/sci/ - Science & Math

Is there a name for a type of numerical series where at each step in the series, it branches into two or more different series, each with a common history until that point? The series basically has a tree-like structure.

This is the single most based faculty page in all history. This man does not give one single fuck about washing his hair or trying to please normies, because it is irrelevant. Here's what the guy looks like, web 1.0. No I won't recommend you, stop trying to ride my dick.

>>10528997
SHOO SHOO DISCORD TRANNY

>>10528948
Exams start in about a month. How should I revise? Should I just pick a few questions out of my textbook everyday?

I'm going through MIT 6.041 and about 30% of problems in psets absolutely whoop my ass, and I'm not even out of discrete probability section. Is this subject/course genuinely hard, or am I just that fucking dense?

>>10529217
based and redpilled

>>10529217
This is what peak math looks like

>>10529360
Surely you must have had some assignments given to you throughout the term? Review the problems found there, seeing as this is the material you have already been expected to know.

hello anons. Precalc Brainlet working through Langs Basic Mathematics book.
Currently on the quadratic formula questions in Chapter 4.

So there is a question: x^2 - 4x + 5 = 0

In the answer key he says: Not possible with real numbers (4 +- sqrt(-4))/2

I can't figure out how he got to that answer (4+-sqrt(-4))/2 at all

I can solve the other one x^2 - 4x - 5 = 0 and I get x = 5 and x = -1 but I'm not sure what I'm doing wrong on the first. question.

>>10530265
>Precalc Brainlet working through Langs Basic Mathematics book.
Lang is a meme.

>>10530305
Y

>>10530265
Just apply the quadratic formula and also >>>/sci/sqt

>>10528948
I wanna take a moment to appreciate the background.
>a bunch of pi digits
>Atiyah-Singer
>the harmonic series
>a bunch of knots
>our good friend the genus 2 surface
>the binomial formula
>the spectrum of a matrix

>>10530436
>harmonic series
I meant Zeta(2).
Also,
> [math] e^{ \tau i} + 1 =0[/math]

>>10529236
What? I just want an answer.

>>10528997
It's just a nested series, or series of series, 2 variable series.

>>10530461
>tau

>>10529217
>This does not apply to ... students I supervised
What kind of faggot asks for a reference off someone that didn't supervise them?

>>10529217
I’m close to a professor with a page like this. My favorite part is the part that says hobbies: none

>>10530752
Related, for grad school are your typical three letters of reference all supposed to be from academia? I've had one supervisor, but not three.

Mochi added a slideshow to his Inter-universal Geometer business card (hover over his picture):
http://www.kurims.kyoto-u.ac.jp/~motizuki/top-english.html

Two new pics

>>10530788

>>10530788
>>10530790
cute

https://en.wikipedia.org/wiki/Igor_and_Grichka_Bogdanoff#Publications
>Éléments de la Géométrie Froéboïde post-Anabelienne
Does any french anon here know if that's a real book? Googling it gives nothing, and the ISBN shows a different book.

>>10531010
>Does any french anon here know if that's a real book?
It's not

>writes about the God function
>writes about the fine structure constant
>dies

>>10531010
We had a guy out school about named "Bogdan Gretchka"
Then he moved to california
Then i googled him after I learned about the Bogoffs
He had some peculiar stuff written about how much he likes "blood sport" which ostensibly was MMA but actually it was pretty weird the way he wrote about it

>>10531017
Thanks, friend.

>>10530788
>>10530819
he's not mocking me for the tension in my neck is he? If he had my life and a little tension to show for it he'd be doing pretty good.

i want to become a large cardinal set theory monk
i know calculus and vector algebra, i know basic discrete math and lots of formal logic

where do i go know

>>10531232
Handbook of Categorical Algebra, then Sketches of an Elephant.

Does an element LIE in a set or does it LAY in a set. This isn't bait, I'm retarded and don't know which is correct. I think it's lie but I'm not sure.

>>10531251
would i need topology and higher calculus/algebra to understand those?

>>10531295
>topology
Yeah.
>higher calculus/algebra
Nah.
If you start feeling unmotivated about category theory midway, flip to the third volume of the Handbook and check out the part about Heyting algebras.

>>10531277
lie - present tense of two homophobous verbs, one meaning roughly to recline, the other meanig to knowingly utter a falsehood
lay - present tense of a verb meaning to put something into a reclined position, past tense of the first of the two verbs whose present tense is "lie"

Does X put Y into a reclining position? If yes the present is "X lays Y down" and the past is "X laid Y down". If X goes into a reclining position itself then present is "X lies [down]" and the past is "X lay [down]"

So because there is no direct object the correct verb is "lie" in the present and "lay" in the past

>>10528948
So i never did too well with math when i was younger, and i still can't do basic 2-digit arithmetic in my head, but tell me if i've got this correct.

If i have some number n, the square root of n^2 will be n^2/n, and the cube root of some n^3 will be (n^3/n)/n.

So if i were to create an algorithm it would follow the rules:
1. take some N
2. divide it by Its prime factor pow-1 times

>>10531506
>can't do two digit arithmetic in your head
I can't do three digits by two digits.
But that algorithm is probably trash, since prime factorizations take time.

>>10531521
The prime factorization part will certainly take time, but i can improve it with a pre-generated sieve to call on.
What about the basic principle of the algorithm though, did i do a good?

>>10529379
yes and yes

I'm worried I like studying established math much more than I like actually preforming research

>>10531908
Well somebody has to write the textbooks

>>10531506
How exactly would this compute say sqrt(2)?

>>10531527
if you have your prime factorization you can just divide each exponent instead of dividing a big number a bunch of times. also i don't know what you mean by 'divide it by its prime factor'. it looks like you're assuming you know the root already so you can divide by it

>>10531927
2/1 :^(
I surrender, is there a better way to compute roots?

proof by induction can only be used to satisfy countably infinite propositions? ie all natural numbers?

>>10531908
what does your research usually entail?

>>10531976
Look up transfinite induction. If you prove the condition is true for an ordinal if it's true for all lower ordinals then you can induct with that.

>>10531990
but cant you map any ordinal to any natural number and they are countable in that sense, i guess my question is, can you prove things about the real numbers via induction in some way?

>>10532001
>but cant you map any ordinal to any natural number
you can map whatever you want i guess. it isn't a bijection though

>and they are countable in that sense
no.

you have to prove something about how your infinite thing has the property if some set of your finite things does, at some point. keep in mind you can induct over any structure that you build out of smaller ones, not just adding 1 to natural numbers.

>>10530265
fuck, no why you don't know the quadratic formula.

its 2+i or 2-i, one of the easier shit I did in high school, its just plug and take dick in the ass as you trivially calculate a retarded value.

>>10531924
kek

>>10530788

Whats so special about the upper half of the complex plain?

Daily Putnam Problem >>10532228

>>10532218
Every number in that part of the complex plane has a positive imaginary part, i.e. is [math]a+bi[/math] with [math]b \in \mathbb R^+[/math]. I don't see why it should be special.

https://www.thetimes.co.uk/article/caucher-birkar-from-asylum-seeker-to-fields-medal-winner-at-cambridge-xrz5t7ktj

>At the highest level of intellectual achievement minds deteriorate as surely as bodies, and there is a short window in which you can do your best work. The Fields Medal goes only to mathematicians under 40 – a stipulation that rarely excludes research of importance.

>>10531947
> I surrender, is there a better way to compute roots?
(a^b)^c=a^(b*c)
=> e^(log(x)*y) = (e^log(x))^y = x^y
=> e^(log(x)/n) = e^(log(x)*(1/n)) = x^(1/n)
IOW, log, divide by n, antilog gives you the nth root. Base doesn't matter. This is how you calculate roots with a slide rule.

The method given in
https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Decimal_%28base_10%29
was commonly taught in school in the early 20th century, but mechanical (and later electronic) calculators made it obsolete (slide rules are only good to about 3 sig. fig.).

>>10532218
.It gives a very nice and simple example of non-euclidean geometry
.When given a suitable metric, it is an example of geometry of constant negative curvature. In particular, it is a model space for most problems regarding geometry with negative curvature: it can be used as an example and surfaces with nonconstant negative curvature are studied locally by comparing them to the hyperbolic plane.
.It is one of the only three simply connected Riemann surfaces. "Most" connected Riemann surfaces (those with at least two holes) have it as a covering.

>>10532241
>ywn even come remotely close to being a fields medalist
feels real bad desu

>>10531981
algebra

>>10532326
how do the calculators do it?

starting HRT tomorrow lads

>>10533588
A moment of silence for the loss of anon. We'll miss him.

>>10533590
What do you mean anon, I'm not going anywhere

Atiyah is a weird name for a mathematician. Is he some kind of A-rab?

>>10533673
lebanese

>>10530265
>Meme book doesn't teach the quadratic formula
what a surprise

>>10533590
F

>>10530753
kek

>>10529217
>t. Elon Lindenstrauss

>>10530265
>he doesn't know the quadratic formula
Never gonna make it

I've been working on this stupid fucking problem for nearly 6 months. it doesn't help I'm shithouse at graph theory and combinatorics.

You have a set of 3 sets named A, B, and C. Each set must contain 4 elements, and at least two pairs of these sets (AB, AC, BC) must share at least one element.

If I gave you three sets that meet those constraints [math]A=\{1,2,3,4\}, B=\{3,4,5,6\}, C=\{5,6,7,8\}[/math] we can see that [math]|A \cup B| = 2, |B \cup C| = 2, |A \cup C| = 0[/math] (A and B share 2 elements, A and C share 0 elements, etc). The graph theory part of this is that the three sets can be converted into the bipartite graph in pic related.

So one could give you the reverse challenge: generate a valid set of {A,B,C} given the numbers [math]\{|A \cup B|, |B \cup C|, |A \cup C|\}[/math]. For example, if given the pairings {3,1,1}, there are two unique sets of {A,B,C} that are valid:

One variant with total 7 elements
A = {1,2,3,4}
B = {1,2,3,5}
C = {4,5,6,7}
Second variant with total 8 elements
A = {1,2,3,4}
B = {1,2,3,5}
C = {3,6,7,8}

I've been trying to write a python script that can generate every possible set {A,B,C} that satisfies the constraints above, and I've gotten nowhere. I've managed to find 20 of them by hand, and I'm almost certain that for 3 sets there is only 20 valid sets. Finding all valid sets {A,B} with the same constraints is fairly trivial (there's 3). I won't even bother finding sets {A,B,C,D} by hand since there's gotta be hundreds.

I have this question as homework<I dare /mg/ to solve this<I'm doing this question for fun<I did this question tell me if I got it wrong<my teacher insists the solution to this is a, but I think it's b.
Did I miss any?

>>10534054
Would filtering a recursive powerset help?

>>10534054
just start from the freest case with the right number of distinct elements connecting pairs of the set vertices. start combining those element vertices, deleting multi-edges. this maintains the intersection condition (which i assume you meant and not union). then you add extra vertices connected to each set to pad out the size

24 too old to get into pure math?

t. recovering doomer

>>10534054
Take k=min{|A∪B|,|B∪C|,|A∪C|}. Define A, B, and C as equal sets having the same k elements. Add elements to A and B to fill out the rest of the intersection, then similarly for A and C, and B and C, with new elements every time.
This gives one possibility, and the rest are obtained by repeating the process with k-1, until k=0.

>>10534054
incidentally the algorithm is generalizable to more sets but you have to think about why >>10534400
only had to vary over one type of collapse

What's up /mg/. I started to relearn math using Khan, then switched when I wanted things better explained: and with proofs. I'm currently reading Basic Mathematics, but I'm having great trouble right off the bat. I've never really learned algebra, and feel this might be what's holding me back on fully understanding this book. Is it possible, that without a good background of algebra; I'm going to have a difficult time with this book? Or I'm I just making excuses and need to keep trying. I'm also reading logic on the side to better understand proofs. Many thanks /mg/.

can someone explain topology. This semester I started topology, but it doesn't really click. All this talk about how one figure can transform into another if it doesn't have any holes really don't have any relation to what we learn in topology. How can I make sense from it?

>>10534369
>24 too old to get into pure math?
Why don't you try it and find out?

>>10529217
*blocks your path*

How do I construct a homeomorphism from the one-point compactification of R to the unit circle?

>>10534677
>How do I construct a homeomorphism from the one-point compactification of R to the unit circle?
What have you tried?

>>10534573
well i don't know what you learn it topology. point set?

the sets that make up a topology can be seen as a chunk of points that are spatially 'together' so you can scoop them out and separate them from surrounding points. a map is continuous when any scooping done in the image could have been done in the domain. so the map somehow doesn't mix points outside of local chunks in when you're sending those chunks to a chunk of the new space.

you can look at whether points move continuously on a path by associating them with time (a real segment) and making sure no togetherness-defying jumps happen.

when people talk about deforming one thing into another they're taking a subset of some ambient space and moving the points of that subset continuously (while preserving togetherness so they're not tearing the object apart) into another subset which looks different if you care about distance and shit instead of just togetherness

I commute to uni for around three hours every day. What's something math related I can do in the car so I'm not losing so much productivity? Any good podcasts about math?

>>10534649

He most certainly does. He most certainly does block my path, and effectively at that. Well met.

>>10534677
lol what the fuck do you think the one point compactification is?
hey, maybe construct it from the one point compactification of the open interval (-pi, pi) to the unit circle first and then take your favorite homeomorphism from (-pi, pi) to R.

>>10533588
take a cyanide pill while your at it you disgusting waste of life mentally ill tranny faggot. you unironically bring shame to all of your ancestors

>>10533588
Why the fuck do you trannies always have to rear your ugly fucking heads everywhere. There is a 6ft 2 adam's appled motherfucker that crossdresses everyday in my graph theory course and I'm sick of seeing it everywhere

get help. no, "transitioning" -- also known as laboring under a DELUSION -- isn't the best treatment faggot. realizing that you were born with a particular gender (i.e. what is reflected by your genitals and chromosomes) is the best treatment

Now kys

>>10535031
lol tell him you think he is cute then murder him and make it look like suicide. mentally ill faggots have no place in society

>>10534690
You can think about maths problems as you drive I guess.
Bumping for podcasts.

>>10535271
That's what I do now, it's pretty comfy but my mind also wanders a lot

help bros

Daily Putnam Problem >>10536135

>>10536033
Stop staring at it and actually try solving it.
>>10534677
Manually.
Or you can prove that the unit circle is the one point compactification of (0, 1) and invoke the homeomorphism between the open unit interval and R.

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

So, Wikipedia defines the polynomial ring R[X] only for commutative rings R.
Why can't we define R[X] for non-commutative rings? Does it not form a ring anymore?

If I have a function that is continuous almost everywhere on a compact set, and that is equal almost everywhere to some continuous function, must both functions be equal?

>>10536264
It's still a ring, the noncommutative case has a significantly more difficult construction from first-principles set theory but the model's actual properties are exactly what you'd expect (everything you can prove about the commutative polynomial ring R[x] without invoking commutativity). Noncommutative rings adjoin several in determinants are on the other hand _very_ awkward.

>>10536292
Hey thanks!
>the noncommutative case has a significantly more difficult construction from first-principles set theory

Why is that? Won't the definition on pic related work just as well as it works for the commutative case?

>>10536284
If the functions are real-valued, then yes. Write h as the difference of both functions. Then h is continuous and zero almost everywhere. If there's a point x s.t. h(x)=/=0, see what you can get in a small enough neighborhood.

>>10536303
Forgot the pic

>>10536308
That's actually the one that works for all rings, the one that doesn't is the algebra of functions one.

>>10536355
Or maybe it was backwards, I don't really remember.
But you can see the difference, right? (ax)(bx)=abx^2 under the one you've posted, axbx under the other one. One is an algebra of functions under pointwise multiplication, the other isn't unless the ring commutes. Also, quotients for finite rings, since the second eventually exhausts all functions.

>>10536374
I'm dumb, I didn't even realize that multiplication doesn't respect the evaluation map

Thank u

>>10528948
does anyone have good tips of making good mathematical definitions? more specifically in the direction of allowing for more elegant solutions to problems? thanks for ur time if u respond

>state theorem/exercise with some unexplained notation
>context for it is one sentence in the middle of some paragraph 20 pages ago
Seriously fuck Hatcher. Why does anyone recommend this meme book?

>>10536977
Because they don't know about Fuchs-Fomenko.

>Find out in a week or so if I get into a math PHD program
>Already have my masters, which means that my chances of getting into the program is significantly lower then young blood
>My interest in math has waned the last year because no job prospects and I'm starting to realize that I just don't have the imagination for math research
>Also discover over the course of the last few years, my cal 2, 3 and Linear Algebra skills have decayed into mush
I think I'm ready lads.

>>10537585
>tfw undergrad about to enter a master's program and calc/linear algebra skills are already rusty
>tfw your post describes my worst fears for the future

>>10537585
>>10537615
>First Semester in grad school
>While the Standard Analysis and Algebra course is an important gatekeeper courses, the true most important course is the Matrix Analysis class
>This is because even if you're shit at standard analysis and abstract algebras, if you know the Jordan canonical form and other advanced topics in linear algebra, you're good to at least churn out a few papers that nobody reads
>Professor was a fucktard that made the class so unendurably hard, 1/2 the class dropped and the other 1/2 essentially ate Fs on both tests and homeworks, including the final.
>Most of us gave up learning the subject as we might be able to walk away with As and Bs in the other two courses
>End of Semester, the fucker passes everyone with a B because he just wants to keep his cushy tenure position and not get any complaints about it
>None of us learned a damn thing besides some rudimentary eiganvalue/vector crap which sabotaged us for the more advanced courses (ODEs, Numerical Analysis ect..)
I think his strategy is to make his course so hard that everyone drops so he can go back to his fucking research in Quaternions in peace

Hi, I'm retarded.
Am I correct in thinking it should be possible to calculate G forces using simply speed lost over a period of time? Say 12mph lost in 850ms.

So the libgen version of Basic Mathematics is full of errors and badly scanned and that there is no errata available for the book, sadly.

Has anyone bought the book from Amazon, does it, at least, contain less errors than the free online version?

>>10537939
Basic Mathematics was written by an error.

>>10537585
Learn to code.

>>10537999
I just want to learn and it is the only precalculus book that is not 1000 pages long full of unnecessary shit. I just wanted to know if the edition in Amazon was sightly newer and therefore with less errata.

I guess I will just go ahead and buy it anyway it seems to be the best option for someone who wants to self-study.

>>10538016
http://booksdescr.org/item/index.php?md5=5AE296C34050FAB50136D08E779DA44C

>>10528997
Eat shit and die

>>10534564
Read “precalc in a nutshell” it covers all of geometry, algebra, and trig you will need

If I want to publish about a topic that I researched anonymously, but I still want to be able to prove it was me if it turns out to be useful/correct how do I do that?

>>10539164
Learn to code

>>10539164
Cryptography

>>10528948
what about his proof has it been officially proven wrong already

>>10539164
put some sort of watermark

>>10539164
Anon, your proof of the RH isn't correct.

>>10539164
I have no idea how well this would work in practice, but you could take a hash of part of your work and publish that on twitter and/or other large platforms with timestamps BEFORE publishing your work, so that the timestamps+hashes show that you had acess to the work some time before it was publically released.

>>10539164
make up a long random phrase, hash it, and embed it in your work. since the inverse hashing problem is difficult if you can provide input that hashes to what you've embedded you're the author

>exam asks me to find a monic polynomial in (Z/(2))[x]

I am trying to learn discrete math.
Is H rosens book the best bet on how to learn it as a brainlet?

>>10540613
Are you sure it didn't ask to ennumerate them?

>>10540834
meant 2Z not (Z/(2))

Is it proven that irrational numbers doens't have repeating numbers?

How? Couldn't irrational numbers have infinitly large blocks which are repeating?

Pic from https://www.youtube.com/watch?v=SqRY1Bm8EVs

>>10540885
sqt is over here
>>10527130

>>10540904
Hey be glad i didn't make a new thread about it

>>10540885
>Couldn't irrational numbers have infinitly large blocks which are repeating?
this doesn't mean anything.
If something repeats, there has to be more than one block of it.
How many spaces after the decimal point do you suggest the second "infinitely large" block should start?

>>10540918
Kek. I'll answer because I laughed, but use /sqt/ next time.
Essentially, if it repeats you can constructively give it as a fraction. I think it was something like check the duration of the part that repeats, and put it over that many nines, then sum normally the part that doesn't.
So 0.444444 has a period of 1 (because it repeats 4) and becomes 4/9.
0.464646... has a period of 2 and becomes 46/99.

>>10540937
>>10540930
Ok so to rephrase the question in more correct terminology: What's there to say that irrational numbers aren't numbers with infinitely large repeating periods?

I mean, take a rational number with the period 21093891238712. That's large as fuck, and it will take a while to find if it in fact is repeating., But until you find that it is repeating, can you really know if it is repeating or not? Similar logic but flipped around: can you construct a rational fraction which has an infinitely large period, making it appear irrational?

>>10540993
nvm

https://math.stackexchange.com/questions/1519752/maximum-length-of-repeating-digits-in-a-decimal

it was sqt mb lol

>>10539164
LOL

ok i just 360 noscoped this mathproof up, did i get a pentakill?

Lads.... Why is [math] 2\mathbb Z\otimes_{\mathbb Z}\mathbb Z/2[/math] not 0???

>>10541167
Because the element [math]2\otimes_\mathbb{Z}1[/math] is in there.

>>10541204
I know, but why can't we pass the 2 to the other side? It belongs in Z right?

What the FUCK is the double line symbol

>>10541480
The equaliser

>>10541480
A long number eleven

>>10541244
Because to pass something from one side to the other we need one side be decomposable in product of two things, then ab \otimes c = a \otimes bc, which is not the case because you can't decompose 2 in product of two things from 2Z

>>10541080
a_1 = 0 - rational number
a_2 = 0 - rational number
....
a_n = 0 - rational number
...
lim a_n = lim 0 = 0 - irrational number

What about book on mathematically rigorous reinforcement learning?

>>10541480
An rubbish ladder design.

>>10541480
tilt your head 90 degrees

>>10541852
But now I can't read the text

>>10541676
Damn I'm dumb, of course, thanks

>>10541879
>he can't read sideways
no seriously, you can't? It's harder but I can definitely read sideways text.

>>10541026
don't feel bad, loads of beginners fall for those kinds of mistake. it's like getting confused why 1.00000(infinite 0's)1 isn't a number

>blocks your path

what's the motivation behind the definition of a topology on a set? is there a similar intuition akin to the motivation of a metric/norm/inner product on a set?

>>10542173
The motivation is that topology is cool
Seriously though it's so you can study properties of spaces that are invariant under homeomorphisms (bijectively continuous maps with continuous inverses). Because the continuity of a function can be characterized by its effects on open sets.
Homeomorphisms don't preserve metrics but they do preserve topologies.

>>10533588
good luck, I wish you the best anon.

>>10542173
The motivation behind a metric is obvious and left to the reader. The motivation behind a topology is essentially the following:
>a metric makes some sets open and others closed
>we can properly clean up this set of open sets by closing it under arbitrary union and finite intersection
>this new, closed up set is capable of determining whether a function on the original metric space is continuous or not, and can determine the limit of sequences, in an extremely natural and simple way
>this implies that skipping the part of inducing through a metric and simply determining that some sets are open generalizes the notions of continuity and proximity
A norm is a comfy, extremely well behaved metric on a vector space.
An inner product is a device that measures angles and distance.

>>10542441
and beyond an inner product?

>>10541480
what book?

Daily Putnam Problem >>10543223

>>10542906
Wedge product I guess. But wasn't the point of the question

>>10534690
>mathematics student
>going to class
What kind of backwards-ass uni doesn't put their math lectures online. I haven't been to uni all year apart from tests.

https://arxiv.org/pdf/1904.05096
>Value patterns of multiplicative functions and related sequences
>Terence Tao, Joni Teräväinen
>Submitted on 10 Apr 2019
>We study the existence of various sign and value patterns in sequences defined by multiplicative functions or related objects. For any set [math]A[/math] whose indicator function is 'approximately multiplicative' and uniformly distributed on short intervals in a suitable sense, we show that the asymptotic density of the pattern [math]n+1\in A[/math], [math]n+2\in A[/math], [math]n+3\in A[/math] is positive, as long as [math]A[/math] has density greater than [math]\frac{1}{3}[/math]. Using an inverse theorem for sumsets and some tools from ergodic theory, we also provide a theorem that deals with the critical case of [math]A[/math] having density exactly [math]\frac{1}{3}[/math], below which one would need nontrivial information on the local distribution of [math]A[/math] in Bohr sets to proceed. We apply our results firstly to answer in a stronger form a question of Erdős and Pomerance on the relative orderings of the largest prime factors [math]P^{+}(n)[/math], [math]P^{+}(n+1), P^{+}(n+2)[/math] of three consecutive integers. Secondly, we show that the tuple [math](ω(n+1),ω(n+2),ω(n+3)) \pmod 3[/math] takes all the 27 possible patterns in [math](\mathbb{Z}/3\mathbb{Z})^3[/math] with positive lower density, with [math]ω(n)[/math] being the number of distinct prime divisors. We also prove a theorem concerning longer patterns [math]n+i\in A_i[/math], [math]i=1,\dots k[/math] in approximately multiplicative sets [math]A_i[/math] having large enough densities, generalising some results of Hildebrand on his 'stable sets conjecture'. Lastly, we consider the sign patterns of the Liouville function [math]λ[/math] and show that there are at least 24 patterns of length 5 that occur with positive density. In all of the proofs we make extensive use of recent ideas concerning correlations of multiplicative functions

As an absolute brainlet how do I know a book is a meme and I am getting bamboozled for some asshole doing his 999th revision of a book but he added one new letter to the book?
Trying to refresh precalc and then calculus, linear algebra and discrete math.
I have also interest in statistics and probably theory.

>>10542140
I see what you did there

I had a lot of fun picking up math with projecteuler, do you know any books with a similiar approach? I've been studying TAOCP 1 by Knuth a bit but having to stop to analyze and understand why formula x works multiple times per page(It's very compressed and reading an explanation first won't give me the level of understanding that studying it will.) is not fun.

>>10540885
It's easily proven that sqrt(2) cannot be expressed as a fraction.

Social science brainlet here, and my PhD supervisor is even more of a brainlet (he doesn't even know how to do a regression for god's sake) so I'm looking to replace him as supervisor with 4chan.

Does anybody know the correct way to follow up a multivariate multiple regression analysis? The multivariate test (Pillai's trace) tells me that x1, x2, and x3 are all significant predictors of my group of outcome variables, but how do I understand what those effects actually are in practical terms, in terms of directionality and effect size on each individual outcome variable?

Daily Putnam Problem >>10545260

>>10540885
[math]\sqrt{2}[/math] is rational if [math]\sqrt{2} = \frac{a}{b} [/math] for some [math]a,b \in \mathbb{Z} [/math] . Suppose [math]\frac{a}{b}[/math] is in simplest form (a and b relatively prime).

then [math]2 = \frac{a^2}{b^2} [/math] or [math]2b^2 = a^2[/math], so [math]a^2[/math] is even.
If [math]a^2[/math] is divisible by 2, then a must be even, so [math]a^2[/math] must also be divisible by 4. Further, [math]b^2[/math] must also be divisible by 2 since [math]a^2 = 2b^2[/math]. It follows b is even as well.
Then [math]\frac{a}{b}[/math] is not in simplest form, and a and b are not relatively prime, leading to a contradiction in the initial assumption. [math]\sqrt{2}[/math] is irrational.

>>10545274
>>10545117
That is completely besides the point. He's not disputing the existence of irrationals, rather he doesn't see the connection between periodicity of digits and rationality, which is a different thing

>>10545288
Ah. The very basic explanation is any number with periodic digits can be expressed as a fraction. Proving irrationals cannot be expressed as a fraction is sufficient proof they aren't periodic.

>Couldn't irrational numbers have infinitely large blocks which are repeating?
If the sequence is infinitely long, how would it be repeating?

>>10545343
Since it's late as fuck you can forgive this shitty proof, just to satisfy:

Consider x with [math]a_1,a_2,....a_n[/math] where [math]a_k[/math] is the kth digit of the sequence of its decimals.
[math]10^n k[/math] has an integer part equal to the sequence, and a decimal part equal to the sequence.
Then [math]10^nk - 1[/math] is solely the sequence as a sequence of integers. Then
[math]\frac{a_1,a_2...a_m}{10^k-1} = x[/math]

>>10545343
The point is: how would you know that it isn't repeating? And if there's an infinite amount of non-repeating digits, wouldn't it eventually reach a point where the digits mimic repetition (due to sheer randomness)? If it does, what's the difference between mimiced repetition and actual repetition?

>>10545370
You mean something like:
>I give you a computer
>this computer is loaded up with a software that, whenever you type a natural number, gives you that digit of a real number
>can you determine if the number is rational?
And the answer is no.
>>10544512
If someone is telling you to buy a newer version of a book over an older one, he's bamboozling you.
If he's telling you to buy a book that's on libgen, he's bamboozling you.
If he's telling you to buy a book because the most recent edition isn't on libgen he's bamboozling.
If he's telling you to buy a book that's not on libgen, solid 50% chance of bamboozling.

>>10545370
>wouldn't it eventually reach a point where the digits mimic repetition
No. Some finite number of repetitions is possible but the probability of that tends to zero as number of digits n grows. I.e. you can always chose n large enough to make the chance to find repeating digits as close to zero as you want.

>>10543102
Bosch commutative algebra and algebraic geometry

I quite like it, it is extremely complete in that it explains every step quite clearly and doesn't leave anything as an exercise

>>10545378
Look. All i wana do is ride the same train you guys do.
at least as a servant, or even walking next to the rails at the same direction you guys are going.
And here I hear from someone like you that all the books that I am trying to research are bullshit?

>>10545378
Uhm, no. I mean like:

pi = 3.1415... and then an infinite amount of non-repeating digits. An infinite amount. In this infinite amount of digits, there will at some point be a sequence of digits ...141..., and also ...1415..., by chance alone. So there's a "substring"(subset?) of repeating digits, in this case it repeated 3 and then 4 of the original digits. If there is a substring of period 4 "pseudorepeating" numbers, there's a chance of of a substring of 5, and 6, and so on, incrementally until the pseudorepeating substring is also infinitely long = the digits are actually repeating. What's the difference between that "mimiced" repetition and actual repetition?

>>10545403
My logic is: If there exists a chance, any chance, and this chance is iterated over and over again an infinite amount of times, it's not only probably that a certain event will occur but inevitable. Is this incorrect?

Why is this true?

That is, why do the a_m generate the unit ideal?

>>10545582
Actually, is it because the ideal generated by the a_m not contained in any maximal?

>>10545112
>having to stop to analyze and understand why formula x works multiple times per page [...] is not fun.
This is the best way to learn maths though anon.

>>10545595
Yes.

>>10545430
It's from the difference between potential infinity and actual infinity.

>>10533588
I hope you die. :)

>>10545436
Not if this chance decreases with each iteration. Again any finite number of repeatings is possible, but you’re talking about infinity...

>>10545120
Nobody knows stats?

>>10545430
You mistakenly assume that the probabilty of appearing of repeating string length n is very small but still fixed, it’s not. It tends to zero if number of digits is revealed ony by one to infinity. I mean, yes, the number of “trials” really tends to infinity, but probability for digits to start repeating tends to zero faster.

>>10530461
e^tau*i = 1 brainlet

>>10534369
No, but don't expect to be a great mathematician that will solve impossible problems and drown in pussy as a consequence of that. You'll be a mere spectator of the show other people with talent and proper nurture will provide to you. Don't feel bad if you can't compute things fast in your head, this comes with time and practice, don't feel ashamed to use a calculator if you're in a hurry. Do attend lectures, go to office hours and study a lot (and I mean A LOT). Pick a field that interests you when you're mature enough and follow that path, don't try to know every nook and cranny of maths, that's nearly impossible.
With that said, you can still be a professional mathematician and write textbooks, make important contributions, be a professor, mentor younger students, etc. There's glory in all that.
Godspeed.
t. also a late learner

>>10539164
Just use a pseudonym, if you're so worried

>>10531251
I wish girls fucking looked like this but NOOOOOOOO we just had to be stuck with 3D foids. LIterally fuck this gay earth.

>>10546619
why do you need girls when you have spaces like [math]\ell^{2}[/math]?

I'm so stupid. For the last 1.5 years of my undergrad I've been forced to solve a bunch of problems but I still suck at problem solving. I'm hopeless. For my linear algebra class we covered a bit of group theory but didn't get very far. So in our problem set homework, one of the problems was to give a proof of the Sylow theorem (it wasn't named in the problem set), and the problem was broken down into 4 steps so as to hold the student's hand throughout the proof. But being the dumb asshole that I am I got lost and since it's due in less than 24 hours I turned on cheating mode and found the proof in a textbook. Turns out it's not even that complicated, it's just mostly combinatorial. But I only found out after the fact.

>>10546925
Why would Sylow's theorems be taught in a linear algebra course. First time I'm hearing this.

>>10546948
Calculus we had to solve a problem that we could only do by delving into set theory.
Math is an overtaking experience
Life consuming ecperience

>>10546948
Well it wasn't taught per se. As I said we covered only a bit of group theory, mainly to motivate the study of algebra in general. The Sylow theorem was just a problem in the problem set

>>10546968
Meh you could just learn group theory in parallel instead of wasting a problem set of linear algebra on group theory

Ok, I have a problem guys
I'm taking Algebra next semester and am reading through Saracino's book right now
I was trying to prove the Third isomorphism theorem and ran into a contradiction, but i dont see an error

A, B, X groups
[math]
X \triangleleft A, X \triangleleft B \triangleleft A \\
\therefore B/X \triangleleft A/X \\
(A/X)/(B/X)=\{ (B/X)Xa, Xa \in A/X\} = \{XbXa,Xa \in A/X, Xb \in B/X \}\\
=\{XbXa,a \in A, b \in B\}=\{Xba, ba \in BA \}=BA/X \text{ but } B \triangleleft A, \text{ so } BA=A\\
(A/X)/(B/X) = A/X
[/math]

but [math]A/B \cong (A/X)/(B/X)[/math]
and this is contradictory
we can take [math]A = \{0, 1, 2, 3\}, B = \{0, 2\}, X = \{0\}\\
A/B \cong B, A/X \cong A, A \not \cong B
[/math]
wheres the error?

What's the elliptic genus?

>>10547484
>wheres the error?
you're studying algebra.

>>10545969
I often say the 'am I too old' question is solely rooted in the desire to get good at said skill and get laid. Why spend 10 years studying math/learning an instrument/working out just for pussy when 2-3 months selling drugs will achieve the same results?
As a 30 year old who fell for the Lang meme, I'm excited at the fact I have another 40 years to get into the top 1% of people who ever lived in my country in terms of mathematical knowledge

>>10547484
Don't write walls of symbols without any words. Everyone who has to grade anything you write hates you for this.

The issue is that [math]\{(B/A)Xa, Xa \in A/X\} = \{XbXa, Xa \in A/X, Xb \in B/X\}[/math] is wrong.
What you should have is [math]\{(B/A)Xa, Xa \in A/X\} = \{ \{XbXa\}, Xa \in A/X, Xb \in B/X\}[/math], since (B/X)Xa is a coset.
Halfway through the proof you deleted the fact that you took a quotient and then you proved that you didn't take a quotient.

>>10547830
sorry, and thanks

>>10531251
tfw no rite of spring ballet gf

Undergradlet here.
I read that a topological space can by expressed as a quotient space for some Hausdorff space.
Can this happen for some regular space or does a counterexample exists?
(Supposing that the regular space is not necessarily the same as the Hausdorff one.)

OI! THIS IS A STICKUP! I'm an engineer that wants to make personal lubricant 2.3% more cheaply! PUT ALL THE MATH IN THE BAG RIGHT NOW! Yeah put that topological whatsit right there, yup taking those algebras. Category theory? What're ya trying to pull? Ya holding out the good stuff on me? Category theorist are going door to door handin' out tha shit.


Fuck me. I'm grasping at straws to solve a nearly impossible problem. I need some new math, but barely have time to learn it. Fuck. Also, fuck category theory. Category theory fucked me over hard.

>>10542441
based answer

Daily Putnam Problem >>10549795

Are there some simple examples of characters on groups that are not just mappings to the unit circle? I think if a group is compact or abelian it will always just map to the unit circle, so maybe something like GL2(Z) would have a character not mapping entirely to the unit circle but I cannot think of one.

Background: not homework. I'm trying to understand the Haar measure and have come across the line "since the character maps to the non-negative reals, it is trivial on compact subgroups of G. If it is trivial on all of G then..." implying the character could potentially give values off the unit circle on non-compact subgroups of G.

>>10549808
take the identity on C^*
> I think if a group is compact or abelian it will always just map to the unit circle
yes, it only has to do with compactness, do you see why ?

>>10549833
This makes sense yeah. If a character maps some element g of a compact group to some x in C outside the unit circle, then we can take g^n which will map to x^n and (possibly needing to swap g for g inverse) we get that g^n tends to a point necessarily in G which maps to infinity which is impossible?

I'm thinking in analysis here rather than topology as I'm not comfortable with topology at all, but that seems to work.

>>10549833
>>10549919
thank you for this.

>>10549919
that works yeah

>>10549919
If you want to rephrase it topologically, you'd have to see that the image of a compact group under the character map is again compact in C^*,
so it is closed and bounded: there is a minimum and maximum norm elements can have.
Then as you say, the sequence g^n will map to a sequence that is not bounded if g maps to something with norm not equal to 1, so the minimum and maximum norm are just 1.

You do algebra exams with or withouth calc?

>>10550003
>algebra exam requires calculator
Lmao wat

>>10550006
>algebra exam requires calculator
what do you mean?

>>10550007
What do (You) mean? You were the one to ask the question

>>10550010
thx, you very helpful

>>10550003
i haven't used a calculator in my four years of maths studies at uni.

>>10550003
>math
>calculator
Utterly plebeian. I haven't seen a number in years.

i'm finna change my major to math starting next semester, wish me luck nigras

>>10550351
>t. algebraist

why are algebraists by and large the most rude, arrogant, and awkward people to work with?

>>10550784
Woah, rude. And I always put so much effort into answering your questions, monkeyposter.

>>10528948
FUCK VECTORS
That's all folks.

I hate calculus and analysis.

>>10550861
FUCK DUAL VECTORS in particular

>>10550784
My algebra professor is actually the nicest person in the department.

>>10550784
Because they know they're at the top of the food chain.

>>10551312
this is the number 1 answer

>>10551312
And all they had to do was simplify the works and theorems of other branches.

>>10550784
huh, in my department it's always the analysts being arrogant twats.

>>10550343
why

Obstruction theory will kill me, send help.

Yeah I've got double D's

>>10552452
On my unfaithfully flat gf ;)

Did grossendieck ever use a cox ring?

>>10550861
>>10550892
FUCK CATEGORY THEORY!

>>10552470
>https://en.wikipedia.org/wiki/Cox_ring
>2000
https://en.wikipedia.org/wiki/Alexander_Grothendieck#Retirement_into_reclusion_and_death
>recluse since 1991
Five bucks say no.

>>10550861
>>10550892
>>10552520
I wish I could, if you can catch my drift.

>>10547830
>Don't write walls of symbols without any words. Everyone who has to grade anything you write hates you for this.
Yeah I fucking hate when students do this

So I'm taking Intro to Real Analysis this quarter and one of the books our prof. listed is Rudin's Principles of Mathematical Analysis/Baby Rudin. It's a lot smaller than I expected but the book is fucking OPAQUE. Is there a companion guide or something that discusses verifying his theorems and explaining them? One section just concluded with "I won't bother detailing this."

>>10553084
>So I'm taking Intro to Real Analysis this quarter and one of the books our prof. listed is Rudin's Principles of Mathematical Analysis/Baby Rudin.
Rudin is a meme.

>>10553092
Yeah, I bought three other analysis texts but our prof. is still working through some Rudin parts.

>>10550892
>vectors
>dual vectors

I'm trying to solve the differential equation
[math]y'=\frac {2x} {x^2+1} y[/math]
Using [math]\int \! f'g \, \mathrm{d}x=fg-\int fg' \mathrm{d}x[/math] knowing that the solution will be [math]Ce^{-G(x)}[/math]
It's mentioned that the fact that 2x being the derivate of x^2 is relevant.
How exactly?

>>10550784
Algebraists have autism. Be more understanding.

>>10553305
Seriously?
[math]y'/y = (\ln y)' = \frac{2x}{x^2+1} = \left(\ln(x^2 + 1)\right)'[/math]

>>10553305
differentiate your candidate solution and plug it into the differential equation and solve for G(x)

>>10553316
>>10553321
No I have to specifically use that integral.
[math]f'g[/math]is supposed to be some form of [math]\frac {2x}{x^2+1}[/math]split up as two equations and the result from that integral becomes [math]G(x)[/math] which can be plugged in over e

>>10550784
algebraists are the mathematical equivalents of toddlers, immature, spoiled, and envious.
>>10551312
>>10551533
imagine seething this hard, logicians are obviously above you morons and analysts and geometers are the only respectable mathematicians.
>>10551599
ever consider you're just blind to the fact that all the smart people in your department think you're a hack and an idiot?
>>10553314
and yep, yukari poster is BASED as fuck. you are a real one my guy.

>>10553332
Idiot.
>>>/sqt/

Daily Putnam Problem >>10553347

>>10553084
>not understanding the most basic mathematics textbook available
>implying rudin is in any way "opaque"
blunt != opaque, rather, it is essential for clarity.
>>10553104
oh, you buy textbooks? yeah, that explains it. never gonna make it.
try pugh (pdfs on fucking line) if you need something that's more comprehensible and readable but on the level of rudin in content.

>got a 4.0 in all my calculus classes
>no longer remember even a single integral or derivative rule unless I manually derive the integration/derivation

>>10553332
Multiply both sides by the denominator.

>>10550784
A few algebraists doesn't represent all algebraists

>>10551312
Honorary algebraist.
>>10553344
>logicians are above algebraists
Give one reason.

>>10553344
>praising the toymaker
out

I've been wondering, now that the classification of finite simple group program has already completed, what are the main focus of finite group theorists right now?

>>10554005
Applying to a new job

>>10554005
field is dead

>>10554005
Inverse Galois problem, which is basically the opposite of the classification. How to build groups from simple groups?

I'm currently in a weird position. I desperately want to find a lower bound for the sequence A161772.

I think I have managed to prove it's unbounded.

https://www.overleaf.com/read/tjjspftfdzwc

Please tell me what you think of this proof.

>>10553363
You remember how to manually derive them.

>forget the quotient rule
>write everything as a product, using negative exponents
>use product rule

>>10554496
Why do people bother showing us the quotient rule anyway? The product rule and is almost always easier anyway.

Why are there calc babbies still itt

>>10554519
What should be the bare minimum for someone to post in /mg/, anon?

>>10530788
Did he get Herpes from getting mouth raped by based Scholtzy?

>>10543634
>mathematics student
>going to class
>gets shot
Now you know what kind.

>>10545343
Replace arbitrarily long for infinitely long. Then explain. That's the point of the question.

>>10553631
t. statfag

>>10554535

PhD in theoretical chain rule analysis

>>10530265
the absolute state of /sci/

>mfw I can't multiply two matrices without physically putting my fingers over the entries I'm multiplying

>>10530265
Don't listen to quadratic formula memers. Complete the square to get:
(x-2)^2 = -1
which has no (real) solutions, since the left-hand side is a square, while the right hand side is negative.

>>10554005
the group extension problem?

Proving that Lusternik-Schnirelmann is one or two is easy. Are there any other convenient cases or does it just get worse and worse as n goes up?

>>10554976
So what ? You do whatever you need to do.
I also make involuntary hand movements when I am multiplying matrices in my head sometimes (I pretty much do what you do on an imaginary blackboard). If it helps you, why not

Will i regret transfering from computer engineering to maths and computation?

In ZFC is set inclusion actually a real relation or is it a feature of the metalanguage?

>>10554286
Provide an example of your construction and people will be more motivated to look at the proof

>>10555963
It is a real relation

>>10555992
how do you construct it without running into circular arguments?

How do I choose my priors in a rigorous way?

>EGA and SGA remain untranslated
Why has no one bothered to translate them? Grothendiek invented modern algebraic geometry, and in turn algebraic geometry has been reinventing and generalizing all other mathematics, yet no one cares enough to translate it. Nothing else even comes close to explaining the etale fundamental group. Also the history of topos theory is buried in there.

Also French is a faggy language.

>>10556104
>faggy
Why the homophobia?

>>10556108
I prefer a world of straight people. Does that bother you?

>>10556108

-t. leftist of the oversocialized type

>>10556108
I have no problem with gays and lesbians. Whatever. Like whomever you want. What I have a giant problem with, however, are trannies. Letting people fuck what they want to fuck is just liberty. Forcing others to play make believe with you and your oozing wound is, on the other hand, totalitarianism.

>>10556108
ass cancer

>>10556104
>he can't read french

>>10529217
>dynamical systems applications to number theory
What have I just read?

>>10556015
What do you mean?

>>10553316
>>10553345
Fuck. I'm retarded.
I had never seen that chain rule thing before. Sorry.
>>10553567
Nah the other guy had it. Thanks anyways.

>>10536033
i think you can just rewrite it as a sum of b_n where b_n ends up being a power of 56/(1+...48).

Daily Putnam Problem >>10556517

>>10533588
Hey tranny you are a mentally ill freak and you will never be the opposite gender. Quit deluding yourself

>>10554286
Your idea works, but please just fix your notation.

Also fun thing to note, the same idea works for higher power operations rather than just squaring.

>>10556104
>Why?
Because G'dick protested its translation until his dying breath, and nobody would have disrespected him. In fact, they did work on a translation and I think they even finished EGA I but big G protested it and that was that. He also wanted the whole of EGA and SGA copies to be burned and taken out of the market, and well, they didn't burn them but they stopped selling them, which is why getting the books is so expensive as they are a rarity, and they're usually super old.

Now that he's dead and a new generation of mathematicians are coming over, it's much more likely that it gets translated

>>10556749
SGA has already been typeset with LaTeX, won't be too long until that is translated. The final volumes of EGA, though. I don't know if we'll see them in the next 30 years.

>>10556749
>protested its translation until his dying breath
I know he's going through a mental breakdown but damn, that was a dick move.

>>10556355
construct the relation "member of" as a subset of the cross product

>>10556113
>>10556115
>>10556149
>>10556165
>retarded /pol/ users falling for the same bait that gets posted every thread

>>10556049
pls respond

I recently realized that if you don't work in mathematical physics (and thus will eventually get a Nature paper published), then you will never be hired into a faculty position in math.

You have all been warned. It's not that hard to publish in Nature, so if you don't have that paper you'll never make it.

Is there a good set of notes / short book on basic CS theory? Like what CS undergrads would learn but presented in a way that's not for brainlets (that is, doesn't take multiple classes over four years).

>>10557192
CS theory is a lot of fields bundled together.
The book, "Concrete Mathematics" is a good start
Look for notes on computability (set theory / recursion theory), complexity theory, formal grammar, logic (mostly lambda calculus is useful), maybe some type theory.

Someone make a new thread.

>>10557192
>>10557208
Oh yeah, and combinatory logic and graph theory are important for algorithms.

>>10547652

I really have zero ambitions to contribute to Math as I know I'm a brainlet and don't have the buddha-like will to persue it.I just need to understand enough of this discipline to be able to not be a codemonkey but an actual engineer.

>>10557365

1. Databases
2. Algorithms
3. Programming language semantics

>>10557157
Okay? What part of that is circular?

>>10557600
it looks like you're wrong in any case, element of is a proposition in the metalanguage of first order logic not a proper in-model relation

>>10557192
The Art of Computer Programming