/sci/ - Science & Math

Math is boring lol

Do you take math notes using LaTeX?
https://www.strawpoll.me/20291441

>>11772940
Apply it to something fun and you won't think that.

>>11772937
>Math general
>Pic is not math related
Holy shit, never create another /mg/ thread man

>>11772962
still mad at the anon that got his dick sucked

/gmmg/

>>11772940
At first, but not after you find your thing.

>>11772937
I'm a retard who got a BS with the minimum courses required (it was my secondary degree) 4 years ago and hasn't touched any math since. What's fun to study during lockdown?

Just a reminder that tooker has an rh thread with some new stuff here >>11769446

Also I assume it's chill for me (an undergrad 50% done) to sit in on one of the OATS things tomorrow?

>>11773164
Dynamical systems is interesting. You could try set theory too if you want to hate yourself for 2 chapters before it gets awesome

>>11773200
>Also I assume it's chill for me (an undergrad 50% done) to sit in on one of the OATS things tomorrow?
Ah merci for reminding me to remind! Have you been on any of them yet? You don't have to show yourself, you don't have to say anything. You can just listen and watch.

8½ hours till
https://sites.google.com/view/nialltaggartmath/oats
>Kathryn Hess (EPFL)
>Title: Calculus from comonads
>Abstract: (Joint work with Brenda Johnson.) The many theories of "calculus" introduced in algebraic topology over the past couple of decades--e.g., Goodwillie's calculus of homotopy functors, the Goodwillie-Weiss manifold calculus, the orthogonal calculus, and the Johnson-McCarthy cotriple calculus--all have a similar flavor, though the objects studied and exact methods applied are not the same. We have constructed a relatively simple category-theoretic machine for producing towers of functors from a small category into a simplicial model category, determined conditions under which such tower-building machines constitute a calculus, and showed that this framework encompasses certain well known calculi, as well as providing new classes of examples. The cogs and gears of our machine are cubical diagrams of reflective subcategories and the comonads they naturally give rise to.
>In this talk, I will assume no familiarity with comonads and only basic knowledge of simplicial model categories.

long story short:

>didn't like math in high school
>want to do CS as a major years after I left high school
>need to take these courses to be able to apply https://www.adelaide.edu.au/learning/adelaidex/programs/mathtrackx
>first course is https://www.adelaide.edu.au/learning/adelaidex/free-online-courses/polynomials-functions-and-graphs
>course goes on for 4 weeks and they expect 3-6 hours of study from you a week

Does this seem slow to you guys? I'm not even great at math, but studying 3-6 hours a week seems kind of slow? Should I just used Khan Academy and jump to the exam portion as soon as I can?

>>11773200
>OATS things
What's that?

>>11773234
De rien, no I haven't gone to any yet, happy that some have been recorded tho. Been a little scared to go because I can follow it but I basically have no idea whats actually going on. This might be the one I finally show up for, but that means I have to go to sleep.

>>11773259
OATS: Online Algebraic Topology Seminar. You can find out more here: https://sites.google.com/view/nialltaggartmath/oats I think there are only two more to go.

>>11773164
The set theory idea isn't actually a bad one. Do that until you can no longer take it, and then maybe a bit of topology.

>>11773259
Thiis >>11773234

>>11773255
You could study other relevant things at the same time if you think you have extra time. Then you get to the exams and ace them!

>>11773268
Nighty night!

I have about 12 hours before a test on infinite series. I didn’t look at the materials at all. What can I study in the next few hours to pass this test?

>>11773313
If its calculus then just use Paul's online math notes, the Calc II notes cover infinite series

If its analysis and you aren't a brain chad you're going to get raped

>>11772937
How smart do you have to be to study math. I'm looking at the University of Toronto and their introductory math course MAT157. Which is called "Analysis 1." Do you have to be a genius to be succesful in mathematics? How smart do you have to be?

>>11773365
Here is what I scraped from a forum.
"MAT157 won't have the introduction to logic and proofs part at the beginning. You'll be expected to pick that up on your own, which I think is a reasonable expectation for people in that class. They're a self-selected bunch of people. Basically, some familiarity with proofs is helpful, but if you're the sort of student who will do well in MAT157, you're also the sort of student who can learn about proofs readily on your own. It's a hard course. "

I'm kind of intimidated.

>>11773372
Analysis is the great brainlet filter for science and math, you either are capable of doing it or you aren't. You should dl Rudin's Principles of Analysis and work diligently on the exercises. If you can manage to do them you will crush the class you're interested in almost guaranteed.

>>11773365
https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/

>>11773383
Listening to geniuses sermonize about who can do what they are naturally masterful at is like listening to Warren Buffet talk about how anyone can become a multi-millionaire. You should not settle for the empty words of people that are already self-satisfied and beyond petty concerns that could destroy you overnight like failing an exam or making one wrong investment.

>>11773365
>Do you have to be a genius to be succesful in mathematics?
Define this success of yours or the question about how smart one needs to be is impossible to answer.
>MAT157 won't have the introduction to logic and proofs part at the beginning. You'll be expected to pick that up on your own, which I think is a reasonable expectation for people in that class
Proofs may seem scary at first, but it's actually pretty easy to get used to them by starting with something easy and imitating the proofs you see in your course material. It's not like they will make you prove anything big at first anyway.
>I'm kind of intimidated.
Now is not the time for fear. That comes later.

>>11773389
He does remark the importance of talent, but I can see your point.

In any case, I realize I'm not qualified enough to answer the question meaningfully. So I'll shut up and let the big boys in the thread give their opinion

>>11773313
>infinite series
Mate perhaps you'd want to study from the definitions first. Series are infinite by definition so what you said is redundant.

>>11773390
>Define this success of yours or the question about how smart one needs to be is impossible to answer.
I have listed goals in increasing difficulty:
1. At the bare minimum would want to graduate mathematics (with a minor in computer science),
2. It would be acceptable to find a job in industry (software engineering preferably, potentially fincance or actuarialism),
3. I very, very satified if I would be able to go to graduate school for computer science (MSC or PHD), and
4. I would be feel incredibly accompished if I would be able to go to gradutate school for mathematics (MSC or PHD).

>>11773383
>https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/
Isn't it foolish to ask a genius for advice on this matter. I can't differentiate weather this article is mindless "follow your dreams" sensationalism or actual advice. I have seen engineers on YouTube responding to questions saying that "you don't have to be talented at math to be an engineer" and that you should "not let anyone stop you from following your dreams." I realize that engineering is a lower caliber of mathematics than what a mathematics major studies by I would assume you have to be reasonably intelligent to be an engineer. Could someone else give their opinion? Maybe Terrance Tao's advice really is correct and I am wrong? I don't know.

About myself:
In my high school of greater than 1000 people, I am probbably the most talented at mathematics. I have a reputaion for helping students with math. And most teachers know I am good at math. I don't have to take notes in high school at all and I have excellent grades. I have read "Structure and Interpretation of Computer Programs." I have thought myself C and C++, I can create non-trival GUI programs using FLTK. I plan to read "How to Prove It" by Velleman.

>>11773423
If that is what you think success is, then I am happy to say you don't need to be genius. Go for it and make us proud!

>>11773423
What does being good at math mean in high school mean where you live? Genuine question. What topics do you learn?

>>11773442
>What does being good at math mean in high school mean where you live? Genuine question. What topics do you learn?
Good question. Canadian schools are a joke in comparsion to Eastern European schools and Asian school. They are on par with American schools and perhaps Western European schools.

The textbook is called "Calculus: A First Course." James Stewart, I believe.
I have attached screenshots of the table of contents to this imgur link: https://imgur.com/a/REGjt03

Here is a link to the full textbook: https://sites.google.com/a/share.epsb.ca/wilde-math/my-subjects/math-31-ap-ab/calculus----a-first-course-textbook
(Obviously this is not my math teachers website, or my school's. I not stupid enough to dox myself on 4channel)

>>11773432
Provided that I have a passion for math and treat mathematics as if it is a job by allocating 40 hours per week (or more) studying it, it is really possible for me to go to gradutate school at a respected school for mathematics (MSC/PHD). I always assumed mathematics gradute school was orders of magnitude more difficult than CompSci graduate school.

>>11773456
Alright, neat. I skimmed the book (I had some familiarity with Stewart) and looked over at the course page for UoT MAT137.

Based on this, if the part about proofs scares you, a good start would be getting yourself aquainted with the formal epsilon-delta definition of limits, derivatives, etc and proofs of their properties, if you haven't already. The book suggested by the UoT course is really good and actually a rather fun read. You can get it at libgen or similar, there are great scans with bookmarks and all that jazz. Be sure to do the exercises.

Hey guys i wanted to study cs but due to high cost i am unable to study it. Now i have chance to study 3 year bsc in mathematics(honors). I am from india. It has courses from cs too but final year is all maths. I am afraid i cant handle those greek theorems or proofs that people talk about like analysis etc. Should i take it? It'd cost me 150$a year. If you guys wanna look at syllabus or curriculum i can share it.

>>11773479
>UoT MAT137
I belive the introductory math course if actaully MAT157, not MAT137. I could be wrong. If you could kindly look at MAT157. I could have also made a mistake.
>The book suggested by the UoT
Are you refering to Spiviak?

Also, I would like to thank everyone answered my questions.

>>11773483
>I am from india.
leave

>>11773456
If you are worried about proofs, I suggest you give this a look. Not only does it have exercises that make you prove and deduce, but also makes you analyse the proofs to find their vulnerabilities, Try them and hit me with questions if you so wish (maybe babby's first proofs but still better than the Trump vs Obama from last thread). https://people.maths.bris.ac.uk/~sz16567/Writing%20mathematical%20proofs%20-%20exercises.pdf

>>11773467
>Provided that I have a passion for math and treat mathematics as if it is a job by allocating 40 hours per week (or more) studying it, it is really possible for me to go to gradutate school
I don't promise you any grand futures as a professor somewhere, but I am fairly sure you would be accepted.
>respected
No idea about this. Perhaps. I wouldn't place my bets on Oxbridge/Ivy League unless there were signs of big talent (and/or a bit of extra money), but I think [math]\text{decent} \le \text{your future grad school} \le \text{respectable}[/math] would be likely. I don't know how the English speakers' system works, to be desu.

>>11773489
My defination of respectable was top 50 in the world. So like University of Toronto, University of British Columbia or McGill.

>>11773485
I was looking at MAT157, apologies for the confusion.
And yes, Spivak. It's a nice book.
I was slightly worried about >>11773380. Rudin's fine but maybe a little harsh for a first brush. Some parts are not even appropiate for the course anyways, it seems to remark geometric intuition and I think Rudin doesn't even show the classic tangent thing for differentiation for example.

>>11773488
Well here is the syllabus link
punjabiuniversity.ac.in/syllabi/index.php?folder=Academic%20Session%202019-20%2FFaculty%20of%20Physical%20Science%28s%29%2FUnder%20Graduate%20Courses

Three year syllabus in three different files. The course is bsc (honours in mathematics)
I can handle calculus trigonometery but i have no idea if there is some thing really hard. It also suggests a textbook for each course. Guys could any one tell me which course are going to be hardest? In our high school (grade 11 to 12 ) we were taught the all kinds of maths and indian maths syllabus is pretty tough so how would you guys see

>>11773501
So you were looking at MAT157 when you mentioned MAT137 in your previous post? If I understood that correctly. MAT157 uses Spivak. Is Spivak the book that was suggested by UoT that "was a fun read."
You confused me a bit. :)

>>11773489
My definiton of repectable is top 50 in the world (University of Toronto, University Of British Columbia or McGill).
My defination of prestigious is top 10 in the world (Oxford, Cambridge, Harvard, etc).

>>11773496
>>11773512
As I said, no idea. I don't know what it takes to be accepted into any of those. If it is what you really want, don't you think it's worth the risk? It is possible you don't get into any of the top 50 schools, it is possible you will be paying your student debt for years to come, it is possible that life sucks and then you die (well, this is certain), but it is also possible that you will make it and you will make it big. Big wins require big stakes. I'd give it a go.

>>11773512
>So you were looking at MAT157 when you mentioned MAT137 in your previous post? If I understood that correctly. MAT157 uses Spivak. Is Spivak the book that was suggested by UoT that "was a fun read."
Exactly.
God I need to sleep.

>>11773518
I appreciate your help. Thank you very much.

>>11772814
Because usually that's how it goes

Making a quiz with my family. One of them is doing a "maths" round, which will likely be pseudo maths problems (for lack of a better term) like you'd see on internet IQ tests.

>>11773856

>>11773861

I believe this is what asian boomers share on facebook

i need a way to turn a cosheaf into a sheaf
any ideas?

>>11773947
Perhaps. Can you solve it? It is a valid problem.

>>11774127
Sheafification.

Given U, V independent random variables from Uniform(-1, 1).

Prove that (U, V) / ||(U, V)|| is independent from ||U, V||.

It seems intuitively obvious, since when you divide with the norm you only keep the "angular" information and nullifying any "length" information, but I don't know how to prove it.

It's not an exercise, just autism
https://en.wikipedia.org/wiki/Marsaglia_polar_method

>>11774201
Not true. If ||(U,V)|| > 1, there are values of (U,V) /||(U,V)|| that cannot occur.
I know it works if U and V are Normal random variables. I don't know what other distributions might work.

>>11773268
Welp, that one went wayyy over my head. The description made it same a lot more accessible then it actually was.

Conclusion: Kathryn is cool, cat theory is scary.

how do you become better at not doing retarded small mistakes in math?
i got a b- despite spending hours studying and understanding everything. what's more annoying is that it was trivial mindless stuff like writing (x+1)^2 as x^2 + 1, 77+33=100 or just writing entirely different numbers for some reason. what's even more annoying is that i checked my answers once to make sure that i didn't do any mistake

>>11774331
spend more time doing math that consists of more big pictures ideas rather than low level computations

>>11772937

Sagbi bases how do they work

Toric ideals; are they based?

>>11774235
>Not true. If ||(U,V)|| > 1, there are values of (U,V) /||(U,V)|| that cannot occur.
like which values?

>>11774603
also, found this here:
https://stat.snu.ac.kr/theostat/course/adv_stat_method/%EA%B3%A0%EA%B8%89%ED%86%B5%EA%B3%84%EC%A0%81%EB%B0%A9%EB%B2%95%EB%A1%A0_5%EC%9E%A5.pdf

>>11774191
Oh wait no, cosheaf isn't presheaf.

Let X be a topological space, [math]\gamma_1, \gamma_2 : [0, 1] \rightarrow X [/math] are two closed loops.
What is the proper terminology for
a) the [math]H_k(X, R)[/math] singular homology module
b) the statement "[math][\gamma_1] = [\gamma_2][/math] in [math]H_1(X, R)[/math]"
also I would like this opportunity to say FUCK TOPOLOGY FUCK GEOMETRY FUCK ANYTHING THAT REQUIRES THINKING ABOUT THREE- OR HIGHER-DIMENSIONAL OBJECTS

>>11774603
if ||U, V||>1+epsilon then (U, V) / ||(U, V)|| cannot be (1, 0) or anything close to that
this is why your picture says "reject (v1, v2) if v1^2 + v2^2 > 1"

>>11772937
So, any of anons participating in a graduate summer school this time around? I'm in ATOM for this summer.

>>11774331
Take the extra 30 seconds whenever there is a computation. There really is no other way to get better at this. No one is immune to it, but as long as you have that voice in the back of your head saying "careful there", you'll be fine.
Also, practice more in order to lower the likelihood of dumb mistakes occurring.

>>11774650
No, I had two of them planned for the end of june but they were cancelled

>>11774356
what kind of big idea math? i am not a math major, i just need to take the basic college math for my major.

>>11773365
It depends what you mean by successful and genius. You don't have to be a genius to graduate. You don't have to be a genius to get a PhD.
Of course, you need a modicum of intelligence, but I am sure that with motivation, dedication and love for the discipline, you will do it.

>>11774640
>What is the proper terminology for
>a) the Hk(X,R) singular homology module
the Hk(X,R) singular homology module
>b) the statement "[γ1]=[γ2] in H1(X,R)"
the statement "[γ1]=[γ2] in H1(X,R)"

>>11774640
a) the k-th singular homology module with coefficients in R
b) gamma 1 and gamma 2 represent the same homology class

>>11774323
She's supposed to come to the YTM next year, so if you can get the uni pay your trip to Stockholm you can see her live https://sites.google.com/view/ytm2021

>>11774640
(a) kth singular homology group/module of X with coefficients in R.
(b) I don't I've ever seen anything else that both loops representing the same homology class.
>FUCK ANYTHING THAT REQUIRES THINKING ABOUT THREE- OR HIGHER-DIMENSIONAL OBJECTS
A big agree with this!

>>11774668
Defined here >>11773423

i try to learn about Central Limit Theorem using python. I have list of 24000 bitcoin prices, i take lot of samples, then take their means, after that i plot density plot. It looks bit like normal distribution, but not quite pic related, why? I am testing on 1000000 means from samples of length 100

here is code

import seaborn as sns
from matplotlib import pyplot as plt
from random import randint
from statistics import mean

def getMeans(n, sample_length,prices=prices):
samples=[]
for i in range(n):
print(i)
piv=randint(0,len(prices)-(sample_length+1))
samples.append(mean(prices[piv:piv+sample_length]))
return samples

samples=getSamples(1000000,100)
sns.distplot(samples)
plt.show()

>>11774773
central limit theorem is a statement about independent random variables
"the value of bitcoin at time t" and "the value of bitcoin at time t+1" are not independent, they are quite strongly correlated

So, my university's curriculum is really shit, we literally start with functions and analytic geometry, calculus I only in the 2nd semester, so I've been reading an analysis book written by an IMPA professor. I struggled a bit with set theory but I think I understood it well enough. I'll probably read book of proof at once to help me with proofs. Am I doing it right or is it a waste of time? I've never had calculus before and I'm 24.
I've been lurking this thread and I've seen at least another brazilian, so maybe he can answer that.

>>11774843
>and I'm 24.
just give up, anon. It's too late for you, don't waste your time.

>>11774843
>24
It’s already too late for you. Also proof books are a meme. Pick up the techniques as you go along.

>>11774847
I don't think it's too late for a bachelors, but for research it certainly might be.
>>11774850
Thanks, I'll do that then.

Has anyone here actually studied from this entire list? If so will it help me create my own math?

>>11774631
yeah lol

and i can't do some gay shit like thinking about F^op since that'll land in the opposite of my target category

>>11774356
> To the question "what is 2 + 3" a French primary school pupil replied: "3 + 2, since addition is commutative". He did not know what the sum was equal to and could not even understand what he was asked about!

>>11774843
I don't understand, what are you trying to do? Learn basic calculus?

>>11774923
I want to find out if I'm smart enough for maths.

>>11774843
You can learn basic calculus at any time. It's too late for higher math.

What is
[math]\sum_{i=1}^\infty \frac{p_i}{2^i} [/math]
where [math]p_i[/math] is the i'th prime number?

>>11774942
the answer is: it's nothing fucking special

>>11774947
Is it a rational number?

>>11774950
no

>>11774954
How do you know?

>>11774640
oh I see, thanks

so we break it like U, V = R exp(iΘ)
and then for any S subset [0, 2π)
P(Θ in S | R=r) = P(Θ in S) = μ(S) / (2*π) as long as Θ can take arbitrary values for that radius

right?

>>11774925
I don't think you're gonna have a hard time learning calculus
just do it

>>11774847
Its not waste of time if he likes it. Will have another job most likely but at some level he could find some tutoring or online course prep math related job. And btw im eurofag so i am speaking from a position where university ed is free. There is nothing stopping you from joining and profs will often go for arrangements to make up for your job related time constraints if you talk to them and show good work.

>>11774964
just summed it in my head

>>11774976
what you wrote isn't exactly correct, because P(R=r) = 0 for a particular r, and conditioning on zero-probability event doesn't really make sense
but yes this is the idea

>>11774964
assume it is a rational number, then it's expansion in base 2 is periodic
from here https://en.wikipedia.org/wiki/Prime_gap use the statement "maximal prime gaps grow more than logarithmically..."
you will arrive at a contradiction

>>11775008
https://en.wikipedia.org/wiki/Conditional_probability#Measure-theoretic_definition
https://en.wikipedia.org/wiki/Borel%E2%80%93Kolmogorov_paradox

weird stuff

If I had the last authority over Wikipedia article on math, a lot of articles would have paragraphs starting with "And this is where shit hits the fan:"

>>11774925
As someone on a similar position, if you never knew how good you were at this stuff you need to immerse yourself hard in the material and try really hard
There's no other way of knowing

>>11774942
https://oeis.org/A098990

>>11775071
Give examples

Suppose [math]\text{Spec}(A)[/math] is irreducible. I need to show it has a unique minimal prime. If there are finitely many minimals [math]\mathfrak p_i[/math], then [math]\text{Spec}(A)=V(\mathfrak p_1)\cup...\cup V(\mathfrak p_n)[/math] and inductively we can show that [math]\text{Spec}(A)[/math] can only be in one of these, hence the result. But what if there are infinitely many? There's no guarantee that an infinite union of closed sets is closed, so the argument breaks down.

>>11775164
The nilradical is prime if the spectrum is irreducible.

>>11775212
Don't you need to assume that A is an integral domain for that?

>>11775120
Would offend someone.

>>11775120
I didn't know that oeis does "the base 10 decimal expansion of some real"
that's frankly retarded imho

>>11775212
nigga, you just rephrased the result

>>11775250
>that's frankly retarded imho
It's not retarded at all. It's incredibly useful to have the function of a searchable "encyclopedia of constants", and AFAIK there's no other place you can do that other than the OEIS site.
It's not like you have to actually splice the digits into a sequence, you can just search for the decimal expansion directly and it'll work
>>11775212
why even bother responding if you're just going to google it and copy something useless off the first stackexchange answer you see? I'm pretty sure he can do that himself

>>11775256
How does that imply the result?

>>11775298
the nilradical is prime iff there is a unique minimal prime

>>11775279
fair enough, I agree that they should be searchable somewhere - but I don't think base 10 digit expansion should stand next to Catalan numbers etc. in the online encyclopedia of integer sequences.
Also fyi WolframAlpha does a search at least for close algebraic expressions, including special function values (see bottom of pic)

>>11775225
No. Argue by contradiction. You need to do is divide the spectrum into two of those V-sets and show that neither of the V's can be empty or the whole spectrum.

>>11775256
Yes. An equivalent claim as a hint.

>>11775279
I didn't google, though. It was an exercise in Matsumura's (I think it was his) book and I remember it because I struggled with it for hours.

>>11775308
>but I don't think base 10 digit expansion should stand next to Catalan numbers etc. in the online encyclopedia of integer sequences.
What's the point of making a separate website for it? It just makes me have to pick between websites instead of going to the same one for everything.
I don't understand what the argument is supposed to be about "stand next to Catalan numbers". Is this supposed to be implying that decimal expansions aren't as important as the Catalan numbers so they shouldn't be on the same site? That doesn't make any sense.

>>11775320
If N is the nilradical, assume ab in N, but neither a nor b in N.
Then if A is an integral domain, we have V(a) union V(b)= V(ab) = Spec(R) because every prime ideal contains (ab), so we're done.
Actually now that I'm writing it i just realized that V(a) union V(b) equals V(ab) even if A is not prime so all is good. I was thinking of classical alg geo.

>>11775320
ah i get it - in fact, i somehow almost proved the fact much earlier in a different exercise but didnt make the connection

[math]\text{Spec}(A)[/math] irreducible iff [math] \text{Spec}(A/N)[/math] irreducible where [math]N[/math] is the nilradical. Then suppose [math]fg=0[/math] in [math]A/N[/math] [math] \text{Spec}(A/N)=V(f)\cup V(g)[/math], so by irreducibility, [math] \text{Spec}(A/N)\subset V(f)[/math] (WLOG) and thus [math]f[/math] is nilpotent, thus [math]0[/math], thus [math]A/N[/math] an integral domain, thus [math]N[/math] prime, thus its unique minimal prime

>>11775350
>Then suppose [math]fg=0[/math] in [math]A/N[/math], so we have [math] \text{Spec}(A/N)=V(f)\cup V(g)[/math] ***

>>11775343
Good. It essentially boils down to V turning sums to intersections and products to unions (and vice versa).

>>11775350
That's a clever one!

>>11772937

I'm a normal guy and I post here

U mad white boi?

>>11775481
post BBC

>>11774781
thank you

>>11774902

>Has anyone here actually studied from this entire list?

Hahahahaha, I LOLed @ that meme image

>>11775543

Is "Basic Mathematics" by Serge Lang a good book to prepare to study mathematics at university? I wish to recapitulate my mathematics knowledge formally.

>>11774902
It's not a typical curriculum.


Side note, I see the "subsystems of second order arithmetic" book at the bottom, which is nice

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

>>11775250
>Would offend someone.
Come on anon

How do I get this power

It seems like a couple people here went to Kathryn's talk. Anyone willing to give a quick run-down or her main constructions. I missed the talk for various reasons.

>>11775772
it tells you in the pic. Simply [math](a-b)^2\sqrt{ct+x}/v[/math].

>>11774655
That sucks man, they didn't try moving to the online format? I mean, I guess some summer schools are more about the environment and what not, but still.

>>11775780
Seconding this.

>>11775772
Not from a jedi.

>>11775780
>>11775873
Note: It was recorded so it should be on the website soon (https://sites.google.com/view/nialltaggartmath/oats))
Like I said above it went right over my head, but what I can say is this part of the abstract "We have constructed a relatively simple category-theoretic machine for producing towers of functors from a small category into a simplicial model category, determined conditions under which such tower-building machines constitute a calculus, and showed that this framework encompasses certain well known calculi" sums it up pretty well

>>11776034
Yeah I woke up from my nap only to notice no recording or slides. Did she drop words like Postnikov tower/system, or maybe pro-isomorphism or something like that? Towers are of many sort, so I wonder if there could be something I could use as an analogue. Especially the mentioning of simplicial model categories makes me think of a tower of fibrations, perhaps Kan, and also of the towers related to for example the Bousfield-Kan completion which itself is simplicial and monadic by nature. If you could remember something like this, I'd appreciate it. Besides, you mentioned you are an undergrad and you were just bombarded with a lot of abstract nonsense by a big algebraic topologist. You may be stupid, sure, but having trouble following what she was saying without spending a few years on those things beforehand, that doesn't prove anything.

>>11776097
>you were just bombarded with a lot of abstract nonsense by a big algebraic topologist
Not talking about my post, btw. Hah! I may be rotten to the core, but not that rotten.

/gnmg/

>>11776097
iirc, she started with taylor towers of functors, of the sort [math] X\cong P_nX[/math] up to homotopy (or something like that, definitely taylor tower tho). I remember her referencing Kristine Bauer, Johnson and McCarthy. The main thing in the talk was a simple way of creating a tower (don't think it was taylor, but could've been) of a simplicial model category using comonads. There were many diagrams, talking about k-coalgebras where they did something to the effect of [math](...,X)\rightarrow(..., kX)\rightarrow(...,k^nX)[/math] (don't remember what those dots actually were) or something to that effect, and something of [math] \mathcal{\Gamma}(\Gamma,...,...)[/math] where the dots didn't really matter in terms of creating the tower (one of them was an epsilon I think). I don't remember every hearing Postnikov, pro-isomorphism or Bousfield-Kan, maybe fibrations tho (50%). She also had moments where things ended up being the homotopy limit of something. Sorry that's all I remember, my brain's a little fried. While trying to remember this I looked up somethings, and it was kinda related to the first little bit of https://www.sciencedirect.com/science/article/pii/S0001870814004289 and this https://books.google.ca/books?id=O7GqCQAAQBAJ&pg=PA30&lpg=PA30&dq=taylor+tower+kathryn+hess&source=bl&ots=uQSwXIuSeu&sig=ACfU3U0GarzCPffGHxy52MunpDjUhQ6dVg&hl=en&sa=X&ved=2ahUKEwi6uKmSw_PpAhUDUt8KHbKNABMQ6AEwAHoECAgQAQ#v=onepage&q=comonad&f=false

>that doesn't prove anything.
Don't worry, I know. I just feel dumb right now, it's inspiration to work harder

>>11776208
Good night!

>>11773504
This seems like a pretty rigorous curriculum. I'd probably guess Analysis I would be roughest. You could read ahead in those provided textbooks; Tao is probably the easiest to start off from that list.

It's your decision. If you really don't think it's a good decision, don't do it, but if you wanna do it, go for it. I know nothing about how the schools work in India, do you get another shot to apply if this doesn't work out?

>proof books
>24

anon ... I'm sorry but you're gonna have to start with the greeks

otakus culiaos

>>11776531
So it'd be tough? Well i have no choice. I cant handle chemistry. Physics seems okay but i cant see what can i do with physics degree. Yes we do get second chance. Like if fail in sem 1 i get to reappear in sem 3. Byt if i fail in final year then i have to appear 1 year later. Also minimum pass percentage is 33%. Do you think this curriculum is not for average student? I already have 3 years gap after 12th grade.

>>11776699

I didn't know there were Indians who are normal people too, most of you I met just solved every class on the first week

>>11772937
What's /mg/ favorite point set topology book?

>>11776718
>>11776718
https://imgur.com/a/hRDo33Z

Just to be sure this is the curriculum. is this still tough?
meet some sikhs, they are the chillest people and probably then one with 0% nerdism or geekism.

>>11776754
Counterexamples in topology

>>11776718
AHAHAHAHAHAHA
someone has seen the IQ stats, you need to go back

>>11776695
Los otakus son los mejores posters en este general

Is the result of a modulus function, ie [math]4 % 3 = 1[/math] just called the remainder, or is it called something else because it's not exactly division?

Is the result of a modulus function, ie [math]4\ mod\ 3 = 1[/math] just called the remainder, or is it called something else because it's not exactly division?

/gmmg/

>>11776237
Thanks! Now that I saw Taylor towers mentioned, I remember actually hearing about a Taylor theorem for Goodwillie calculus. What you described makes sense.
>Don't worry, I know. I just feel dumb right now, it's inspiration to work harder
That's the spirit! Get cornered by things you don't quite understand and let the fight-or-flight response make you defeat them. Why not give the last one a listen, too? I conjecture the following: Markus Szymik will give a nice talk next week and he will call one of the results he references the prison lemma.

>>11776689
Babylonians and Egyptians... it is by no accident that Eukleides lived in Alexandria, a hellenistic city, sure, but in Egypt and after Alexander the Great had conquered Persia, the two countries of which rich cultures one should have learned everything by the age of 13 before moving onto Greek texts following the publication of Elementa. Naturally, reading these in Greek.

>>11776754
For me it's Dugundji. It may hurt a bit, but it will teach a lot when you start to get into it. Also a good reference.

>>11776852
Si amigo.

>>11777031
I'd call it remainder class because [math]\cdots \equiv -5 \equiv -2 \equiv 1 \equiv 4 \equiv 7 \equiv \cdots \text{ mod }3[/math].

>>11777312
Oops forgot:
https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminar
>The seminar takes place on Zoom (see information below) every Tuesday at 16:00 CET (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).
>Boyu Zhang (Princeton)
>Instanton Floer homology for tangles and applications in Khovanov homology
>In this talk, I will present an excision formula for singular instanton Floer homology where the excision surfaces intersect the singular locus. This formula allows us to define an instanton Floer homology theory for sutured manifolds with tangles. Similar to the non-singular case, the instant Floer homology for tangles is non-vanishing on taut manifolds with tangles and detects trivial products. As applications, we prove several detection results for Khovanov homology. This is joint work with Yi Xie.

>>11772947
Exactly and THAT is what's missing in the curriculum.

>>11777312
>I'd call it remainder class because [eqn]⋯≡−5≡−2≡1≡4≡7≡⋯mod3⋯≡−5≡−2≡1≡4≡7≡⋯mod3\cdots \equiv -5 \equiv -2 \equiv 1 \equiv 4 \equiv 7 \equiv \cdots \text{ mod }3[/eqn].
I'm leaning towards that too. It's not EXACTLY division, but it's pretty damn close.

>>11777324
It is an equivalence relation and each equivalence class is represented by the remainder.

>>11777331
>>11777312
He's talking about the mod fuction, not equivalence classes.
>>11777031
Yes, it's called the remainder.

>reading up on a subject in math
>notation you've never seen before (I'm assuming Greek) starts popping up out of nowhere
Goddamn

>>11777370
>He's talking about the mod fuction, not equivalence classes.
Oops, true.

>>11777374
Examples?

>>11777378
[math]b^e = b^{\left( \sum_{i=0}^{n-1} a_i 2^i \right)} = \prod_{i=0}^{n-1} \left( b^{2^i} \right) ^ {a_i}[/math]
Whatever the fuck that Roman column thing is. Also in some other articles there were other Greek letters (I'm assuming)

>>11777399
It's Sigma for Sum and Pi for Product.

>>11777399
it's sigma, equal to 1+2i, and pi, equal to 3.14

>>11777406
you can just round pi down to 3, you know

I am writing an undergrad thesis. Is it good or bad style to try to make proofs as detailed and rigorous as possible? My proofs are all pretty long because they are verbose. Books normally skip a lot of steps to let the reader fill it in, but I felt like it is much nicer if I just write down how it works.

>>11777418
I would write it as if I were explaining it to another undergrad.

>>11777399
As the other anon said, it's a formula relating a sum of powers to a product. When you some day have to write stuff that involves Greek letters, it is good to know which letter is which, as the code will then simply be \letter or \Letter. Also, notice how here you have the Greek S for sum and the Greek P for product. Clever, don't you think? https://en.wikipedia.org/wiki/Greek_alphabet

>>11777418
My supervisor's rule of the thumb is that you shouldn't make the reader hate you. Can you for example show one of your proofs to us. We won't bully (too hard).

>>11777432
I don't want to show too much but maybe this is an example of what I mean. For context: We want to show something for the set M, and we know a previous theorem shows it for slices of M (in a certain sense). In a lecture or book the prof would write "Approximte M and apply theorem x.y to slices of M". Then you say okay that makes sense, but to rigorously write it down would take me a few pages and half an hour. Well, I did write down a bunch of notation to do it more rigorously (the pic just shows the approximation of M by cubes).

>>11777508
it's okay to write down every obvious step in your undergrad thesis

>>11777508
I don't think that is too verbose, far from it. You are explaining what you do and why, but not writing a page for every single thing you do. I think that looks very good. You should also notice that you are comparing yourself, a soon to be bachelor, to profs with years of experience. I'll actually copy-paste a bit of what my supervisor told me, a bit of censorship to avoid getting doxxed. We were discussing the lengths of proofs, so he told me this:
>The short version: My first substantial theorem achieved independently took 10 pages in print. If you look at my thesis, it's the - theorem. It also took about 2-3 weeks of hard work.
>Some time later I gave a talk about it, with B in the audience. B liked the theorem. That's good news.
>Two months later he met me and F in a conference. He handed F two sides of A5 hand written with a proof of my theorem by a different method.
So don't worry. If your supervisor thinks you should shave a bit off from here and there, then do that, but I think that looks fine.

pls rember that wen u feel scare or frigten
never forget ttimes wen u feeled happy

wen day is dark alway rember happy day

>>11777514
>>11777528
alright thanks anons, appreciate the feedback.

>>11777508
That seems perfectly fine. It would get bad if you were endlessly ranting about trivial points, but clearly you aren't.
You are also missing a "the" in the first sentence before the "case" and your spacing before quantors like \forall is a bit off, I would separate them with a "\" from what is behind them.
I personally also prefer the for i \in \{1,...,n\} Notation as that is closer how you would actually read the text.
Sorry for the nitpicking...

HOT NEWS: Any homeomorphism [math]f: X \rightarrow X[/math] has a periodic point, where X is the double torus, as pictured on the attached illustration.

>>11777571
proofs?

>>11777571
proof ?

>>11777571
What's a periodic point?

>>11777579
It is a point [math]x \in X[/math] such that [math]f^k(x) = x[/math] for some integer [math]k \geq 1[/math].
>>11777572
>>11777573
Sorry, I cannot disclose my sources.

>>11777571
>double torus
you mean smooth manifold of genus 2

>>11777584
why not?

is it similar to this?
https://www.ams.org/journals/proc/1989-107-02/S0002-9939-1989-0965243-2/S0002-9939-1989-0965243-2.pdf

>>11777571
Not doing your homework.

HOTTER NEWS: Any homeomorphism f:XX has a fixed point, where X is the double torus, as pictured on the attached illustration.

>>11777592
it's no homework my friend
>>11777588
a more general statement is:
let X be a manifold with the euler-poincare characteristic [math]\chi(X) \neq 0[/math].
Then any homeomorphism [math]f:X \rightarrow X[/math] has a periodic point.
here's a 1-page proof although it requires some knowledge
sci-hub. tw/10.2307/1969856
>>11777610
FAKE NEWS

>>11777616
>FAKE NEWS
Prove it.

>>11777592
>>11777616
the question you are replying to is solvable by a uni student right? i have vague memories from uni doing similar type of statements as HW or class exercise

>>11777617
Put the double torus into a 3D coordinate system, as pictured. Then the double torus is centrally symmetric with respect to the point (0,0,0). So, [math]f(x) = -x[/math] is a homeomorphism without a fixed point.

>>11777646
Nice. Do you think there are more such homeomorphisms, up to homotopy?

>>11777646
Why isn't 0 a fixed point?
Am I retarded?

>>11777670
0 is not on the surface. By double torus anon means only the surface of it, without the inside.

>>11777619
no idea
>>11777670
you're not retarded it's a misunderstanding
we're talking about a surface
the torus is empty inside
>>11777655
no idea
it makes me wonder how many "homeomorphisms up to homotopy" are there? eight maybe?

>>11777672
>>11777677
Oh, sure. That makes sense, thanks.

>>11777677
I think you get at least 6 homeomorphisms from the S_3 on the three handles. So together with your homeomorphism, there seem to be at least 7.

>>11777710
Wait if you reflect horizontally you get at least 12 homeomorphisms like that.

>>11772944
Doing it real time is practically impossible or at least will destroy all understanding you could have gained from the lecture.

What I did do was write up my hand written notes in LaTeX after the fact.

Say [math]g\in C([-\pi,\pi],\mathbb{C})[/math] is a [math]2\pi[/math]-periodic function with Fourier-coefficients [math]\left \{ c_n \right \}_{n\in\mathbb{Z}}[/math] and [math]\sum _{n\in\mathbb{Z}}|c_{n}|<\infty [/math]. How do you show that the Fourier series of g converges uniformly to g?

If I wanted to use geogebra to graph polar imaginary numbers, how would i make the full circle without manually typing out a long list of angles?

>>11777828
try Fejér's theorem?

>>11777828
you don't because it's not true

>>11777828
>How do you show that the Fourier series of g converges uniformly to g?
trivially

>>11777889
Can you please explain why? I'm a brainlet

>>11777906
let [math]g_n(x) = \sum_{k = -n}^{n} c_k e^{ikx}[/math]
then [math]|g(x) - g_n(x)| \leq | \sum_{|k| > n} c_n e^{i k x} | \leq \sum_{|k| > n} |c_k|,[/math] and this converges to zero

>>11772937
Does anyone know about a collection of warm-up problems?
By a warm-up problem I mean something that doesn't require any advanced concepts, isn't trivial but isn't exceptionally hard either. Like a little problem you can do at the start of the day or after a pause that won't take long and will get your mind up and running.

>>11777725
Based. I write problems that will be on the exam in latex after solving them once and thats enough to ace it even if you dont look at them again

>>11777944
One of the interesting components of developing basic mathematical competence is learning to think for one self and make informed decisions based on limited information, and prior experience.

>>11777725
i always wanted to do this, then never had the will to do so. especially when i have 5+ pages after every lecture handwritten. what i did instead is try to make good notes to begin with or read them thru after the fact and patch it up while i still remembered

>>11777950
What?

>>11777933
you're assuming that g_n converges to g pointwise

>>11777956
ha said
>spoonfeeding
in a sophisticated way.

what type of warm up problem are you looking for?
combinatorics? calculus? etc

i think a lot of entry level textbooks have good exercises

anyone know what the name of the template is? or do you have the one of /a/?

>>11777966
I'm not looking into anything speicific, and textbooks aren't ideal because they are exercises in the material they propose. Guess I'm just looking for mathematical puzzles.

>>11777994
i think usually high school math competitions have puzzles which don't require much background theoretical knowledge but you need to think hard to figure them out

>>11778000
Yeah, those have the problem of taking up too much time. Maybe I should look into problems for the qualifications for high school maths comps, since they tend to be easier...

>>11778000
This, pick some AMC12 problems, preferably from 15-25, that should get you warmed up, however they still require some material such as eulers totient theorem, euclidean geometry etc. But you can just pick the ones you like

Can someone explain to me what this functional determinant has to do with branching? I don't see the connection and the author doesn't explain it.
This is from Klein's book "Lectures on the Icosahedron".

>>11778114
I'd not be surprised if something happens where the Jacobian becomes degenerate?

>>11772025
I added 5000 characters to this page
https://en.wikipedia.org/wiki/Constructive_set_theory

>>11778230
Right, I get that. I'm not surprised either, I would just like to see a justification. The equation states that the gradient of the numerator is collinear with the gradient of the denominator.

>>11778230
Why is that pastry thing staring at me with such a shocked face?

I haven't done math in a month and I feel like I'm forgetting everything, this had never happened to me before, what do I do?

>>11778249
lel

>>11778247
>The equation states that the gradient of the numerator is collinear with the gradient of the denominator.
Which sounds like it ought to be a constant while it isn't.

This reminds me of counterexamples to holomorphic but naively nice looking functions (althought this isn't in the domain of several complex variables). One would hope
[math] f(z):=\overline{z} [/math]
to have a somewhat constant derivative, but in fact
[math] \dfrac{f(z)-f(0)}{z-0}=\dfrac{\overline{z}}{z}={\mathrm e}^{-2i\,\mathrm{arg}(z)} [/math]
(and the same is thus true for Re and Im as functions)
The thing is constant along rays, but even when f goes to 0 when z becomes smaller, the derivative fluctuates arbitrarily along the angle direction.

I can't help more with just that one page, but maybe that helps somehow.

>>11778331
Yeah you didn't help at all.

>>11778230
>I added 5000 characters to this page
Nice! You could write the German page if you think it would provide you some extra insight when you would have to rephrase things.

>>11778317
It comes back. I had a 6-8 month break at some point, but managed to recap. You just have to start doing it again.

>>11772947
>>11777321
This is true, maths thought the way in school is soi and soulless. But since studying numerology and ancient equations its now beautiful.

>>11777725
How the hell do you have time for this. I dropped that in favor of more math practice.

Is there any algorithm for ranked voting of rankings?

So in other words, rather than voting for A, B and C to pick just one of the three, we're voting on an order to place A, B and C in. I'm considering a phased reduction of failed orderings to their component parts, so that CAB reduces to the three orders of CA, AB and CB, and letting these count as second-phase votes, but if this is old ground I'd rather skip to the good bit.

Guys, I need some ideas.
I'm looking at a weird differential equation and my brain has just fucking died for a few days. I've got a function [math]f[/math] which is involved in the equation with terms like [math]f(z\pm a)[/math]
So the first thing I've done is to get a rough idea of what the behavior of solutions is like for small [math]a[/math] which is easy because you just take a series around [math]z[/math]. But I'm also interested in what the solutions look like if [math]a[/math] is large.
Do you guys know how I could approximate functions [math]f(z\pm a)[/math] for large constants [math]a[/math]? It's not enough for me to just make a change of variable [math]t=z+a[/math] because I've also got another term [math]f(z-a)[/math] so I probably do want to just look at some trick to look at a series expansion for large [math]a[/math] somehow.
Any ideas would be really appreciated.

>>11778933
Can you post differential equation here?

>>11778553
sadface.jpg

>>11778928
voting is a field on its own, here's some algorithms, maybe you find what you want

https://en.wikipedia.org/wiki/Schulze_method#Comparison_table

>>11777863
[math] x^2+y^2=1[/math]

>>11778959
That would be awkward for me because I derived it and it look a bit weird if someone ever googled it and saw me posting my own preprint on /mg/. But the idea is I've got some problem terms which are like [math]\frac{d}{dz}f(z+a)f(z-a)[/math] and these terms make it a nonlinear pain in the ass. The rest are basically linear or not that bad. So for small [math]a[/math] I've been able to reduce the equation to a more familiar nonlinear equation with known solutions. But because of the way in which it was derived, it should also be interesting for large [math]a[/math], and most annoyingly, even when [math]|z/a|>1,[/math] so I can't necessarily assume that [math]|z/a|[/math] is near zero and expand that way. So this is really fucking me off.

>>11778959
That would be awkward for me because I derived it and it look a bit weird if someone ever googled it and saw me posting my own preprint on /mg/. But the idea is I've got some problem terms which are like [math]\frac{d}{dz} f(z+a)f(z−a)[/math]
and these terms make it a nonlinear pain in the ass.The rest are basically linear or not that bad. So for small [math]a[/math] I've been able to reduce the equation to a more familiar nonlinear equation with known solutions. But because of the way in which it was derived, it should also be interesting for large [math]a[/math], and most annoyingly, even when [math]|z/a|>1[/math], so I can't necessarily assume that [math]|z/a|[/math] is near zero and expand that way. So this is really fucking me off.
(Going to delete the first post in a sec, fucked up the latex)

>>11772944
Learn to script and use snippets

How do you train to explain math?
I was talking to my advisor and he was barely able to follow what I said and had to repeat "say it again" multiple times.
It's probably not helping that I'm an ESL.

>>11778979
I know, plenty of voting systems, but very few of them seem to give much of a shit about how they calculate the sequence of the ranking, particularly once it gets to the lower end.

>>11779169
I talk to him before I talk to my supervisor. Then I sort of know how to phrase things.

>>11779169
learn and apply basic pedagogy.
no more than three points at a time, keep a central theme, pic=1000 words, and get them (through conversation) to repeat key points to you in their own words before moving on

>>11779227
do you have studies that show the optimal decomposition of novel abstractions for humans happens to come in groups of 3’s, something regarding memory storage or retrieval? No? Perhaps you should rethink posting on the Science board then.

>>11779183
????
What does this mean?

>>11779265
>most voting systems
>input is loads of votes of a given selection of options, sometimes just selecting one per vote, sometimes a ranking of the options per vote, sometimes assigning points, or something along those lines
>output is a single winner, or sometimes several winners for proportional voting or a vote for more than one successful option

>what i want
>input is a load of votes, each of which is a ranking of all options
>output is a winning sequence ordering all options

If I just chose FPTP for this, it'd be something like
ABC: 200 votes
ACB: 350 votes
BAC: 100 votes
BCA: 50 votes
CAB: 500 votes
CBA: 300 votes

In the above case, sequence CAB wins. The trick is that you can't just use ranked voting and rerun the vote excluding the winner each time, because who comes in last is just as important as who comes in first.

Brief question, all of you here can do stuff like pic related completely on your head right? I was curious.

>>11779589
No, but I can do the first 4. I like the problem and its drawing, though.

>>11779589
I can do everything except for the sharp corners, I'll have to think on those for a minute

>>11779589
>>11779680
Okay I got it.
A cross of slidy ropes.

>>11779602
It's pretty cute. I searched for the book or whatever it's from for a bit but found nothing sadly.

>>11779876
>I searched for the book or whatever it's from for a bit but found nothing sadly.
It's from here.

If you want to reverse-search for a book given a page or a quote you can usually do it by taking a chunk of text from the pic and googling it in quotes. The Google Books of the textbook will usually pop up or something like that. I searched for "today's problem set deals with goats" and it's the only match.

>>11779900
I actually did something similar but didn't check google books.
In my defense my searching for this was part of a wider procrastinating effort

>>11779876
At least you tried. I wish I had a goat farm of my own.

>>11779900
This is what you need to solve before you can tackle the Verbitsky list. Nice digits, btw.

>>11779589
>>11779900
>(standard for 8th graders in Russia)

>>11779602
I'm in a similar position, except I actually can't do the eye shaped one, I feel like an idiot.
Some of the latter ones feel free though, like the dog one.
>>11779906
>This is what you need to solve before you can tackle the Verbitsky list.
Explain. As in, tackle the courses he teaches?

>>11779922
I interpreted the eye as an ellipse, and using this interpretation it is quite simple. By the list, I mean this list.

>>11779915
Yes?

>>11779915
>>11779941
The AMS store says its for Undergraduate students, hah.
>I interpreted the eye as an ellipse, and using this interpretation it is quite simple.
I learned basically no geometry ever, but I thought the ends had to be like, sharper (I dunno if that's an ellipse). I got that you get a what I just googled is called a lens when two circles touch but thats it

>>11779997
I don't know either. Actually the ellipse thing I had in mind doesn't work, so that can be scrapped. However, the lens thing could be achieved if you attach the goat into two poles with ropes of equal length.

what's the official, general way of transforming stuff like line 1 into line 2? google isn't helpful

>>11779997
Also the shape created by a lens rotating around an axis through it's tips is called a lemon and I found that neat

>>11780030
Find the zeroes of line 1. Call them a and b. Write (x-a)(x-b). You will notice that in your example they are -1 and 2, giving you x^2 -x -2 = (x+1)(x-2).

>>11780031
Well, the shape is quite similar.

>>11780041
Well, if you have cx^2 + something, then c(x-a)(x-b), but yeah. In your case c=1.

>>11780041
>>11780057
this is surprisingly easier than what i've been doing in my mind up to now
thanks

>>11780060
Have you heard of double roots? It's when your 2nd degree thing has only one zero. It took me ages to understand why it would be double when there is only one root, but then I realised it's because your polynomial is then of the form c(x-a)^2. I hope they are double roots in English.

/gnmg/

>>11777985
i think it's simply called derail comic

>>11780041
Aren't you supposed to yell at them to go to /sqt/
>>11780083
It's called that in spanish I think, actually

>>11780097
>Aren't you supposed to yell at them to go to /sqt/
not her style

I tried using Cauchy on this:
[math]x+y+z = \frac{x\sqrt{y+z}}{\sqrt{y+z}} + \frac{y\sqrt{x+z}}{\sqrt{x+z}} + \frac{z\sqrt{x+y}}{\sqrt{x+y}}[/math]
But I only get
[math]\sqrt{2x+2y+2z}(\frac{x^2}{y+z} + \frac{y}{x+z} + \frac{z}{x+y})[/math]
How do you get the final inequality in the exercise?

Daily reminder that if you use [math]\blacksquare[/math]
you are racist.

>>11780289
[eqn](\frac{x^2}{y+z}+\frac{y^2}{x+z}+\frac{z^2}{x+y})((y+z)+(x+z)+(x+y)) \geq (x+y+z)^2[/eqn]

>>11780398
Oh fuck I'm dumb.

>>11777508
>>11777528
>>11776237
don't mind me EE fag here just mirin this shit, is that what a pure maths major is? We do a lot of maths in EE, the most in any engineering field and my uni is known for its pure maths and physics focus, but I have no fucking clue what any of this shit is
kinda feelin like a brainlet now godspeed

>>11780337
why yes I do hate niggers and make liberal use of the tombstone to remind them of the abyssal grave most of their ancestors lie entombed within at the bottom of the lowest circles of hell, how could you tell?

>>11780555
NIce trips. No, this isn't what a math major is necessarily (in reference to my post >>11776237), this was research level category theory/algebraic topology. Some people do this, most don't. Other areas of specialization are still filled with obscure terminology, but can be at least a little more approachable. For instance, the study of elliptic curves in number theory or fractional derivatives can have some layperson explanations. That being said, for >>11777508 >>11777528 it's pretty standard (from what I've heard). I've "read" my professors Ph.D. thesis, and I could only get through the introduction chapter. That's why we study for 6+ years

/gmmg/

>>11780097
Maybe I'm supposed to do that, but that doesn't stop me.

>>11780337
>not using the empty box to express one's own hollow self

>>11780555
>kinda feelin like a brainlet now
If you think you are dumb for not knowing about things you have never done anything with, then the dumb part is this belief instead of your ignorance of that stuff. Occasionally helping an energy engineer out with his stuff has lead me to a similar position where I can only bow my head in shame and tell him I have no idea what is going on. Two separate fields, and some branches are pretty far from any sort of engineering (except maybe functional programming & stuff which I know nothing about), like >>11780592 said. No need to worry.

>>11780592
You are giving me a gut feeling that you will be a PhD at some point.

>>11780745
i hope you die in your sleep

>>11780745
I like you anon

It seems arxiv is on strike. No daily mail for a while, I guess.

>>11780758
I actually just woke up almost choking on my gastric acids, so it was pretty close.

>>11780763
Nice contrast between the two replies, don't you think? <3

>>11780745
Thank you, that's actually super encouraging right now

what jobs can i get with a degree in math that i can't get with a degree in cs?

Is Lie Algebra worth learning, if your goal is to learn the most general / widest varieties of mathematics? Are the objects and concepts in Lie algebra applicable beyond modeling spinors and shit?

>>11780949
Now go make that reality!

>>11780987
>Are the objects and concepts in Lie algebra applicable beyond modeling spinors and shit?
This obviously depends on the exact nature of shit, but here's a good list https://math.stackexchange.com/questions/1322206/what-are-applications-of-lie-groups-algebras-in-mathematics and the MO link leads to seemingly quite detailed a discussion on the matter. Maybe those will give you a glimpse of the reach of Lie algebras.

>>11780977
Napoleon of crime. Prof. Moriarty wasn't a CS guy.

>>11781059
Have you studied Lie algebras? Are there ways to study it that don't involve having to suffer through calculus on complex manifolds? I'm more of an algebraist than an analyst type and I'd prefer to stick to the former.

>>11781097
Not too much. I've managed to avoid going too deeply into the internal affairs, but I've used Lie groups for embedding purposes when trying to get some cohomological info out of a group, for example. I've been planning to go deeper into them at some point, but all that calculus business is something I am horribly bad at, and I am quite afraid it is something neither of us could avoid.

>>11781117
Well fuck. Thanks for replying anyway. Fuck calculus.

>>11780857
>arxiv is on strike
What is wrong with these people?

>>11781154
virtue signalling is a scourge on humanity

>>11781154
The death of the west
Read spengler

>>11781154
>mfw live /innawoods/ doing math like uncle ted
>"they won't be able to fuck with me here"
Jews and nigs still find a way.

>>11781154
oversocialization, mass psychosis, high genetic load.

>>11781292
>high genetic load
POZZED

What did they mean by this?

>>11781245
Virtue signalling as a concept is a scourge on discourse

>>11781329
Jesus christ. Its like a worldwide parody. White man catering to black manchildren - okay we will play along, just stop burning shit up okay?

>>11781329
Oh fuck off
This black lives bullshit shouldn't be our fucking problem, politics should not be involved in mathematics or the sciences.
And I wish they'd stop capitalizing black.

>>11781337
Virtue signalling as a concept being a scourge on discourse is a scourge to reasoning.

L: Quantity of Learning that was achieved
p: progress in the task
D: difficulty of the task

I claim that [math]D = \frac{dL}{dp}[/math].
Or simpler, [math] L = Dp [/math].
When you solve an easy task, you don't learn much. When you struggle at a hard task but don't make any progress, you don't learn much either. Only when you struggle *and* make progress, do you learn.

Does [math]a*\frac{b}{c}=\frac{a}{\frac{c}{b}}[/math] hold for all complex [math]a,b,c\neq 0[/math]?
I can't remember.

>>11781564
Yes except infinities and shit

>>11781567
[math]\{ \infty, \text{shit}\} \subset \text{Idxaaak@}\subset \mathbb{C}[/math]?

>>11779922
put two stakes and a rope with a bit of slack of equal length tied to each stake. The goat can then move through the line that is the perpendicular bisector of the line through the stakes, and it will reach maximal distance from either stake when its on this line. In particular, this creates a corner

>>11775780
The slides and recording are there now https://sites.google.com/view/nialltaggartmath/oats

What's the name for the set of quadratic equations with solutions [math]a+bi,a-bi[/math]?

>>11781941
quadratic equations over the real numbers

>>11781974
with non-positive discriminant

>>11781977
b=0 is a thing you know

>>11781979
give an example of quadratic equation with positive discriminant and solutions in the form a+bi, a-bi

>>11781941
there is exactly one such quadratic equation up to multiplicative constant, bro

>>11772937
I took my undergraduate abstract algebra course a year ago and I am about to try to crack open an ANT book, what should I review before I give it a go? I am under the impression that all I'll need to review is some basic ring theory (as far as algebra prereqs go) as I am pretty sure introductory group theory is permanently stuck in my brain.

>>11781845
I watched them last night. desu the whole thing seems pretty unconvincing.

Perhaps a dumb question, but what are quotients in the category of chain complexes? I guess more specifically cochain complexes, but still.
I should probably be able to figure it out based on cokernels or something but I've turned myself around in confusion. It's abelian so there should be a general notion of quotient right?

>>11782457
You need basic galois theory.

Let [math]X = \{ 1/2^n : n \geq 1\}[/math].
Let's also use the standard notation [math]aX + b = \{a/2^n + b : n \geq 1\}[/math].
Does there exist a set [math]S \subseteq \mathbb{R}[/math] of positive Lebesgue measure, such that [math]aX+b[/math] is not a subset of [math]S[/math] for all [math]a, b \in \mathbb{R}, a \neq 0[/math]?
Look up "erdos similarity problem" if you care, but no one knows the answer. SAD!

>>11782876
How did you come across this question? i.e. why do you care?

>>11782907
>How did you come across this question?
random clicking stuff on the internet
>why do you care?
how could one not care? it's an extremely simple question about simple stuff

>>11782749
Have you tried applying the categorical definition of a quotient?

>>11781344
I feel this way but I fear that if I don't get better at towing the party line my career will be in trouble.

>>11782749
taking a subcomplex and quotienting every term doesn't work ? what goes wrong ?

I wanna learn graph theory just because it sounds kinda neat.
I wanted to know if there's any prereqs I should know about. Chapter 1's been fun so far but I don't know if I'll hit a wall soon.

>Applications
I dunno, people linked me the book.

>>11782649
I haven't taken a look yet. Was there some seemingly shaky limit argument or something?

>>11782457
Dedekind domains, valuation rings, fields of fractions, basic Galois theory. Not much.

>>11782749
Take a subcomplex of your complex and apply the quotient morphism degreewise. This induces differentials between your quotient objects, and so you have a new complex.

>>11782946
I realized soon after I posted it that that does work, because the cokernel is degreewise. So the algebraic quotient C/D is the cokernel of D into C and that guy is taken as the degreewise cokernel of D_n into C_n...When I posted the question I had momentarily forgotten that all algebraic quotients are just cokernels.

>>11782936
Categorical quotient? No, I try to avoid starting from scratch...but it's gotta be true that the quotient object C/D in the categorical sense is the same as the algebraic cokernel of D into C, since the quotient object is defined by a coequalizer.

thanks for the help guys

>>11782950
Pure graph theory has literally no prerequisites other than being comfortable enough reading mathematical arguments that you can hang on when stuff gets complicated (which depends on the author, not the subject), so you ought to be able to read a substantial portion of any non-specialist text. It might help if you know a little bit about matrices, but even that's not strictly necessary.

Also the book you posted is a 700 page graduate-level brick. I don't mean that as "don't read it", but as "don't think you have to read all or most of it". A couple chapters probably corresponds to your average undergrad graph theory course.

>>11782943
Firstly, it's toeing, as in not putting a toe over the line, and secondly fuck the line, nothing will ever get fixed if nobody makes any effort to unfuck the place themselves.

>>11783053
And thirdly, before you ask "but aren't you just PC irl yourself?" my advisor and I routinely have discussions about Chinese and Indians and why they can't do anything right (they can't) which make other people get up and leave the general vicinity, and nothing ever fucking happens because people are terrified of conflict. We've been saying borderline racist shit for years and nothing ever happened.

>>11783019
>No, I try to avoid starting from scratch...

The definition of an abelian category is an abstract categorical definition. Checking what that implies with the other axioms and the category you're working with at the moment gives you a clue as to the construction you need. Then you'd need to check that your guess agrees with the actual definition of a quotient to really be sure.

>>11781323
I think that may be why we see more homosexuals these days, yes.
>>11781329
They want to extirpate brainlets from research science. Everyone who participates is outing themselves as a conformist lemming to the true brain chads.

>>11783007
Quite the opposite. This is as far as I can tell 40 minutes of model category bs that didn't need to happen and 10m of building a functor that outputs sequences of reflective subcats of a functor category. I'm neither convinced the endpoint is something that deserves to be called a calculus nor that the input is much easier to produce.

In the cases where a good calculus hasn't yet been constructed, but is believed to be out there somewhere neither side of what was written has an obvious candidate.

>>11783139
That's disappointing. I'll probably just check the slides and decide whether to watch the video based on those. Thanks!

>>11782950
probably not a bad idea to brush up on some basic combinatorics, but other than that, basically no prereqs

>>11782950
prereqs is being able to solve IMO combinatorics problems

Hello can anyone help me with this cauchy problem? the task is proving that a solution exists/doesnt exists around (0, 0) with alpha not equal to 0

>study motives
>no motive to live

>>11783443
They're supposed to be called motifs, blame whoever translated it to English first for botching it

>>11783053
>nothing will ever get fixed if nobody makes any effort to unfuck the place themselves.
And what is the alternative? Telling the unironic antifa presence at your campus to fuck off and getting beat up?
Does that accomplish anything?

>>11783066
>We've been saying borderline racist shit for years and nothing ever happened.
The fact that you haven't had your life cancelled by a lynch mob yet is not a good argument that it's never going to happen to anybody.

>>11783066
>saying racists shit but not working towards actually getting them out of the country
are you a boomer by chance?

>>11783497
the apathy of the majority of students and meek cowardly assent of administrators and neutral faculty is what enables these people to make terrorist demands for students and professors to be dismissed when they fail to worship the same gods as them. I don't see how you could win even a small victory by yourself, they'll isolate you, out you as a racist heretic and destroy your life even if you are tenured. But, with the support of sufficient numbers of students, even if not directly stating opposition to their ideology, you could negate much of their influence. They thrive upon disinterest and mutually reinforced conflict avoidant silence.

>>11783443
What a coincidence! - IAS just uploaded a video on them by Deligne :D
https://www.youtube.com/watch?v=n9AtEtED640

>>11783568
>and mutually reinforced conflict avoidant silence.
But they are *very* loud in every sense of the word.

I would bet that half of the students would identify themselves as Antifa and 10% would be willing to engage in violent conflict if their positions are relatively threatened.

It also seems to me that the silence is the only thing that is hurting them. It gets hilarious if the anti-anti-semitic student party (not kidding, that is literally their entire program) gets shit flung at them by the radically leftists (orthodox Marxists I believe) student paper because you should be allowed to criticize Israel.

Hello /mg/, did you remember to put down the math pen today and listen, learn, reflect and focus on racial inequity in mathematics?

>>11783678
My small act of defiance was studying a bit more.

>>11783691
fuck you nazi

>>11783703
Let's not be rude.

>>11783707
sorry i am so triggered by what he said
i am literally shaking

>>11783678
I think we should shut down maths indefinitely until more negros join the subject.

>>11783722

>>11783587
yea thats what brought it into my thoughts

>>11781483
>I claim that D=dLdpD=dLdp.
>Or simpler, L=DpL=Dp.
Damn is THIS the Lp Fourier transform shit they were talking about in PDEs today?

>>11783722
>Cornell shuts down arxiv
>Cornell math department has 1 (one) black grad student
Reminder that all this is literally just meaningless virtue signalling. Most math departments have 0 black profs and 0 black grad students. A handful of them have 1. This will not change. It CAN'T change, because black applicants are basically rejection-proof and most departments still struggle like hell to find one.
This is nothing more than an opportunity to take a mini-vacation while scoring some social justice points.

>>11783793
>because black applicants are basically rejection-proof and most departments still struggle like hell to find one.
That's why we, as white people, need to fight racism!

>>11783793
I loved watching my department eat claims of racism. They were more diverse than the actual diversity-centric departments. It really shows liberal racism and lack of math knowledge that they somehow think math isn't diverse.

>>11783793
My ~2000 person school (with no grad students obvs) has 2 maths profs + and engineer for labs, one prof is white, one is black and the engie is brown. Anything is possible

New Thread:
>>11784117

>>11783722
based