/mg/ maths general: big boy edition

[Anonymous No.11464544]

talk maths, formerly >>11446627

[Anonymous No.11464563]

First for COVID-19, today's research:

>Generalized logistic growth modeling of the COVID-19 outbreak in 29 provinces in China and in the rest of the world
https://arxiv.org/pdf/2003.05681

>Rational evaluation of various epidemic models based on the COVID-19 data of China
https://arxiv.org/pdf/2003.05666.pdf

>Similarities and Evolutionary Relationships of COVID-19 and Related Viruses
https://arxiv.org/pdf/2003.05580

>Prediction and analysis of Coronavirus Disease 2019
https://arxiv.org/pdf/2003.05447

[Anonymous No.11464564]

>>11464544
>actually using my two minutes shitpost for the OP
Jesus Christ anon.

[Anonymous No.11464990]

Can anyone recommend an undergraduate/intro level algebraic geometry textbook that actually offers solutions to some exercises? I want to understand wtf is happening. Even ones that work through examples amidst the chapters would be fine. I'm currently using Fulton's algebraic curves and he constantly peddles very important results off as exercises which of course have no solutions.

[Anonymous No.11465301]

>>11464990
you're supposed to do the solutions yourself

[Anonymous No.11465372]

What's a good intuitive way of distinguishing two topological spaces being homeomorphic vs. being homotopic? I know that homotopy equivalence is more general, but I keep getting confused thinking about it.

[Anonymous No.11465379]

Reading suggestion on noncommutative geometry?

[Anonymous No.11465409]

Shitpost or not, being able to properly understand a question and communicate properly is a useful skill to have

[Anonymous No.11465434]

>>11465372
The following fact is useful: two spaces are htpy equivalent iff they're both deformation retracts of a same space. Try toying with this and the letters of alphabet.

[Anonymous No.11465439]

>>11465372
Homeomorphic: If the objects are made of putty, can you squish one into the other without any cutting or tearing?

Homotopic:Can you find functions f and g from one to the other (and vice verse) whose composition is homotopic to the identity? This would mean that there is a continuous path in function space from one to the other.

[Anonymous No.11465460]

>>11465301
Not him but how am I supposed to know if my work is right? Should I go full descartes and believe anything that I clearly and distinctly perceive?

[Anonymous No.11465473]

>>11465434
OK, this helps. The deformation retract picture is something I can visualize. Thanks.

[Anonymous No.11465653]

How the FUCK do I take a limit? AAAAAAHHHHH

[Anonymous No.11465660]

>>11465379
Connes

[Anonymous No.11465695]

>>11465660
Do you say that because that's the one fat book you know, or because it's actually good?

[Anonymous No.11465754]

How important is statistics in the modeling of infectious diseases? How far do you get with just differential equations and computer simulations?

[Anonymous No.11465762]

>>11465439
>Homeomorphic: If the objects are made of putty, can you squish one into the other without any cutting or tearing?
That's isotopy, a much stronger notion than homeomorphism.
You don't seem to know what you're talking about.

[Anonymous No.11465993]

Is there any relation between topological spaces and measurable spaces?

[Anonymous No.11466040]

>>11465993
honest answer: no, there's not much relation
yukaritard style answer:
The following setting comes up very often: there is a topological space, then you can have the Borel sigma-algebra (i.e. sigma-algebra generated by the open sets of topology), then you can have a measure on this Borel sigma-algebra.
For example in topological dynamics and ergodic theory, one starts with a top. dyn. system [math](X, T)[/math] where X is a compact metric space and [math]T:X\rightarrow X[/math] is a continuous transformation, which allows you to define the pushback [math]T_* :\mathcal{M}(X) \rightarrow \mathcal{M}(X)[/math], where [math]\mathcal{M}(X)[/math] is the space of Borel probability measures on X.
The Bogolyubov-Krylov theorem then states that the set [math]\mathcal{M}^T(X) := \{ \mu \in \mathcal{M}(X) : T_*\mu = \mu \}[/math] consisting of invariant measures is nonempty. Not only that, it is also a compact metrizable Choquet simplex.

[Anonymous No.11466059]

Only math for me is graph theory and numerical analysis boiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

[Anonymous No.11466067]

>>11466059
That's a solid commitment to topology right there, good for you man!

[Anonymous No.11466165]

>>11465993
Yeah, as the other anime lad said you've got the Borel sets which generate "the" smallest sigma-algebra of the topology.
Whether or not it is interesting depends on that topology.

[Anonymous No.11466184]

best books to study vector calculus and linear algebra?

[Anonymous No.11466198]

>>11466184
"Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach" is a great read

For linear algebra I also recommend Hoffman and Kunze.

[Anonymous No.11466222]

>>11465653
Just fucking use Bernoulli’s (L’Hopital’s) bro easy

[Anonymous No.11466226]

>>11466198
That was my freshman year textbook. It should only ever be used once you know linear algebra and mutlivariable

[Anonymous No.11466338]

>Hi, I worked on a problem for 2 hours and can't figure it out
>>Oh 2 hours minutes is far too short.
>Oh okay, can you please prescribe an upper bound so I know when
>>....Upper bound?
>Yes, I'd like to get an upper bound for efficiency's sake. Otherwise if I encounter a problem I simply can not solve, I know when to cut my losses and move foward.
>>REEEEEEEEEEEEEEEEEEEEEE YOU SHOULD TAKE AN ENTIRE SEMESTER IF YOU HAVE TO TO SOLVE A PROBLEM EVEN IF ITS DUE IN A WEEK SOLVING THE PROBLEM ON YOUR OWN IS THE MOST IMPORTANT THING HERE EVEN IF YOU FAIL THE COURSE REEEEEEEEEEEEEEEEEEEEEEEEEEEE

Baby with the Bathwater shit

[Anonymous No.11466377]

>>11465301
"just figure it out." Sure in some cases I'd give this advice to anyone, but he's legit just putting whole proofs to propositions and thrms that are very important to the subject in the exercises! That's bullshit. I want a better book and that's why I'm asking

[Anonymous No.11466422]

>faisceau
how did he come up with the name?

[Anonymous No.11466425]

>>11466422
it literally means "bundle" or "ray", or "bundle of rays" (depending on the context) in French.

[Anonymous No.11466481]

>>11466040
cool. does it matter if the space is metriziable or not?

[Anonymous No.11466487]

>>11465993
If the topology is not too horrible (eg. locally compact) and you take the Borel sigma algebra, then yes.
Integration theory allows you to relate (sufficiently nice) measures to the algebra of compactly supported continuous functions.
There is also an interesting analogy between Baire-negligible sets (countable union of nowhere dense sets) and measure-theoretic null sets. This is explored in a nice short book by Oxtoby called Measure and Category

[Anonymous No.11466500]

>>11466487
thanks for the book recommendation.

[Anonymous No.11466516]

>>11466198
Can support H&K. Let my brainlet ass pull a ninety in two LA courses

[Anonymous No.11466578]

Mathematica or Maple?

[Anonymous No.11466619]

>>11466578
>Mathematica or Maple?
Sage.

[Anonymous No.11466628]

>>11466487
>>11466500
Rudin gives a nice and readable relation between measure theory and Baire theorems in Real & Complex Anal. (Chapter 5).
Of course, not everything is handed out to the reader, but the little gaps in the proofs help to understand it.

[Anonymous No.11466634]

>>11466628
>Rudin gives a nice and readable relation between measure theory and Baire theorems in Real & Complex Anal. (Chapter 5).
Rudin is a meme.

[Anonymous No.11466637]

>>11466634
he is, but he's an enjoyable one. You can't attack it head-on as a first plunge in analysis, but with some basic math knowledge, intuition, and if you've got a sheet of paper to note equations and do the missing steps, it's a very good book to properly understand measure theory and analysis.

It's a reference for a reason.

[Anonymous No.11466658]

>>11464544
I don't know if this is the right thread to ask this question, but I am pursuing a degree in pure mathematics and I am planning to enroll in upper level courses next fall. I was hoping another anon could help guide me. what are some must take courses? aside from the analysis and algebra sequence, I for sure want to take topology and complex analysis at some point. I also am interested in proof based linear algebra.

[Anonymous No.11466661]

>We have too many graduate students this year, what should I do.
>I know!
>*makes Rudin the primary text for the course*
Based Rudin destroying scrubs that enter into his discipline

[Anonymous No.11466662]

>>11466578
>Mathematica or Maple?
Depends. If you are into functional programming - Mathematica. If you are into C-like syntax - Maple.
>>11466619
If you are into Frankenstein's Monster of programming, SageMath uses libraries of ATLAS, GAP, R, Singular, Maxima, PARI/GP, FLINT, NTL, GLPK and much more. (if you don't know these names, stay away)

[Anonymous No.11466683]

ENTER the Funk metric.

[Anonymous No.11466778]

>>11466683
Can I get a quick definition plz?

[Anonymous No.11466780]

>am 18
>started doing math a few years ago and genuinely enjoy it
>in high school atm
>taking college classes at an R2 (currently algebraic number theory, graduate linear alg, analysis, algebra)
>have professor friend who has connections
>her collaborator gives me (low-tier) research projects to work on, we published recently
>at the same time, I suck complete dick at competitions (88 on AMC12, <65 on usamts, 1/120 on putnam, never placed high at state competition)
>feel like world is trying to tell me something

should i take the hint on my low iq and give up on math while I still have my life left?

[Anonymous No.11466792]

>>11466780
never give up, if you enjoy math go for it, if you fail then go for the schizo route

[Anonymous No.11466796]

>>11466780
AMC competition math is different from actual math. Doesnt matter, stay motivated king

[Anonymous No.11466851]

>>11466792
>>11466796
<3

[Anonymous No.11466862]

>>11466796
This seriously. Both are quiet different.

>Here is a problem on the AMC/Olympiad/Putnam
Just a few creative utilizations of skills and tricks I built up over the years. Also this time limit prevents me from doing anything novel, so I keep to my same well paved ways.
>Research problem
I didn't solve it, but it motivated me to create this new mathematical object in an attempt to solve it. Also here are a few easy theorems about that object. Also here is a question about the object I couldn't solve.

[Anonymous No.11466877]

>>11466780
If you really do have publications and are taking upper classes that might be a sign that you do have potential as a research mathematician. There's plenty of time to work on that. Competitions are a huge circlejerk and they won't land you a job nor an academic position, and moreover they don't reflect the experience of working months or years in an actual open problem, so either take them for fun or ignore them altogether.

[Anonymous No.11466941]

>>11466780
you're doing fine, don't worry
having said that: you're in high school, there is no need to hurry into university-level topics and research
a good mathematician is someone who can solve math problems. learning more advanced topics and fancy theorems is only a tool to that end. At my uni I see a lot of people who can regurgitate definitions but will fail to solve any problem that isn't an obvious application of a theorem they learned
i have been doing math competitions as a high school student and I feel they are worth more than people say. I don't mean "you need to score high to be a good mathematician". But time spent on them is not wasted.

[Anonymous No.11467083]

>>11466780
>I'm doing research and grad subjects in high school but I'm also bad at this one thing, please pat me on the back and tell me I'm good
You disgust me.

[Anonymous No.11467094]

>>11466578
Learn a real language

[Anonymous No.11467100]

>>11466578
python

[Anonymous No.11467109]

can you solve coronavirus?

[Anonymous No.11467111]

>>11467094
>Learn a real language
Define "real language"

[Anonymous No.11467180]

>>11467111
C

[Anonymous No.11467203]

>>11467180
ok boomer

[Anonymous No.11467245]

>>11467083
I had actually expected this thread to call me retarded and an attention seeker. Regardless, I agree: I'm pretty pathetic, and I have absolutely no business enacting that on this thread and the people in it. Thank you for calling me out, and thanks to everyone else for all the kind words!

[Anonymous No.11467318]

>>11467111
Javascript

[Anonymous No.11467320]

>>11467203
If you ever need to do some calculations fast you'll end up using C, so you're better off learning from the beginning
t. someone first learned a meme language (Java/Python) then had to move to C to optimize Pari/GP code

[Anonymous No.11467375]

>>11466040
...pushback?

[Anonymous No.11467462]

>>11465434
OK, same anon here who asked about homotopies earlier. Suppose [math]f , g : X \to Y[/math] are homotopic. Then considering their images [math]f(X) , g(X) \subseteq Y[/math], are these spaces of the same homotopy type. I'm trying to write down the explicit homotopy equivalences but I'm having trouble doing it.

[Anonymous No.11467472]

>>11467462
Consider the full image of the homotopy and apply the deformation retract definition.

[Anonymous No.11467501]

>>11467472
Got it, thanks desu.

[Anonymous No.11467579]

>>11466780
>published in math as an undergrad
>"guys should I give up?"
What was the paper about though

[Anonymous No.11467584]

>>11467579
Fun fact: many people writing papers nowadays about Langlands correspondence are actually babies in a womb using it as practice for real math they're gonna do when they come out.
Things are looking up for mathematics!

[Anonymous No.11467588]

>>11467584

[Anonymous No.11467620]

>>11467579
>>published in math as an undergrad
No, anon, read it again. He said high schooler.
Bit old for high school, tho.

[Anonymous No.11467727]

>>11466780
Exams test your on-the-spot thinking and recall. They do not test your ability to internalize and understand subtle ideas. Research is a far better predictor of your abilities and academics know this.

[Anonymous No.11467795]

>>11467727
>They do not test your ability to internalize and understand subtle ideas. Research is a far better predictor of your abilities and academics know this.
Cool. Lets give out preliminary tests as a barrier to PHD research rather then a panel of professors evaluating students.

I'm sure that won't have any kind of consequence

[Anonymous No.11468026]

>>11465762
https://en.wikipedia.org/wiki/Isotopy
Kill yourself.

[Anonymous No.11468074]

>>11466377

Those are some pretty old set of notes, so the solutions are online. Just gotta look for them

[Anonymous No.11468076]

From the math grad students or above here, who doesn’t drink coffee? If you don’t drink coffee, do you drink tea?

[Anonymous No.11468119]

>>11465695
He's the king of NC Geometry

[Anonymous No.11468121]

/mg/pill me on motives

[Anonymous No.11468126]

https://en.wikipedia.org/wiki/Richard_K._Guy
30 September 1916 – 9 March 2020

[Anonymous No.11468129]

>>11468121
When someone has been murdered, the cops are looking for people who had both the opportunity and the motive to kill this person.

>>11468076
Tea and energy drinks. Coffee is for conferences or if it is gives as a dessert drink in a restaurant.

[Anonymous No.11468130]

>>11468129
>gives
given*, silly me.

[Anonymous No.11468150]

>>11468026
Your point?

[Anonymous No.11468253]

>>11464544
*farts*

[Anonymous No.11468541]

>professor ignored my entire page long answer because he couldn't understand my handwriting

[Anonymous No.11468545]

Question: Which quadrilaterals gave point symmetry?
Student A: Parallelograms, rectangles, rhombi and squares.
Student B: Parallelograms.
Which student is right?

[Anonymous No.11468556]

>>11468541
mathematics is not just about solving the problem, but being able to communicate a solution.

[Anonymous No.11468571]

>>11468541
>prove half of the test for Hilbert spaces instead of Banach spaces out of sheer dyslexia
>still get a 7

[Anonymous No.11468578]

>>11468541
You deserve it

[Anonymous No.11468592]

>>11468541
Should you perhaps learn to write?

[Anonymous No.11468625]

>>11468592
how? my normal handwriting is already trash and it's even more trash when i am writing fast and under stress and even even more trash when i am writing symbols i have never learned how to write.
how the fuck do you write
[math]∫ , R, \mathbb {Q} ,\varphi, Σ, \pi , \prod , \zeta, \delta , \aleph [/math]
not that i have all those symbols but i think that a lecturer should at least show how to write a symbol and how to organize an answer, it wouldn't take 5 minutes and it's extremely helpful

[Anonymous No.11468632]

>>11468625
>how?
practice
>how the fuck do you write
how do you think you write them. it isn't rocket science

[Anonymous No.11468634]

>>11468625
You are clinically retarded.

[Anonymous No.11468635]

>>11468625
it will take you 5 minutes to look up how to write ζ and ℵ
how can you fuck up the other ones is beyond my comprehension

[Anonymous No.11468831]

>spend 300 hours learning all the theorems and proofs by heart
>exam time
>cannot solve simple problems because have no developed any intuition because I invested all my time learning the theory
>get a pass, basically the lowest grade

>spend 300 hours working on the hard problem sets
>get 10% bonus grade
>exam time
>all problems are theory based and have barely any overlap with problem set
>get a pass, basically the lowest grade

I am trying my best but I keep getting fucked over. I feel like there is some secret that everyone else is in on and I am not, because some other people who work no harder than me, seem to do quite well.

[Anonymous No.11468850]

>>11468831
>learning all the theorems and proofs by heart
I wonder where the problem is

[Anonymous No.11468870]

>>11468850
What should I have done? How do you learn your theory and proofs?

[Anonymous No.11468894]

>>11468870
you're supposed to understand the arguments, not memorize them.

[Anonymous No.11468899]

>>11468571
I guess you used the correct techniques and some of the hypothesis overlapped.
Most things are way easier to prove in Hilbert than in Bannach, though.

[Anonymous No.11468904]

Peano axioms are incomplete. Is there any problem that was proven to be independent from PA?

[Anonymous No.11468906]

>>11468870
>>11468831
rewrite/relearn it in your own words, see connections with other areas of math, get some intuition, etc, etc.

[Anonymous No.11468909]

Were books on calculus by GM Fichtenholz ever translated to English?

[Anonymous No.11469087]

>>11468904
interesting question

[Anonymous No.11469094]

how do you create a new mathematical object that isn't classified by something that already exists?

[Anonymous No.11469104]

>>11469094
why don't you take a problem and try to solve it, instead of "creating" useless rubbish

[Anonymous No.11469105]

>>11469094
At this point I'm pretty sure every "low complexity" algebraic structure possible already exists.

[Anonymous No.11469143]

>>11468904
Many ways of how to read that question.
The one you're probably looking for is
>Yes, e.g. the Paris–Harrington theorem
https://en.wikipedia.org/wiki/Paris%E2%80%93Harrington_theorem
>For any positive integers n, k, m one can find N with the following property: if we color each of the n-element subsets of S = {1, 2, 3,..., N} with one of k colors, then we can find a subset Y of S with at least m elements, such that all n-element subsets of Y have the same color, and the number of elements of Y is at least the smallest element of Y.
Similarly, to quote from
https://en.wikipedia.org/wiki/Goodstein%27s_theorem
>It was the third example of a true statement that is unprovable in Peano arithmetic, after Gödel's incompleteness theorem and Gerhard Gentzen's 1943 direct proof of the unprovability of ε0-induction in Peano arithmetic.

That said, with the more autistic reading of it the answer is more trivially yes in that all undecidable statements are some natural number claims and thus "problems". But yeah, okay.
As it's the core of the incompleteness theorem that you can encode Turing complete expression in the theory, the answer is yes less autistically also in that "problem about algorithms expressed in this way" also work. E.g. the Halting problem is a problem "in" the theory. But yeah okay, you wanted a practical natural number example I guess.

Related to the above encodings is also that you can encode countable structures (count through all polynomial p(x) with coeffs in N and \forall quantify over the argument x) and thus grab problems from those realms.

Interesting undecidable problems are Hilberts tenth
https://en.wikipedia.org/wiki/Hilbert%27s_tenth_problem
or the moral matrix problem
>Two 15 × 15 matrices A and B either can be multiplied in some way to yield the zero matrix or not

And then we have the nonstandard models (but I'm out of characters), you can read up explicit ones and any diverging fact about them will be undecidable

[Anonymous No.11469165]

>>11464544

I need a good idea for a term paper in undergraduate differential geometry. I wanted to write about a famous paper by Milnor about differentiable structures on the 7-sphere, but I don't think I know enough about algebraic topology or homology/cohomology theory

[Anonymous No.11469173]

>>11469143
The mortal matrix one also pops up on this list
https://en.wikipedia.org/wiki/List_of_undecidable_problems

I can't find a good overview about the simple non-standard models, but a good way to think of some is just take ordinal'ish structures that go one, ordinally beyond all the naturals you comfortable with, i.e. add additional numbers, but in ways which don't break the Peano axioms. Then if you got some of those non-standard models, find a claim about them that just so happens to not be true for the standard model (i.e. a distinguishing predicate) and then this property can't be provable from Peano arithmetic (otherwise the non-standard model wouldn't be a model for the axioms in the first place)

There's also interesting short Peano arithmetic problems that aren't proven, so they could well turn out to be undecidable. Bauer I think thinks the shortest one at all is:
∀a.∃b.∀x.∀y.(a+b)·(a+b)≠SS((SSx)·(SSy))
Roughly: “Are there infinitely many primes of the form c2−2 for some c∈ℕ?” (c=a+b),
were “prime” is being captured as not being of the form X⋅Y (for some X:=x+2≥2 and Y:=y+2≥2).

As another aside, I like to point out how not even ZFC can decide statements such as
>|Z|>|X| => |2^Z|>|2^X|
>"If a set Z has more elements than another set X, then Z also has more subsets than X."
This is basically because there's models of set theory where two sets X and Y with |Y|>|X| exponentiate to the same power set (a set Y between N and R may also have |R| subsets, like N does.)

>>11469165
I have a need of understanding averaging of Lie groups such as SE3 at the moment. Relates to interpolation of generating/tangent vectors as well as cost functions (and if you want to get into metric territory).

Some more hands-on papers I found were
https://core.ac.uk/download/pdf/19128027.pdf
https://projecteuclid.org/download/pdf_1/euclid.pgiq/1436795020
Would be thankful if someone looks at that :^)

[Anonymous No.11469178]

>In a discussion with Grothendieck, Messing mentioned the formula expressing the integral of exp(-x2) in terms of pi, which is proved in every calculus course. Not only did Grothendieck not know the formula, but he thought that he had never seen it in his life.

Has there ever been a more chad algebraist?

[Anonymous No.11469200]

>>11468906
Cool
>throws an exam at you that doesn't give a fuck about your own words, connections or intuition

[Anonymous No.11469217]

>>11469178
That's extremely sketchy, given Grothendieck worked in functional analysis before going full algebraic geometry.
He's known for the theory of nuclear spaces and even has some hands on theorems such as
https://en.wikipedia.org/wiki/Grothendieck_inequality
I remember reading some comp sci guy on SE who only knew Grothendieck from this and related theorems.
So anyway, if Grothendieck was writing papers related to Schwartz early work on distribution theory, there's no way getting around known what comes out when integrating exp(-x^2).

Of course, if you read that one 60 paper Grothendieck bio/essay (I think it's called "A land of which nothing is known but the name" or something similar), you can also read that Grothi went pretty mad at the end and babbled about why the devil made the speed of light c close to but not exactly 300something something, i.e. delusional stuff. I mean don't judge Gödel for starving to death or Nietzsche for eating his own shit, live's tough when your parents get killed off in WW2 etc.

[Anonymous No.11469223]

>>11469217
this is the essay btw., would recommend

http://xahlee.info/math/i/Alexander_Grothendieck_cartier.pdf

[Anonymous No.11469238]

>>11469217
I have a suspicious that beyond genius level intelligence will always strongly correlate with perceived insanity. You can convince yourself of some pretty seriously divergent ideas, and there's nobody out there smart enough to prove you wrong. And also the comorbidity with autism/high disagreeability means they won't seek social approval anyway.

>>11469223
This will be an interesting read, thanks

[Anonymous No.11469275]

>>11469217
>>11469238
Eh, I have less sympathy for Grothendieck's breakdown considering it was mostly his own fault. Can you even imagine receding from the subject you love dearly just because a couple of teens told you that you were "working for the man"? He had a lot of friends and followers who tried reaching out, but he was acting like a brat it seems, getting pissy that people wanted to work on their own things whilst simultaneously decrying that too many mathematicians were simply working on the same tracks laid out by their predecessors.
Also, despite what people seemed to say about him being humble, he seemed to be pretty fucking elitist imo. He constantly talks about how people aren't doing the right (e.g. his) research, how different pieces of mathematics are somehow less valid because they didn't fit into his vision (rather than proving his vision himself), and generally complaining that, heaven forbid, mathematicians need funding in order take on students and not starve to death. He could never see outside himself, and that was his strength and weakness.

[Anonymous No.11469294]

>>11469143
>https://en.wikipedia.org/wiki/Goodstein%27s_theorem
Cool. Maybe 3n+1 problem will be solved in similar way?

[Anonymous No.11469325]

>>11469238
np.
what's also a cool "read" is "I have a photographic memory" by Halmost, which is 500 pages of him instagramming mathematics conferences throughout his life.

>>11469275
Not sure if I recall someone reporting about him being genuinely humble (in the sense of being really nice to other people, not as a political statement)

>>11469294
I'm certain there's forum question online about that. I know for sure that there are generalized versions of it that have been found to be undecidable.
(Just googling it, I found that the original question >>11468904 also has an SE thread here: https://mathoverflow.net/questions/284921/undecidable-easy-arithmetical-statement
Anyway, here is what I remembered
http://people.cs.uchicago.edu/~simon/RES/collatz.pdf
)
Btw. if you want reading material, there's also funky modal logic stuff that validate a notion of consistency (or PA) that's not all too far away from the one Gödel tackles in his work, pic related

Anyway, coming back, probably the answer to questions along the lines of "could it be found to be undecidable" will generally tend to be yes - I happen to know no result about undecidability being undecidable, but I'm certain there questions have also been asked before (maybe in the guise of discussing Turing jumps).
But in some cases like this, it's a one-sided thing: If it's not possible to find a terminating sequence, it could be undecidable, while if it's possible to find one, then by the nature of the termination, you can decide it by brute forcing all numbers until you find the one that terminates. There's some statements, e.g. the Riemann hypothesis in analysis, which turn out to be of that type
https://en.wikipedia.org/wiki/Divisor_function#Robin's_theorem
I do some explicit dovtailing
(in the sense of https://en.wikipedia.org/wiki/Dovetailing_(computer_science))
here

https://youtu.be/Ox0tD58DTG0

[Anonymous No.11469326]

>>11469325
>I have a photographic memory
pic related is a random page of it, so you get the idea

[Anonymous No.11469328]

>>11469325
Halmos*

pic related is a random page of it, so you get the idea

[Anonymous No.11469334]

>>11469325
>Not sure if I recall someone reporting about him being genuinely humble (in the sense of being really nice to other people, not as a political statement)
You know, the more that I think about it, I suppose it is less about being humble and more generous with one's ideas.

[Anonymous No.11469356]

>>11469334
Ah yes, I suppose he wasn't prepping dem theorems and covering up how he got some results like maybe Gauss did :P

There's this (long, but still) talk by a logically minded guy (McLarty) who goes into some detail about a long talk series by Grothendieck of which the recordings exist and it's fun to hear his descriptions and elaborations on him

https://youtu.be/vmcbm5FxRJE

[Anonymous No.11469394]

>>11466377
>I want a better book
write one. there isn't a better book

[Anonymous No.11469413]

>>11469325
>turns out the consistency Godel used is too strong
Wait, you can weaken consistency?

[Anonymous No.11469533]

>>11469413
Gödel's incompletness theorem says that
>there exists no (I) proof (II) in Peano arithemtic (PA) that shows all (III) proofs are not inconsistencies.
The proofs are encoded as numbers, so "all" in "all proofs" (III) is a PA universal quantifier (\forall, in first order logic (FOL) although funny enough, sidenote, Peanos first paper was SOL). And the proof (II) is one of those proofs/numbers.
This is arithmetization and one approach to answering Hilbert.

But note that this approach naturally is arguably more than what Hilbert asked for (in any case, this is the line of argument about what's to be proven here by the author.). Hilbert wants consistency proofs of his math from modest assumption. Gödel here approaches is by showing PA can't show self-consistency (there's no II proof) and, thus (e.g. if you have a set theory like ZF that can model PA) PA surely can't ever punch upwards and say something about ZF that we'd believe.

Now since PA has non-standard models (e.g. extensions beyond all 1,2,3,...), you can think of a PA quantifier as one that can live in all those universes, it doesn't speak about a categorical world of numbers but is forced to speak about them all, and this is where using it to speak about all proofs makes problems - the forall of this theory is too weak to prove that is-not-inconsistency statement about its numbers.

Now what the author shows is that
>for all theorems of PA, you can show ("in logic") that for all proofs in PA, you can find a proof that the proof is not one of inconsistency.
Not that this formulation doesn't start with (I), i.e. it's not formally a non-existence statement of an arithmetized proof of a (self-reflecting) statement. In fact iirc the forall in the authors version isn't the same as in the body of the statement and that helps and is why it works.
Instead of arithmetizing proofs and showing that consistency is rejected, he inserts a modal provability operator and proofs "constructive consistency"

[Anonymous No.11469543]

[Anonymous No.11469553]

>>11469413
Gödel's incompletness theorem says that
Theorem (Gödel, PA):
>there exists no (I) proof (II) that shows all (III) proofs are not inconsistencies.
The proofs are encoded as numbers, so "all" in "all proofs" (III) is a PA universal quantifier (\forall, in first order logic (FOL) although funny enough, sidenote, Peanos first paper was SOL). And the proof (II) is one of those proofs/numbers.
This is arithmetization and one approach to answering Hilbert.

But note that this approach naturally is arguably more than what Hilbert asked for (in any case, this is the line of argument about what's to be proven here by the author.). Hilbert wants consistency proofs of his math from modest assumption. Gödel here approaches is by showing PA can't show self-consistency (there's no II proof) and, thus (e.g. if you have a set theory like ZF that can model PA) PA surely can't ever punch upwards and say something about ZF that we'd believe.

Since PA has non-standard models (e.g. extensions beyond all 1,2,3,...), you can think of a PA quantifier as one that can live in all those universes, it doesn't speak about a categorical world of numbers but is forced to speak about them all, and this is where using it to speak about all proofs makes problems - the forall of this theory is too weak to prove that is-not-inconsistency statement about its numbers.

Now what the author shows is
Theorem (Artemov, provability logic about PA):
>for all proofs, you can find a proof that the proof is not one of inconsistency.
Not that this formulation doesn't start with (I), i.e. it's not formally a non-existence statement of an arithmetized proof of a (self-reflecting) statement. In fact iirc the forall in the authors version isn't the same as in the body of the statement and that helps and is why it works.
Instead of arithmetizing proofs and showing that consistency is rejected, he inserts a modal provability operator and proofs "constructive consistency"

[Anonymous No.11469769]

>>11467111
FORTRAN

[Anonymous No.11469777]

>>11469200
That doesn't even make sense

[Anonymous No.11469881]

>>11469777
Sure it does
>doesn't give a fuck about your own words
Exam asks you to state a definition or theorem from the book verbatim. I've had two professors do this to me.
>connections or intuition
simply ask them something along the lines of :
"Prove that Given a solid ball in 3‑dimensional space, show that there doesn't exist a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball." with the original goal of making the students realize that this can't be proven and that in fact there does exist a decomposition. However, given some time limit and initial trust that you would never, ever mislead them, you fuck with their intuition on both a mathematical and rational level while also rendering any connections they happen to make moot.

[Anonymous No.11469889]

Can anyone explain cohen forcing?

[Anonymous No.11469914]

>>11469889
>just force the counterexamples to CH into existing bro

[Anonymous No.11469918]

>>11469889
cohen forcing is rape
#girlmathematicans #futureisfemale #coronavirus

[Anonymous No.11470084]

>>11469889
I suppose the page
https://en.wikipedia.org/wiki/Forcing_(mathematics)#Cohen_forcing
gives a rough idea of >>11469914, but not sure what you want or want to get at

[Anonymous No.11470092]

How does one teach to re-love math again? I have had trauma ever since I got out of high-school.

[Anonymous No.11470097]

>>11470092
Learn physics

[Anonymous No.11470103]

>>11470097
I am about to re-apply on CS program next semester, so that's a big no.

[Anonymous No.11470109]

>>11470103
Then it's over for you, sorry

[Anonymous No.11470125]

>>11470109
Don't be a dick anon.

[Anonymous No.11470187]

>>11466226
I agree. For example, it defines matrix multiplication, then in the next chapter proves that it is a composition of transformations. As opposed to the correct way of matrix are transformations from the start.
See pic. Even Lay doesn't do this.

[Anonymous No.11470195]

>>11470187
chapter [math] \rightarrow [/math] section

[Anonymous No.11470618]

Why do trigonometric substitutions work? Sin and cos are bounded, you could be replacing a variable that would take values larger than 1 or smaller than -1.

[Anonymous No.11470626]

>>11470618
This comment is in regard to integrals.

[Anonymous No.11470675]

>>11464544
e is a mirror of pi. Dimensional area of curve between is 1. Pi is the dimensional representation e is the kernel

[Anonymous No.11470682]

>>11470675
No matter how I look at it, it's you guys' fault I'm not popular.

[Anonymous No.11470700]

>>11470682
You're welcome anon. Why be popular for a moment in your life when you can make eternally beautiful mathematics.

[Anonymous No.11470705]

>>11470700
How do you deal with not having anyone to talk about interesting stuff you "discover". In CS there is usually a software that implements that thing and that software has a community.

[Anonymous No.11470713]

>>11470705
The Toilet paper situation is community based. The discovery is the reward.

[Anonymous No.11470756]

>>11470675
can u explain

>>11470705
same

[Anonymous No.11470776]

>>11470756
>can u explain
https://en.wikipedia.org/wiki/Mirror_symmetry_(string_theory)

[Anonymous No.11470783]

>>11470776
where is the pi and e in that?

[Anonymous No.11470822]

>>11470783
[math]\pi \sim \frac{1}{e}[/math] and T-duality maps the K-group of the circle of radius [math]\pi[/math] to the K-group of the circle of radius [math]e[/math]

[Anonymous No.11470835]

>>11470783
See OPs picture.

[Anonymous No.11470919]

>>11464544
>Yukari
https://www.youtube.com/watch?v=m9rGni-DJJc

but actually, wtf is yukari

[Anonymous No.11471229]

>>11470919
Japanese Yokai that manipulates the boundaries between things.

[Anonymous No.11471278]

All this stupid hysteria. I wanted to go to conferences and shit. I wanted to get the nice hand drawn diagrams with essentially undecipherable hand writing from my supervisor. No, says the man in the office, you stay home.

[Anonymous No.11471293]

https://terrytao.wordpress.com/2020/03/14/course-announcement-math-247b-classical-fourier-analysis/
>Next quarter, starting March 30, I will be teaching “Math 247B: Classical Fourier Analysis” here at UCLA. (The course should more accurately be named “Modern real-variable harmonic analysis”, but we have not gotten around to implementing such a name change.) This class (a continuation of Math 247A from previous quarter, taught by my colleague, Monica Visan) will cover the following topics:

>Restriction theory and Strichartz estimates
>Decoupling estimates and applications
>Paraproducts; time frequency analysis; Carleson’s theorem

>As usual, lecture notes will be made available on this blog.

>Unlike previous courses, this one will be given online as part of UCLA’s social distancing efforts. In particular, the course will be open to anyone with an internet connection (no UCLA affiliation is required), though there is the possibility that some restrictions on participation may be imposed if there are significant disruptions to class activity. For more information, see the course description.

[Anonymous No.11471294]

>>11470084
Don't you just hate it how 75 % of maths is by Jews and 75 % Jews are Cohens, so Cohen is basically the Bourbakified Grothendieck where everything is Cohen this or Cohen that, but Cohen is not a single person?

[Anonymous No.11471391]

>>11471293
Any other such courses offered like this?

[Anonymous No.11471403]

>>11471294
Same thing as hating Et al

[Anonymous No.11471412]

>>11471403
I really hate that guy. I'm glad Et al isn't specialised in étale stuff, otherwise I'd find him and pull his fucking spine out of his ass.

[Anonymous No.11471464]

>>11471293
Ironic.... only Corona could kill Tao

[Anonymous No.11471484]

>>11464544
cringe image

[Anonymous No.11471486]

>>11471293
based
but I doubt I will have the time for this

[Anonymous No.11471509]

>>11468831
I know people who do fine research, but got average gre scores. IMO while being good at keeping a large chunk of disparate definitions/theorems/intuition/techniques to get correct answers when faced with a problem in lower division and elementary is a helpful skill to have, it is more of a warning sign if you do very bad. Research is called as such as its mostly about reading and being creative with what you learned from the reading, knowing the product rule by heart can only help you in very limited situations but knowing how to internalize some theorem you just read will help you in many more.
I suggest proving the theorems before looking at the proof. If this is to difficult spend as much time as you can on it, read only the first word etc
You arn't wasting your time by proving every theorem. You are wasting your time if you don't.
Even if your proof is wrong it is likely salvageable after reading the book's proof. Honestly it is important to write incorrect proofs as you know for a fact that you learned something. Think of it like this: You can either write no proofs or you could write 1000 true proofs and 100 false proofs. In the second example even assuming you learned nothing from writing the 1000 true proofs, you for sure know 100 things you didn't, that is if you finish class in the first example you think 100 false things are true. The proof writing method is also good for building humility and confidence. The memorize method is good for building arrogance and incompetence. Final note, most hard textbooks problems fall from the proofs of the theorems, or at least you understand what the problem is "really" asking.

[Anonymous No.11471519]

>>11471509
>I know people who do fine research, but got average gre scores
Cool, we'll just keep using the GRE scam I mean, score as a gatekeeping mechanism- Every University

[Anonymous No.11471534]

>>11471519
Honestly just make graduate students teach some class and tell them to fuck off if they suck and have bad grades.

[Anonymous No.11471760]

[Anonymous No.11471766]

>>11471464
If only it would. Every dead chink is good news.

[Anonymous No.11471771]

I browsed openproblemgarden today and I just want to say that 90% of problems posted there are rubbish

[Anonymous No.11471991]

>>11471771
Its like I stumbled upon a old museum that only the caretakers keep up... does anyone actually use this site?

[Anonymous No.11472013]

>>11471766
you are just envious of their high iq
fucking moron

[Anonymous No.11472307]

>>11472013
Nope. I am disgusted by their ugly faces.

[Anonymous No.11472359]

Let [math]f, g \in \mathbb{C}[x,y][/math] be two irreducible polynomials.
Suppose that [math]f(x,y)=0[/math] iff [math]g(x,y)=0[/math] for all [math]x, y \in \mathbb{C}[/math].
Prove that the polynomials are the same up to a multiplicative constant, i.e. [math]f=ag[/math] for some constant c.
I know it follows instantly from nullstellensatz but I was looking for something simpler.

[Anonymous No.11472380]

>>11466683
Get Up or Get Down, though?

[Anonymous No.11472417]

>>11472359
Interesting question! I suspect not, but I'd like to know too.

[Anonymous No.11472467]

>>11472359
direct application of the fundamental theorem of Algebra ?

[Anonymous No.11472470]

>>11472359
>Suppose that f(x,y)=0 iff g(x,y)=0 for all x,y∈C

wouldnt i just be supposing that both functions are equal to the zero function if every f/g(x,y) is zero?

[Anonymous No.11472475]

>>11472359
i think you mean for any two polynomials with all the same roots strongly implies they are similar by at most a linear transformation?

[Anonymous No.11472479]

>>11469889
Let M be a model of set theory and consider the poset of all finite sequences of zeros and ones in the M ordered by extension. We can use partial information (only information about the initial segments of the reals in M) in M to build a new real c that differs from all the reals of M by making sure that c differs on at least one digit from every real in M. You do this by having a filter meet every dense subset of the poset that exists in M. Such a filter is called generic, and will be a infinite branch through the poset (which is a tree). An interesting fact about Cohen forcing is that it can be effectivized. You can ask that your filter only need to meet certain definable dense sets. In this way you can control the complexity of the real being created. in a way Cohen forcing is a generalization of finite extension arguments in computability theory.

[Anonymous No.11472480]

>>11472475
i think the only linear transformation that would allow that is a dilatation of space.
if they have the same roots, they share their Lagrange interpolation polynomial (of degree n) based on those roots.

if they have n roots, then they are of degree n with the TFA.
but f is equal (up to a multiplicative constant) to its Lagrange interpolation polynomial, being itself a polynomial

the result follows

tell me if I'm wrong here

[Anonymous No.11472498]

>>11472467
please elaborate
>>11472480
these are polynomials in TWO VARIABLES

[Anonymous No.11472532]

>>11472498
are they complex also or R2?

[Anonymous No.11472544]

>>11471519
The GRE actually gives very good information about potential graduate students. The only part that's a scam is how expensive it is, and the fact that they charge you extra to fucking email your scores out if you want more than 4. It's true that it has nothing at all to do with research talent, but it does indicate other things that are very important for students to have.

There are exactly two real reasons anyone does badly on the GRE; either you didn't take it seriously and spend a month or two practising, or you suck balls at calculus. Anything else is cope from people who got their egos hurt by it.
If it's the first, what message does it send to schools that an hour or two a day of practice for a month was too much to ask to get into their program? If you could have succeeded but didn't, then you're too lazy to do things that you really should do just because they aren't fun.
If it's the second, that's an even bigger issue, because almost all PhD programs in the USA pay their PhDs to teach calc courses. How can you be trusted to grade/teach calculus if it takes you 7 minutes to do an integral in polar coordinates?

[Anonymous No.11472548]

>>11472532
They're indeterminants anon...

[Anonymous No.11472551]

>>11472470
Yes, this holds for arbitrary fields K as long as they're infite

[Anonymous No.11472691]

>>11472532
both complex, I guess, if x and y are real then it's easy-ish.

>>11472498
damn I'm thinking about this one since 40 minutes and I've got no other ideas. most of what comes to my mind is only valid for single-variable functions. maybe I'm the real brainlet after all.

I was thinking a local approach using local inversion theorems could work, but at the same time what's interesting is that the functions are equal in points "distinct" from each other.

will be thinking about it, but why not try to show that the sets of points at which [math]f(x,y) = g(x, y)[/math] is both closed and open?

it's obviously closed, could try to show it is also open because it's a neighbourhood of every single of its points?

[Anonymous No.11472695]

Sunday evening book peak

https://youtu.be/MAL6rz3FyVw

[Anonymous No.11472727]

Hey lads, humanities bro here, what is the mathematics community's consensus on corona?

[Anonymous No.11472743]

>>11472727
It sucks ass. I wanted to attend some seminars and shit, but the cowards cancelled those.

[Anonymous No.11472747]

>>11472359
[math]f/g[/math] is an holomorphic function defined in a nicely large space, so you can probably borrow some results from several complex variables to analytically extend it to the null set and then spend three hours doing fucking estimates with muh maximus modulus to show it's constant.

[Anonymous No.11472803]

>>11472747
Meromorphic*

[Anonymous No.11472810]

>>11472803
not really, it's analytic in any compact subset of C^2, a few isolated points (zeros of f and g) expected.
i guess that's what the other anon meant by "holomorphic in a nicely large space".

[Anonymous No.11472822]

>>11472803
No.

[Anonymous No.11472839]

>>11472359
Either GCD(f,g) = 1 or f = ag.
In the case that gcd is 1, you can use undergrad ring theory arguments (Gauss to pass from C[x,y] to C(x)[y], then use Bezout's formula) to get the contradiction that the zero set is finite.

[Anonymous No.11472928]

>>11470822
what is a K group? is this just using something implied by complex analysis? if so it doesnt seem very special

on second note why do we even call e^z a thing, its just a label, its only sin and cos that exist and de moivres theorem. where is the e^iy thing from other than an arbitrary label when you come to derivatives being same?

btw i made a proof based on the fact that there is some f(theta) where f(th1)f(th2) = f(th1+2) implies this function equals its own derivative at all theta, and also must equal e^1 at theta=0. but idk what else to do to get it filling the complex plane? pls help

[Anonymous No.11472934]

>>11472928
Ever heard of K-theory?

[Anonymous No.11472940]

>>11472928
>on second note why do we even call e^z a thing, its just a label, its only sin and cos that exist and de moivres theorem.
No.
Let
[math] f(x):= \sum_{k=0}^\infty \frac{x}{n!} [/math]
(This is just the exponential series, also denotes [math] \exp [/math])
Then, if [math] a_n [/math] is any Cauchy-sequence of rationals converging to the (non-rational) real number [math] f(1) [/math], then the sequence [math] a_n^b [/math] converges to [math] f(1)^b [/math] and that's then actually [math] f(b) [/math]. I.e., the exponentiation of e is really special in that sense.

[Anonymous No.11472942]

>>11472940
and e is the real number 2.71.. etc.

[Anonymous No.11472943]

>>11472928
Sorry anon I was just making a joke post before

[Anonymous No.11472950]

>>11472839
thank you, I typed the solution just to make sure i understand it:

gauss lemma => the polynomials f, g are irreducible as elements of C(x)[y]
bezout identity (which only works in PIDs) => we can find u, v such that uf + vg = 1, where u,v are elements of C(x)[y]
multiplying by denominators, we get u'f + v'g = h, now u', v' are in C[x,y] and h is in C[x]
So if f(x,y)=g(x,y)=0, then h(x)=0 so x is one of (finitely many) roots of h.
Everything is symmetric so we can do the same for y, and we get that the zero set of f is finite.

Claim: f any two variable polynomial, zero set finite. Then f = nonzero constant.
proof: Assume otherwise. For any fixed x0, we can view f(x0, y) as a polynomial in y. This polynomial is either
(1) a nonzero constant or
(2) something else, but then we have some zero at f(x0, y0)
So it must be that (1) holds for all except finitely many x0. But then we get f(x,y) = h(x) for some h polynomial. And again if h has a root we get infinitely many zeros.

[Anonymous No.11472971]

>>11472934
no, pls explain

>>11472940
oh yeah, taylor series. that one is weird, i feel like its an emanation of higher looping based on differential structure rather than multiplicative and additive structure, and sin/cos matching e comes from their differential structure being somehow symmetric. but how/why? confuz

[Anonymous No.11473018]

>>11472950
The first part looks good.
The second part is correct too, but I think you could write it out a little cleaner than you did.

[Anonymous No.11473074]

>>11472971
[math]\exp[/math] maps algebras to groups (the simples case being the hom [map]\exp(A+B)=\exp(A)\cdot \exp(B)[/math] between addition and multiplication). If E is the two-dimensional identity matrix, then the matrix J=[[0,-1],[1,0]] has J^2=-E so exp maps the matrices generates by J into a group (the generated elements by J are all matrices of the form [math] x*E+y*J [/math], with e.g. real x,y). Since J has no real eigenvalues, the exp(x*J) are just SO(2). Then sin and cos pop up because those are just the two projection of the vectors in the standard representation of SO(2), i.e. if T is a 2-dim vector exp(xJ)*T just circles around the origin and it's components have sin and cos in it.

For the more general low dimensional context in which this split-off of a trigonometric function happens:
if F is characteristic not 2, with particular elements a and b, then if you have any (unital) F-algebra with two anti-commuting elements i, j such that their squares are central (in the sense that i^2=a*e and j^2=b*e, those are constant examples of a Clifford algebra behaviour), then the generated algebra is 4-dimensional.
If you got any 2x2 matrix representation of it, and v=t*e+w is a generic element (w is in the 3 dimensional part, also let r=sqrt(det(w))), then
[math]exp(v) = e^t * (\cosh(r) + \cosh'(r) * w / r)[/math]
Note that cosh' is just sinh.
cos and the Euler formula come into play if a and b is choosen so that the above reduces to the Hamiltonian quaternions.

[Anonymous No.11473080]

r=sqrt(-det(w)))

[Anonymous No.11473084]

>>11473074
>exp maps algebras to groups
whats an algebra and whats a group and why does it do that?

[Anonymous No.11473090]

>>11473074
>explaining advanced maths to freshmen
It's just not as funny without the yukari.jpg, the broken Latex and the TQFT.

[Anonymous No.11473097]

>>11472544
>you suck balls at calculus
...you've never actually taken the general GRE have you

[Anonymous No.11473104]

Oh Reminder to work with physicist fag... come out to play!!!

[Anonymous No.11473105]

>>11473090
im not a freshman im a neet! = D

[Anonymous No.11473106]

>>11473090
to be fair, it's just 2x2 matrix functions. I thought I'm being more or less hands-on, pic related

>>11473084
https://en.wikipedia.org/wiki/Exponential_map_(Lie_theory)

Also
https://www.wolframalpha.com/input/?i=MatrixExp%5Bx+*+%7B%7B0%2C-1%7D%2C%7B1%2C0%7D%7D%5D

[Anonymous No.11473127]

>>11473106
matrix.. exponentials? woah. i know these lie algebra things are important, should i read a book on them next? im doing linear algebra right now but im interested both in non euclidean geometry and abstract algebra. what should i do next?

[Anonymous No.11473145]

>>11473127
If a matrix has all real finite eigenvalues, then any convergence question will be measured by the biggest eigenvalue.
E.g. if [math] f(x):=(1-x)^{-1}=\dfrac{1}{1-x}=1+x+x^2+x^3+\cdots [/math] converges for |x|<1, then a matrix like A={{0.3,0}, {0, 0.6}} who's biggest eigenvalue has |0.6|<1 will also behave well with the above series expansion. I.e. "[math] \dfrac{1}{1-A} [/math]" will make sense, if you just take the power series and plug in A.

Donno. Borrow some books in the library and find out I guess. It won't hurt, even if you give it back quickly.

[Anonymous No.11473160]

Analysis and forecast of COVID-19 spreading in China, Italy and France
https://arxiv.org/pdf/2003.06031.pdf
>In this note we analyze the temporal dynamics of the coronavirus disease 2019 outbreak in China, Italy and France in the time window 22/01−09/03/2020. A first analysis of simple day-lag maps points to some universality in the epidemic spreading, suggesting that simple mean-field models can be meaningfully used to gather a quantitative picture of the epidemic spreading, and notably the height and time of the peak of confirmed infected individuals...

SARS-CoV-2 Entry Genes Are Most Highly Expressed in Nasal Goblet and Ciliated Cells within Human Airways
https://arxiv.org/ftp/arxiv/papers/2003/2003.06122.pdf
>The SARS-CoV-2 coronavirus, the etiologic agent responsible for COVID-19 coronavirus disease, is a global threat. To better understand viral tropism, we assessed the RNA expression of the coronavirus receptor, ACE2, as well as the viral S protein priming protease TMPRSS2 thought to govern viral entry in single-cell RNA-sequencing (scRNA-seq) datasets from healthy individuals generated by the Human Cell Atlas consortium. We found that ACE2, as well as the protease TMPRSS2, are differentially expressed in respiratory and gut epithelial cells. In-depth analysis of epithelial cells in the respiratory tree reveals that nasal epithelial cells, specifically goblet/secretory cells and ciliated cells, display the highest ACE2 expression of all the epithelial cells analyzed. The skewed expression of viral receptors/entry-associated proteins towards the upper airway may be correlated with enhanced transmissivity. Finally, we showed that many of the top genes associated with ACE2 airway epithelial expression are innate immune-associated, antiviral genes, highly enriched in the nasal epithelial cells...

SIR Model-based Prediction of Infected Population of Coronavirus in Hubei Province
https://arxiv.org/ftp/arxiv/papers/2003/2003.06419.pdf

[Anonymous No.11473164]

>>11473145
in such case are you then treating 1 and division like identity and matrix division?

[Anonymous No.11473186]

>>11473160
>https://arxiv.org/pdf/2003.06031.pdf
>"The model places the peak in Italy around March 21st 2020, with a maximum number of infected individuals of about 15,000"
>25k infected as of today
shit model

[Anonymous No.11473554]

>>11473097
I'm not talking about the general GRE dumbass
No one looks at your general scores unless you're a FOB who got 5% on the verbal

[Anonymous No.11474117]

>>11472950
I vaguely remember this as an exercise I saw somewhere. I think it was in algebraic curves by Fulton

[Anonymous No.11474247]

>>11473164
The 1 is identity matrix and I'm computing a power series. (And the result of summing up infinite of those powers then happens be be the same as what you get from the inverting algorithm.)

[Anonymous No.11474679]

Did someone ever attempt to apply Newton method to Riemann Zeta function?

[Anonymous No.11474833]

When did you realize that mathematics is spiritually closer to philosophy than it is to science?
Math is about exploring the world of ideas, same as philosophy. Science doesn't care about ideas unless they happen to be applicable to the outside world.

[Anonymous No.11474856]

>>11474679
Great idea. And then when it gives you that -2 is a zero, what do you do next?

[Anonymous No.11474922]

>>11474856
Check different number.

[Anonymous No.11474940]

>>11474922
Good thinking. And if you then find -4,-6,-8, and so on, then you will apply Newton to finding complex roots?

[Anonymous No.11474972]

>>11474940
Check different number.

[Anonymous No.11475101]

Has anyone here done tripos iii
Or even better gone from a different university to do a MAst
Is it a meme?

[Anonymous No.11475233]

>>11475101
I'm in part ii atm, but I've been to some part iii courses and have friends doing it, albeit they also did their undergrad here
It's absolutely not a meme and insanely hard, but also really cool.
Except if you want to do functional analysis. Then you'd have to be retarded to come here, as there is only one course that's even vaguely related to that area

[Anonymous No.11475411]

>>11475233
Nah I've done my functional anal time already in undergrad
Do you know if 6 lots of 3 credit courses is a normal choice or is that a madman move
I'd be crossing my fingers a little bit even getting in seeing as I got a 2:1 from a redbrick and it'd be returning to education after work

[Anonymous No.11475418]

>>11475411
>not being a madman

[Anonymous No.11475425]

Anyone here have whiteboards for home use they would recommend?

While portability would be convenient, I've been considering but am not absolutely sold on a tablet solution either.

[Anonymous No.11475428]

u guys r fuckin dweebs lmao

only maths i need to know is me + ur mom = u loooooooooool

i was gonna tell u to have sex but u dont know what that is so let me put it this way

have se^x loooool

[Anonymous No.11475447]

>>11475428
weird notation, something to do with the exponential e^x, i need help deciphering this guys

[Anonymous No.11475486]

>>11475428
>is me + ur mom = u
d...daddy???

[Anonymous No.11475884]

Pre-symptomatic Transmission in the Evolution of the COVID-19 Pandemic
https://arxiv.org/pdf/2003.07353

Understanding Epidemic Data and Statistics: A case study of COVID-19
https://arxiv.org/pdf/2003.06933

Propagation analysis and prediction of the COVID-19
https://arxiv.org/pdf/2003.06846

Predicting COVID-19 distribution in Mexico through a discrete and time-dependent Markov chain and an SIR-like model
https://arxiv.org/pdf/2003.06758

Can the COVID-19 epidemic be managed on the basis of daily data?
https://arxiv.org/pdf/2003.06967

Covid-19 spread: Reproduction of data and prediction using a SIR model on Euclidean network
https://arxiv.org/pdf/2003.07063

[Anonymous No.11475909]

>>11475425
Get a blackboard instead, if you can. They're much sturdier (you buy one, it basically lasts forever), less maintenance to keep from turning into a smudgy pile of unreadable shit, and you get a bigger math peen for using chalk.
I'm not sure how much they cost commercially though. I got lucky with mine, one of my dad's friends ran an elementary school and I bought four fuckhuge classroom boards off him when they refurbished some of the classrooms.

[Anonymous No.11476137]

Can someone mathematical-elegance-pill me on Conic Sections?

[Anonymous No.11476141]

>>11475884
These models are pretty shit.

[Anonymous No.11476375]

Why is it that mg is basically dead in the middle of a pandemic which has forced everyone to be quarantined in their homes?

[Anonymous No.11476629]

>>11476375
Too busy enjoying Big Brother Canada 8.

[Anonymous No.11476641]

>>11476375
Here they told all foreign undergrads to go home if they so wish, which means that the local Yukari fan clubs got dismantled.

[Anonymous No.11476697]

>>11475411
>6 lots of 3-unit courses
Yeah, that's a madman move. People do at least 4-5 courses each term (without looking at the number of units) and then cut down for exams so they get in the 17-19 range. But if you're set on 6 specific courses from the beginning it might work.
Which courses/ areas are you looking at?

[Anonymous No.11476837]

Anyone knows where is first cluster of EXACTLY four nines in Pi?

[Anonymous No.11476871]

Yo, I've started studying algebra and the professor is using a book called 'Algebra - Lang', on the cover it says it's a graduate book, so is the professor actually crazy or is the book easy and good for a first exposition to Algebra?

[Anonymous No.11476912]

>>11476871
Depends. If your professor is lecture heavy (he supplies a lot of examples and stuff that doesn’t show up in the book), then it’s ok.

[Anonymous No.11476992]

>>11476837
how do you know it exists ?

[Anonymous No.11477005]

>>11476992
a simple computation

[Anonymous No.11477104]

>>11476992
>how do you know it exists

http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html
ctrl-f nigga

[Anonymous No.11477404]

>>11476697
Algebra, Cat theory then a mix of diff and alg geometry

[Anonymous No.11477577]

>>11476912
I've tried reading the chapter on Ring Theory (professor is starting with rings for some reason) and it looks like quite a difficult book for a newcomer like me, well, for now I guess I'll just read Dummit&Foote and the class notes. He also recommended doing exercises 1 to 12 from chapter 2, I'm quite scared of this class now desu.

[Anonymous No.11477720]

What is the virtue of studying automorphic forms over arbitrary groups like GL(5) or Sp(4)? Do they tell us anything about solutions to polynomials? How?

[Anonymous No.11477730]

>>11464563
https://www.globalresearch.ca/covid-19-further-evidence-virus-originated-us/5706078/amp

[Anonymous No.11477741]

>>11468121
The talmud commands them to dominate the cattle.

[Anonymous No.11478546]

>>11477741
AAAAAAAH FUUUUCK

I can't fucking stand this shitty life anymore, I'm a fucking brainlet I'm never making a breakthrough in mathematics, I'll never crave my name in history.

But that's OK. It really is. That would be fine by me if only I could have a little happiness in life, why nobody loves me? I want a fucking girlfriend to love, to depend on me, anyone, why can't I even have that motherfucker fucking piece of shit? I was born a brainlet and on top of that I'm not dear or important to anyone else.

WHAT KIND OF FUCKING LIFE IS THIS GOD? WHY WAS I FUCKED UP LIKE THAT? LET ME AT LEAST HAVE SOMEONE THAT LOVES ME, I WOULD BE FINE WITH MY EXISTENCE, WITH MY MEDIOCRITY IF I AT LEAST HAD A FEMALE THAT LOVED ME DEEPLY. I WOULD ABANDON ALL MY DREAMS FOR HER, FUUUCK.

I'll never have that will I? Having so much self-counciousness is hard, I can't cope with failure, if at least I had intelligence I could make my dreams come true

[Anonymous No.11478596]

This man legit having a breakdown in the middle of a 4chan thread

[Anonymous No.11478899]

>>11476871
Often it means that the prof will roughly follow the structure of the book but might skip some topics or put a different emphasis.

[Anonymous No.11478999]

>>11478546

The second part doesn't have to be true forever.
Go to therapy anon, and live your life before its too late. Go outside, meet people, develop hobbies, find your purpose. For family. For country. For loved ones.

[Anonymous No.11479070]

>>11478999
I don't think I need that, I'm not crazy or mentally ill, it's the people around me, they're the ones making my life hell, or rather they've been making my lfe hell since I was a little kid, it's all their fault, they fucked me up from the start, Ibcould be a IMO medalist if I had the training, but they were so clueless that they just let me do whatever I wanted, no that's wrong, they let me do whatever THEY wanted and it never crossed their fucking minds that I could be something big, I always dreamed of that golden medal ever since I was 15 but it was already too late for IMO, then it became too late in college as well and now it's too late for everything.

All that is in the past anyway, I don't care anymore, I can cope with my dreams being wasted, or rather, I could if I at least had a girlfriend. Actually not A girlfriend, I'm talking about THE girlfriend. It's probably too pathetic for all of you, but I've been in love for the same girl for about 2 years and you know what's funny about all that? I never even talked to her once. HAHAHAHAHAHAHAHAH, IT'S SO FUCKING PATHETIC, I THINK ABOUT HER ALL THE TIME, I KNOW A TON OF THINGS ABOUT HER LIFE, I KNOW HER NAME, HER FACEBOOK ACCOUNT, THE PAPERS SHE PUBLISHED, WHY CAN'T I FUCKING DO SOMETHING? WHY AM I SUCH A COWARD?

I've already gave up on my dreams, all that's keeping me alive is the light of hope that she feels the same about me, I mean it is possible isn't it? I noticed she looks at me sometimes, maybe it's just my imagination but I like to think she finds me attractive at the very least, but even then I can't talk to her, if her answer is not what I expect then it would truly be the end of the line for me, so I guess I'll just have to keep living in doubt forever until she marries another guy, but even then maybe she'll still think of me who knows. God has cursed me in this terrible, pathetic, humilliating life.

If only I was born intelligent, then I could forget about love and all that stuff.

[Anonymous No.11479100]

Day Level Forecasting for Coronavirus Disease (COVID-19) Spread: Analysis, Modeling and Recommendations
https://arxiv.org/pdf/2003.07778

Machine Learning the Phenomenology of COVID-19 From Early Infection Dynamics
https://arxiv.org/pdf/2003.07602

A Novel AI-enabled Framework to Diagnose Coronavirus COVID 19 using Smartphone Embedded Sensors: Design Study
https://arxiv.org/pdf/2003.07434

COVID-19: The First Public Coronavirus Twitter Dataset
https://arxiv.org/pdf/2003.07372

[Anonymous No.11479427]

why didn't you major in physics, anon?

[Anonymous No.11479440]

Why are there so many Mersenne primes (one less than a power of two) with more continuously being discovered, but so few Fermat primes (one more than two to the power of a power of two)?

[Anonymous No.11479455]

>>11479070
shoot ur shot, you only live once. Im a brainlet and Im graduating in physics. I stopped believing I can't do things and just started giving it my best effort. perseverance goes much farther than talent could in the long run.

I don't know you or your experience, but remember that nothing comes from nothing.

[Anonymous No.11479473]

>>11477720
Because the partition function [math]Z[/math] of a CFT on a symmetric [math]G[/math]-space [math]X[/math] naturally must be invariant under the mapping class group [math]\Gamma\subset G[/math] of [math]X[/math], hence can be expressed as a sum over automorphic forms. For instance, with [math]X = \mathbb{T}^2[/math], [math]G = SL(2,\mathbb{R})[/math] and [math]\Gamma=SL(2,\mathbb{Z})[/math] the modular group, this gets us the natural setting for a CFT partition function [math]Z[/math] on the moduli of the torus [math]\mathcal{M}_1[/math] as a section of a V-bundle over [math]\overline{\mathcal{M}}_1[/math] (modulo the action by Dehn twists [math]\mathbb{Z}[/math]), and we can in fact write [math]Z[/math] as a sum over modular forms such as the Jacobi theta.

[Anonymous No.11479479]

>>11479440
Fermat primes grow really, REALLY fucking fast due to the double exponential. They're just rarely feasible to work with computationally if n is not very small.
We've confirmed tens of millions of Mersenne numbers to be composite, and a couple hundred Fermat numbers.

Comparatively speaking, we've done thousands of times better discovering 5 Fermat primes in a few hundred tests than discovering 51 Mersenne primes in tens of millions of tests.

[Anonymous No.11479482]

>>11479473
>math typesetting messing up all over the place
> just Yukariposter things

[Anonymous No.11479483]

>>11479427
What is physics compared to mathematics? Nothing more than trash. Physics is simply a failed human attempt at describing natural phenomena, but mathematics goes beyond the natural, you could say it's almost a supernatural thing, it's the study of the complete abstract, it's the structure of the structure, it doesn't depend of humans or nature. Pure mathematics is the only truth this world can comfort us with.

[Anonymous No.11479650]

>>11479483
>Pure mathematics is the only truth this world can comfort us with.
(Don't tell them about Gödel's incompleteness theorems. They might snap.)

[Anonymous No.11479652]

>>11479440
Maybe it's because beyond 65537 every Fermat number is composite?

[Anonymous No.11479897]

>>11479652
Any source on that?

[Anonymous No.11479929]

>>11479897
it's a joke, anon. This is an open problem.

[Anonymous No.11479930]

Rate my tinder bio

What are the chances I find a cute mathematician gf?

[Anonymous No.11479932]

>>11479930
>if you can't name all the properties of a ring
can you?

[Anonymous No.11479946]

>>11479932
You kidding?
I)A is an abelian group with respect to addition
II) multiplication is associative
III) multiplication ha a unit element
IV) distributivity holds

[Anonymous No.11479956]

I double majored in math and physics at one point. My advisor looked at the math courses I had taken so far and said "Yea this is about all the math you'll ever need" and it bummed me out really bad.

Also, everytime I study physics I find myself just wanting to focus on the math and it feels like the physics is getting in the way.

No philosophical reasons here. Just like what I like.

[Anonymous No.11479959]

>>11479930
>ring with a upper case r
>kähler with a lower case k
Well, at least you did get ä right instead of using a or ae.

[Anonymous No.11479967]

>>11479959
What difference does it make?

[Anonymous No.11479970]

>>11479427
the post about liking math more than physics is a reply to this post.

[Anonymous No.11479977]

>>11471991
I just finished writing my prospectus based on some problems from there.

[Anonymous No.11479980]

>>11479946
>forces his ring to be unital
Just laughing at your attempt while I read Hecke theory. Nice try, kid.

[Anonymous No.11479982]

>>11479967
Is the cause of your lowered IQ one of the following:
>your alcoholic/junkie mother didn't stop her substance abuse while pregnant
>your alcoholic/junkie parents kept dropping you on the floor as a baby
>your brain was deprived of oxygen while you were sucking your dad's dick too hard

[Anonymous No.11479983]

>>11479980
Well, at least this dyke didn't claim they are all commutative.

[Anonymous No.11479993]

>>11479982
I'm a low IQ because I wrong the word 'ring' with an upper case R? Wtf

[Anonymous No.11479997]

>>11479993
I'm a low IQ because I wrote the word 'ring' with an upper case r? Wtf

[Anonymous No.11479999]

>>11479930
Did anyone here ever found a mathematician/physicist girl on tinder?

[Anonymous No.11480001]

>>11479993
>i wrong
:^)

[Anonymous No.11480099]

>>11479930
pure cringe.

[Anonymous No.11480111]

>>11479980
>>11479980
desu desu both you and he said "Ring", not "Rng"
;^)

[Anonymous No.11480123]

>>11465653
When x tends to infinity you just divide each term by the x of highest order and simplify
Anything that's x^m/x^n with m<n is 0
If x tends to values other than infinity you do algebraic shit to remove the trouble term, which usually is a denominator that equals 0 (a good example for this is the definition of derivative where f'(x)=lim when h tends to 0 of [f(x+h)-f(x)]/h)

[Anonymous No.11480142]

>>11479983
Banned from /algeo/

[Anonymous No.11480148]

What is good resource material to PRACTICE linear algebra and calculus? I am deriously tired of looking for s good bunch of fucking exercised and just finding pages with a small handful of exercises and absolutely no explanation whatsoever (that if you can find exercises with the solutions to them)
I NEED TO FUCKING PRACTICE FOR MY FINAL EXAMS

[Anonymous No.11480195]

>>11480148
Just make up problems, its calc and lin alg, it's not hard

[Anonymous No.11480225]

>>11466422
GOAT mathematician right there
shame there isn't much about him on the internet (as far as i could find)

[Anonymous No.11480231]

>>11470125
he's right tho
you'll spend your first 2 years doing dumb shit with binary trees red black trees and it doesn't really use any math besides basic logic

in the first two years of physics you learn what an integral means at least

t. ex comp sci student

[Anonymous No.11480327]

What's the meaning of doing mathematics if it is ultimately a human creation? Nothing in mathematics exists, it's all a human made game, nothing more, mathematicians are no better than e-sports pros.

[Anonymous No.11480329]

>>11480327
yes
being an esport pro is a great thing

[Anonymous No.11480333]

>>11479930
if anything, you're gonna get a handful of "OMG I LOVE SCIENCE" roasties who'll buy into any buzzwords you feed them; that happened to a physicist friend of mine, albeit he was much less pretentious on his bio (merely stating his major and "nerdy" personality along with normie interests).
>>11480148
>I am deriously tired of looking for s good bunch of fucking exercised and just finding pages with a small handful of exercises and absolutely no explanation whatsoever (that if you can find exercises with the solutions to them)
just check your answers in WolframAlpha or something. if you want exercises that involve proofs, grab a book and see if you can find a solution manual online, or if you can find explanations on Math StackExchange. learn to search properly

[Anonymous No.11480334]

>>11480329
No, it's not, you're not searching for the truth of life and the universe, you're not doing something transcendental, you're not changing the world, you're not even changing yourself, all you're doing is playing a fucking man-made game.

[Anonymous No.11480338]

>>11480334
lmao @ u if you think you will "change the world" or "search for the truch of life and universe" by doing math

[Anonymous No.11480342]

>>11479930
My main interests are rectangles, triangles and morse theory on holomorphic fuctions. I'm also fond of cunny. Trying to find pussy around here.
If you can't even suck dick properly, then just swipe left please.

[Anonymous No.11480346]

>>11480338
You idiot, I'm saying the opposite of that, I was making a comparison between mathematicians and e-sports pros, both are never doing any of the things I metioned, both are merely playing games for a living.

[Anonymous No.11480347]

>>11480327
it's fun and sometimes it illuminates perspectives in other fields such as physics, the natural sciences and engineering. Math gets funding ultimately because of this last reason, but we all do it solely because we like to tackle abstract problems

[Anonymous No.11480349]

>>11480333
He didn't even find at least one mathgirl or physicsgirl there?

[Anonymous No.11480352]

>>11480346
nothing wrong with playing games for a living if you enjoy the game

[Anonymous No.11480369]

>>11480352
It is wrong when you consider life as a whole. Why are we here? What's the meaning of life? Deluded people will say that there isn't any or that you should create your own meaning. That's wrong, the meaning of life is searching for the truth, what is the truth though? Does it even exist? One thing I know for sure is that the truth can't come from a man-made creation and mathematics is just that, a human made game, why are we wasting our time with that game when we should actually be searching for the truth of the universe?

[Anonymous No.11480384]

>>11480369
how about you fuck off back to /pol/ or /r9k/? they might like your vaguely spiritual motivational garbage

[Anonymous No.11480752]

>>11479482
It's not my fault ok, the 4chan TeX fucks up if there are too many [math]math[/math] environments in one line.
>>11479956
Your advisor is a physicist, of course he'd want you to focus on the physics instead of the math. Once you've had enough experience you'll find that focusing too much on the formalism in fact hinders you from making progress.

[Anonymous No.11480813]

>>11480349
no, they're either too autistic to use tinder (dated such a mathgirl once) or just not interested in someone in the same major, if not already taken

[Anonymous No.11480817]

Is anyone good at Propositional Logic and converting wffs into DNFs?

[Anonymous No.11480843]

How do I get 4chanX to display TeX?

[Anonymous No.11480973]

>>11480813
>they're either too autistic to use tinder (dated such a mathgirl once)
Based, that's my dream, how was it?

[Anonymous No.11480987]

>struggled with drug addiction
>literally homeless
>born in a shithole country
>became fluent enough in english to publish in academic journal
>immigrated to america alone
>became the most prolific mathematician of all time

what are you doing, /mg/?

[Anonymous No.11480992]

>>11480843
>How do I get 4chanX to display TeX?
What have you tried?

[Anonymous No.11481011]

>>11466578
Emacs Calc is the thinking man's choice

[Anonymous No.11481018]

>>11480195
Explain why it took the human race 10000+ years to discover it.

[Anonymous No.11481114]

>>11480987
Based suitcase man has blessed this thread

[Anonymous No.11481120]

>>11480987
to be fair, he only became a "homeless" drug addict after he already has been an established mathematician for years

[Anonymous No.11481162]

>>11480992
I obviously tried googling the problem, but nothing came up.

[Anonymous No.11481379]

>>11481018
Dude, creating calc is not the same thing as: what's the integral of x*sinx, or is the set [math] s=span\{(a,b,b),(1,0,1)\} [/math] a subspace of [math] R^3[/math]?

[Anonymous No.11481452]

>>11481379
>is the span of these vectors a subspace

[Anonymous No.11481492]

>>11481018
the basic ideas of linear algebra and calculus were known to ancient greeks or something
just because the modern formalization was only done 200-300 years ago doesn't mean there is anything extremely difficult there
do you remember the meme paper where a biologist rediscovers "a method to determine area under a curve" i.e. integration? these are really intuitive things for a somewhat smart person

[Anonymous No.11481539]

>>11480817
there's programs for that

[Anonymous No.11481546]

>>11479930
I wouldn't date anyone who doesn't capitalize names like Kähler you fucking piece of shit

[Anonymous No.11481565]

>>11481546
Ah well, I see it has been pointed out in >>11479959 already

[Anonymous No.11481589]

>>11481452
I know, but if he can't make up problems for lin alg and calc, I don't know if he does

[Anonymous No.11482882]

>>11476871
Anyone who uses Lang is crazy. Try Undergraduate Algebra by Lang instead. That guy knows what he's talking about.

[Anonymous No.11483135]

New Bread when?