/mg/ maths general: Eulerian Edition

[Anonymous No.10101820]

talk maths, formerly >>10090014

threadly reminder that 0 is not an element of \mathbb{N}

https://ilaba.wordpress.com/2011/03/28/why-im-not-on-mathoverflow/

[Anonymous No.10101824]

Befriend Euler, ignore Gauss.

[Anonymous No.10101832]

What's more fundamental, graphs, digraphs, or simplices?

[Anonymous No.10101867]

>>10101832
Digraphs are more fundamental. They are nothing but relations.

[Anonymous No.10101870]

Where the math bio fags at? Who's at NIMBioS rn?

[Anonymous No.10101965]

There's no such thing as 'applied' or 'pure' mathematics, only mathematics. If you felt unmotivated to learn it just because it's categorized in applied math, that means you don't truly love math. You're worth nothing more than garbage.

[Anonymous No.10101983]

>>10101965
I agree that if you truly enjoy math then you will also enjoy its application, but to say that the distinction does not exist just shows you are ignorant and probably not even an undergrad. An applied course will just give you a surface understanding of the theory and then jump right into applications. A pure course will be completely focused on the theory and will either ignore applications or leave applications as exercises in which you 'discover' the application. The difference in method is also very different as applied courses are based around hand holding so that most students can pass.

TL;DR: When you get into college you'll understand.

[Anonymous No.10101991]

>>10101983
Maybe he means that over time, the line between applied and pure mathematics has blurred. Math that was done for its own sake and not motivated by application gets applied to things later (e.g. number theory/elliptic curves and cryptography). Likewise, pure mathematicians may take interest in generalizing and abstracting what the applied mathematicians are doing.

[Anonymous No.10102002]

>>10101991
Well, even then I'd have to disagree. What you see is true but in research, there is also a huge difference in method. Maybe it is true that the results in pure mathematics will appear in applied mathematics journals 100 years later, but when they do the way they are used will be completely different from how they were studied in the pure setting.

Applied mathematicians do not work like pure mathematicians, and vice-versa. Motivations, method, and goals are completely distinct. At best you could say that there is a semi-permeable membrane separating them and every now and then stuff passes through.

[Anonymous No.10102010]

>>10102002
Oh okay, I understand your argument more and I agree with you. I was thinking just in the grand scheme of things the lines get kind of blurred, not trying to say that the work applied mathematicians do is the same as what pure mathematicians do. As you pointed out, methodology and motivations are very different.

[Anonymous No.10102096]

>>10101965
dumb faggot stop trying to cope with the fact that you are to retarded to pursue pure math.

[Anonymous No.10102131]

>>10102096
>faggot
Why the homophobia?

[Anonymous No.10102214]

>>10102131
>LOL LE EBIN MEME

[Anonymous No.10102230]

>>10102214
>LOL LE EBIN HOMOPHOBIA

[Anonymous No.10102236]

>>10102131
>homophobia
Why the Islamophobia?

[Anonymous No.10102239]

>>10102230
if(right.creates_meme()) {
download.file('newmeme.png');
edit.file('newmeme.png').addmagahat();
}

>WHO SAYS THE LEFT CAN'T MEME

[Anonymous No.10102242]

>>10102236
>Islamophobia
Why the antisemitism?

[Anonymous No.10102248]

>>10102239
if(right.creates_meme()) {
download.file('newmeme.png');
edit.file('newmeme.png').addmagahat();
edit.file('newmeme.png').addTextBlockFromCommieBooks();
}

[Anonymous No.10102251]

>>10102242
>antisemitism
Why the anti-white?

[Anonymous No.10102269]

>>10102251
>anti-white
Why the suppression of black lives?

[Anonymous No.10102275]

>>10102269
>Black lives
Why the rape culture?

[Anonymous No.10102281]

>>10102275
>rape culture
Why the feminazism?

[Anonymous No.10102283]

>>10102281
>feminazism
Why the anti-feminism?

[Anonymous No.10102288]

>>10102283
>feminism
Why the anti-trans?

[Anonymous No.10102296]

>>10102288
>anti-trans
Why the anti-TERF?

[Anonymous No.10102301]

>>10102296
>TERF
Why the literal Hitler?

[Anonymous No.10102304]

>>10102301
>literal Hitler
Why Hitler Hitler?

[Anonymous No.10102309]

>>10102304
>Hitler Hitler?
Hitler Hitler Hitler

[Anonymous No.10102333]

>>10101832
Simplixes, since pretty much all category can be represented by its nerve.

[Anonymous No.10102458]

>>10102230

[Anonymous No.10102465]

>>10102333
>Simplixes
is there actually a country that uses this autistic spelling or did you fuck up

[Anonymous No.10102608]

Explain the intuition behind ultraproducts please thanks.

[Anonymous No.10102649]

>>10102608
ultrafilter on I = voting system (input a subset of I and it tells you yes or no)
ultraproduct indexed by I = set of sequences up to voting equivalence (two sequences are equal if the set of indices where they coincide is in the ultraproduct)
Los's theorem tells you that an ultraproduct of structures X_i has a first order property P iff the subset of I such that X_i has P is in the ultrafiltrer (hence properties of an ultraproduct are decided by "consensus").
Ultraproducts also allow you to construct "limits" in the sense that if the structures "almost" have a property, then the ultraproduct might have that property. The most emblematic example of this is the non-standard real line: Let R* be a non standard countable ultrapower of R. Then, the class of the sequence (1, 1/2, 1/4, 1/8, ...) is smaller than any positive real, since it is case for almost all terms of the sequence.
Hence, we have constructed an ordered structure with infinitesimals starting from a structure that did not have them

[Anonymous No.10102719]

>>10102649
>>10102649
>>10102649
This helps; the equivalence relation definition is what's confusing to me:

Two elements of the Cartesian product a and b such that { i in I: a_i == b_i } in U

What *are* these two elements, a and b, in the cartesian product?

If the cartesian product is Product(i in I) A_i = (A_1, A_2, ..., A_i) what are these "Two elements a and b [in the cartesian product]?"

[Anonymous No.10102870]

>>10102309
>Hitler Hitler Hitler
Heil Hitler

[Anonymous No.10103024]

I think /sqt/ is too brainlet to confirm this answer. Halp pls.

[Anonymous No.10103066]

how to prove this?

[Anonymous No.10103070]

>>10103066
>how to prove this?
What have you tried?

[Anonymous No.10103113]

>If [math]f:[a,b]\to\mathbb{R}[/math] is bounded and [math]f(x)=0 \hspace{0.1cm} \text{a.e}[/math], then [math]f[/math] is Lebesgue integrable with integral equal to zero.
Could I just evoke the result from Riemann integration

[Anonymous No.10103142]

>>10103113
Rule of thumb is if there's a theorem that makes a question trivial, then you probably aren't supposed to use it.

[Anonymous No.10103149]

>>10103142
that's dumb.

[Anonymous No.10103151]

>>10103142
>that guy who keeps trying to use feit-thompson in a group theory class

[Anonymous No.10103165]

>>10103149
The theorem itself isn't important. The reason why it's a theorem is, and that's what you're supposed to be learning.

[Anonymous No.10103371]

>>10103113
What if f i not Riemann integrable? say it's the indicator function of the rationals

[Anonymous No.10103711]

>>10103113
Use the definition of Lebesgue integral and estimate.

[Anonymous No.10103726]

>>10103113
Latex isn't loading, but can't you literally just make the Lebesgue measure function f(0)=1, f(x)=0 otherwise, and say that integrating that gives zero?

[Anonymous No.10103765]

>>10103726
Anon needs to prove it for all functions that satisfy his criteria.

[Anonymous No.10103786]

>>10103024
It's wrong. How did you even get that first determinant expression. Remember that [math] dx \wedge dy = dx \, dy - dy \, dx [/math]. And (a b; c d) isn't even a scalar matrix so I don't know what property you used to factor the determinant.

[Anonymous No.10104089]

How do you get over the fact that you are low IQ and will never achieve anything akin to the great mathematicians? If you do not possess the raw IQ to succeed in pure mathematics, would it be a waste of your life?

Gauss has over double my IQ. How could I ever compete?

[Anonymous No.10104175]

>>10104089
>a mediocre brainlet has over double your IQ
(You) should definitely give up.

[Anonymous No.10104231]

>>10104089
>How do you get over the fact that you are low IQ and will never achieve anything akin to the great mathematicians?
Blaming your low IQ for this is missing the point. Being remembered as a great mathematician means you were lucky enough to work on something at exactly the right time that big changes were ready to happen.
The majority of geniuses don't achieve anything earth-shaking either. Scroll through a list of putnam fellows sometime, or a list of stanford faculty. You'll recognize a few of them, but not most; the majority of them ended up making niche contributions to a niche field just like you will.

[Anonymous No.10104635]

>on the math reddit
>someone mentions one of the people in my department by name
>another one mentions that he'll speak with him when he sees him the next day
>tfw i see these people every day at seminars

[Anonymous No.10104711]

>>10103024
it's wrong

[Anonymous No.10104775]

>>10102608
Ultraproducts allows you to glue structures in an interesting way (less trivial than the product, which is not so interesting).
You should also be familiar with this construction from analysis: functions equal almost everywhere.
Think.

[Anonymous No.10104847]

What does relate mean in the context?
-t. complex analysis retard

[Anonymous No.10104857]

>>10104847
it wants you to do some algebraic manipulation to write the top sum as some expression of the bottom sum

[Anonymous No.10104864]

>>10104847
>basic sequences
>complex analysis
Weird, innit?
α=(Υ^2-1) and I don't remember how to adjust for the zero.

[Anonymous No.10104865]

>stuck on problem
>make totally random bullshit guess
>it werks
>go from nothing to publishable result in <1 week
god I love combinatorics

[Anonymous No.10104881]

>>10104847
Is it just (z^2 + 1)^-n?
Have I really spent the last 20 minutes on something that simple?

[Anonymous No.10104885]

>>10104881
It isn't because of the zero, but I don't remember the solution. Something something Laurent series.

[Anonymous No.10104891]

>>10104885
What about [math]((z^2) + 1)^n)/((z^2) + 1)^n+1)[/math]? That would make the numerator 1 when n = 0

[Anonymous No.10104892]

>>10104891
That's not of the form alpha^n.

[Anonymous No.10104897]

>>10104891
I'm too stupid to even use math tags right

[Anonymous No.10104902]

>>10104897
Righty, I think I've remembered.
https://en.wikipedia.org/wiki/Laurent_series
Take that original function, write up sum of alpha^n from 0 to infinite, equal that to the Laurent sum, solve for the function, calculate the complex function, solve for alpha.
Man I ought to reread my complex analysis.

[Anonymous No.10104925]

>>10104902
Thanks for the help
>Take that original function, write up sum of alpha^n from 0 to infinite
I can't even do this right oh my fucking god

[Anonymous No.10104955]

>>10104925
Right, sorry, I'm autistic and got hyped with using complex numbers, then got hyped with finding a real number (not explaining) and now I'm back.
Since gamma squared is positive, one divided by gamma squared plus one is smaller than one, so you can use ye old to calculate the sum. From there on, literally make a sequence that goes from one to infinite and converges to that sum, and the zero adds itself.

[Anonymous No.10104978]

>>10103786
I’m not saying I was right, but to clarify, these are just forms and wedge products, not differential forms. The output should be a scalar.

[Anonymous No.10105001]

>>10104955
This is a dumb question, but how do I calculate the sum of the original series?

[Anonymous No.10105005]

>>10101820
>numberphile does a video on your seminar topic
>it's shit

[Anonymous No.10105198]

got a retarded question comin up
is there an integral equivalent of curl? does it have any neat properties?

[Anonymous No.10105292]

>>10105198
A curl isn’t really just a derivative though. Its a map that takes a 2-form and spits out a vector field. If you reverse that you get the area of a parallelogram, I guess.

[Anonymous No.10105299]

>>10105005
exceptionally well composed, unbelievably handsome, how does he do it lads?

[Anonymous No.10105304]

>>10105292
i understand that, i'm asking if there's such an operation as ∇-1⨯F or really just ∇-1 in general

[Anonymous No.10105325]

>>10105304
Yes, you would get a covector space.

[Anonymous No.10105406]

>>10104847
Try alpha = (1+gamma^2)^(-1), brainlet.

[Anonymous No.10105733]

What if Atiyah was right all along?

[Anonymous No.10105809]

>>10103151
I really like this post, I lost

[Anonymous No.10105818]

>>10102230
>>10102236
>>10102239
>>10102242
>>10102248
>>10102251
>>10102269
>>10102275
>>10102281
>>10102283
>>10102288
>>10102296
>>10102301
>>10102304
>>10102309
>>10102458
>>10102870
Why aren't these cancerposters permabanned?

>>10103113
It's been a long time since I proved those theorems but don't you just need to show that the essential support of the function is empty?

>>10101832
Digraphs, because it requires the least amount of theory and definitions as pre-requisites (if you define them the right way).

[Anonymous No.10105823]

>>10105733
Then a bunch of dumb pop-sci bloggers and shitposters will eat their words. Most mathematicians haven't said much except for how his argument is supposed to work and that he hasn't put out sufficient details about the Todd function for us to know if his approach works or not.

[Anonymous No.10105834]

>>10105818
>Why aren't these cancerposters permabanned?
>not including the "why the homophobia"

faggot

[Anonymous No.10106000]

Guys, I need to revisit high school stuff. Is Lang's book enough for that?

[Anonymous No.10106019]

So I need to proof equivalence between A and B.
Can I do that by showing:
>not A => not B
>not B => not A
The only logical conclusion is:
>A => B
>B => A
or am i retarded?

[Anonymous No.10106032]

>>10105001
If 0<a<1, sum a^n from one to infinite is 1/(1-a).

[Anonymous No.10106041]

>>10106019
Yes. More formally:
(not a implies not b) if and only if (a implies b). You should have this one as a theorem somewhere on your book. Otherwise it's still accepted.
Since you have not a implies not b and not b implies not a, you have a implies b and b implies a, which is all you need.

[Anonymous No.10106044]

>>10106041
Mixed up:
(not a implies not b) if and only if (b implies a).

[Anonymous No.10106067]

>>10106041
>>10106044
yea i was just unsure, my prof used it and i was just wondering if its really in a generell case so i can use it myself

thanks bud

[Anonymous No.10106105]

>4 volumes
>more than 400 pages average
Holy fuck Hormander, calm down.

[Anonymous No.10106212]

>>10106105
>four books about linear partial differential operators
This is why I'm not a mathematician.

[Anonymous No.10106448]

>>10106212
Worse than a bourgeois.

[Anonymous No.10106623]

I agree, it is denoted as N0 if it includes the zero, otherwise it does not.

Last thread some homo linked me elements of information theory and the statistics students graduates association from Berkeley for linear algebra, probability and stats.

Thanks! I'll try finding them online as I find a need for them

I am currently doing pattern classification by Heart, Duda and Stork.

[Anonymous No.10106859]

Proofs in analysis > Proofs in algebra. Change my mind.

[Anonymous No.10106885]

u_1 ... u_n is linear independent, so is w_1 ... w_m

[math]w_j \notin \space <{w_1, \cdots, \hat{w_j}, \cdots, w_m}> \wedge \space w_j \notin \space <{u_1, \cdots, u_n}> \implies w_j \notin \space <{w_1, \cdots, \hat{w_j}, \cdots, w_m,u_1, \cdots, u_n}>[/math]

is this true? i mean it only makes sense...

[Anonymous No.10106910]

>>10106859
dirty epsilons and shit <<<<< godly structure

[Anonymous No.10106912]

>>10106910
t. failed analysis
proofs in algebra are literally "le use this secret trick that you never heard of".

[Anonymous No.10107001]

>>10106912
>le use this secret trick that you never heard of
That's the beauty of it, though, it keeps you excited.

[Anonymous No.10107035]

>>10107001

[Anonymous No.10107043]

>>10106912
>>10107001
there is an elegance to it if you know the secret, otherwise its really just aids mixed with aids

[Anonymous No.10107096]

>>10106000
>Is Lang's book enough for that?
Lang is a meme.

[Anonymous No.10107130]

>>10107096
I’m at the past-disbelieving Lang is a meme stage of the meme. Will I later take Lang seriously again?

[Anonymous No.10107173]

>Proposition follows from the definitions.

[CA Tutor No.10107468]

>>10105733
At a number theory seminar I had the other day, someone was speaking about L functions and he mentioned (jokingly) that what he did would disprove RH, and someone else said "with apologies to Atiyah" and they all laughed. idk what it means tho

[CA Tutor No.10107478]

>>10106885
I wouldnt use a wedge when speaking about linear algebra when you mean "and"...

and its obviously not true. Consider [math](1,1)\not\in \langle (0,1)\rangle[/math] and [math]\not\in \langle (1,0)\rangle[/math], but clearly [math](1,1)\in \langle (0,1),(1,0)\rangle[/math].

[Anonymous No.10107501]

Yo this is the wrong thread for this but I am doing some research and this fucking paper is defining shit in a language I do not understand and they dont even explain or define it at all so I cant even google to find what these mean

Not asking to be spoonfed, just some name I can google

and yes I understand most of the individual symbols but I have never seen anything written out this rigorous

At some point I wonder if they are just purposely dense in their papers to look smart

[Anonymous No.10107521]

>>10106912
>he's never done any functional analysis
LMAO

[Anonymous No.10107574]

>>10106019
Yes, you can. What you're doing there is called "proving the contrapositive" or "proof by contrapositive".
More precisely, the contrapositive of a conditional sentence is a statement that is true if and only if the original statement is true. It is produced by flipping the direction of the conditional and negating both sides. For example, given a conditional sentence like, [math]A\Rightarrow B[/math], the contrapositive would be [math]\lnot B \Rightarrow \lnot A[/math].
Note: [math]\lnot[/math] is the logical symbol for "not".
So essentially you would say you are proving [math]A \Rightarrow B[/math] and [math]B \Rightarrow A[/math] by contrapositive. Google contrapositive for more information.
As a sidenote, if your proving the statements via proof trees, natural deduction, sequent calculus, or some other special proof system then you should prove the equivalence using those tools and not by argument. If not you can justify the notion of taking the contrapositive by looking at truth tables or doing some fancy stuff with other equivalences and De Morgan's Laws.

[Anonymous No.10107609]

>>10107501
Nevermind I figured it out, this dude is using some weird syntax he made up from 2003 and acting like its just known shit

[Anonymous No.10107622]

>>10107501
>At some point I wonder if they are just purposely dense in their papers to look smart
Of course they are.

[Anonymous No.10107629]

>>10107622
I am a lowly engineering student and am not even doing a thesis, but I have to do some work with a professor and I never realized how bad it was until I started reading all these papers. I went down a rabbit hole on one topic thinking it was amazing until my professor pointed out the papers are only cited by the same authors writing more papers later, completely changed my perspective

[Anonymous No.10107632]

>>10101820
Help

[Anonymous No.10107695]

>>10107609
The sequent calculus notation is extremely standard in programming language theory related areas of comp sci (including category theory, type theory, and formal logic stuff). That said there's a ton of different proof systems each with their own conventions and notations for sequent calculus type stuff so you'll often have to check the type of sequent calculus used and maybe read up on the paper where the specific system was introduced. It's pretty standard procedure but there's so many systems and they're developed in such an ad-hoc way that there's really no good alternative.

[Anonymous No.10107700]

>>10107629
>until my professor pointed out the papers are only cited by the same authors writing more papers later, completely changed my perspective
It's not uncommon for a lot of this non-mainstream stuff. On occasion someone will figure out that it's connected to some other area of research and things will really become interesting but often times it will continue for years with just one or a few people working alone on the topic.

[Anonymous No.10107856]

>>10107521
>Marisafag is a analysisfag
No, bad Anon.

[Anonymous No.10108064]

>>10107096
What do you suggest, then?

[Anonymous No.10108067]

>>10107632
Shhhh, shhhh, it's okay.
What's the problem?

[Anonymous No.10108083]

>>10108067
Has anyone here ever been raped before?

[Anonymous No.10108085]

>>10108083
my analysis professor fucks me in the ass every day so yes

[Anonymous No.10108353]

>tfw fallen out of love with math again
>tfw wishing I had studied the humanities again
I'm not worthy. Is anyone else here extremely capricious with this subject?

[Anonymous No.10108356]

>>10108353
Lmao exactly on the opposite end brah

[Anonymous No.10108454]

>>10106105
>>10106212
I used to think the only hard questions in the study of PDEs related to nonlinear PDEs. Nope, turns out even linear PDEs are a bitch. Even the fucking Helmholtz equation has nontrivial analysis related to it, and it's one of the simplest PDEs out there.
>>10108353
>tfw wishing I had studied the humanities again
Why not become one of those historians of mathematics? I always considered that to be my fallback if things went south.

[Anonymous No.10108490]

Help me to stop being a mathlet. I was thinking of a particular free-fall physics problem.
I started with the formula of "travelled distance" as a function of time and acceleration, for constant acceleration.
[math] x(t) = x_0 - \frac{1} {2} at^2[/math]
where, for this case, [math]x[/math] = distance respect to center of gravitational mass, [math]x_0[/math] = initial distance, and [math]t[/math] = time elapsed of course.
This is enough for small distance and mundane scenarios, but it's obviously very lacking when studying a long free fall, because acceleration won't be constant. It will be a function of distance, at every "instant".
Now, there's well known derivatives of acceleration ("jerk") which are easy to calculate, but our changing acceleration is a function of distance, so jerk is not useful and probably not a thing here.
Messing around, I came up with the following:
[math]x(t) = x_0 - \frac{\mu}{ 2(x(t))^2 }[/math]
Where [math]\mu[/math] is the standard gravitational parameter (a constant, around [math]4\times10^{12}[/math] for our planet. And [math]x(t)[/math] is the function itself.
So how the hell do you compute a function that has itself as a "variable"? Is that algebra even remotely correct? I know this must be all wrong and abominable. So please lecture me. I beg you.

[Anonymous No.10108493]

>>10108490
Sorry, the last equation would be as following (forgot time):
[math]x(t) = x_0 - \frac{\mu}{ 2(x(t))^2 } t^2[/math]

[Anonymous No.10108514]

>>10108454
History is the humanity I'm the least interested in

[Anonymous No.10108664]

The proper definition of a ring does not require unity, prove me wrong.

If you don't require unity you have ideals that are actually subrings.
If you don't require unity then an "ideal with unity" (an ideal containing an idempotent that satisfies the identity axioms for members of the ideal) becomes a sensible concept

[Anonymous No.10108803]

>>10108353
Interestingly I used to really love math, until I started studying it at uni. I still like it, but not the same degree as before. It's become much more tempered, a part of my routine, and no longer feels special to me. I miss it, but I guess it was inevitable. I'd recommend doing some fun projects, that makes me relive that "honeymoon" period again. Really, you're going to have different topics and subjects in math you find interesting to different degrees, perhaps you're currently just studying something you don't enjoy?

[Anonymous No.10108839]

>>10108803
I think it's more the realization that actual math research (what I spend most of my time doing now) is largely tedious and frustrating and rarely produces any results of much interest. I also feel like I'm not learning as much anymore, as odd as that may sound. Like I get exposed to loads of new material but it's always just aimed at gaining tools to produce new results. I never have the time to fully grasp the meaning of a something like I could in undergrad. That depresses me. Then I'll read a nice paper or something that proves an elegant or surprising result and I'll get all hyped for math again and start planning on self-studying texts, etc, only to get dejected again after realizing how much I dislike the routine of a working mathematician.

I don't know what to do with myself desu. I always assumed I would go get a PhD but I'm not sure I have the passion for it. But I also don't want to be a wage slave so I don't know what the fuck to do.

[Anonymous No.10108845]

>>10108664
Ring without unity is just a rng

[Anonymous No.10108887]

category theorists display the same symptons as shizophrenics
prove me wrong

[Anonymous No.10108905]

>>10108887
>1
t.set theorist

[Anonymous No.10108911]

>>10101820

I have a "real" IQ of between 115-120. Should I just give up on the dream of pursuing pure mathematics? Why even bother when every one of my colleagues would be higher IQ than me?

[Anonymous No.10108914]

>>10108911
Just give it a go. IQ simply CORRELATES with things like aptitude for abstract reasoning, only morons on /pol/ treat it as an objective and absolute measure of potential.

[CA Tutor No.10109234]

>>10108664
No matter if a ring has or doesn't have unity, it doesn't solve the problems that modules solve, that is, making rings an abelian category.

Also no identity means Z can have more than one ring structure which is just disgusting

[Anonymous No.10109520]

Does anyone else get frustrated easily when they encounter difficulty in solving a problem, or just in general? I'm an underage (junior) working through Spivak's Calculus right now and every time I hit a wall and can't solve something, I get fed up quickly and resort to checking the answer key. I'm very impatient, and not really used to having to spend time solving problems. For problems that I don't immediately know how to do, I usually just don't do them (if possible). So, is there any way to overcome this? Will I get used to it? Any useful tips or techniques for increasing attention span? Also, as an aside, how long should you be spending per problem for Spivak? I'm pretty insecure about it and was wondering what is considered average or normal. Any responses would be appreciated. Thanks!

[Anonymous No.10109555]

>>10107856
>muh analysis-algebra dichotomy
>what is categorification
Yeah whatever dummy

[Anonymous No.10109569]

fuckin hell generating functions are weird. or is it just me?
how do I get an intuitive grasp on this?

[Anonymous No.10109572]

>>10109520
^im the same as you. interested in an answer

[Anonymous No.10109803]

>take test
>do almost perfectly
>all 4 parts of the first question was really easy
>get home, take test out of my bag
>see that first question actually had 5 parts
Whoops

[Anonymous No.10109886]

>>10109520
>So, is there any way to overcome this?
Grow up.
>Any useful tips or techniques for increasing attention span?
JUST DO IT.
>Also, as an aside, how long should you be spending per problem for Spivak?
If you mean the *shitty book*, something like 5 seconds. You would be better off learning the basics from a decent book (that is, if you are not a physicist). Before learning differential geometry you should also have decent basis of first year undergraduate real analysis and second year potato topology.
If you mean the *golden book*, you should attempt all the relevant ones (or all) whitout hints. Notice that differential geometry exercises can have very long solutions even if they seem immediate. If after enough attemps (say few hours or more) you can't solve one exercise, you can postpone it, ask look for hints on mse, or ask yourself why you are so stupid and jump out the window.

[Anonymous No.10109973]

I'm reading Book of Proof and having fun. I managed to do every exercise, that has a solution provided, right, in the chapter on disproofs.

Do you have fun studying?
Pic unrelated

[Anonymous No.10110020]

What went wrong with physicists?

http://ap.io/home/
>This web site is owned and administered by Prof. A.W. Peet of the University of Toronto.
>How to get my name and pronouns right
>Being transgender
>Being disabled
>How to accommodate me

>I have (co-)organized enough conferences, workshops, and social events in my time to know how the associated workload feels. Accordingly, I never ask event organizers for unnecessary disability accommodations. The information below is a distillation of over fifteen years of hard experience. Taking it seriously will make all the difference between me being able or unable to participate fully in your event.

>At a single-day professional event, I need (1) a reserved top-quality chair, and (2) barrier-free accessibility. At a multi-day professional event, I also need (3) a decent bed at a relatively quiet hotel which can receive shipped luggage, and (4) maps showing barrier-free entrances to all venues and the locations of all-gender restrooms. At a local social event with friends, I just need a high-backed chair with soft surfaces and a picture of it ahead of time so that I can plan ahead. Please see below for specifics. Thanks!
>1: Chair

>Most chairs are not comfortable enough for me to sit on them for more than a few minutes, even on a good pain day. At a professional event, I need to sit on a high-backed adjustable ergonomic office chair with all of the following six properties. At a local party with friends, the first two are usually sufficient. In order of importance, the six requirements are:-

>High back: at least 26in/66cm high.
>No hard surfaces pressing on shoulder blades.
>Adjustable seat height and seat tilt.
>Adjustable arm rests.
>Adjustable lumbar support.
>Sturdy five-wheel base.

[Anonymous No.10110035]

>>101100201
http://ap.io/home/disability/medis.html
>My primary disability is chronic neuromuscular pain, affecting my neck, shoulders, back, left arm, and left leg. It originates in accident traumas, primarily a bad skiing accident at the end of the 1990s. [...]

>Frustratingly for an academic, chronic pain makes it harder to sit and to work at a computer. I manage the physical discomfort by frequently changing working positions (sitting, standing, lying), stretching, doing aerobic exercise, getting physiotherapy, and being extremely disciplined about managing workload and sleep. Chronic pain also affects my concentration, making me less tolerant to background noises and other interruptions (some of my CPU is busy just handling the pain). Supervised by expert doctors, I take two medicines that attenuate the worst signals in the pain spectrum and let me think clearly. An annoying side effect of one of them is that it can hinder my ability to find words. This is why I sometimes digress more than other people in a normal conversation or lecture.

>Generally, pain significantly limits the functionality of my shoulders and arms. For instance, I cannot comfortably write at a blackboard for more than five to ten minutes per hour, and there is no way that I could carry a backpack with books inside or paddle a kayak. In order to carry papers, I scan them and "transport" them electronically. When I have a laptop or other gear with me, I have to transport it in a rolling briefcase, which I cannot lift up stairs or steps. It is astonishing how much of a university and its surrounding area can become inaccessible on wheels, so I usually carry an extremely minimal amount of gear, usually in my pockets. I am also thankful for every electric door opener mechanism that saves me from having to wrench my good shoulder to open a heavy door.

[Anonymous No.10110040]

Hi boys, I got a peculiar request. My father is an archaeologist and he is doing research on celtic art. He has shown me some of the shit they make and it's pretty impressive. He is wondering what kind of techniques they are using, so that we can infere what kind of mathematics they know. I figured that they must have the same techniques as the greeks, so synthetic geometry, but I'm not sure since they make really impressive use of curves in 3D.
I was wondering if you knew a good book on synthetic geometry or on the state of mathematic knowledge in Europe around the 5th and 3rd century before Christ, or better if you knew a mathematician that would like to work on some of those problems.

[Anonymous No.10110109]

Well /mg/? Will you become a mass murderer or a savior?

[Anonymous No.10110126]

>>10110035
I don't get your issue, they're disabled of course they're going to need accommodates

[Anonymous No.10110134]

>>10110109
>Reimann

[Anonymous No.10110136]

>>10110126
Different anons. I was replying to the fuckwad who tried to make it sound like his accommodations were due to being transgendered.

[Anonymous No.10110165]

What is an "inductive limit topology" in the context of [math]C_0^\infty ( \mathbb{R} ) [/math] functions?

[Anonymous No.10110176]

>>10108911
>>10108914
i refuse to believe these two anons are even human
>>10109520
underage
>>10109555
>>>/toy/
>>10109973
what the fuck is this filename?
>>10110109
>>>/pol/
>>10110165
>>>/trash/

[Anonymous No.10110225]

>>10110176
Kill yourself

[Anonymous No.10110592]

>>10108353
This anon here again. I spent the rest of yesterday and this morning fucking around some other stuff (philosophy and some papercraft I've been working on), feeling very refreshed now. Maybe I just need to take a rest from mathematics every few days. Which isn't great for my PhD prospects but will work for the present.

[Anonymous No.10110662]

[Anonymous No.10110676]

>>10110662
nice one

[Anonymous No.10110702]

>>10110662
What do analysis people even fucking do? I asked my real analysis professor what he was working on once and he just showed me this hideous inequality he said was better than the currently known one.

[Anonymous No.10110703]

>>10110040
You don't need to know math to fucking create a pleasant-to-look-at curve

[Anonymous No.10110917]

>>10110703
You'd be surprised. Celtic art from this period incorporate a surprising amount of intricate geometric patterns and symetry. Those can't really be done by drawing freely; there has to be some kind of technique behind these. We know that celts were very close to the Greeks, frequently trading with them and sharing religious belief along with scientific ideas.
I'd just like to know what kind of techniques those crafty fuckers used, anon. Making similar objects is hard, even with modern smelting techniques and ideas about geometry.

[Anonymous No.10110945]

ok, this is epic

[Anonymous No.10110947]

>>10110662
could have been way better
>>10110702
apply cauchy schwartz

[Anonymous No.10110950]

>>10110947
Feel free to make it better, well's a bit dry today.

[Anonymous No.10110981]

>>10110950
no cos if i do one and its worse, then it's definitely going into someone's cringe compilation

[Anonymous No.10110983]

>>10110981
You're pretty funny, shouldn't worry that much.

[Anonymous No.10111256]

>>10110662
cringe
>>10110676
>>10110702
>>10110947
the absolute state

[Anonymous No.10111263]

>>10111256
seething analcyst

[Anonymous No.10111327]

>>10106859
Proofs in algebra are for the most part constructive. Analysists don't know what constructive even means.

[goes in all fields No.10111343]

>>10111327
nice bait
try harder

[Anonymous No.10111350]

>>10110662
Leave German out of this

[Anonymous No.10111355]

>>10111350
true since most of them are virgins anyway
and failed mock physicists

[Anonymous No.10111362]

>>10111343
Name one (ONE!) constructive proof in mainstream analysis. I'll wait.

[Anonymous No.10111367]

>>10111362
>mainstream analysis

[Anonymous No.10111369]

>>10111367
ie not something like numerical analysis where everything is gimped constructive results.

[Anonymous No.10111373]

>>10111362
I don't have the constructivism autism but I do feel that analysis proofs are often weaker due to their reliance on non-constructive arguments desu. Like none of the constructions of the reals are even implementable. They basically exist purely by their axioms. Which is fine, but the rationals and friends feel "realer", ironically.

[Anonymous No.10111598]

I'm working through Hartshorne, section II.3. I want to show that if [math] f: X \to Y [/math] is of finite type, then for any open affines [math] V = \operatorname{Spec} B \subseteq Y [/math] and [math] U = \operatorname{spec} A \subseteq X [/math], [math] A [/math] is a finitely generated [math] B [/math]-algebra.

I've already shown that [math] f^{-1}(V) [/math] can be covered by a finite number of affines with this property. Since adjoining inverses preserves the property of being finitely generated, I can reduce this to showing that if [math] A_{s_i} [/math] are all finitely generated over B, and [math] s_i [/math] generate the unit ideal, then A is finitely generated. This works by kinda standard pushing algebra around.

I'm confused because I didn't actually use the full finite type assumption, really only locally finite type. Does this hold for morphisms of locally finite type as well, or am I missing something?

[Anonymous No.10111668]

>>10109886
I said I was working on Spivak's CALCULUS. Do I need to spell that out for you? C - A - L - C - U - L - U - S. I won't take advice from someone who can't read, sorry.

[Anonymous No.10111680]

>>10101820
[math] \displaystyle
\boxed{ \mathbb{O} \;
\boxed{ \mathbb{H} \;
\boxed{ \mathbb{C} \;
\boxed{ \mathbb{R} \;
\boxed{ \mathbb{Q} \;
\boxed{ \mathbb{Z} \;
\boxed{ \mathbb{N}}}}}}}}
[/math]

[Anonymous No.10111695]

>>10111668
To be fair to that guy, Spivak wrote another book called "calculus on manifolds," and several books on differential geometry, which for which he is better known.

[Anonymous No.10111698]

>>10110662
Based

[Anonymous No.10111704]

>>10111668
I didn't know Spivak had a book on calculus, I must have thought it was 'calculus on manifolds'.
So you can't solve american calculus problems.

[Anonymous No.10111714]

>>10111695
yes, but (a) I'm in high school so I clearly would not be doing diff. geo. or his Calculus on Manifolds and (b) I wrote specifically Calculus and nothing else. As far as 'rigorous' calc textbooks go (as opposed to analysis), Spivak is the go to, and the book, I at least, have seen most. often.

[Anonymous No.10111717]

>>10111704
I'm still in highschool, I'm not an undergraduate. Again I'm a junior.

[Anonymous No.10111723]

>>10111704
>>10111695
Sorry for being a cunt.

[Anonymous No.10111758]

>>10111714
>he is in high school so he can be brainlet
So what is your problem exactly?
Getting frustated when you see an easy exercise that you can't solve is fair enough, you should not look to the solution and try to do it even if it takes hours, at least if it is the subject of your interest. Reread the theory, the examples, think of all techniques that you know, do the sums, draw pictures, find inspiration in your dreams. Wouldn't you feel a little better after solving it?
Also, it get easier with time, but the first time you learn a subject it is always somehow difficult. You can end up putting too much effort into something which you should have prospective and fail to go on (for example getting stuck on the Alexander horned sphere exercise from the first reply without even caring about it; but if you came afterward knowing the meaning then you would enjoy to solve it). This is one reason why it is good to have someone teach you.
Also my advice is general and not related to Spivak, so it is out of line for sure.

>>10111723
Don't be a pussy now.

[Anonymous No.10112226]

>>10111680
>no sedenions
woow

[Anonymous No.10112236]

>>10112226
The octonions are already disgusting, why would you want to go further?

[Anonymous No.10112245]

>>10112236
if you're already including octonions its just rude to leave sedenions out

[Anonymous No.10112269]

>>10112245
The octonions are your friend who, if you're honest, is a complete degenerate loser but you still like him because you've known him forever and he's nice enough and it's fun to look in on that lifestyle. The sedenions, by comparison, are a homeless drug addict who tried to rob you when you offered him half of your sandwich.

[Anonymous No.10112278]

>>10112269
sedenions should still be treated with some level of respect despite their ugly algebraic properties, leaving them out wouldn't be mathematician-like

[Anonymous No.10112303]

>>10112278
>sedenions should still be treated with some level of respect despite their ugly algebraic properties
what algebraic properties? The sedenions have almost no structure left in them at all. There's absolutely nothing interesting you can say about them or do with them.

[Anonymous No.10112309]

>>10112303
a-at least they're flexible

[Anonymous No.10112339]

>>10112226
octonions are the last one works in Division algebra

[Anonymous No.10112342]

>>10112226
octonions are the last one that works in Division algebra

[Anonymous No.10112358]

>>10112342
https://www.youtube.com/playlist?list=PLNxhIPHaOTRZMO1VjJcs7_3dgyJ2qU1yZ

[Anonymous No.10112363]

>>10112342
Huh, I didn't know this, I thought they had just lost anything even resembling associativity and so were basically intractable to study

[Anonymous No.10112651]

>>10101820
Is the commutator of [math]F_n[/math] always just [math]F_\infty[/math] for [math]n \geq 2[/math]?

[Anonymous No.10112801]

FUCK I CANT FUCKING CONCENTRATE
WHY DO NIGGERS HAVE TO LIVE UP TO THEIR STEREOTYPES EVERY TIME FUCKING PLAYING LOUD MUSIC AND CHIMPING AROUND
AND WHY DO I GET A ROOM NEXT TO ONE FUCKKKKKKKKKK

[Anonymous No.10113134]

>>10112651
>Is the commutator of [math]F_n[/math] always just [math]F_\infty[/math] for [math]n \geq 2[/math]?
What have you tried?

[Anonymous No.10113165]

>>10112651
>[math]F_\infty[/math
What did he mean by this?
Seriously I don't know help a brainlet out.

[Anonymous No.10113169]

>>10113165
Linear infinite dimensional space.
Function space is a good example.

[Anonymous No.10113178]

>>10113169
What do you mean by commutator then? This question doesn't make sense to me.

[Anonymous No.10113202]

>>10113178
>me
No, I'm a random dude. This definition is a bit harder, so I'll link you to wikipedia.
https://en.wikipedia.org/wiki/Commutator

[Anonymous No.10113208]

>>10103113
>all closed intervals of reals are lebesgue measureable
>there are countably many members of f(x) not equal to 0
>all non-zero members of f(x) are finite and bounded
>integral reduces into the measure of a countable number of finite value which is just zero.

[Anonymous No.10113215]

>>10113134
I'm not even doing group theory right now. This is just a fact that I want to whether it's true or false.

[Anonymous No.10113218]

Imagine being such a brainlet that you think everyone understands your shitty notation without stopping to realise that F is the standard notation for at least 10000 things

[Anonymous No.10113227]

>>10113202
I know what the commutator is, I don't see how the commutator of a finite field could ever be a infinite dimensional space

[Anonymous No.10113229]

>>10113227
No one knows desu.

[Anonymous No.10113380]

>>10112651
>>10113134
Yes.

[Anonymous No.10113517]

>>10113229
Are you drunk anon?

[Anonymous No.10113553]

>>10111362
Mountainpass theorem
>he ACTUALLY has never done any function analysis
Jesus

[Anonymous No.10113583]

>>10113553
fuck off 2hu fag
go back to your containment trash board and stay there you subhuman >>>/jp/
take your analysis friend with you

[Anonymous No.10113611]

>>10113553
>inf max
Can you construct this fampai?

[Anonymous No.10114051]

Can anyone advise me how to get started on the link between Modular/Maass Forms and Representation Theory? I've tried reading Bump's book on Automorphic Forms, and also Bushnell-Henniart's book on Local Langlands, and they both read like complete moon-math. There must be some simpler middle-ground material somewhere?

[Anonymous No.10114052]

>>10113553
._.

[Anonymous No.10114200]

>>10111362
>Let H be a space on which the integral along any closed curve is zero.
>Theorem: the integral along any curve depends only on the first and final points
>Let γ be a curve from a to b. If we cannot draw a different curve from a to b, the argument's done. If we can, we construct a closed path using the first curve, and since their integrals must sum zero, they have the same value and can be given from the first and end points.

[Anonymous No.10114350]

>>10114200
>If we cannot
>If we can
LEM spotted

[Anonymous No.10114383]

>>10114350
Do you even need that part? Proof still works without it I think

[Anonymous No.10114899]

how difficult do you think is the following lemma in terms of proving it?
sum of all Ф(d) where d divides n is equal to n, where Ф is the totient function.
i cracked my head to prove this on my own, couldn't do it. am i a mega brainlet?

[Anonymous No.10114914]

>>10114383
Right, my mistake.
Let gamma and sigma be curves from a to b. Since gamma then -sigma forms a closed path, the integral along gamma is equal to the integral along sigma. Since gamma and sigma were any paths from a to b, the theorem follows.

[Anonymous No.10114924]

>>10114899
Medium difficulty.
But you shouldn't worry too much. Number theory is weird, and you're still beginning. There's still time to get the hang of things.

[Anonymous No.10115060]

>all holomorphic functions are complex analytic
What the FUCK.
Why are the reals so shit lads?

[Anonymous No.10115185]

>>10114899
Very easy.

T(p^k)=p^k-p^{k-1}
T(pq)=T(p)T(q)
sum_k(T(p^k))=p^k-p^{k-1}+p^{k-1}-p^{k-2}+...=p^k

and you're pretty much there

[Anonymous No.10115214]

>>10114383
Yeah I realised this after I posted but was too tired to correct myself

[Anonymous No.10115255]

>>10114899
It is hard in that proving it usually requires you to use every result about cyclic groups you've gone through in that class/book, usually for the first time, but otherwise medium-easy, since I could solve it. You just have to think what do the terms mean.

[Anonymous No.10115263]

>>10115060
because being holomorphic is a much much much stronger requirement than being real differentiable, brainlet

[Anonymous No.10115277]

>>10115263
But holomorphic is the natural extension of differentiability to the complex plane, I just think it's staggering that C just werks

[Anonymous No.10115284]

>>10115263

[Anonymous No.10115385]

>>10115284
retard
>>10115277
If you check out the definition of holomorphicity, it's real differentiable + satistfies the cauchy-riemann equations, ie the real/imaginary parts satisfy the laplace equation, ie they are harmonic

But it is a general fact that equations in the real plane that satisfy the laplace equation are real analytic, so there is no "deep" difference as to why holomorphics are so special as opposed to reals

[Anonymous No.10115394]

>>10115385
>it's real differentiable + satistfies the cauchy-riemann equations
Nah. f'(z)=lim Idelta zI ->- of [f(delta z+z)-f(z)]/delta z

[Anonymous No.10115404]

>>10115394
you should really stop posting, you are actually making a fool of yourself

[Anonymous No.10115408]

>>10115404
https://en.wikipedia.org/wiki/Holomorphic_function#Definition
No one defines it as satifying the Cauchy-Riemann, you twat. You define it by having a limit as z's module near zero and show that it satisfies Cauchy-Riemann.

[Anonymous No.10115430]

>>10115408
>what is an equivalent definition
>what is a criterion
so, how's second year doing for you?

[Anonymous No.10115440]

>>10115385
How do you formulate the laplace equation for a real function?

[Anonymous No.10115444]

>>10115430
>discussing holomorphic functions on the reals and complex numbers
>purposefully uses the explicitly different definition for a holomorphic complex function while saying some autism about complex numbers also satisfying Cauchy-Riemann
How's business school?

[Anonymous No.10115467]

>>10115440
Double derivative is equal to zero.
https://en.wikipedia.org/wiki/Laplace's_equation

[Anonymous No.10115469]

>>10115444
you are such a fucking doublenigger
>f(z) is complex differentiable IF AND ONLY IF each part is REAL differentiable AND satisfies the CR equations, ie: when it satifies LAPLACE equation
>a REAL 2 VARIABLE FUNCTION is ANALYTIC when it satisfies LAPLACE equation

>HURR DURR holomorphic functions are analytic haha wow, so deep!!!!!

>>10115440
[math]f_{xx}+f_{yy}=0[/math]

[Anonymous No.10115485]

>>10115469
>[math]f_{xx} + f_{yy}=0[/math]
Oh I see, nothing about the fact that the field is C is particularly important for proving analyticity from that. Thank you friend

[Anonymous No.10115548]

Okay, this is epic

[Anonymous No.10115558]

>>10115548
What am I looking at?

[Anonymous No.10115566]

>>10115558
It's a coequalizer and the joke is that coequalizers are epimorphisms

[Anonymous No.10115567]

>>10115566
and they are also called "epic morphisms"

[Anonymous No.10115650]

>>10113583
How about this instead - I will pull your entrails out and make you eat them, if you manage to retain your consciousness i shall numb any feelings of pain that might arise due to that.

[Anonymous No.10115664]

>>10115650
Go back to the botanist thread sweetie

[Anonymous No.10115669]

>>10115566
I really need to get into the category theory autism, sounds comfy

[Anonymous No.10115930]

What's your favorite function?

[Anonymous No.10115970]

>>10115930
Why the jewphobia?

[Anonymous No.10116004]

is differential equations an enjoyable course?

[Anonymous No.10116016]

>>10116004
Depends, but I liked it way more than calculus.

[Anonymous No.10116165]

Does anyone know any good youtube education playlists for game theory? I've got a bit under two weeks to cover picrelated, I don't think it will take two weeks to cover but I want to do very well for this exam
Thanks lads

[Anonymous No.10116179]

>>10115970
underage

[Anonymous No.10116410]

>>10112801
Why do you surround yourself with niggers? Idiot.

[Anonymous No.10116516]

>>10116165
>studying through youtube videos
Pretty sure most people here have long since lost that habit.
>>>/wsr/
>>>/sci/sqt

[Anonymous No.10116540]

>>10116410
I got randomly placed here in student accomodation... we're all postgrads but that doesnt make him any less chimp

[Anonymous No.10116759]

https://arxiv.org/abs/1401.0300
Kourovka notebook is such a cool concept. I wonder if other math branch has something similar.

[Anonymous No.10116804]

>>10116540
>we're all postgrads
You literally need to man up and tell him to turn it off. File a complaint with whoever manages your accommodation too. This is not fucking first years.

[Anonymous No.10116809]

>>10116540
>>10116804
Also talk to your other neighbors. They are getting pissed two. If all of you knock on his door at once that is much more effective than if you do it alone.

[Anonymous No.10116837]

>>10116804
>You literally need to man up and tell him to turn it off
How can he man up if he’s a pussy?

[Anonymous No.10116873]

>>10116837
Life experience turns you into a man. You you to confront your fears repeated until you stop giving a shit.

[Anonymous No.10116877]

Oh god I hate my geometry teacher, she literally don't know how to teach, she is morbidly obese and she don't even know how to write pretty LaTeX (she literally use things like "sin" instead of "\sin") and she like to tell how nice LaTeX is. God this is the second woman I have a course with and it's HELL, she is so obese she need to sit the entire lecture, when she writes we can't read because of her fat ass. She can also barely write proofs, she always use a different notation (vectors with arrows or without, changing letters for no reasons etc). God i would love to have a required textbook to follow the course, teachers in my country are so arrogant they thinks their course is the best in the world even if they struggle to share some first year algebra knowledge.

[Anonymous No.10116919]

>>10116877
The notation confusion is typical of any geometry course.

[Anonymous No.10117009]

>>10116804
>>10116809
I'm the only one that can hear him through the walls because he's right next to me. And what do you think, if I go tell a pack of 5 chimps to keep it down, that they're gonna say something other than fuck off whitey?

[Anonymous No.10117027]

>>10117009
If you weren't racist you'd realize that he is just a normal human being with the same sensibilities and understand as you are. He is just unaware that he is causing you such frustration. How is he too know that music is escaping his room if you don't tell him?

[Anonymous No.10117068]

>>10117009
Don't have a conversation.
"You're too loud, turn it down", and go back home.

[Anonymous No.10117108]

>>10117027
I'm 100% sure he's dumb because I know he couldnt follow his math for economics class and failed the exam
>>10117068
>ok whitey
>close door
>HAHAHA did you see that dumb HONKEY?? HAHAHAA

[Anonymous No.10117172]

>>10117108
You know what, suffer then.

[Anonymous No.10117179]

Has anyone here done H&K's Linear Algebra? I'm coming from a background devoid of any abstract algebra and I saw various conflicting reports on the need of it. Is it really self contained or should I brush up on some abstract algebra before I start? Thanks in advance.

[Anonymous No.10117183]

>>10117179
>Is it really self contained or should I brush up on some abstract algebra before I start?
Why don't you read it and find out?

[Anonymous No.10117467]

>>10115548
I made this joke threads ago you mong.

[Anonymous No.10117520]

there's not enough documentation on the code that I'm debugging. it was written in 2005 or something. I think I found an error that, when corrected, slows down the algorithm significantly. so it must not be an error, but the algebra disagrees...

[Anonymous No.10117523]

>>10117520
Can the error produce a wrong result?

[Anonymous No.10117533]

Open question: Why do you faggots use LaTeX when it is in fact faster to write out the problems by hand? you're effectively always adding extra characters to every single problem you work out at every step. Seems extremely autistic. I know WPM varies among you and that being big brain niggers you are likely to have higher WPM so you can compensate for the extra characters with significantly faster rate of transcription, all the same I just am not convinced it wouldn't be better to learn to write faster and to make use of paper and pencil, where formatting and compression are much more freely modulated. Just my opinion, feel free to rebut or expand.

[Anonymous No.10117535]

>>10117533
I'd draw if /sci/ had the oekaki engine, but it doesn't.

[Anonymous No.10117544]

>>10117533
the benefit of latex is copy + paste, and when you're writing technical documents this is really useful. I think it speeds up my work. I still prefer writing by hand.
>>10117523
nah it's solid code I'm just screwing something up and venting about it.

[Anonymous No.10117553]

Quick run down on cyclic, permutation, and normal groups?

[Anonymous No.10117565]

>>10117553
>cyclic group
There is some a such that every element of the group can be written as a^n.
>permutation group
A permutation is a bijection from a set to itself. The group of permutations is the group of those bijections along with the operation composition.
>normal group
Imagine I have a group H within a group, and an element a. A coset is a set of the form aH. A normal subgroup has aH=Ha for any a.

[Anonymous No.10117699]

>>10117553
>>10117565
An alternative way to think of two of those:
A cyclic group is a quotient of (Z, +). (Take the map sending 1 to the generator. This will be a surjection since every element is of the form g^n where g is the generator. Then apply the 1st isomorphism theorem.)
A normal subgroup is the kernel of a group homomorphism. (i.e. a kernel is always a normal subgroup, and any normal subgroup H < G is the kernel of the map G -> G/H)

[Anonymous No.10117714]

>>10117533
It depends on what you're writing whether LaTeX is a worthwhile time investment or not. For baby linear algebra problem sets I agree it's probably a waste of time.
But, for example, I think it's annoying as hell to teach from a set of ratty handwritten notes with shit scribbled over and crossed out everywhere because it's a pain in the ass to make edits.
And as an extension of that even taking down notes for a class you're a student in in LaTeX isn't a bad idea, because you end up with basically a teachable set of notes at the end if you ever need them, which will save you many hours when you're much busier than you currently are.

[Anonymous No.10117721]

How to check whether three vectors in orthonormal basis are laying on one line (not sure how to formulate it in English)?
Should I just check if their coefficients are proportional for each combination? Or just calculate its triple product?

[Anonymous No.10117723]

>>10117721
>three vectors are laying on one line
In other words, if the vectors are x, y, z:
y=tx+a, and z=sx+a, for some vector a, and scalars t and s?
Test whether y-z=(t-s)x can be solved for t-s.

[Anonymous No.10117733]

>>10117721
What anon >>10117723 said. You can also check if any two-combination of the three lie on the same line by calculating the determinant of the two vectors.

[Anonymous No.10117739]

>>10117565
>normal
Funnily, in my language this is called a distinguished (sub)group.
It is interesting that if you define an equivalence relationship R on your group, it is compatible with the operation of your group (ie, xRy implies axRay for all a), then you have

xRy <=> x - y is in H, with H being a normal subgroup.

This is useful as it illustrate a link between equivalence relationships and sets.

[Anonymous No.10117785]

>>10117533
Because with LaTeX you can heavily amend without having to rewrite all the previous work on the page.

[Anonymous No.10117835]

>>10117553
what the other anons said, but normal is the "weakest" type of subgroup such that you can form a quotient and get a group. That is, a subgroup H of G is normal iff G/H is a group.

Obviously, this is a very useful criterion, since you can form a subgroup H consisting of "relations that you dont want in your group", find the smallest normal subgroup N containing H by taking the intersection of all normal subgroups containing H, then quotienting G by N will give you a group without those characteristics.

As an example in the abelian case: Consider a group G of order pn. Let g be any element, and consider its cyclic subgroup generated by g, that is {1,g,g^2,...}. Since G is finite, then there is some m with g^m=1, so it is indeed finite cyclic. But every finite cyclic group has elements of prime order q, where q divides m. If q=p for any of these, then there exists an element of order p, if it is not the case, then quotient G by {1,g,g^2,...} and you get a subgroup of order pn/m, but since p and m have no common factor, then you only take off primes "belonging" to n. So by quotienting you remove elements of order that isn't p. Hence you can inductively proof that there exists an element of order p by repeating this procedure.

[Anonymous No.10117862]

Can someone recommend books/papers/research on Gaussian hypergeometric series? I'd write a coursework on this topic. I won't be able to invent something but it's not required of me either. Just interesting proprieties, applications, etc.

[Anonymous No.10117887]

>>10117862
Hypergeometric functions are solutions to the conformal blocks of a conformal field theory with the affine Lie algebra [math]\mathfrak_\mathbb{C}{sl}(2)[/math] on the Riemann sphere (complex projective line) [math]\mathbb{A}^1_\mathbb{C}[/math]. The coupled ODE they satisfy are the Knizhnik–Zamolodchikov equations, which is a necessary condition on the conformal blocks in the highest-weight Verma modules [math]V_\mu[/math] satisfying the quantum Clebsch-Gordan gauge condition for the existence of a singular (cyclic vacuum) vector.

[Anonymous No.10117897]

>>10117887
nice one nerdlord

[Anonymous No.10117957]

I'm trying to prove that the union of a set and its limit points contains all its limit points. Here's my attempt, is it correct? I don't know if the step from line 5 to 6 is right

[Anonymous No.10117976]

>>10117957
Please explain the notation. More specifically, D* and Br(x).
Eighth line is outright stupid tho.

[Anonymous No.10117977]

>>10117533
I only use LaTeX for final documents

[Anonymous No.10117984]

>>10117862
Anon if you ever want to know anything about any special functions just go here
https://dlmf.nist.gov/
Either this will have the answer or one of its many references will.

[CA Tutor No.10117987]

Welp, took a nap for too long and my comm algebra thread died... well, im not gonna start a new one because i've barely gotten through 3 chapters in 2 weeks at this rate with the posting and all

[Anonymous No.10117993]

>>10117533
This >>10117785
This year I'm given written exercises for a course (find a counterexample why such a result cannnot hold if we use weaker hypotesis or use families of sets of different kind), and while I start by solving them with paper and pen, I write the final version in latex; it takes not so much time, but had I written it in paper, I would have needed to rewrite the whole thing few times.

[Anonymous No.10117999]

>>10117987
>making less progress because shitposting
I feel you.
>three chapters in two weeks
Not that bad.

[Anonymous No.10118001]

>>10117987
It was a good thread.

[Anonymous No.10118003]

>>10117987
If it's any consolation thanks to that thread I finally started studying the subject and am still doing the problems. It kind of gave me the motivation to tackle the subject, so thanks anon.

[Anonymous No.10118017]

>>10117957
D* is the set of all limit points of D. Br(x) is standard notation for the open ball of radius r around x. Line 8 is trivially true but I was just stating it explicitly.

[Anonymous No.10118025]

>>10118017
meant for
>>10117976

[CA Tutor No.10118035]

>>10117999
i know it's not technically bad, but I dont have much to show for it. Also a lot of the time was wasted in putting up polished solutions, but oh well.
>>10118001
thanks, sadly this is the least "advanced" topic im going to be doing in the near future so i cant really do any other thread of this style that's accessible
>>10118003
im still going to be doing the problems, so if you're stuck on something just ask here, im always lurking

[Anonymous No.10118036]

>>10118017
Righty.
Fifth line is wrong. Rather, it isn't, but you need to show it. Imagine I have a set A, then I take all the limits of sequences on A, and put them in a set B. What you need to show is that there are no sequences on B-A that converge to some point outside B union A. In the fifth line, when you claim any open ball around x has intersection with D, you're assuming what you need to show.
This is honestly one of those cases where the proof for topologies is easier than the one for metric spaces, low-key do that one.
By the by, for any point in D we can form the sequence x, x, x, ..., so you can compress some notation by just writing D* instead of DUD* all the time.

[Anonymous No.10118058]

How do you study maths? It's so different from college to university and the difficulty spike is insane. Any tips for a brainlet?

[Anonymous No.10118062]

>>10118058
Read the book
take notes on the book
do the exercises

[Anonymous No.10118071]

>>10118036
>need to show 3 times
Man I ought to get back into literature.
Anyhow, I completely forgot to say that you can just write:
Let D be a set. Let B be the set of points x such that every open ball around x contains some point in D. Let C be the set of points y such that every open ball around y contains some point of B. Assume that there is some y that is not an element of B. This is false, since if an open ball contains x, it also contains some open ball around x. Therefore C=B and we're done.

[Anonymous No.10118078]

>>10118058
practice

[Anonymous No.10118087]

>>10118058
Do fundamentals until you shit fundamentals

Start tackling individual subject areas like fun problems and try to figure out how they tick and then practice the fuck out of them until your brain starts to reflexively think in them

Keep doing that with more specialties until you ascend to real high level math

Don't be afraid to layer and redo online courses, use MIT free shit, use pirated textbooks, use whatever you want, just keep doing it and do it seriously and make it part of your life

[Anonymous No.10118102]

>Weierstrass' theorem
>Taylor's theorem
>Rolle's theorem
>Mean value theorem
>Intermediate value theorem
>Lipschitz continuous, uniformly continuous functions
>all the stuff on monotonicity and continuity

What are some calculus books that go in depth with these things, including proofs? Most of them ignore stuff like these and skip to the classics.

I want to keep it real and one-variable so I don't get too much into metric spaces and the like.

[Anonymous No.10118115]

>>10118102
Better off just using an analysis book for full proofs of those. Rudin, Royden, Abbot, pick your poison.

[Anonymous No.10118118]

>>10118102
Real Analysis books.
>Weierstrass's extreme value theorem
Let I be a closed interval and f(x) be a continuous function on I. Assume f(x) is unbounded on I. Then I can form a sequence of values of f(x) inside I that diverges, and by the definition of continuity, the value of f(x) at some point in I is infinite or minus infinite, which contradicts the function's counterdomain.
Since f(x) is bounded, Dedekind's axiom guarantees suprema and minima. Assume there is no a for which f(a)=sup f(x) in I. We can once again form a sequence of values of f(x) which converges to sup f(x), and continuity guarantees the existence of a.
I can post some of the others, if you really want me to.

[Anonymous No.10118151]

>>10118115
I don’t think you can go in full raw without rubber into analysis. You need to finish a book on calculus first.

[Anonymous No.10118177]

>supposed to meet with advisor tomorrow
>did basically nothing last week
oh no oh no oh no oh no
why am I like this

[Anonymous No.10118186]

>>10118177
Has happened to me a lot. I basically just say some combination of "TA work + course work took too much time" "I had family/personal business to attend" "I've been reading up on related literature to gain a deeper understanding/new perspective" or "I'm stuck on some problem." I will say this though, you should aim to at least have something tangible to show you've been doing work. Even if it's nothing but dead ends and false paths your advisor will at lest appreciate the effort you're putting in. Likewise it's okay to not have results once in a while, just don't make it a habit of showing up with your proverbial cock in your hand.

[Anonymous No.10118203]

>>10118151
I'd argue the opposite. Whilst calculus does offer exposure, I'm sure a basic introduction to proof/logic would prepare anyone sufficiently to tackle intro-analysis. Any good course should be building everything up from the reals anyways.

[Anonymous No.10118228]

>>10118217
any thoughts?

[Anonymous No.10118273]

>>10118228
It's false. Take f to be the delta function.

[Anonymous No.10118283]

>>10118203
>the reals
No such thing.

[Anonymous No.10118286]

>>10118273
Kek

[Anonymous No.10118290]

>>10118273
http://mathonline.wikidot.com/functions-of-lebesgue-integrals

[Anonymous No.10118293]

>>10118283
Proof?

[Anonymous No.10118299]

>>10118293
>Proof?
The burden of proof is on you.

[Anonymous No.10118306]

>>10118299
Construction from Cauchy sequences.

[Anonymous No.10118313]

>>10118306
>just construct the set of all the cauchy sequences bro

[Anonymous No.10118314]

>>10118313
Do you know what an equivalence class is?

[Anonymous No.10118326]

>>10118314
I'm a different guy and I believe in the reals, I was trying to point out that the issue the constructivists take is that all attempts to construct R rely on the construction of uncountable sets (eg, the uncountable set of cauchy sequences you quotient to define the reals as limit points). If you can't give a procedure to construct an uncountable set (which is clearly impossible) then you're not going to convince them that R exists.

[Anonymous No.10118366]

There are things so deeply imbedded in my anus they are, for all intents and purposes, lost. My poop river diverted and regrooved a new channel to open air. No one will ever guess what or how I got these medium sized office supplies into my ass. I fantasize about someone masturbating my poop chute, reaching in and pulling out the stapler that they just do happen to need to perform their work. They exclaim in eureka! Looking for my supplies they defy logic and crawl into my massive shit cave and I swallow them hole. Nasty

[Anonymous No.10118370]

>>10118326
For reference, a definition of the real numbers from a constructivist viewpoint is the following: a sequence, [math]\{ x_{n} \} [/math] of rational numbers if regular if [math] |x_{m} - x_{n}| \leq m^{-1} + n^{-1}[/math] for natural numbers, [math]m,n[/math]. A real number then is a regular sequence of rational numbers. From Foundations of Constructive Analysis by Errett Bishop

[El Arcón No.10118388]

>>10118326
>you're not going to convince them that R exists.
interesting

>>10118370
>A real number then is a regular sequence of rational numbers.
Could you explain what this technical definition means?

[Anonymous No.10118393]

>End of year exam finish
>Professor suddenly asks me if I'd like to work for him
>I've never been employed before and this really surprised me
>give the most awkward smile and blank stare

Guess this is why I'm stuck being a socially inept NEET for years

[Anonymous No.10118469]

>>10118388
best I could find on it.

[Anonymous No.10118478]

>>10118393
Well did you say yes?

[El Arcón No.10118481]

>>10118469
I see. I like this definition better.

[Anonymous No.10118482]

>>10118478
"n-no" was my response in panic

guess it's back to burger flipping

[Anonymous No.10118488]

>>10118482
FUCKS SAKE ANON
Go talk to him, apologize for being an autist, and ask if the offer is still available.

[Anonymous No.10118495]

>>10118482
Yeah, you fucked that up. Maybe email your prof and see if you can still get hired?

[Anonymous No.10118537]

>>10118482
Better to have tried and failed, than never to have tried at all.

[Anonymous No.10118647]

>>10118366
I imagined such a magical world inside your anus.

[Anonymous No.10118667]

Anon wtf. You need to contact them ASAP. You mother fucker.

[Anonymous No.10118997]

>>10108490
I'm not a mathematician, so I'm not sure how would you solve it with that particular approach. Why don't you just write a differential equation for it? Something like

[math]dx = -\frac{\mu}{x^{2}}tdt[/math]

Also, gravitational acceleration is proportional to the inverse square of the distance.

[Anonymous No.10119078]

>>10119075
>>10119075
>>10119075
NEW THREAD
>>10119075
>>10119075
>>10119075

[El Arcón No.10119314]

>>10118537

[Anonymous No.10120157]

>>10118102
My introductory calc/analysis course had some of these as required known proofs, although unfortunately the book wasn't in english.
Proving Rolles theorem is simply:
since f is continuous, the extreme value theorem means that f has a minimum and maximum.
If both minimum and maximum are at the edges of the interval, then the function is clearly constant, and so has derivative zero.
Otherwise, at least one extreme value is at an interior point, so the derivative there is zero.

From this, the mean value theorem simply follows from considering the function [math]\varphi: x \mapsto f(x)-\frac{f(b)-f(a)}{b-a}x[/math], noting that [math]\varphi(a)=\varphi(b)[/math] and applying Rolles theorem.

Now I haven't had much analysis beyond that, but the theorems in the picture don't seem that difficult to prove if you're used to the proofs of elementary properties of continous functions.
The first two don't require much more than assuming the negative and noticing the contradiction, if you just take help from graph intuition to see where the contradiction can be found.