple.

>you literally click and drag shit across the screen
>somehow this is supposed to help you understand formal logic
Is Tao just as shit at teaching in the classroom?

>>9904160
You prove it's commutative later. Also Brendle is giving a talk at the IMC so maybe he will get the fields medal. Just one more day.

>>9904309
It could be that Shigefumi Mori being the president of the IMU means we'll be spared any "progressive" shenanigans when it comes to who gets the Fields this year.
Now if only we could get rid of the applied maths shitheads (like Helge Holden). Physishits have polluted our sacred domain for far too long.

Any other recommendations for a resource that teaches propositional logic in a similar manner, ie by showing you how to prove it step by step from first principles?

>>9904399
Don't waste your time with silly things; just learn coq or any other proof verifier.

How do I get good??

>>9904514
If you have the potential, persevere. If you don't, pray someone discovers a real nootropic.

Fuck it. I'm leaving EE to do math and cs. Don't care anymore. All I want to do is solve math problems.

>>9904707
I hope you have a source of passive income 'cuz you're going to need it.

>>9903930
>Prove me wrong?

This is wrong right? From the theorems in the book I can only conclude that it's real on the points of continuity of that function or is at most complex in a set of measure 0?

How do you guys dispose of textbooks you don't need anymore?
They're mostly grad level and/or niche and all my usual sources of book disposal for undergrad texts aren't really good choices. There's nobody local to sell them to, no buyback service wants them, Goodwill would take them but I may as well just throw them in the recycle bin at that point.

>>9904938
Nice picture for ants. We're all dying to strain our eyes for you.

>>9904955
I don't care what some poor eyesight cuck has to say about it. I can see it from 2 meters away.

>>9904947
Why not just keep them? What's wrong with building yourself a library? Math textbooks are perennially usable, since they're filled with eternal truths.

>>9904962
I'm not getting rid of every book I own, just the ones I will never have any reason to open again. Keeping them all would just be clogging up a bunch of space with shit I don't need.

>>9904964
>I'm not getting rid of every book I own, just the ones I will never have any reason to open again.
How do you know you won't need them in the future? And if you're so sure, why the fuck did you waste money buying them in the first place you absolute retard? Borrowing books is possible. Pirating them is also possible.

>>9904995
>Borrowing books is possible. Pirating them is also possible.
This is exactly why I don't need them anymore.

>why the fuck did you waste money buying them in the first place
because I was not aware that libgen existed four years ago

>>9903802
>is it just me or are there fewer anime posters nowadays?

What are some good basic econometrics books?

Can someone please explain this to me ?

>>9905227
Look at figure 5.2.

>>9905227

Can you post the previous page? Is the part you're having trouble with the fact that P and Q are in the intersection or that it's easy to find the other factor?

>>9905237
The fact that he could easily find the other factor. Here's the previous page.

>>9905245
and the one before that

>>9905245
Just use synthetic/long division.

x^3-(49/9)x^2 - (121/9)x + 161/9 =
(x-7)(x^2 + 14/9 x - 23/9) =
(x-7)(x-1)(x+23/9)

>>9905245
>>9905250
I honestly don't understand what it is that you don't understand. It's literally spelled out to you: you have a polynomial of degree 3 and you know two of the roots, so you can factor out (x - firstroot)(x - secondroot) and get (x - thirdroot), which gives you the coordinate.

>>9905265
Thanks.

What happened to that guy who wanted us to go through a textbook together?

What's the Spivak/Apostol of linear algebra?

Of abstract algebra?

>>9905386
>the Spivak/Apostol
What do you mean?

What is a logical sequence to study the following subjects

Algebraic Topology
Differential Topology
Differential Geometry
Algebraic Number Theory
Algebraic Geometry

>>9905488
Diff Geometry (Curves surface and submanifolds)

Diff Topology +Diff Geometry (General topological manifolds, differential forms)

Diff Topology + Algebraic Topology (Finally setting that shit straight)

Power Gap

The rest.

>>9903802
I’m a Touhoufag, reporting in. I won’t stop until I name a new theorem after my waifu, Murasa.

>>9905544
Shit taste dude

>>9905546
How dare you. Murasa is the most beautiful girl in Gensokyo. Post your 2hu sort.

>>9905488

General Theory of Smooth Manifolds
Algebraic Topology 1: i.e. Fundamental Groups and Singular (co)homology
Differential Topology
Riemannian Geometry & Kahler Geometry
Algebraic Varieties (mainly over C)
Algebraic Number Theory & "Classical" Arithmetic Geometry
Schemes, Sheaf Cohomology (Zariski & Etale)

>tfw fell for the 300k starting meme

>>9905698
Someone I know who just finished their undergrad maths degree got a job consulting on AI having never done anything but pure maths. They weren't a particularly bright student either.

Is Coxeter a good place to start to learn 'classical' geometry?

>>9905708
I take it you live in a 1st world country.

A little over 24 hours left until we find out who gets the Fields this year. Any last bets?

>4th year university course
>first assignment
>draw addition and multiplication tables of finite field with 9 complex elements
>we have to handwrite everything

My hand hurts

why do I have to do this

>>9905856
Australia

>>9906027
>not writing a program to do it

>>9906064
>we have to handwrite everything

>>9906027
>draw addition and multiplication tables of finite field with 9 complex elements
Why though?

How do I outsource my homework to some poor Asian country

>>9906118
How much are you willing to pay me?

>>9905016
do you not prefer reading a physical math book as opposed to your screen?

>>9905278
I'm here but I'm going on vacation soon so i thought there's no point

1 + 1 = 2

>>9906162

>>9890073
>https://mathoverflow.net/questions/226277/what-is-a-grossone
Opinions on the witch hunts on this guy?

I feel that if you've published several papers that passed peer review in several journals, some of those papers even winning large awards, published a book and been invited to several conferences then you should have some credibility. Or are we all just quietly publishing a bunch of shit to keep our faculty jobs?

The tl;dr of the critique against him is this:
>His constructions, when formalized by others, are essentially based on primitive properties of a non-standard arithmetic.
>Therefore the essential complaint against him is not using modern math terminology.
>His papers area overly long and filled with philosophical fluff (to everyone's credit, no one critiques him on this).
>The applications of his constructions on solving unsolved problems are undisputed except for his latest paper his work is applied on two Hilbert problems.

>https://retractionwatch.com/the-retraction-watch-leaderboard/top-10-most-highly-cited-retracted-papers/

Two editors from the EMS Surveys in Mathematical Sciences have resigned over this shit. I find this tactic despicable. Regardless of the validity of his work, he did pass peer review and he should've been picked up by an editor before acceptance, which is something they should've been doing to begin with rather than complaining after the fact.

Why don't they write polemics and papers that either generalizes/disproves his work, instead of throwing a literal hissy fit in the media and making it a personal attack.


I thought we had grown out of this dark age academic practice, as a species.

>>9906183
* Wrong link:
https://retractionwatch.com/2017/12/19/editors-chief-math-journal-resign-controversial-paper/

>>9906183
It's interesting to note that the most significant contingent attacking Sergeyev is made up or lead by jewish mathematicians.

>>9906183
It is interesting that cranks can get papers into publication, so long as they are extremely long and use obscure enough terminology and notation.

>>9906215
Hmm, yes, very interesting indeed I had not noticed that.

Perhaps he was responsible for some of the anti-Semitic postgrad acceptance policies in the USSR in an earlier life (back when virtually half the departments were dominated by Jewish supremacists and the commies didn't want to stand for it).

I don't like his papers either, but there doesn't appear to actually be anything wrong with it. Definitely not retraction worthy in any case. Guess that's why they had to resign instead of actually trying to retract it in their own fucking journal. Good on the chief editor for not falling for it.

>>9906223
>It is interesting that cranks can get papers into publication, so long as they are extremely long and use obscure enough terminology and notation.
Yeah, man, fuck these cranks and their irrelevant work. They should be banned from all journals since they aren't using standard math.

Anyway what's happening with Shinichi Mochizuki these days?

>>9906104
I don't know
I seriously don't know

>>9906236
That's the spirit man!
Logically then, Shini is a crank. How about you ask him if that is not correct?

>>9906229
>back when virtually half the departments were dominated by Jewish supremacists and the commies didn't want to stand for it
Why do you say that they were supremacists?

how do you celebrate scholze fields?

i celebrate by watching korean drama

>>9906310
Not that I particularly care about this issues, but I say this due to statistical observation and experience.

As a practical example my adviser was rejected for postgrad from a third rate (ranked in the 300-400s) university in the 70s. Because the faculty was over 80% Jewish and they tended to favour admitting Jewish students over academically more deserving students from other ethnicities.

That same year he applied to the PhD programme at MIT and got in.

The only place where in the world where this bias was completely reversed at the time was reversed was in Moscow (which of course many Jewish writers are still (fairly) complaining about).

In addition there are Jewish only scholarships all across the world even today. Many Jewish professors make light public jokes about Jews being smarter than other races on average (including many famous professors).

This is all still fine (at least in my own ethical framework) because it's true, Jews are over represented per capita for awards and breakthrough papers etc. But this should be expected due to the historical hiring and admission bias whether that practice was intentional and organised or not (given that there is public formal organisation I would personally have to conclude that it is in many cases intentional).

>>9906310
Not that I particularly care about these issues, but I say this due to statistical observation and experience.

As a practical example my adviser was rejected for postgrad from a third rate (ranked in the 300-400s) university in the 70s. Because the faculty was over 80% Jewish and they tended to favour admitting Jewish students over academically more deserving students from other ethnicities.

That same year he applied to the PhD programme at MIT and got in.

The only place where in the world where this bias was completely reversed at the time was in Moscow (which of course many Jewish writers are still (correctly) complaining about).

In addition there are Jewish only scholarships all across the world even today. Many Jewish professors make light public jokes about Jews being smarter than other races on average (including many famous professors).

This is all still fine (at least in my own ethical framework) because it's true, Jews are over represented per capita for awards and breakthrough papers etc. But this should be expected due to the historical hiring and admission bias whether that practice was intentional and/or organised or not (given that there is public formal organisation, I would personally have to conclude that it was/is in many cases, intentional).

This is the solution to Kirkman's loli problem

>>9906327
A lot of mathematicians are very un-PC about it (surprisingly so, even), especially in the countries that used to comprise the Habsburg empire (Austria, Hungary, Romania, Czechia, Slovakia etc.). It might be because mathematicians tend to care a lot about their (mathematical) lineage (hence the plethora of very good bibliographies of mathematicians), and have a much more mature sense of community compared to the other academic fields, so this kind of banter is widely accepted over a coffee or beer. Other scientists get really uncomfortable when you bring this sort of shit up.

"I have to start with a distant past. In 1954 Fields medals were awarded to J.-P. Serre and K. Kodaira. If you look at the composition of the committee, this choice is anything but expected. If you were well versed at the time into what is going on inside of the Institute for Advanced Studies in Princeton, you perhaps knew that the chairman of the committee and the most respect mathematician at the time, H. Weyl, was quite interested in the works of Kodaira and guess that Kodaira has a chance. But he was not the only member of the committee, and I am not aware of any hints that he could be interested in new French algebraic topology. Only one committee member, H. Cartan, definitely knew about Serre's work. The point is that representatives of the "classical" mathematics unanimously voted for awarding the medal to two mathematicians who just started to develop completely new methods. These methods are still not universally accepted, and are disliked by many."

>>9906383
"The situation changed dramatically over the past 15-25 years. Now it is not hard to see the correspondence between the members and the winners. There are, say, 8 members and 4 medalists, and for each of medalists there are 2 or 3 members for support: they are either from the same area of mathematics (using much more fine division that Algebra-Geometry-Analysis), or they are from the same country, or something else. "

>>9906378
Yeah, I remember the adviser of a friend of mine started talking about (((them))) without any hesitation, which we all found funny as I make a lot of jokes on the issue.

>>9906386
"I claimed in this blog both a year ago and this year that I would be able to guess the winners if I knew the composition of the committee. Well, may be I was overconfident or assumed that some traditions would still be in place. The main relevant tradition is to award Fields medals only to pure mathematicians (well, E. Witten is ever not a mathematician, but he made some contributions to mathematics, and this was very pure mathematics). I definitely would be able to guess an applied mathematician, at least not by a glance on the list of members. I would not be able to guess M. Hairer at the spot. Perhaps, I would be able after doing some research with the help of Google and MathSciNet. The chances of success depends on how applied he is, and if applied, would it be the Computer Science (much more chances) or traditional ODE-PDE style applied mathematics (much less). I am not inclined to explain now the reasons beyond saying that I extremely rarely find an applied work to be of comparable with the pure mathematics depth."

>>9906390
"There are 4-5 members of the committee for supporting Hairer. I am sure that the main concern of the President of the IMU was awarding a medal to a woman, but I doubt that she has enough background to understand what the work Mirzakhani is about, or what are the works of Avila and Bhargava about. The same about 3 other members of the committee. One more is very far from the works of any of the winners, but he may (only may, I am far from being sure) have others reasons to support Hairer. There is no such a definite support for Mirzakhani. After looking at the list of the committee members, it seems that a specific support wasn’t needed. Everybody knew and accepted that one of the winners will be a woman, no matter how good she is, either absolutely or relatively to the other winners or other workers in her area. And only few cared about who will be this woman."

>>9906398
"Anyhow, knowing that awarding a medal to a woman was a priority (nobody I knew doubted this since 2010); the excessive support for Hairer seems suspicious. Another priority of the establishment is to award medals to applied mathematicians or at least looking like applied ones. This is to a big extent due to the desire of the various governments funding agencies to shift all mathematics in the applied direction (this is also a recent phenomenon – in 1960 the US Office of Naval Research funded works in differential topology). If an applied mathematician is really good (well, like Claude Shannon was), there will be no difficulty in awarding her or him a medal and no need for special support. This immediately led to two questions: is M. Hairer applied or pure mathematician? How good is his work? I don’t know the answers. If they emerge later, I will take a note. If not, my curiosity would be limited by the downloading a couple of his papers the day before yesterday. They turned out to be more interesting than I initially suspected, but far from being interesting enough to stimulate me to go further. I will better study the work of Mirzakhani. Or, even better, of J. Lurie – but the papers of Mirzakhani are much more accessible simply because they are much shorter."

>>9904933
who's this cute little girl?

>>9906311
>how do you celebrate scholze fields?
Masturbate violently.

Who are the other strong candidates for Fields 2014? What is their research about?

is applied topology useful? Worth learning?

>>9906378
Banter is one thing.

Excluding non-Jews from positions and admittance to postgraduate programmes due to racial bias is another.

>>9905405
very rigorous, widely accepted as a good book

>>9906517
shilov is rigorous, concise but not so challenging

>>9906461
Is it?

>>9906579
cringe
>>9906461
no

>>9906632
Edgy.

I want to become a meme.

>>9906636
What are some applications of topology?

>>9906688
Neuroscience and market stuff.

>>9906843
Embarrassing response.

>>9906027
>finite field
>complex elements
what did he/she mean by this?

>>9906398
who wrote/said this?

>>9906517
Cool. What about abstract though?

>>9907261
The extension F3[x]/(x^2+1) behaves essentially identically to the extension of R to C. I don't think it's out of line to call the elements "complex".

nth for intuitionistic type theory

>>9907405
>The extension F3[x]/(x^2+1) behaves essentially identically to the extension of R to C.
In what sense?

>>9907413
In the sense that it's composed of elements a+bi with i^2 = -1, which add, multiply, and invert exactly like complex numbers over R do. Also there's the fact that the automorphism group is just the identity and conjugation of i.

>>9907378
why don't you read your linear algebra book before you start planning your abstract algebra book

>>9907413
nigga can't you see the ideal x^2+1??

>>9907424
I like to look over the 'whole' of a thing before I dive into granular study. I find that early exposure to 'the ends' helps motivate me through the foundational stuff.

>>9907448
Fair enough. At least you have a reason unlike the classic dipshit on here making a list of books he's never going to read.
You sound like you would enjoy reading Mac Lane's Algebra. It's somewhat of a hidden classic among algebra texts and it has a very structurally-focused "big picture" style to it.

Can you put the roots of a polynomial in terms of relatively known transcendental functions?

>>9907501
Probably not by your definition of "relatively known".
But there is a method of doing it: https://en.wikipedia.org/wiki/Thomae%27s_formula

https://www.businessinsider.com/the-17-best-universities-in-the-world-to-study-math-2018-7
1. Princeton University, United States — 349.5
2. University of Paris-Sud, France — 291.1
3. Stanford University, United States — 283.7
4. Oxford University, United Kingdom — 278.4
5. New York University, United States — 276.4
6. MIT, United States — 274.4
7. University of Cambridge, United Kingdom — 266.7
8. University of California Los Angeles (UCLA), United States — 264
9. Paris-Sorbonne University, France — 254.4
10. University of California, Berkeley (UCB), United States — 243.9
11. University of Warwick, United Kingdom — 243.2
12. Harvard University, United States — 237
13. The University of Texas at Austin, United States — 232.6
14. University of Wisconsin–Madison, United States — 230.6
15. Stony Brook University, United States — 229.5
16. Rutgers University, United States — 228.4
17. Kyoto University, Japan — 218.9

https://news.google.com/articles/CBMiMmh0dHBzOi8vd3d3Lm5hdHVyZS5jb20vYXJ0aWNsZXMvZDQxNTg2LTAxOC0wMDUxMy040gEA?hl=en-CA&gl=CA&ceid=CA%3Aen
>The Fields Medal should return to its roots

>This idea of giving a top prize to rising stars who — by brilliance, luck and circumstance — happen to have made a major mark when relatively young is an accident of history. It is not a reflection of any special connection between maths and youth — a myth unsupported by the data2,3. As some mathematicians have long recognized4, this accident has been to mathematics’ detriment. It reinforces biases within the discipline and in the public’s attitudes about mathematicians’ work, career pathways and intellectual and social values. All 56 winners so far have been phenomenal mathematicians, but such biases have contributed to 55 of them being male, most being from the United States and Europe and most working on a collection of research topics that are arguably unrepresentative of the discipline as a whole.

>When it began in the 1930s, the Fields Medal had very different goals. It was rooted more in smoothing over international conflict than in celebrating outstanding scholars. In fact, early committees deliberately avoided trying to identify the best young mathematicians and sought to promote relatively unrecognized individuals. As I demonstrate here, they used the medal to shape their discipline’s future, not just to judge its past and present.

>I think that the Fields Medal should return to its roots. Advanced mathematics shapes our world in more ways than ever, the discipline is larger and more diverse, and its demographic issues and institutional challenges are more urgent. The Fields Medal plays a big part in defining what and who matters in mathematics.

>The committee should leverage this role by awarding medals on the basis of what mathematics can and should be, not just what happens to rise fastest and shine brightest under entrenched norms and structures.

>>9907554
Mathematics should be about promoting gender and LGBT issues.

To become a master geometer, does one need to read all of Euclid's Thirteen Books of Elements?

>>9907582
>To become a master geometer, does one need to read all of Euclid's Thirteen Books of Elements?
No.

>>9907582
you can probably skip the 3-4 books on number theory

>>9907592
>>9907594
Thanks friends

How much depth in abstract algebra do I need for public key cryptography implementation purposes? I'm mildly familiar with Galois fields in the context of error correction codes and network coding but the extent of that was pretty much just polynomial arithmetic and I'm guessing cryptography requires more background?

Do I need number theory beyond modular arithmetic and are there recommended books for either of these 2 areas if I'm not overly concerned about rigorous and just want to get stuff to work?

>>9907542
>all those US universities
Shit list.

>>9907672
You have more than enough background to start reading papers in the field.

More background is obviously always better, but you should balance the time you invest in this with your work and its applications.

>>9907542
>tfw made it

dubs decide what I read tonight

>>9908078
Is Eisenbud good for a first exposure to Commutative Algebra?

I only have a modest Abstract Algebra foundation.

>>9908078
Rolling for Rosenburg.

>>9907571
Finally someone who really gets it.

>>9907582
You need to be able to rederive them by yourself.

>>9908078
Rolling for Bao-Chern-Shen, so that you can do proper general relativity. Also, Ratcliffe is a reference book, not so good to study from in my experience. It's better if you pick something else (An introduction to Geometry Topology by Bartelli, or Thurston's lecture notes, for example) and check Ratcliffe if you want further details.

>>9908078
k theory and its applications

I'm gonna build a koch snowfake out of some old chains

256 links = one 4 iteration side