/sci/ - Science & Math

> tfw you realize your undergraduate Analysis course was just some small-talk

I have a question about group extensions (of abelian groups). If I have two extensions
[math]0 \to A \to B \to C \to 0 [/math]
[math]0 \to A \to B' \to C \to 0 [/math]
and I know that B and B' are isomorphic as groups, are the above extensions then equivalent?

Reality Dynamics in Conversation

IN any discussion (defining discussion as language and sub-language conveyed between any number of participants over any duration), all factors brought to attention are valued and thus given reality. Giving a concept or a material reality increases its range of effect, and pushes it forward in time towards its final aim, and towards its next aim in succession.
IF a concept is not explicitly referenced, but only the recieving party is aware of it, the concept has hijacked the speaker.
IF a concept is not explicitly referenced, but both parties are aware of it, the speaker is supporting said concept. The only way they can avoid supporting it is to explicitly or inexplicitly avert its aim, rather than just giving it existing.
HOWEVER, the mere act of giving it existence fuels its aim more than not letting it exist in the first place. Thus, a sufficiently powerful concept relative to a sufficiently weak speaker will always hijack the speaker to its purpose, even if the speaker opposes it.
THE only way to defeat a concept is to wield enough power that it does not enter thought, even inexplicitly. This requires control not only over speech, but of matter as well.

How could you approximate [math]f(x-x_0)[/math] for [math]x_0\to\infty[/math] when you know [math]f[/math] is analytic, won't blow up for any values of [math]x_0[/math] but don't know the form of [math]f[/math] in advance, besides that?

>>12042691
What function is that? Where in physics and computer science is it relevant?

>>12042719
If I interpret correct, this is the same as asking
>f(x) as x-> - inf
In that case you would need to know the end behavior of f, and there are many functions that are analytic, don't blow up, and have different end behaviors. So I assume you could not approximate it.

>>12042725
So we don't have any kind of analogy to Taylor's theorem for asymptotic series? I've almost never actually needed to use them before except for integrals, so know very little about them.

>>12042712
All the group operations are preserved

>>12042737
Oh, you meant "doesn't blow up" as in no infinite growth, not no vertical asymptotes.
Even still, there are different asymptotic functions with different y-values towards -inf. How do you know which one you arrive at?

>>12042737
Also, Taylor's theorem applies to "k-times differentiable real functions." So, for example, you can make a Taylor series of the sigmoid function.

>>12042755
Yeah, I get your point and I do see why it's somewhat implausible to expect an analogy there.
Mostly I'm working with a nonlinear PDE at the moment and have derived approximate behaviour and solutions for a small parameter and I'm frustrated I can't get the asymptotic behaviour for when the same parameter is large, since it would round off my paper so nicely.

>>12042743
so?

>>12042765
Have you tried induction?

>>12042771
Think about what's being "extended."

>>12042781
C

>>12042691
What happens if you continue this shape until it joins up, is this just a section of a torus given unwarranted significance?

>>12042802
>for any such short exact sequence, f is a monomorphism
>a monomorphism is an injective homomorphism
>a homomorphism is a structure preserving map

>A-->B preserves structure
>A-->B' preserves structure

Are there any books on intuitionistic analysis?

>>12042816
Read Newton

What are the most amazing or unexpected results when studying geometry over fields other than C or R? For example in finite fields or the p-adics.

>>12042712
I don't think so
>>12042815
what are you trying to say exactly?

>>12042815
I know, but I don't see how that tells me anything useful

>>12042825
I'm trying to lead him to the conclusion that his replacing B with B' leads to equivalent extensions. But I know zilch about group theory, I'm just going off of Wikipedia and trying to guess. It seemed like a fun thing to try.

>>12042834
>I'm trying to lead him to the conclusion that his replacing B with B' leads to equivalent extensions
but it doesn't

>>12042836
I guess not. I guess I was wrong. However I refrained from any overt statements and just gave him information, so I didn't do anything illegal.

Just got started with definite integration. What am I doing wrong here?

My answer is coming out at 8190, but the boom says 227.5.

So lads, I'm returning to uni after retaking a year out of attendance (due to mental health problems i couldn't attend exams).
I still have an issue of self doubt in my abilities and I want to be able to just do math without thinking about it. By this i mean without trying to find some fucking analogy or deeper understanding or shit like that. It's just distracting and a waste of time. How do i get over it?

>>12042858
bounds

>>12042863
?

>>12042866
the 0 and 1 at either end of the cool S change

>>12042859
learning historical uses as motivation is a good thing. try to look for application instead of philosophical conspiracy

>>12042858
Where are you getting that factor 2? I'm getting a factor of 1/18.

>>12042879
Sound advice - this seems like it'll work perfectly. Thank you

>>12042858
You have to divide by 6, not multiply.

>>12042859
Get used to finding intuition in pure logic rather than geometry. Focus on how symbols can move, patterns in symbol manipulation itself.

>>12042840
nigger

>>12042887
Next time I'll be more cautious with my play, alright?! Sometimes you just have to try :}

>>12042884
I did divide by 6. 1/3 divided by 6 gives 2

>>12042884
>>12042890
Nevermind, I am retarded

>>12042890
No it does not, silly anon. Dividing by a positive integer means braking into N parts. Imagine a piece broken into 6 parts. Each part is 1/6th of a whole. Now imagine that the original piece is 1/3 of a whole. Thus, each piece is 1/6th of 1/3. 6 of them make 1/3, so 18 make 1. So each piece is 1/18th of the whole.
>breaking a piece into smaller pieces doesn't make it bigger

>>12042884
>>12042894
Thanks, anon. I did it like 1/3/6 when I should have computed it as 1/3 ÷ 6

>>12042897
1/(3/6) is valid too. I like to do 1/3 * 1/6 so I match up my denominators.

>>12042901
>>12042897
Woops, 1/(3/6) is not valid, sorry

Division is not commutative under / notation
(1/3)/6 =/= 1/(3/6)

>>12042816
>Are there any books on intuitionistic analysis?
https://ncatlab.org/nlab/show/intuitionistic+mathematics#feel

huh, never knew it was called a solidus
The diagonal slash "/" used as the bar between numerator and denominator of an in-line fraction (Bringhurst 1997, p. 284). The solidus is also called a diagonal.

Special care is needed when interpreting the meaning of a solidus in in-line math because of the notational ambiguity in expressions such as a/bc. Whereas in many textbooks, "a/bc" is intended to denote a/(bc), taken literally or evaluated in a symbolic mathematics languages such as the Wolfram Language, it means (a/b)×c. For clarity, parentheses should therefore always be used when delineating compound denominators.

a Virgule is similar but less slanted than /

>>12042889
kys

Let [math]X_1 \dots X_{2N+1}[/math] be i.i.d., such that [math]\mathbb{P}[X_i = ()] = p[/math] and [math]\mathbb{P}[X_i = ()]=1-p[/math]. Think of it as traffic signs that guide you towards some target - either to your right or to your left - and the signs are affected by random noise. Taking the majority vote over [math]2N+1[/math] signs, by the Chernoff bound we get that the probability of error is [math]\leq \mathrm{e} ^ {-\Omega(N)}[/math], where we modeled the [math]X_i[/math]s as Bernoullis taking on the values [math]\{0,1\}[/math].

Now suppose we have [math]Y_i[/math]s taking the values [math]\{,,,\}[/math]; only *one* of these directions is the correct answer. How can I bound the probability of error in these settings (when taking the majority vote)? I need a nice way to model the [math]Y_i[/math]s as if they're taking numerical values.

Let [math]X_1 \dots X_{2N+1}[/math] be i.i.d., such that [math]\mathbb{P}[X_i = (\rightarrow)] = p[/math] and [math]\mathbb{P}[X_i = (\leftarrow)]=1-p[/math]. Think of it as traffic signs that guide you towards some target - either to your right or to your left - and the signs are affected by random noise. Taking the majority vote over [math]2N+1[/math] signs, by the Chernoff bound we get that the probability of error is [math]\leq \mathrm{e} ^ {-\Omega(N)}[/math], where we modeled the [math]X_i[/math]s as Bernoullis taking on the values [math]\{0,1\}[/math].

Now suppose we have [math]Y_i[/math]s taking the values [math]\{\rightarrow,\leftarrow,\uparrow,\downarrow\}[/math]; only *one* of these directions is the correct answer. How can I bound the probability of error in these settings (when taking the majority vote)? I need a nice way to model the [math]Y_i[/math]s as if they're taking numerical values.

>>12043096
I think you're making this more complicated than it has to be. But it might be fun to solve with Chernoff bounds and modeling directions as [math]\{1,-1,i,-i\}[/math]

>>12042720
It's a saddle point.

>>12042894
We stan a humble king.

>>12043096
Why'd he delete it, bros?

>>12042712
I assume you mean that the exact sequences are isomorphic. Under this definition, I think no. For instance, in the case [math]A = 0[/math] this yields the statement that two subgroups of an Abelian group which are *abstractly* isomorphic must be carried to each other by some isomorphism of the larger group.

I'm not the best with finite group theory, but I think this fails on examples such as [math] \mathbb{Z}/2\mathbb{Z} \oplus \mathbb{Z}/4\mathbb{Z} [/math]; there are two subgroups abstractly isomorphic to [math] \mathbb{Z}/2\mathbb{Z}[/math], but it's reasonably easy to see that there is no isomorphism of [math] \mathbb{Z}/2\mathbb{Z} \oplus \mathbb{Z}/4\mathbb{Z}[/math] relating them to each other, since every isomorphism of that group preserves each direct summand.

>>12043227
oki upon googling what "equivalent SES" means, my answer is stronger than needed; the answer is obvious for the case [math] A=0 [/math], and any distinct isomorphic subgroups yield an obvious counterexample (they clearly can't be related by the identity automorphism of [math]C[/math] because they are distinct).

>>12043239
>oki
Osmi?

>>12043360
?

>>12043371
Nevermind your syntax made me wonder if you were someone who went by a name starting with "osmi". He was into math too.

redpill me on symplectic integrators

>>12043227
>>12043239
>for A=0 this yields the statement that blablabla
are you >>12042834
or just another guy who has no idea about exact sequences and tries to give some retarded wrong answer.
Anyway, >>12042712
is not true, consider for example
[math]A= Z \oplus Z [/math]
[math]C= Z/2Z [/math].
Then [math]Ext(C,A) = Z/2Z \oplus Z/2Z [/math]. So, there are 4 extensions up to equivalence. But B can only be [math]Z \oplus Z [/math] or [math]Z \oplus Z \oplus Z/2Z [/math] up to isomorphism.

How do we prove that
>lim n>inf (1+1/n)^n
converges, and how do we prove that it converges below a certain bound, say, never goes above 2.75

>>12043506
Take the derivative.

>>12042816
https://www.youtube.com/watch?v=wuhbxJahVRE

i still hate set theory.

>>12043536
If you're the same poster from before, you don't know any math beyond basic arithmetic because you can't even into a collection of numbers.

>>12043536

>>12043544
to be fair, you can drop Regularity (or, equivalently, Set Induction, if you want to not use Regularity for some reason) and still get far in ZFC.

>>12043536
I'll bite, why?

Why do people use Landau-notation and don't take the effort to note what the constants depend on?

https://www.mathtrainer.org/

Do you even operate?

>>12042840
The fucking state of /mg/

>>12043698
Yeah that was pretty fucking shameful. I'm the one who brought up Prüfer groups in a question about arbitrary Abelian groups without taking the effort to check whether they were actually a counterexample to the statement under consideration, but at least I had a decent reason to think they would be worth looking at.

>>12042719
I might be naive here but don't we typically define a function [math]g(z)=f(1/z)[/math] and then consider behaviour near the origin?

I'm trying to find a formula for the Mclaurin series of [math] f(z)=sin(2z^2) [/math]. I've calculated the first 4 derivatives of [math] f(z) [/math] and evaluated each at [math] 0 [/math]. The third derivative evaluates to [math] 12 [/math], but the rest evaluate to [math] 0 [/math]. When I substitute into the form of a Mclaurin series, I get [math] 0+0+0+2z^3+0+... [/math]. Where do I go from here? Any help would be appreciated.

>>12043874
Oops, that should read [math] f(z)=zsin(2z^2) [/math].

>>12043874
Just use the series for sin(z). Plug in 2z^2 and multiply by z.

>>12043606
based, fuck Regularity
S = {S} is the best set.

>>12043683
Dude, why is it only +-*/ I want more

>>12043892
Thanks, anon

>>12043969
Cheers, lad.

>>12042713
Stop confusing ontology and gnosiology.

>>12042920
Imagine confusing commutativity with associativity

I'm reading stewarts calculus just for to get a stronger grasp of calculus, up to this this point i've done around 50% of the exercises of each chapter but at chapter 11(sequence and series), I'm kinda bit dead inside through the end. How much will it hurt inside if I don't ever practice taylor series properly? I'm a software eng. student. I haven't done any multi var. calculus in my life yet and my brain tells me to skip what is left of chapter 11. Is taylor the basis of a more advanced thing I don't know the existence of?

>>12044138
>Is taylor the basis of a more advanced thing I don't know the existence of?
Yeah, and it has lots of applications in engineering too.

>>12042858
Hopefully you can read my handwriting

>>12044138
There is this meme that everything you learn is uni will be what you use everyday for the rest of your life. As a software eng obviously you shouldn't worry that much if you don't know the same amount of calculus a math student knows, but the point is that if something relevant comes up, then it will help you. For example, neural networks seem like some really innovative field with state of the art techniques, but really it only seems like that because few people know how to program and statistics well enough to see it's really a pretty simple thing that got over memed. So if you want to understand the theory behind it obviously knowing statistics (which requires calculus) is going to help you massively. Just look at uni as a way not to get hyperfoccused on your field, but as a way to get a great baggage and formation that will help you generally in life. Not everything has to be get good job and repeat same meme till you die.

What are the pre-reqs for tensor calculus?

>>12044138
get the main ideas but don't force it down, it's pretty disconnected to the rest of what you learn at that point so you'll forget most of it anyway. when it reappears you will have more contextual motivation to study it

>>12044123
associativity is commutativity of the action

>>12044183
I honestly wish I knew as much as math than a math student. Thanks for writing this much, I appreciate, I get stressed over missing something important when learning for fun.
>Not everything has to be get good job and repeat same meme till you die.
I agree for the last part, but I'm in uni for a specific job in a specific field because it's better for contact making through teachers and internships. I'm trying to grind as much math as possible since my uni doesn't go over proof since it's engineering oriented.
>>12044248
>you'll forget most of it anyway. when it reappears you will have more contextual motivation to study it
thanks, I'll go with that

>>12044153
Fuck me, didn't see you were a software engineer. You don't need to know any math unless you want to be in the top 10% of positions.

>>12044241
If you weren't raised as a gymnast you'll just break your neck.

>>12044241
multivariable calculus and linear algebra

>>12044335
Really, that's it?

>>12044342
You can do multilinear algebra if you'd like.

>>12044320
>You don't need to know any math unless you want to be in the top 10% of positions.
that's what I'm looking for, I was a another front-end web-dev before uni.

>>12044241
The word tensor is a fucking mass mostly because of physicists and partly because of mathematicians. So your question depends for what? For physics? Well Yeah just vectory calc and linear algebra for physicists. Just a heads up, nothing will actually make sense. For math? Well if you have a rigorous multi-variable calculus class you will see that for the most part, there is really nothing new about tensor calculus until you see most of this comes from its use in differential geometry, so really tensor calculus is just differential geometry in coordinates.

Scientifically speaking, what is a tensor?
Can I see it?
Can I touch it?
Can I smell it?
Can I taste it?

>>12044349
Then you want a graduate degree in mathematics.

>>12044398
math degree usually doesn't come with easy contact and 3 paid intership.

>>12044395
Hint: It starts with an A.

I have the series [math] f(z)=\sum_{n=0}^{\infty}\frac{i^n}{4^n}(z-2+i)^n [/math] and tried using the ratio test to find the radius of convergence. However, I end up with [math] (\frac{z+i-2}{4})^n[/math] which doesn't have an [math] n [/math] term in it, so I can't take the limit as [math] n [/math] approaches [math] \infty [/math]. Is the ratio test not applicable for this problem or did I do it incorrectly?

>>12044439
Goddam it. I ended up with [math] (\frac{z+i-2}{4})^i [/math], it should be to the power of [math] i [/math], not [math] n [/math].

>>12044409
Alright, so that's why you won't get those prestigious jobs. You are not independent enough to find those opportunities outside of a rigidly-defined system. You can still do well as an engineer and work on cool stuff, you're just going to have a hard time getting those most competitive positions.

>>12043212
go back

>>12043960
To me it's also attractive since afaik the graph model (e.g. the Hereditarily finite sets are exactly rooted graphs with automorphisms ruled out by the extensionality axiom) is particularly simple without it.

I.e.
>all accessible pointed directed graph are sets
e.g. the graph with one vertex 'S' and one arrow 'S in S' is what your example

>>12044439
You have seriously fucked up using the ratio test or doing arithmetic.

>>12044241
Lin Alg up to multilinear maps, multivariable calculus but taught somewhat rigorously, good geometric intuition and possibly a book on diff geo if you would like some motivation.

>>12044449
Not him, but I understand why some people don't pursue internships, especially if they aren't paid. I live in the middle of nowhere and even after grants and scholarships, I have to take out loans for tuition. I commute to university to save money rather than dorming, and for me to take up a job that doesn't pay and would require me to commute likely at least 30 minutes either way (15-20 miles), I would need way more hours of work that did pay to sustain doing that.

>>12044475
internships are for students with full-ride scholarships and/or rich well connected parents, the same way that just being yourself and networking is for facially attractive normalfags.

>>12044449
I don't care about prestige I just want to do something I like. I don't live with the maxim of "independent enough to find those opportunities" but more with "keep on learning and opportunity will be easier to grab". in uni I get one call per 5 resume while outside of it I get one call per 50 resume. I'm from a mostly poor background, I can't afford to do a bachelor with no or unpaid intern. The "rigidly-defined system" exist and i'm going to use it. All my free time should be on learning(and friends), not by being a waiter for rich kids. Paid inter give me that opportunity.

>>12044508
>>12044478
also,
>the same way that just being yourself and networking is for facially attractive normalfags.
not my problem if you're insecure about yourself and can't socialize properly.
>internships are for students with full-ride scholarships and/or rich well connected parents
unpaid inter*

>>12044508
You should have mentioned that you skipped the most important step in starting a strong career, which is being born into a wealthy family. Coming back from this error is nearly impossible, and I wish you all the best in your journey.

>>12044473
I take the original function and change every [math] n [/math] to [math] n+1 [/math], right? And then divide by the original? So, it should be [math] \frac{i^{n+1}}{4^{n+1}} (z-2+i)^{n+1} [/math] divided by [math] \frac{i^{n}}{4^{n}} (z-2+i)^{n} [/math]. So I multiply by the reciprocal [math] \frac{i^{n+1}(z-2+i)^{n+1}}{4^{n+1}} \times \frac{4^n}{i^n(z-2+i)^n} [/math], and this time I ended up with [math] \frac{i \times (z-2+i)}{4} [/math]. Does that seem right? I still can't take the limit, so I assume not, but I don't know where I'm going wrong.

>>12044523
First of all, you need to take absolute values. Secondly, think about what the number 2 does as n goes to infinity.

>>12044520
>I wish you all the best in your journey.
thanks I'll do my best you to.

>>12044478
>internships are for students with full-ride scholarships and/or rich well connected parents
>I understand why some people don't pursue internships
lazy brainlet cope

>>12044535
Thanks. :)

>>12044475
forgot one of the copers. the point of the internship is that you pay for your gas money with wages, zoomer
>>12044540

>>12044519
>not my problem
I wasn't saying it was your problem I was saying that the people who preach this are normalfags that already have good success socially. It's not actionable advice for autistics. Yes, unpaid internships, getting your foot in the door so to speak, is for people who have resources to fall back on. Some poor fuck who is working a full-time job and taking out loans for uni has no business devoting more time to other ventures.

>>12044540
I didn't say don't do an internship, I was going off what they said which was that they did not have a full-ride. Learn to read the thread brainlet.

>>12044551
>>12044520
this is you too? keep coping and blaming your lack of success on money

>>12044528
I'm aware I need to take the absolute value, but does that have any effect on the outcome prior to taking the limit? I left it out because I assumed it wouldn't be relevant if I wasn't even multiplying properly. The number 2 doesn't "do" anything, but it's effectively 0 compared to infinity, right? The issue is (at least what I think the issue is), the answer I'm getting from performing the ratio test doesn't have an n in it.

>>12044560
No. I don't know what that person's predicament is but they're not me. I was just off-handedly stating that internships and the idea of networking aggressively during undergrad are for: wealthy and/or full-ride students; and for normalfags especially facially attractive people that are good at getting others to see them as part of their in-group in a short amount of time (respectively). That was the whole of the statement(s) that I made. The other person seems to be retarded and to have taken out loans and committed to wagecucking while doing a technical degree, something I would never do.

>>12044547
I spend $80 a week on gas just to get to college. A parking pass is $300 per quarter. Fortunately, I have a paid internship I work when I'm not in school that more than covers those expenses, but if you're someone who has similar expenses and works a minimum wage or slightly above minimum wage job, I could understand why taking an unpaid internship would be financially impossible, especially if the hours you're expected to work for the internship overlap with your regular work schedule.

>>12044577
>unpaid internship
boomer meme, equivalent to slavery
>>12044572
>stating that internships and the idea of networking aggressively during undergrad are for: wealthy and/or full-ride students; and for normalfags
more cope and you're still missing the obvious fact that they care way more about grades/intelligence

>>12044395
Start with a vector space. Every vector space has a “field” associated with it, for simplicity let’s assume it’s the real numbers. The covector space is the set of functions that map vectors to real numbers (with the requirement that those functions are linear). Incidentally, the covector space is also a vector space. A tensor is a map which takes a bunch of covectors and a bunch of vectors and maps them to a real number. The dot product for instance maps two vectors to a real number. A matrix maps a vector and a covector to a real number.

>>12044609
yeah right but I mean like can I smell it ?

>>12044582
what? I'm not talking about graduate school I'm talking about someone feeling compelled to do interships or network to land a good job after undergrad or graduate school. I'm talking about industry work, and while I agree that grades and intelligence are as important if not more so in some cases than networking its still true that those who reach out to well connected people early on have a big advantage. I'm not saying I wouldn't network or that I wouldn't do an internship (I wouldn't probably), only that it appears to me that internships are for those who can reasonably spare the time and lost income and networking is necessarily beneficial for people that can actually make other people like and trust them. How the fuck is this hard to understand? I'm not making a prescriptive statement.

>>12044623
I love the smell of tensors in the morning.
Smells like vectory.

>>12044609
ok but whats a field, scientifically speaking?

>>12044626
>I'm not talking about graduate school
neither am i, you keep bringing it up. you also keep bringing up networking like it's the same as internships and like you cant apply to shit online
>>12044626
>internships are for those who can reasonably spare the time
what does this even mean? it's your job

If I just copy a proof should I cite were I took the proof from even if I did some modifications to it?

>>12043218
There is a reason, so don't repost it (not that anon).

>>12044561
The problem is you need to learn how to take limits. The limit as n goes to infinity of 2 is just 2. If you can understand that you should be able to solve your problem.

>>12044654
>what does this even mean? it's your job
Traditionally internships are unpaid. It's just a learning experience. Poor people need a job so they can't take on an internship.

brainlet question:
my uni offers both cal 3 which they treat as intro to vec calc and multivar calculus. They also offer Vector Calc, which has cal 3 as a prereq, but the syllabus has all the same shit on it as cal 3. Are they essentially the same thing or is Vector Calc typically just a more in depth look at topics normally treated in Cal 3?

>>12044682
Yes, absolutely.

>>12044776
Oh I'm sorry I mean if it's in a paper you're publishing then yes. If you're writing a textbook or something you don't have to cite it specifically, just include your source in the references to established literature.

How do you treat the integral of a square root? Is it just x^(1/2 + 1), with n = 1/2?

>>12044771
>Traditionally
>internships are unpaid
ok boomer

>>12044758
Ok, so I'm looking for [math] \lim_{n \to \infty} |\frac{i \times (z-2+i)}{4}| [/math], right? Do I ignore the [math] i [/math] and [math] z [/math] terms? If 2 remains 2, I would assume [math] i [/math] and [math] z [/math] remain the same as well. I am not very good with limits, you have me there, so that's probably why I'm so confused.

>>12044785
You need to divide by 3/2.

>>12044792
How do you write equations like that on a keyboard? Probably a brainlet question, but I'm not a regular poster in the maths general.

>>12044792
I'm pretty sure i is the square root of -1 here, not a variable. Also, z is a constant as far as n is concerned. You really need to go back and review basic limits or these convergence tests are not going to be your friend.

>>12044649
A section of a bundle.

>>12044795
[math] /math with brackets around the second thing too

[math] n^ea_to [/math]

>>12044795
It's Latex, you can find a list of symbols and their code online if you just google "Latex symbols". Just type [ math ] equations/symbols/whatever [ /math ] (no spaces between "math" and the brackets). You can click the "TEX" in the top left of the reply window and copy/paste what you're typing to see how it will look when you post it.

>>12044776
>>12044782
It's for my thesis. It is already based on an article but it's supposed to be selfcontained in a way a typical student with only certain prerequisites can read it. It's just that there are some technical lemmas that I really don't see how to adapt better and so I end up basically just using the idea but as explicit as I can in many different steps. So I don't know if I should put something like "the next 5 lemmas" were taken from this article or something.

>>12044771
>Traditionally internships are unpaid
where are you from? I feel bad for you.

>>12044809
I'd just say «The following five lemmas and their proofs are substantially the same as those appearing in...»

>>12044813
Why? It's not like I've ever been an intern. There's really no reason to pay them.

>"ah, the proof is almost done and I can go to sleep soon"
>spot an error

>>12044797
Yes, [math] i [/math] is just [math] \sqrt{-1} [/math] and [math] z [/math] is a constant, however, [math] z [/math] is not the equivalent of [math] n [/math]. Every example I've looked at ends up with an [math] n [/math] as part of what is being evaluated for inside the limit. You say that 2 remains 2, which I understand. Based on that, I would assume there is no change to [math] i [/math] or [math] z [/math], which basically means the function does not change as [math] n [/math] approaches [math] \infty [/math]. The implication of that for finding the radius of convergence, I do not know, unless that function is indeed the radius of convergence, which I do not think is the case.

>>12044792
expand the definition of the length of a complex number
that would turn it into just a real valued function

>>12044649
A set equipped with two binary operators (+,*) that satisfy the field axioms.

>>12044852
You should really take a class or at least watch a lecture online. There are a lot of gaps in your understanding and although you are getting closer I have other things to do.

Why is it I can solve equations when they're handed to me, but if you put some flavour text around it my brain shuts down? I did quite well in English class in school, so it's not a language thing.

Thoughts?

>>12044825
>There's really no reason to pay them
he's doing work and you expect him to do that fulltime for the next 4-8 month with no remuneration? If he has to pay rent and university has mandatory intern what do you expect him to do? Deliver pizza another 40h a week? In my uni, paid intern are at 20h$/h average because of that, a third will do their intern at the same place accounting for 12-20 month of work and ~70% of them will work in a company they've done an intern. It's about securing potential employees in the futur of your company instead of finding one guy in 320 resume on linkdin. Unless you're google, nobody wants to work in a company that didn't pay their intern. Also, unpaid intern are most likely to not be given actual and useful work since they aren't paid, making "work experience" being not real. My university doesn't consider unpaid inter to be actual work but kinder garden slavery for adult.

>>12044859
Are you saying to take the absolute value of [math] i [/math] or to find the modulus? The former would result in 1, which then the function would become [math] \frac{z-1}{4} [/math]. The latter would be [math] \sqrt{z^2-4z+5} [/math]

>>12044884
he maybe fat, but he look like a chill dude, I'd drink a beer with him.

>>12044879
I've taken 1 or 2 classes that discussed limits, but they never went very in depth as the classes weren't specifically about limits. If you have any resources you think to be particularly helpful, I'd appreciate you letting me know.

>>12044884
>Volver
>Cerrar

>>12044775
Vector Calc is generally an effort to establish Stokes Theorem, usually the Generalized Stokes theorem in a coordinate independent sense. Multi is going to focus on introducing partial derivatives, lagrangian multipliers and tangent planes, and multiple integrals. Vector calc you would deal with line, surface integrals and change of variables theorem. They usually expect you to be comfortable with retard lin alg whereas in multi they'll only use vectors in the most superficial sense like the way they do in an intro to mechanics course. Vector Calc is like a retarded version of advanced calculus where you develop analysis on R^n and eventually on abstract manifolds. If you can self-teach multi and take vector calc and if not I would take the multi and avoid vector calc as there is a lot of retreading involved and its a waste of money if they aren't teaching you the real stuff that requires analysis to understand. My school does the same thing but I had to take both for my core requirements unfortunately.

>>12044775
Scratch what i said at the beginning, Vector Calc culminates in the Kelvin-Stokes theorem usually and some retarded applications to EM w/Maxwell's equations. Advanced Calc is meant to establish the coordinate-free baby diff geo Stokes Theorem with differential forms.

>>12044884
CHI

>>12042691
>finished undergrad in 2019
>decided to work for two years so I could afford to move for grad school
>work shitty IT jobs
>start brushing up on undergrad topics for subject GRE
>start preparing my CV
>start writing a personal statement
>fall 2020 rolls around
>rumors that 2021 application cycle will be competitive as fuck
>subject GRE gets cancelled
>suddenly (very) worried that I will get rejected from every school I apply to
>can't bring myself to study/do fun problems for the last week
Has anybody else been here? What should I do bros?

>>12044930
>What should I do bros?
1. Do more math.
2. Make friends.
3. Get more money.

>>12045025
2 is the most important thing you can do for your mental health. If you've made enough of money, try to work less and do more math.

>>12044930
Well, grad school is for most a means to get paid to do math and to meet others who do math. Supposing you have no grand visions of prestige and that you do not want to teach, you can try getting creative about the way you make money and the way you make friends. If you can find a good position that balances income and time, you can learn a lot of math. If you can find friends to talk about math with, you can learn a lot of math.

It's not clear to me why so many insist on going to grad school. It sounds hard, gruelling, and competitive, yet in many ways it is the path of least resistance. The total refusal of many would-be mathematicians to try and forge different paths has always been very frustrating to me. I am guilty of this myself. My current position pays jesrly double what a typical professor of mathematics would make, so you'd think I would figure out how to turn this into a position that pays the same as a professorship with half the time, leaving me free to learn math at a much quicker pace. Yet every day I fail to do this.

Of course, this js all just silly cope. I hope that you just get into grad school. But supposing you do not, maybe you will take this as a challenge to succeed where I have failed.

What is the general path for someone who studies Mathematics. After you get your degree do most pursue a PHD? Or do most just go on and find a job? What are most of the jobs offered? Does it usually pertain to the branch of mathematics your studying? Thinking of specializing in statistics. Oh and you can talk about your path through math too.

>>12045633
I'm finishing my PhD and probably expect to go back to wagecucking it

>>12045638
This.

>>12045633
Most programs are usually formed with the idea of either to go into a teaching position or to research.

>>12042691
So im hugely into science and logic and math makes me more angry than anything ive ever encountered

It seems math homework/tests are more on the tier of trickery than process, every fucking question with a slight nuance instead of just making the intention OBVIOUS BECAUSE IT IS THE FUNCTION THAT MATTERS AND NOT THE TEACHERS FUCKING SWITCHEROO OF WORDS HOLY FUCK

>>12045680
How do I cope with this? There is no reason to not make things obvious in math. You literally have every reason to make it fucking obvious. Why try to hide shit? Lol hurr durr looks like you werent paying attention!!! Fucking whore bitch ill set you on fire

>>12045680
>so im hugely into science and logic
kys you are not

>>12045683
Weak statement that was easy for you to make and therefore you expose yourself as weak

>>12045682
>>12045680
This just sounds like your bad at math. Are you saying you understand the general concept and when it is put into detail you fail? Like what a derivative is but can't apply it to a tricky problem??? Get Gud

>>12045687
Math is extremely easy, as it never actually exceeds 1+1. My time is 95% dealing with teacher's pseudo-witty undertones in questions and 5% the actual question at hand.

>>12045680
>yugely into science and logic
>doesn't use oxford comma so it looks like contradictory statement
>math makes me angry
>y-you tricked me with your symbol magic
Anon I have some very bad news for you

>>12045690
You're just as bad as my teachers, you degrade efficiency for the sake of game playing. You are cancer.

>>12045689
>Math is extremely easy, as it never actually exceeds 1+1
I'm pretty sure you have to be 18 to post here
>My time is 95% dealing with teacher's pseudo-witty undertones in questions and 5% the actual question at hand.
it just sounds like your not carefully reading it or your not practicing enough to do the sub-problems or special cases.

>>12045697
What level of math are you struggling with anon?

>>12045698
>>12045698
Nobody should have to carefully read a math problem. It is literally just right in front of you. Having to treat it like a fucking seek and find is antithetical to the whole purpose of math.
>>12045699
I'm not I'm just angry at human beings

>>12045700
If it makes you feel better you will stop seeing word problems when you start doing real math around freshman/sophomore year real analysis and abstract linear algebra. most actual math texts don't rely on the framing that you see in shitty computational plug and chug texts like Stewart. You'll still have to carefully read the problem but that is more for understanding what it is you're being asked to prove rather than what the problem is saying.

>>12045700
>nobody should have to carefully read a math problem
Yes you are just a fucking brainlet

>>12045705
This has nothing to do with word problems. I wish I could show you screenshots, but I know better. I have a teacher that thoroughly believes in just spamming rare outliers at you. Each day I believe more and more it is because he is mostly teaching the "blind" and has to show them walls. It's an excessive waste of time.

>>12045706
You nor your children will be as smart as me

>>12045711
Post them faggot

>>12045715
This will not happen, sorry to say.

>>12045718
Anon people ITT really don't give a shit about somehow doxxing you from a single math problem, just do it

>>12045711
what class is this that you're complaining about specifically?
>spamming rare outliers
Analysis? Topology? What is it?

>>12045697
>you degrade efficiency
Efficient writing for the author is different to efficient writing for the reader. As the author your job is to prioritize the reader. Please write better in the future and stop making excuses for your failures.

How should one prioritize depth vs breadth in undergrad math? The grad analysis course I'm planning on taking is apparently extremely heavy workload, equivalent to roughly 2-3 undergrad courses. Not sure if the tradeoff is worth it.

Am I a bitch for not taking grad level courses? Everyone jerks off to them online but the upper level undergrad courses at my uni seem plenty rigorous.

>>12045736
addition
the whole numbers are fine but then there are these 3 number fuckers and weird horizontal lines

>>12045680
It sounds like you're struggling with questions framed to test whether you actually understand what the function represents in an applied context, rather than just pattern-matching with no comprehension of what you're doing.

>>12046008
some of the grad courses at my old uni were just the undergrad one with a few extra lextures, proofs and exercises, the module had a 10 credit and 15 credit version

>>12042691
Anyone here work in a biology research group?

How do I prove a polynomial with r roots has a derivative with at least r-1 roots?

Using Rolle I can see how that would be the case if the roots were all multiplicty 1 but then I get filtered

>>12046719
trivial.

>>12045025
>>12045065
Thank you for your help, guys.
I forgot to mention that I'm in the middle of changing jobs (going from installing network equipment at slaughter houses and jails to working IT helpdesk from home). The latter should be more conducive to studying. I will also be working with my old undergrad buddy, so that will be nice.
I'm going to visit my old professors next month to ask for letters of recommendation, hopefully that will help too.
>>12045488
Grad school is definitely the path of least resistance. I loved tutoring and mentoring as an undergrad and I would be more than happy if my role as a professor was mostly instructive.
I entertained the idea of being my own boss this year, but I chickened out and took another IT job. I will probably take the path of least resistance when I finish grad school too.
Out of curiosity, what field do you work in?

>>12046731
pls tho

What do you do against writer's block, mathematically speaking?

>>12046875
Wait or force.

>>12046758
Yeah I mean, grad school is often the smartest move, I'm just a little bitter. I definitely wish you maximum luck in your endeavor.
>Out of curiosity, what field do you work in?
I work at a small (or at least recently-small) company doing some weird mix of "data science", JavaScript stuff, IT, and loads managerial/customer facing junk. Interest in the topics decreases as you move through that list, and time spent of the topic increases as you move through that list.

>>12045680
>I'm hugely into science and logic
Me too, I just fucking loooove science :D

Edit: Wow. Thanks for the gold, kind stranger!

>>12045697
You have to be 18 to post here

>>12046719
if z is a root of f(x) with multiplicity n, then it also is a root of f'(x) with multiplicity n-1

Is it normal for students to find initial proof solving difficult. And especially inductive proofs? Could they get over this with practice e.g. Velleman?

>>12047256
>Is it normal for students to find initial proof solving difficult.
No, most students are able to prove Dickson's lemma within 5 days of learning proofs.

>>12047269
I'm at the end of my bachelor degree and never heard about Dickson's lemma. I fucking sucks

>>12047381
It's a nice result.

I need nj wildeberger memes/images

>>12045700
>Nobody should have to carefully read a math problem.
man, i remember when i was that dumb
but i was never dumb enough to be bad at them,
just wanted to do them quicker, youre just seething and copeing and crying

https://youtu.be/U_6AYX42gkU

>>12047509

i just want to do DEs and make pretty pictures

>>12047606
https://www.youtube.com/watch?v=rNUfiQgj6ZI

>>12046354
>>>/r/eddit
>>12046522
I’m going to be in like a year. How is it, desu?

Is there a way for me to test if the Mclaurin series I made from a given equation is correct?

>>12047606
>4
me but with complex analysis and colorful diagrams

>>12047662
Graph it

>>12047662
Graph it on Desmos.

>>12047662
>>12047712
>inb4 "thats cheating"
Plot the points by hand :}

>>12047718
kill yourself

>>12044882
It is a symbol thing, and a symbol-embeddedness thing, you need to think abstracter

>>12047712
>>12047714
Thanks
>>12047718
It's not cheating if I'm just checking my work.

>>12043517
The derivative is in terms of ln though, doesn't that make it circular?

>>12047515
why did he do that?

>>12047739
Calculators make the mind weak. Checking by hand makes your milieu more difficult, makes your baseline capability higher.

>>12047767
>Calculators make the mind weak
it depends
would you really prefer to waste time on mundane things?

>>12047269
Is this a troll?
how do I get better a proofs bros pls help me

>>12047767
Monotonous tasks are for ditch diggers whose time is of little value.

>>12047805
Of course it's a troll, dumbo. Unless you're Abel or Riemann incarnated, you're not going to just pick up on proofs right away. The way to get better at them is to do a lot of them and always right down definitions of the relevant information at hand.

Here's the proof for Dickson's lemma, though, if you were curious.
http://pi.math.cornell.edu/~dmehrle/notes/old/alggeo/09MonomialIdealsDicksonLemma.pdf

>>12047797
Rote memorization is a powerful tool, and strengthens working memory, attention span, and mood regulation. The fact that Von Neumann could memorize books upon reading and retain it for decades - it wasn't unrelated to his genius and mathematical skill.

>>12047814
Ditch digging builds character, willpower, and strength. Ditch digging feels good. Have you ever dug?
Of course time isn't infinite. This is why you become fast at computation through effort, and speed up your brain long term. And use your intelligence on immortality research.

>>12047860
Strength is for the weak.

>>12047865
Physical pain is the same neural network as mental pain. Physical labor builds mental strength.

>>12047860
Based
>>12047871
>neural network
Cringe

>>12047882
>everything my grandfather wasn't aware of is jewish mysticism

>>12047904

>>12047904
No, you’re just a pseud for using CS metaphors when they have no place in neuroscience. I agree with everything said about working memory being integral to general intelligence and the value of doing computations by hand.

>>12047961
It's not pseudoscience. Referring to cognition as a network is the most accurate thing, because it's not just neurotransmitters, and it's not just specific regions.

>>12047976
>cognition
Not real, if you mean neurobiological function then sure but you can just as easily say neural circuit or neural architecture. mathematically and physically mammalian brains function nothing at all like the digital neural networks which people have retroactively and ironically, given the name comes from biological structures being misapprehended, applied to organic brains.

>T is a non- uppertriangular matrix
>the eigenvalues are blabla, as you can verify
How do I verify? If I construct a polynomial that nullifies T, I can't be sure it's the characteristic polynomial, unless there is a unique polynomial of each degree such that p(T)=0, and I am unsure/doubt that that's true.

>>12047986
>neural circuit
Network is a preferable term, because the circuit is highly non-parallel (except in the cerebellum) and refers to itself often. I'm not intentionally referring to CS here.

>>12047860
Digging is more cardio than strength, you would know that if you ever dug, which you clearly haven't. There are more efficient methods of doing cardio anyway, so why waste time digging if my goal is to do cardio?
>willpower and character
Everything you do builds onto those.

>>12048034
Clamped
Unclamp

Hello from Arrondissement Rennes, Ille-et-Vilaine

>>12048113
Bonjour M. Clause

>>12047990
I think it's possible with a bunch of gaussian elimination given I know the eigenvalues.

Just realized complex numbers make factors much more comfy to work with

>tfw no inner model for supercompact

I have the series [math] \sum_{n=1}^{\infty} \frac{n+i}{2n^2} [/math] and am trying to determine if it converges or diverges. So, I split it up like this [math] \sum_{n=1}^{\infty} \frac{n}{2n^2} + \sum_{n=1}^{\infty} \frac{i}{2n^2} [/math] which I simplified to [math] \frac{1}{2}\sum_{n=1}^{\infty} \frac{1}{n} + \frac{i}{2}\sum_{n=1}^{\infty} \frac{1}{n^2} [/math]. It's my understanding that [math] \sum_{n=1}^{\infty}\frac{1}{n} [/math] diverges and [math] \sum_{n=1}^{\infty}\frac{1}{n^2} [/math] converges. Based on that, I would think the series I am working with diverges. Am I correct?

>>12048253
Why does this make you sad anon?

>>12048276
Yes, I would agree this looks correct-though, perhaps depending on the level of rigor of the class, might need to be rephrased a bit. After all, the sum rule only applies if the sum is convergent in the first place. This is just a minor tweak.

>>12048208
The true beauty of complex numbers really comes in complex analysis-complex differentiability is much nicer then real differentiability.

>>12048289
I want Woodin-sensei's V=Ultimate L conjecture to be true.

>>12048306
It's not very rigorous, but I do have rules/tests written out to show that the first series diverges and the second converges. I think that will suffice. If there is something I can add to make my case better, I wouldn't mind adding it, but I think I have enough. I just wanted to make sure I was right about the series diverging.

>>12048319
In what way? I'm aware of how complex differentials are performed btw

>>12048333
Triple trips confirm it, anon.

Can any anons tell me what this equation relates to?

>>12048383
>there are "people" with handwriting this atrocious
Another piece of evidence strongly supporting the need for eugenics

>>12048388
His handwriting is legible

>>12048399
that's a pretty low bar

>>12048399
That's a sexist assumption btw

>>12048367
The way I see it is real analysis is trying to sort through the mess and all kinds of sticky convergence and existence questions relating to limits, continuity, derivative, and integral. We know of differentiable, non-analytic functions. Of only singularly differentiable functions. One needs to specify the whole domain for it to make sense. In complex analysis, it is remarkable that every differentiable function [to be clear, we are referring to a function from complex numbers to complex numbers, not real to complex] is infinitely differentiable, is analytic, and is 'unique' in a sense by analytic continuation. Cauchy's formula is interesting, since it would mean the function within the interior of a circle is determined by the values on the boundary of the circle. [it is used to prove these results, in fact] In fact, it can go even more general in terms of winding numbers. This stark contrast between the types of things that are looked at astounds me.

>>12048420
That is indeed interesting. Correct me if I'm wrong, but aren't all holomorphic functions conformal? My intuitive guess would be that being forced to preserve structure in a plane rather than on a line tightens things up. I don't understand complex numbers very well, philosophically, so I find noticing things in a simpler domain such as arithmetic to be more insightful since there's fewer moving parts to be confused by, more direct application. Ease of division relates to ease of rotation, motion, interaction.

>>12048418
Assume everyone is the same gender for the higher sake of non- chimpanzee-tier discussion. I go with male because more anons are male overall, and because the general style is male rather than female.

>>12048443
Yes under a few conditions of it being when the derivative is non-zero. Certainly, the restriction of complex differentiability is a lot more strict. They have to satisfy, for instance, the Cauchy-Riemann equations.

Complex numbers shouldn't be too hard to grasp philosophically, when one realizes so far as science is concerned, math models. i appears in solutions of plane waves for instance.

>>12048499
What is the proof that if Cauchy-Riemann holds, holomorphism holds? I tried to find it online but I couldn't find a good one.

>be reading
>says the trace equals 5
>says the trace equals the sum of diagonal entries always
>diagonal entries are 3 and 2
>3+2=4
>4 =/= 5 , what gives?
Above is a post I almost made.

>>12048511
It's actually in general false. For instance, the function e^(-1/z^4) with it being equal to 0 and z=0 satisfies cauchy-riemann but is not holomorphic. Terrance Tao made a post about this here: https://terrytao.wordpress.com/2016/09/22/246a-notes-1-complex-differentiation/..

>>12048383
distribution theory (the delta function is explained in analogy to the Kronecker delta)

>>12048577
>If {U} is open (that is to say, every point in {U} is an interior point), and {f} is complex differentiable at every point at {U}, we say that {f} is complex differentiable on {U}, or holomorphic on {U}.
>Conversely, if f : C>C is a function which is differentiable, then f is complex differentiable if and only if the Cauchy–Riemann equations hold
Second greentext is from wiki, first is from Tao's paper

But if CR imples differentiability for the whole plane, that means its differentiable thus holomorphic for all {U}

>>12048577
>(ii) Conversely, if {f} is Fréchet differentiable at {z_0} and obeys the Cauchy-Riemann equations at {z_0}, then {f} is complex differentiable at {z_0}.
The blog also says this, and Frechet differentiability just seemed like requiring the PDEs to exist in the first place if I read right

>>12048399
It’s visually offensive and shameful to share with others.
>>12048418
There are no women on 4chan worth talking to. Everyone I address is white and male until they prove otherwise.

>be reading final chapter of textbook
>author becomes more loose, jokes around more, leaves more steps of the proof to the reader
>author even makes the book self referential by referring to page numbers rather than definition/theorem/lemma numbers
Comfy feeling

>>12048713
Hello, I'm the guy you sucked the dick to in a previous mg thread, and I'm a woman.

Isn't algebra weird and almost platonic about infinitesimals?

Is it possible to do undergrad in math and phd in a different science?

>>12048863
No, it has never happened. Don’t even bother trying, just kill yourself now.

>>12048893
I almost ammended my post to say "plausible" but I didn't want to excessively bump the thread.

How should a math major go about getting an internship in undergrad? Would you have to know shit like programming and excel?

>>12048919
What are you applying for?

>>12048939
Gonna be a freshman this fall lmao. Just want to try to get ahead on this stuff if I can through networking and shit.

>>12048863
I believe some math undergrad people will take the LSAT and get a law degree.

Friends, I have come up with a new form of indices. It is regular polygons, up to pentagon, acting like base-6 in that if you need more than 5^n indices, you write n pentagons and then a fewer-sided shape. The benefit of this over using a letter and subscript is that they look to similar and are confusing, and you can't write actual numbers for your indexes because those will be mixed up in calculation.
>for a small enough quantity, you can also write a polygon within another polygon instead of writing them side by side to indicate going to the next place value

>>12048958
I wouldn't worry about applying to internships straight out of high school. Take the calc sequence + linear algebra your first year so you can put it on a resume.

>>12048959
Ah, I'm not interested in law. It's either physics, neuroscience, or biochem that I'd want to do. Neuroscience/biochem for immortality research, physics cause advanced physics is interesting

>>12048967
I'm using this rn btw. It works nice but pents are a bit hard to draw so you may stop at squares. For 1 and 2, draw a forward slash and a + or T

>>12044852
remember that's the ratio, not the value of the function. The function converges when that value is less than 1. So what needs to be true?

>>12048979
To be honest, I don't know. I ended up starting over and found an easier way to solve the problem and went with that instead.

>>12048972
There is mathematical physics. Maybe look into something along those lines. So differential geometry, Lie algebras, etc.

>>12049064
Nothing wrong with mathematical physics.

Why does every algebraist I encountered in my undergraduate career try to shill algebra to me? No, I want to do Analysis and that's what I'm doing, fuck algebra.

>>12049266
Algebra > analysis
Simple as.

>>12049279
why not do both?
>t. harmonic analysis chad

>>12048766
I don't know what you're referencing I only remember events that are important for my survival and things that surprised me. What was the nature of our conversation?

>>12049441
I enjoy both, but I find algebra a lot more fun and interesting.

>>12049457
>fun
there's your problem, math isn't about fun.

>>12049467
I disagree.

>>12049474
You're confusing the process with the aim. Math exists to elaborate human reason, people that are mentally ill have fun pursuing this goal. There's nothing to disagree about this is an objective and inviolable truth about the world.

my math department requires taking a silly computation-based linear algebra class before taking the real one (plus a homo "proofs" course)
realized so in the first lecture
would the professor let me in if i asked nicely during office hours?

Has anyone here played with 3D modelling programs like Blender? It's like a playground applying mathematical knowledge, I feel like a kid again

>>12049521
Yes, I did exactly that and got to skip the tard Lin Alg course for engineers. Just make sure you can back up your claims to being ready for the course. Often that might include having to show some type of self study or previous competence in classes at that institute. Showing your transcript might be a good substitute or telling them you've been studying out of a more difficult book. Don't pay for classes that are insultingly low level if you can help it.
>>12049523
Not Science and not Math get the fuck out.

>>12047860
>Rote memorization is a powerful tool, and strengthens working memory, attention span, and mood regulation
seethe... there's nothing "powerful" about doing arithmetic (as you explicitly mentioned calculators (not TI ones))
>This is why you become fast at computation
computer can still do it faster. making sure you didn't make fundamental errors is way more important.
number literally don't matter that much as

>>12047961

>and the value of doing computations by hand
if some isn't interested in numerical methods, or isn't stranded on the desert then what's the value of calculating actual "numerical" result by hand, other than just winning dickwaving contest?

>>12049534
>3d graphics
>not math
keep your salt in the drawer

>>12049521
My university partitions linear algebra and diff eqs into courses for e*gineering majors and math majors, so I never had to take a computational based one. I'm confused as to why linear algebra isn't universally taught proof based, though, if you actually learn the underlying machinery of the field, all the calculations will be really intuitive and fall into palce.

>>12049546
It isn't taught that way because of engineers and computer science idiots that have to take it as a core requirement for their degrees. Almost all unis make these kids take Calc I-III, Lin Alg, Intro Stats, and Diff Eq if engi and they are too fucking stupid to do any of this in a rigorous or interesting setting so they create separate classes for the computational and "formal" aspects of the topics. It's the same reason that "analysis" is really calculus plus intro real analysis in some places in europe but that isn't a thing at all here in the states. Universal education was a terrible mistake.
>>12049545
I'm not talking about adding things in your head though of course that is a very valuable practical skill which you would know if you had ever worked in a lab before. I'm talking about working out any kind of computational problem in your head or on a piece of scratch paper quickly.

>>12049534
redpilled
i was partway through hoffman&kunze over the summer, i'll be ready to bring it up.

>>12049580
I understand that, I just think that regardless of major everyone would benefit from LA being taught in a mathematical way. Without any sort of rigor, almost all the computations you do will seem very arbitrary and unmotivated. There's not much use in computing things if you don't actually know what it is you're computing and why.

>>12049580
That's sort of the way aroudn here yeah. Engineers and the like have the worst of both worlds. Rigurous classes with purely computational excersises, and requiring you to maybe recite a proof from memory

>>12049441
>Harmonic analysis
Elaborate? I enjoy both analysis and algebra

>>12048383
This image is so awful that it makes me laugh

What's an example of [math]\sup (A \cap B) < \min \{\sup (A), \sup (B)\}[/math]?

>>12049741
A={0,1}
B={0,2}

>>12049713
https://en.wikipedia.org/wiki/Harmonic_analysis
>>12049606
good luck, if you come off confident but not pushy they'll probably ascent to your request.

I'm taking abstract algebra this semester and I am curious as to why relations and as a consequence equivalence relations are so important in math? I understand what they are, but I think i'm missing how they play an important role in math, and why we study them.

>>12049940
Equivalence relations let you partition any set into a disjoint set which allows us to compare elements to one another even if they aren't equal in the traditional sense.

They also show up everywhere and are very useful; for example, the construction of [math]\mathbb{Q}[/math] is done with an equivalence relation.

>>12049940
Equality in terms of strictly element identity is quite trivial. Equivalence relations allow one to essentially collapse down into a set by mapping equivalence classes to a point and define 'internal structure' in this manner. In turn, they essentially define the entire concepts of quotients, which are utterly important, showing up in abstract algebra, analysis, and topology. It should be noted they serve another role and that is being able to define certain structures with certain 'equality' even if if their sets are not equal [say, think of an isomorphism, which is an equivalence relation on the class of groups]. In the the application mentioned by anon, two rational sequences are defined as equal if their difference converges to 0.

>>12050004
(Whoops, I should extend a bit-the real number identified is what that rational number should 'approach', but the real number is defined by this sequence since we don't apriori have the numbers that these rationals approach (say, root 2)-the equivalence relation allows this unique definition since all sequences that 'converge' likewise are identified as the same sequence or real number. In fact, this process can be used to complete any metric space and it is called the completion.

>>12048511
if f is differentiable at z (in the real sense), then there is a linear mapping J such that
f(z + v) = f(z) + J(v) + r(v), where r(v)/|v| approaches 0 if v approachea 0. In this case J is the jacobian at z. cauchy riemann equations now just says that you can view J as a complex number

I wonder if there's a good reason to except the particular four polynomials P(x,y,z) that make for this fraction.

An ant searches an [math]N \times N[/math] grid [math]\mathcal{G}[/math] for some target node [math]\tau[/math]. Each node [math]v \in \mathcal{G}[/math] is equipped with a pointer to one of its neighbours, and following all such pointers forms a shortest path from [math]v[/math] to [math]\tau[/math]. That is, the pointers guide the ant towards the target. But due to noise, each such pointer points in the wrong direction instead, with some probability [math]q[/math] (independently of other nodes).

For this task, the ant keeps track of a "heat map" of [math]\mathcal{G}[/math], estimating [math]\tau[/math]'s location based on all the advice it has seen so far. It assigns scores to unexplored nodes (nevermind how), and greedily walks to the highest-scoring node, until it discovers [math]\tau[/math] and terminates.

Let [math]d[/math] be the distance from the ant's starting point to the target. How do I even begin to analyze the expected number of moves w.r.t. [math]d[/math]? This isn't a random walk - the ant's decisions are deterministic, yet the environment itself is random. Does anyone have a reference for this sort of analysis on graphs? Or any ideas just to get me started?

some good undergrad stat books for mathematicians to recc? I'm taking it next semester, want to read up on it

>>12050698
It’s called fuck stats. Anything you do at an undergrad level will be horrible uninspired trash.

>>12049769
sperged out. he called the proofs class "important"
it's over lads

>>12048383
what a pic