/mg/ maths general

[Anonymous No.12051256]

talk maths
formerly >>12042691
good vibes edition

[Anonymous No.12051288]

Bit of a math noob here
How do you know if a series converges or diverges?

[Anonymous No.12051316]

>>12051288
There is a list of commonly known convergence criteria you can check.

The most convenient case however is in the p-adics. There a series converges iff its sequence of summands converges to 0.

[Anonymous No.12051320]

>>12051288
This belongs in the stupid questions thread. Read up on series convergence tests - D'Alembert's ratio test, Cauchy's [math]n[/math]th-root test, etc. In general, there's no bullet-proof technique, in fact for some series it's an open question whether they converge or diverge.

[Anonymous No.12051336]

Can one hear the shape of a boob?

[Anonymous No.12051493]

>>12051256
Currently learning about Pareto-optimality, and it occurred to me that [math]\inf[/math] is not a norm (unlike [math]\sup[/math]), but it does satisfy all the axioms if the triangle inequality is inverted; i.e. [math]\inf(|x+a|,|y+b|) \geq \inf(|x|,|y|)+\inf(|a|,|b|)[/math]). Is there a name for this kind of function?

[Anonymous No.12051521]

>>12051493
reverse triangle inequality

[Anonymous No.12051548]

>>12051336
haha it would be hilariously if she had armpit hair haha

[Anonymous No.12051560]

Seeking help, I think its 2eq 2 unknowns

[Anonymous No.12051570]

hi bros, don't know if this is the right thread.

i'm in the UK and about to go into final year for my BSc Mathematics course and I cant decide on which of 2 modules to pick.
I'm not really sure what I wan't to do with my degree, and I feel kind of lost career path wise, can anyone break down the modules and what careers they open my up to and what you would recommend.

Financial Maths:
"The first aim of this module is to introduce students to the main instruments that are traded in the financial market place and to their practical uses for investment, hedging and speculation. The second and major aim is to equip students with an understanding of mathematical models and solution techniques that are currently used in the newly emerging field of financial engineering. Practical calculations with real and current financial data will illustrate the theory."

Coding and Cryptography:
"This module provides the student with a fundamental knowledge of contemporary mathematical communication theory, ranging from entropy as a measure of information, through robust methods of encoding data via error correcting codes, to means of making messages secure by encryption."

[Anonymous No.12051582]

>>12051570
Financial maths: Finances/Business
Cryptography: Comp sci or fbi

[Anonymous No.12051591]

>>12051560
>>>/sqt/

[Anonymous No.12051592]

>>12051570
financial math sounds boring as fuck, unless its has a lot of stochastical analysis

[Anonymous No.12051602]

>>12051162
don't get your panties in a bunch, recommend a good statistics book then
doesn't have to be undergrad because I'm not retarded

[Anonymous No.12051619]

>>12051591
Ty
Hours of thinking, ask once and it answers itself

[Anonymous No.12051627]

>>12051582
comp sci isn't really that interesting to me, im in the UK so im not sure FBI would apply.
I've also picked fluid mechanics so I'm leaning towards Financial, still not sure what I do career wise though.
Does it really matter what I pick if I'm unsure what I want to do career wise?
>>12051592
I emailed the lecturer and he said he would be covering things like the Black-Scholes model

[Anonymous No.12051630]

What's the difference between arbitrarily chosen, randomly chosen and related statements?

[Anonymous No.12051651]

>>12051630
Arbitrary chosen means that it doesn't matter how it is chosen. Randomly chosen implies that there is some probability distribution. If the distribution is not given, and a uniform distribution exists, then that is probably the default. Note that there is no uniform distribution over the integers as a whole,or over the real numbers as a whole.

[Anonymous No.12051652]

>>12051627
Oops meant nsa not fbi. Wrong type of spying. UK should have an equivalent probably.

Honest to god it doesn't matter a ton what classes you take unless there is a job that specifically requires them. Coding and crypto is basically %100 algebra, so if you don't like that, then go with financial

[Anonymous No.12051730]

Shamelessly reposting from former thread. Any ideas would be appreciated.

An ant searches an N-by-N 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 [math]v \longrightarrow \tau[/math]. That is, the pointers guide the ant towards the target. However due to noise, each pointer might point in the wrong direction instead, with some probability [math]q[/math] (independently of other pointers).

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 position to the target. How do I even begin to analyze the expected number of moves w.r.t. [math]d[/math]? This isn't quite 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?

[Anonymous No.12051800]

>>12051652
thanks bro, big help, I prefer the more 'practical' side of maths like calculus so this makes it easier for me to pick, ty for the help

[Anonymous No.12051895]

>>12051800
>I prefer the more ‘practical’ side of maths
Please go and never return.

[Anonymous No.12052191]

>>12051316
How are those criteria proven to begin with, like 1/n converging and 1/n^2 not? Is there a formalism for seeing if there's a linear basis of functions that spans some set of functions?

[Anonymous No.12052196]

>>12052191
er 1/n not and 1/n^2 yes converge

[Anonymous No.12052208]

>>12051288
just calculate the first few terms

[Unclamped No.12052515]

>>12052208
How do you know the series doesnt have two asymptotes like chemistry titration sometimes does

[Anonymous No.12052520]

>>12052208
How do you know it doesnt have two asymptotes like a chemical titration function

[Anonymous No.12052522]

redpill me on symplectic integrators

[Anonymous No.12052523]

>>12052191
Nigger read a fucking real analysis textbook

[Anonymous No.12052541]

>>12052523
Rec me one?

[Anonymous No.12052551]

>tfw got so absorbed into math today that I forgot going to the gym before it closed
math olympiad style problems are a lot of fun but they take too much time

[Anonymous No.12052577]

>>12052520
fuuuuckk

[Anonymous No.12052747]

Can you work in Aerospace with applied math?

[Anonymous No.12052748]

>>12052520
god i fucking hate titration

[Anonymous No.12052815]

>>12052541
tao or rudin

>>12052747
>applied math
not math or science

[Anonymous No.12052900]

What do you think about Bourbaki's elements ?

[Anonymous No.12052907]

>>12052900
all bourbakist criminals should be shot

[Anonymous No.12052919]

Is there a more satisfying feeling than reaching that blank page between chapters?

[Anonymous No.12052947]

>>12052919
Yes, turning the page.

[Anonymous No.12052954]

>>12052919
yes, having sex

[Anonymous No.12052968]

>>12052919
Coming up with a nicely constructed proof.

[Anonymous No.12052977]

>>12052196
>>12052191
[math]\sum_{n=1}^{\infty}\frac{1}{n^x}[/math] converges for [math]x\leq 1[/math] and diverges for [math]x> 1[/math].

You can find many proofs by googling. Talking about googling, one of the first results would be
https://mathcs.clarku.edu/~djoyce/ma122/posseries.pdf
which describes many different convergence tests.

[Anonymous No.12052992]

>>12052947
True, the new beginnings of a new chapter is a great feeling.

>>12052954
No, I have had sex and it doesn't compare. It is carnal, while the page turning is pure.

>>12052968
A nicely constructed proof is a different feeling. More like setting things in order. An elegant proof is the best, most clean order there is. But it is different in the same way tidying your room is to climbing over a hill. The hill is unexplored, and inviting. The tidying is satisfying, yet does not call to the soul.

[Anonymous No.12053045]

>>12051800
Yeah no worries bro, have fun! Nice dubs btw

[Anonymous No.12053052]

/mg/ is dead lol

[Anonymous No.12053087]

>>12053052
The semester started.

[Anonymous No.12053096]

Does /mg/ prefer semester system or quarter system. My uni does quarters

[Anonymous No.12053102]

>>12053096
How do you even get anything done in a subject that only runs for a quarter?

[Anonymous No.12053108]

>>12053096
trimesters

[Anonymous No.12053140]

>>12053087
summerfags haven't fucked off yet.
>>12053102
you just work slightly harder and learn slightly less than semesterfags. it sucks

[Anonymous No.12053148]

>>12053087
The semester doesn't start for another week and a half

[Anonymous No.12053168]

>>12053102
Most undergrad classes are broken up, so if a normal uni would just have one intro to analysis class, we’ll have one in fall quarter and the next in winter

[Anonymous No.12053264]

>>12052747
Yeah but you're going to be competing with actual engineers who have domain knowledge. Applied math is a little bit of an awkward undergrad in my opinion (I am assuming you are an undergrad). Unless your school has a well structured major (i.e. you have to take some basic comp sci and your math classes are actually still rigorous), I recommend you either double major or just do a proper math major.

[Anonymous No.12053329]

>>12051256
Let [math]A[/math] be an invertible matrix such that all elements of [math]A[/math] and [math]A^{-1}[/math] are integers. Show that [math]|A| = \pm1[/math]
Help anons

[Anonymous No.12053391]

>>12053329
Kinda tired so I don't know if this will work, but if the inverse matrix also only has integer entries, then because the determinant of the original matrix must be an integer, then it must divide every entry of the inverse matrix. Then by using the Laplace expansion of the determinant, Y think you can prove that this can only happen if it is 1 or -1.

[Anonymous No.12053447]

What are the prerequisites for learning algebraic geometry?

[Anonymous No.12053472]

>>12053447
Finish analysis first before falling for a meme

[Anonymous No.12053489]

>>12053391
You don't really need any of this, you just need that the determinants are integers and that det is multiplicative.

[Anonymous No.12053491]

>>12053489
lmao you are right

[Anonymous No.12053509]

>>12053447
Basic commutative algebra and basic point set topology. Learn classical algebraic geometry (varieties) before you learn modern algebraic geometry (schemes).

[Anonymous No.12053614]

>>12053447
classical algebraic geometry:
>linear algebra
>projective geometry
>basic algebra/ commutative algebra (any course that covered galois theory should be enough)
>basic notions of topology
modern algebraic geometry:
>classical algebraic geometry
>autism

[Anonymous No.12053617]

>>12053329
undergrads are not allowed to post anime girls

[Anonymous No.12053723]

>>12052977
looks like you got your domains flipped

[Anonymous No.12053783]

Can you do anything interesting with sequences that have a beginning and an end?
If you have a tuple of sequences a_n and b_n, you could consider this a double ended infinite sequence
a_1, a_2, a_3, ....., a_3, b_2, b_1
Maybe there could be interesting variations of the usual definition regarding sequences.

[Anonymous No.12053849]

>>12053783
I believe this is called a vector

[Anonymous No.12053857]

>>12053849
sequences are already vectors. He's just giving a finite list.

[Anonymous No.12053926]

>>12053783
I think Cantor's first proof for the uncountability of the reals makes use of a sequence like this.

[Anonymous No.12053961]

>>12053045
Thank you!

[Anonymous No.12054055]

>>12053849
>>12053857
they're supposed to have infinitely many numbers in the middle. It's literally just 2 sequences where we "interpret" them as a sequence with an end... But that would only be interesting if there is one can find some nontrivial structure

[Anonymous No.12054056]

>>12052907
>>12052900
bourbaki is the best after category theory

[Anonymous No.12054073]

>>12051256
When you're done with your algebraic abstract nonsense, here's something you should be able to solve if you're any good at complex analysis.
Let [math]\psi(t)=\sum_{n\in\mathbf{Z}}e^{-n^2\pi t}[/math], and show that
[math]\psi(1)=\frac{\sqrt[4]{\pi}}{\Gamma(\frac34)}[/math]

If you can't do this, don't post about sheaves ever again.

[Anonymous No.12054098]

>>12051336
you can with enough LSD

[Anonymous No.12054184]

>>12053723
>looks like you got your domains flipped
Yep, fuck. Not sure how I fucked that up.

[Anonymous No.12054218]

>>12051560
r0 = 0 m , r = -46 m, a = 10 m/s^2, t = 5 s,
solve for v0 = -34.2 m/s

[Anonymous No.12054414]

>>12054073
>something you should be able to solve if you're any good at complex analysis
/mg/ fucking sucks at analysis though

[Anonymous No.12054497]

[Anonymous No.12054589]

>>12054055
Look up ordinal numbers. You can use those numbers to index your sequences which are infinite but have a final entry.

[Anonymous No.12054598]

>>12054073
muh gamma

no

[Anonymous No.12054599]

>>12054414
Those analysis people must not like 4chan very much for some reason.

[Anonymous No.12054614]

>>12054599
almost no nontrivial analysis problems ever get solved here
The only one I remember seeing recently was that one that Slovenian posted and even then /mg/ pussied out with not a single serious attempt before asking him for the answer

[Anonymous No.12054617]

https://math.stackexchange.com/questions/1734104/what-is-advanced-calculus

Is this true?

[Anonymous No.12054632]

>>12054497
muh primes

no

[Anonymous No.12054639]

>>12054073
>When you're done with your algebraic abstract nonsense
ok pussy, have fun with your shitty analysis

[Anonymous No.12054651]

>>12054073
kek this won't get solved
it's actually shameful how badly this general gets triggered by analysis

[Anonymous No.12054688]

>>12054073
Bruh
I remember a problem like this was posted a few months back, someone did solve it, I praised him for what I thought was an excellent solution, and then someone felt the need to insult the solution for no reason at all.

[Anonymous No.12054958]

>>12054599
wdym? We have Tooker, the king of analysis

[Anonymous No.12054967]

>>12054598
>>12054632
>>12054639
>>12054688
such bad attitudes to math

[Anonymous No.12054976]

>>12054967
It's just a troll, don't feed them. I think it's true that this group skews towards algebra and topology, but I don't think most of us have any real dislike of analysis.

[Anonymous No.12055148]

i^3 written in a+bi form is 2i.
can someone tell me how? I'm stuck. :(

[Anonymous No.12055185]

>>12054617
Yes. What about the answer to this question was unclear to you?
>>12055148
>>>/sqt/

[Anonymous No.12055260]

>>12055148
[math]i^3=-i[/math]

[Anonymous No.12055276]

>>12051256
I have an odd goal here.
I'm creating a table in FreeCAD and to calculate the height of the bar I want to multiply the width of the bar top (2ft) by phi ((1+sqrt5)/2).
Then I would like to take that result and find the closest multiple of 1/16th or 0.0625, greater or lower than the original result.
I'm not good at math so how would I find the GCF, the LCD, compare the two and see which is closer?

[Anonymous No.12055299]

>>12054073
what have you tried?

[Anonymous No.12055304]

>>12055299
Pretty sure from the wording it's put to anyone in the thread who wants to solve it as an analysis challenge.

[Anonymous No.12055346]

>>12051256
Ok that's nice and all but what do you do with all these vectors pointing in different direction, how do you begin describe them, what about the distance of each charge, do you have a function that can give you them? How does this work in paractical terms?


fucking physics professors introducing conecpts before the math, fuck handwaving !

[Anonymous No.12055355]

>>12055346
>>12055276
please post these questions in /sqt/ this is not the place to ask.

[Anonymous No.12055361]

>>12055346
That seems fairly clear to me though

[Anonymous No.12055373]

>>12055355
Shut up, it's not like you guys are solving the reimann hypothesis here, i'm sure some math anon would be happy to answer my question.
>>12055361
What do you do with all the infinitesemal vectors factor, the idea is nice but how would this actually work? and how about ''r'how do you define a distance function for each point on the surface to integrate in the first place?

[Anonymous No.12055399]

>>12055346
Vector fields

[Anonymous No.12055402]

Can you guys solve IMO problems? can you even begin to understand the solutions? can you solve pic related in 1.5 hours? do you have a future in math if you can't?

[Anonymous No.12055417]

>>12055402
I just do them for fun and don't get hung up if I can't figure it out. If I can't I usually read through some correct answers and try to learn.

[Anonymous No.12055419]

>>12055417
I mean if you can solve any of them, you're 20 steps ahead of the curve, like i said, i can barely begin to understand the solutions.

[Anonymous No.12055424]

>>12055419
Rome wasn't built in a day, and neither is knowledge. Just keep trying, I believe in you.

[Anonymous No.12055427]

>>12055373
you’re asking an utterly retarded question that you could answer by reading your fucking textbook you drooling nigger monkey freshman. get the fuck out of this thread

[Anonymous No.12055436]

>>12055424
>>12055427
The duality of /mg/

[Anonymous No.12055440]

>>12055436
I try to support my 4chan bros because I know that most of us are borderline schizoid and positivity helps

[Anonymous No.12055442]

>>12055304
That poster was implying it was some kind of homework question posed as a challenge in order to elicit an answer.

[Anonymous No.12055448]

>>12055427
We've solved some examples but it was through symmetry, i'm just wondering what the maths is actually like.

[Anonymous No.12055449]

>>12055304
>analysis
>challenge

[Anonymous No.12055453]

>>12055402
Lmao in some cases several judges have been shown to be unable to solve problems from their own area. I wouldn't get too tweaked out about it.

[Anonymous No.12055456]

>>12055442
There's no chance that's a homework problem. That's not an easy series to evaluate in closed form.

[Anonymous No.12055461]

>>12055453
it's true, and the problems have gotten exponentially harder over the year, but still the kids who solve this in 1.5 hours are the one who's going to win field medals and make names for themselves, the rest would just wagecuck.

[Anonymous No.12055473]

>>12054688
kek that was me
Felt pretty shit to have someone insult me for knowing too many identities, not gonna lie

[Anonymous No.12055474]

On the topic of it, can somebody explain Vietta Jumping to me as if I am 5 years old?

[Anonymous No.12055501]

>>12055440
kys

[Anonymous No.12055509]

>>12055474
maybe

[Anonymous No.12055512]

>>12055501
I love you too, buddy.

[Anonymous No.12055545]

>>12055474
You should really use the subjunctive

[Anonymous No.12055559]

>>12055474
>>12055509
>>12055545
What are you my mother?
WOULD somebody please explain Vietta Jumping as if I am a 5 year old?

[Anonymous No.12055596]

>>12051630
no difference

[Anonymous No.12055608]

>>12053329
since det is calculated solely by multiplying and adding elements of the matrix, the result is an integer in both cases.
but it also holds that det(A^-1) = 1 / det(A)
so 1 and -1 are the only possible solutions, otherwise we'd have an integer 1/n with n>1

[Anonymous No.12055620]

>>12054617
yes

[Anonymous No.12055626]

How do I integrate using u-substitution when there is no du/dx/dt, etc, at the end of the integral?

[Anonymous No.12055634]

>>12055626
Are you integrating over a manifold or something?

[Anonymous No.12055683]

The math here is probably trivial, but you guys are high IQ so this place is my best bet. Can you do this one faggots?

[Anonymous No.12055715]

>>12054073
Because [math]\phi(1)[/math] appears in physics as the partition function for a quantum particle in single infinite well and I've never seen such identity i'm afraid that maybe the identity just holds for those particular values put not in general. Anyone who knows if this is true?

[Anonymous No.12055769]

>>12054073
that was in ramunajan's notebooks, jacobi theta
>>12055715
retarded physics nigger. lmao

[Anonymous No.12055778]

>>12055715
drooling retard

[Anonymous No.12055788]

>>12055769
>>12055778
I know it's not a fucking proof faggot, but I was trying to see if there was a more general relation between the gamma function and [math]\psi[/math] defined for the real positive plane. But then I remembered that in that class there was never such a nice identity and we used the gamma function a lot, so I was just asking if it is pointless to try and find a more general identity.

[Anonymous No.12055828]

>>12054497
kek retarded math, better than 3blue1shit tho

[Anonymous No.12055844]

>>12055683
low iq post, try /x/

[Anonymous No.12055850]

>>12055828
tbf he said he doesn't really prefer doing the olympiad videos they just get a lot of views.

[Anonymous No.12055870]

>>12055683
It’s E. The numbers at the top repeat exactly the same except dubs are changed. If you look at the dubs it corresponds with what number the dominos add up to and the final dubs is nine

[Anonymous No.12055890]

>>12055870
eggstremely based

[Anonymous No.12055899]

>>12055870
Can you do this one??

[Anonymous No.12055907]

>>12055899
nvm, I got it, Im retarded, [\spoiler] B[\spoiler]

[Anonymous No.12055919]

>>12055870
How about this one

[Anonymous No.12055950]

>>12054497
cunny

[Anonymous No.12055958]

>>12055950
CUNY as in City University of New York, Michael is volcel and hates pedophiles

[Anonymous No.12055960]

>>12051336

https://youtu.be/sL73RYikETw

tl;dw, problem is open in 3d, but for 2d shapes close enough to a ball yes, so you can hear the shape of a boob provided it belongs to an anime girl with perfectly formed cups.

[Anonymous No.12055963]

>>12055958
>hates pedophiles
didnt he explicitly say that somewhere? kind of a weird thing to articulate

[Anonymous No.12055970]

>>12054967
math =/= analysis

[Anonymous No.12055974]

>>12055963
When he declared loyalty to the coming 4th Reich in one of his now private videos he said that he was going to personally scalp and immolate all cunny posters on /tv/. I expect him to consecrate the completion of his analysis series with a ritual sacrifice of at least a half dozen cunny posters in the manner of the ancient vedic fire rites.

[Anonymous No.12055977]

>>12055974
>/tv/
no complaints here

[Anonymous No.12055980]

>>12052522
they are like the numerical analysis equivalent of writing software without memory leaks, i.e. always prefer them

[Anonymous No.12056084]

>>12055974
>vedic fire rites
based

[Anonymous No.12056129]

>>12055919
A but I am terrible at these.

[Anonymous No.12056188]

>>12055919
It’s E. This one was really hard. The “shape” that the dominos are in is completely irrelevant so just put them all in a line in your head. The bottom domino with an x on it must have its number on the top half cause that’s all our options. Then the top domino with an x on it has its number on bottom, that way the pattern goes 4 ups 6 downs then 8 ups. Now just take one string of continuous ups or continuous downs; I’ll use the 8 ups so it’s easier to see the pattern. It goes blank 1 blank 2 blank 3 blank 4 etc. so for the string of 8 ups it goes 41424344. For the string of 6 downs it goes 313233. For the string of 4 ups it goes 2122

[Anonymous No.12056222]

>>12053391
I don't understand but thanks
>>12053489
>>12055608
Thanks, it's the answer that I needed
>>12053617
I'm not a math student

[Anonymous No.12056289]

Is there a good way to define the exponential function (that is a^x, where a is non-negative) that does not involve the power series?

For example the trigonometric functions can be defined in terms of a power series, but also have a more immediate definition in that of the unit circle, or even of a right triangle. Does the exponential function for non-rational powers of x also have something like this?

[Anonymous No.12056386]

>>12056289
How on earth you reach power series without ever having seen the exponential function? Usually you start with shit like compound interest...

[Anonymous No.12056423]

>>12056289
[eqn] e^x=\lim_{n\rightarrow \infty} \left(1+\frac{x}{n}\right)^n \\
\ln(x)=\int_1^x \frac{1}{t}dt \\
a^x = e^{x\ln(a)}=\lim_{n\rightarrow \infty} \left( 1+\frac{x\cdot\int_1^a \frac{1}{t}dt}{ n}\right)^n [/eqn]

[Anonymous No.12056427]

>>12056386
Exactly, it would be nice to have a more "basic" definition of it.

>>12056423
e^x there is just the power series definition in disguise.

[Anonymous No.12056433]

>>12056427
[math] {\displaystyle e^{x}=1+{\cfrac {x}{1-{\cfrac {x}{x+2-{\cfrac {2x}{x+3-{\cfrac {3x}{x+4-\ddots }}}}}}}}} [/math]

[Anonymous No.12056453]

>>12056433
I'm not sure that's any better. Seems unfortunate that there is no basic definition when generalizing a^x to irrational x. Leads to a strange break when explaining it to young children, they easily understand a^x when x is an integer, as well as when x is a fraction (Provided you define a^1/x for integer x before). Having to go on a tangent about e and power series, and then redefining arbitrary a in terms of e, and then showing that this new definition behaves as our old one for rational x is such a bore.

[Anonymous No.12056461]

>>12056453
>Seems unfortunate that there is no basic definition when generalizing a^x to irrational x
Just say it's continuous

[Anonymous No.12056496]

>>12056461
This is a good suggestion. Thanks.

[Anonymous No.12056528]

>>12056289
Define exp(x) to be the function such that it equals its own derivative. And exp(1)=0. I think Picard-lindelöf says that definition is unique

[Anonymous No.12056532]

>>12056453
Literally just define it using Cauchy sequencea like you do for the square root of an arbitrary real number. NBD

[Anonymous No.12056692]

Is there a simpler/more compact way to express [math]i^{n \: \mathrm{mod} \: 2}[/math] for [math]n \in \mathbb{N}[/math]? I just want to bounce back and forth between the positive real and imaginary axes in the complex plane, rather than cycling through the negatives (like [math]i^n[/math] would do).

[Anonymous No.12056715]

>>12056692
[math] i^{2n} [/math]

[Anonymous No.12056719]

>>12056188
genius, I have some moar if you like.

[Anonymous No.12056730]

>>12056692
[math] |i^n| [/math]

[Anonymous No.12056748]

>>12056692
[math] \frac{\cos(n\pi)+1}{2}+ i\frac{\sin(n\pi)+1}{2} [/math]
Hope I didn't fuck it up this time

[Anonymous No.12056758]

>>12056719
Sure but where are you getting these from?

[Anonymous No.12056780]

>>12056748
I appreciate the effort, but I would hardly call that more compact.
It's just an aesthetic thing, so it's fine anyway.

[Anonymous No.12056786]

Is teichmuller theory the highest level of math?

[Anonymous No.12056787]

>>12056758

[Anonymous No.12056793]

>>12055769
>>12055788
There is a more general relation for rational values but it's very complicated.
You can actually attack this via the residue theorem or otherwise whenever you see ratios of radicals of pi to the gamma function it's almost always a clue it's coming from a singular value of the elliptic modulus.

[Anonymous No.12056795]

>>12056758
A friend sent me these some time ago, its from a high end IQ test, 160+.

[Anonymous No.12056822]

>>12056795
Do you know how much time they had on these and how many they had to answer?

[Anonymous No.12056900]

>>12056822
Its like 40 questions total, ~20 are trivial if you can get the above ones. In total it's a full day thing, 10hours recommended minimum.

Wat iz your IQ if you don't mind me asking? I imagine you have PhD in triple integrals or something.

[Anonymous No.12056955]

>>12056900
I haven’t taken an actual iq test so I don’t know. I honestly don’t think they test anything other than solving puzzles

[Anonymous No.12056983]

Lads i can't do algebra beyond knowing bomdas but i plugged this cunt into 3 algebra solvers on the internet and each one gave a different answer
Can you give me a site that actually works? only need to chimp my way through one actually hard economics course

[Anonymous No.12056989]

>>12056793
>You can actually attack this via the residue theorem
How? The only thing I can think of is to integrate [math]\oint e^{-\pi z^2}\cot\pi z dz[/math] over a circle enclosing some poles and then let the radius go to infinity, but that integral seems hard to evaluate

[Anonymous No.12056995]

>>12056955
>anything other than solving puzzles
yeah but solving puzzles is useful in literally all of life, correlates well to everything

[Anonymous No.12056997]

>>12056955
Yeah solving puzzles you haven't seen before is literally how they measure fluid intelligence.
People who say it doesn't work because you can train to get good at an IQ test by practicing these and therefore it only measures your skill at taking an IQ test are doing nothing more than destroying the ability of the test to give you a new type of problem and thus inflating their scores artificially.

[Anonymous No.12056998]

>>12056983
have you tried not being a brainlet?

[Anonymous No.12057000]

>>12056998
I'll pass it on to my mums uterus to do better next time

[Anonymous No.12057131]

>>12054614
what slovenian? post his question

[Anonymous No.12057137]

Math is all about memory. Being able to hold a lot of things in your mind while also being able to manipulate them.
It's not a coincidence that Euler could repeat the Aeneid of Virgil from beginning to end without hesitation, and for every page in the edition he could indicate which line was the first and which the last.

[Anonymous No.12057209]

>>12057137
All learned European men could recite the Aeneid from memory back then. It was part of the curriculum.

[Anonymous No.12057418]

>>12051256
How much of this would you feel confident doing in a timed setting where your future is at stake?

I’m thinking about applying to the UPenn Applied Math program and apparently first year grads are required to do a test like this:

https://www.amcs.upenn.edu/sites/default/files/prelim_review2.pdf

[Anonymous No.12057421]

>>12057418
https://www.amcs.upenn.edu/exams/written-preliminary-exam

[Anonymous No.12057425]

>>12057209
All 9,896 lines?
Highly doubt it.

[Anonymous No.12057436]

>>12057131
Not analysis, more linear algebra, but it was:
Show that in [math]\mathbf{Z}/2\mathb{Z}[/math] the diagonal of any symmetric matrix is in its column space.
I'll admit the answer isn't exactly obvious, but /mg/ gave up pretty much instantly.

[Anonymous No.12057447]

>>12057436
I still don't understand the solution...

[Anonymous No.12057464]

>>12057447
The proof was fine, he just omitted simplification and some explanation of why you didn't need to consider other cases, but there aren't any fancy concepts being invoked.
I followed the thing through myself and that clarified it for me.

[Anonymous No.12057704]

>>12057209
Absolutely not

[Anonymous No.12057737]

I made this math puzzle where you have to determine the length of the red line segment. With the given numbers 1, sqrt(2) and 3 the result is 6. I found a way to show this by using the area of kites. However, do you see a simpler solution or a different way? I feel like I am missing something very obvious.

[Anonymous No.12057738]

>>12057436
It's not exactly shocking that a lot of stuff like that goes unsolved. We're mostly undergrads plus a few grad students (or beyond). Most of us don't have the ability to do these problems and those who do typically can't be assed to tex a solution to a problem on a Himalayan jetski aficionado forum so some sperg can roll into your local math department claiming it's theirs.

[Anonymous No.12057751]

>>12057737
Use the 3 and the sqrt(2) to show the dotted line passes through the point (2,4), the find the y-intercept of that line.

[Anonymous No.12057773]

>>12057738
>We're mostly undergrads plus a few grad students
Oh
I thought it was mostly grad students or beyond lol
That's disappointing
>>12057436 is still an undergrad problem though

[Anonymous No.12057777]

>>12057751
ahh, thanks! That looks simpler. Also, I didn't notice that it's just the sum of the coordinates of B'.

[Anonymous No.12057791]

>>12057773
>I thought it was mostly grad students or beyond lol
No, if you actually know some math you'll see that a lot of people are just spamming stuff they don't really understand. You'd think anonymity would cut down on the posturing, but people are very insecure.

[Anonymous No.12057798]

>>12056692
i(-1)^n
or
i^(2n+1)

[Anonymous No.12057808]

>>12057791
Last time I remember being here people were organising a read through of Hatcher's Algebraic Topology or something and I remember Hartshorne being discussed here, and as someone who doesn't know much about algebraic geometry since I went elsewhere with my own interests, I'd assumed there were a fair number of grad students here.

[Anonymous No.12057822]

>>12057808
¯\_(ツ)_/¯

[Anonymous No.12057879]

>>12057808
They're just outnumbered by the horde of undergrads. The most depressing posters in /mg/ are mathematicians who failed to make it. At worst this place can be like a realm of damned souls

[Anonymous No.12057900]

>>12057879
Who here failed to make it? I've never seen anyone talk like that here.

[Anonymous No.12057929]

>>12057900
Hm? I've seen a few. Often complaining aggressively about academia

[Anonymous No.12058148]

Algebra is the gayest subject, literally just homosexual symbolic manipulation where all intuition is based heavily on working memory. Compare this to analysis where one can intuit things by working with concrete examples and drawing and only needing algebra as machinery to verify your result.

[Anonymous No.12058160]

>>12058148
Yes, but we need to keep the trannies occupied with something. Also computing homology groups is a fucking chore so it's good to have autists give us tabels.

[Anonymous No.12058170]

>>12058148
you have to be 18 to post here

[Anonymous No.12058206]

>>12058148
You have that backwards.

[Anonymous No.12058274]

Why do we care about lattices?

[Anonymous No.12058283]

>>12058274
Symmetries of lattices are a fundamental idea that can be explained very simply, but when we actually construct the symmetries and invariants of lattices, we are led suddenly to some of the most gorgeous objects in analysis.
If you study up to this level in complex analysis the topic suddenly explodes into all of these different connections. It was the thing that really got me seriously into analysis, which I'd hated up to that point.

[Anonymous No.12058313]

>>12058148
what do you think "algebra" is ?

[Anonymous No.12058339]

>>12058313
They think it means «arithmetic», 100% for sure.

[Anonymous No.12058345]

>>12058313
The study of algebraic structures.

[Anonymous No.12058346]

>>12058274
The symmetries of objects form groups, the way subobjects are contained in each other form lattices. These are two very related and fundamental constructs.

[Anonymous No.12058363]

>>12057209
Based, its trve.

[Anonymous No.12058374]

>>12057209
Based.

[Anonymous No.12058391]

>>12057209
>>12058363
>>12058374
Source?

[Anonymous No.12058393]

>>12058391
Divine will

[Anonymous No.12058481]

>>12058339
>>12058313
>>12058206
>>12058170
Algebra trannies plz dialate and then kys

[Anonymous No.12058485]

>>12058481
Cope.

[Anonymous No.12058499]

>>12058481
As long as my bf keeps fucking my pussy on the regular I don't need to do that so I have more time to do algebra.

[Anonymous No.12058504]

>>12058499
>axe wound
>pussy
>>12058485
>look at this friking structure, it's so awesome!

[Anonymous No.12058528]

>>12058504
>axe wound
that would be extremely painful

[Anonymous No.12058536]

>>12058504
There's no chance that you actually do mathematics. You're definitely here to troll people, either because you think it's funny or because math is too gay/Jewish/liberal in your mind and this is how you rail against it.

[Anonymous No.12058539]

>>12058536
Ok nigger, keep telling yourself that while I finish my PhD in actual math.

[Anonymous No.12058540]

>>12058528
you're a big guy

[MD,500k,138IQ,GOD No.12058547]

>>12058499
>>12058528
Can I fuck you while Ur bf watches?

[Anonymous No.12058569]

>>12058547
I'm only one of those two posts, but yeah as long as you're a hot girl.

[Anonymous No.12058570]

>>12058528
>>12058540

[Anonymous No.12059053]

>>12056983
You entered it differently in each calculator you brainlet. The first one has the last term in the denominator put over 100 and the rest of them have it over 200. And in the last calculator you put 175 instead of 1.75

[Anonymous No.12059069]

Complex analysis >>> real analysis

[Anonymous No.12059081]

>>12059069
Yes

[Anonymous No.12059091]

>>12059069
>>12059081
Functional analysis shits on both of them.

[Anonymous No.12059094]

>>12059069
>>12059081
>>12059091
Harmonic analysis>Functional Analysis>Complex Analysis>Real Analysis

[Anonymous No.12059212]

Be careful with that complex analysis guys, the algebra people might hear you and start up with their abstract nonsense, claiming that it was invented to deal with this situation.

[Anonymous No.12059263]

>>12059212
But it was.
https://en.wikipedia.org/wiki/Fundamental_pair_of_periods

[Anonymous No.12060473]

Taking discrete maths this semester--which one of these are meme textbooks? Most of them are "supplementary readings" but I just want to know which ones are a waste of my time.

[Anonymous No.12060698]

>>12060473
anon where can I find these, I fucking looooove discrete

[Anonymous No.12060706]

>>12060698
I love discrete and higher combinatorics as well, but I'm afraid to ever talk about on here, I'm afraid /mg/ will make fun of me.

[Anonymous No.12060712]

>>12060706
you shouldn't care what other people think about you unless they're your close friends or family. everyone else is just a gauge for how close you are to the social average for that group and otherwise should be treated as noise. discrete is gay but that doesn't mean you have to be a faggot, if that makes sense.

[Anonymous No.12060726]

>>12060706
okkkkkk but can I have the twxtboox

[Anonymous No.12060731]

>>12060726
libgen, lurk moar if you didn't know how to get textbooks

[Anonymous No.12060854]

What other ways you can you construct the reals besides Cauchy sequences and Dedekind cuts?

[Anonymous No.12060860]

>>12060854
You take the complex number line and expand it

[Anonymous No.12060886]

>>12060854
this probably doesnt satisfiy your idea of constructing something, but the reals are the unique complete ordered field (up to isomorphism), so you can simply define them as such.

[Anonymous No.12060943]

Does it feel good to be back /mg/? I'm starting what is probably my last year in Bachelor's, should I kill myself?
>>12053447
in addition to what the other anons have mentioned, you should have some differential geometry under ur belt

[Anonymous No.12060954]

>>12060943
>I'm starting what is probably my last year in Bachelor's
I started mine 2 weeks ago.

[Anonymous No.12060957]

>>12060954
how close are you to rope

[Anonymous No.12060983]

>>12057418
looks incredibly doable
>>12057900
You must be new here
>>12060706
Discrete is based, talk about it
>>12060943
>should I kill myself?
Do a masters first, that'll make sure you don't regret it

[Anonymous No.12060986]

>>12060957
Not very. I very much enjoy both my classes and professors this semester.

[Anonymous No.12061158]

Alright, not a regular in /mg/ but thought I'd ask here because you guys are smart. Is an expression like x^2/x defined at 0 or not? Like, we can simplify it to just x, but the original seems to imply that it's not supposed to work at x=0.

Obviously this is a contrived example, but you get what I mean.

[Anonymous No.12061193]

>>12061158
You can make it defined at 0

[Anonymous No.12061205]

>>12061193
I know we can extend it to be defined at 0, but is it actually defined there as it stands?

[Anonymous No.12061219]

I have a linear maps f: V-> W and g:range(f) -> V. I want to extend g from the range(f) to the entire space f. V,W are not assumed to be finite-dimensional. Every proof I see of extending a linear map requires having V,W as finite dimensional. Any ideas how to proceed where V,W are arbitrary vector spaces?

[Anonymous No.12061223]

>>12061158
>>12061205
>is it actually defined there as it stands?
No
>we can simplify it to just x
Not at 0
>I know we can extend it to be defined at 0
Well that cuts on limit talk and the like

[Anonymous No.12061350]

There is a major drawback to this proof that every vector space has a basis:
unless the dimension is finite, or at least countable, it doesn’t give us any idea how
to actually find a basis. In fact, this is a serious problem with the concept of a
basis for infinite dimensional spaces in general. Although Zorn’s Lemma tells us a
basis exists, in practice, this fact may be useless if we do not have a procedure for
finding one. For this reason, bases are not often used for infinite dimensional spaces,
and mathematicians have come up with alternative ideas. A basis for an infinite
dimensional space is also called a Hamel basis to distinguish it from different but
more useful notions that will also be (confusingly!) called bases.

[Anonymous No.12061363]

>>12061350
what are you quoting from and what is your point?

[Anonymous No.12061377]

>>12055907
Why not D?

[Anonymous No.12061452]

>>12060854
You could honestly just take any set with the same cardinality as the reals and you could just find a way to give every element a “name” that corresponds to our normal representation of the reals. First thing I could think of is the set of functions from the natural numbers to the natural numbers. The only thing is that in order to call it a construction of the reals in good faith, you’d have to also define addition, multiplication, and an order and prove that it meets all the axioms that define the reals

[Anonymous No.12061458]

>>12061158
a/b is defined only if b is nonzero.
Therefore if we set x to 0 in x^2/x, we get 0^2/0, which is not defined because division by 0 is not defined.

[Anonymous No.12061469]

>>12061377
I’m the guy who solved the other ones I thought it was D too I just didn’t say anything. On a related note I always wondered how the creators made sure that there was only one “solution” to these puzzles, it’s not like you could ever make a proof that any solution is right

[Anonymous No.12061473]

>>12060473
Check exercises. I remember my discrete maths class had the best exercises of all first year math.

[Anonymous No.12061483]

>>12060854
yea, there is this rather obscure construction via almost linear functions, called Exodus reals

[Anonymous No.12061607]

>>12061483
Genuinely surprised I'd never heard or seen of this before. This is pretty clever and neat.

[Anonymous No.12061710]

>>12057137
>Aeneid of Virgil
Good thing you specified what Aenid you meant, I would never have been able to guess.

[Anonymous No.12061736]

>>12061710
Kek

[Anonymous No.12061868]

Anyone here into topoi theory ?

I'm reteaching myself Algebraic geometry, aiming for number theory.
How much do I need to know before I start learning topoi theory? Should I go for books about etale cohomology or is there another entryway into this all category theory generalisation of geometry thing?

[Anonymous No.12061886]

>>12061868
I hope you get AIDS

[Anonymous No.12061901]

>>12061886
Cheers, lad.

[Anonymous No.12061902]

>>12061868
Topoi by Goldblatt is a nice intro that doesn't speak about geometry much at all

[Anonymous No.12061904]

>>12061901
I’m not kidding I hope you die of a painful deadly disease you fucking faggot.

[Anonymous No.12061907]

>>12061350
A statement that can't be proven without using a statement that implies the law of excluded middle is not a "theorem", it's merely a consistency condition.

[Anonymous No.12061946]

>>12061904
We don't die of AIDS anymore in my country. We have decent healthcare and research has produced very efficient drugs for this disease.

[Anonymous No.12061965]

>>12061946
Norway?

[Anonymous No.12061985]

>>12061350
your point?

[Anonymous No.12062081]

>>12061965
No, but what I say probably applys to most rich enough European countries.

>>12061902
Thanks, I checked it out. It looks pretty cool and accessible, but I'm a bit afraid it's a bit far away from what I'll want to learn.

[Anonymous No.12062212]

Is there a book 'Topology of Euclidean spaces for dummies'?

[Anonymous No.12062286]

>>12053614

[Anonymous No.12062301]

hey fellas, i'm taking real analysis this semester, heard it was hard so i wanna prepare, any good advice/sources ?

[Anonymous No.12062305]

Is it a good idea to derive Bolzano-Weierstrass directly from Peano axioms during an undergraduate course?

[Anonymous No.12062338]

>>12062301
Just study really hard and always ask the professor if you don't understand something. Young people nowadays think everyone knows everything and instantly understands everything, then they get discouraged after a few analysis courses and fall for the siren song of alg*bra. First exposure to real analysis is actually hard and it's supposed to be that way, so just study like hell and you will probably be fine. You don't need to prepare, but if you want to anyway you can just look up any book or lecture notes from your university/library. Or check Terry Tao's Analysis PDF.

[Anonymous No.12062353]

>>12062305
the hat says yes

[Anonymous No.12062386]

>>12062301
start reading baby rudin right now lol
best way to pass a course is to already know it

[Anonymous No.12062456]

>>12060854
That's various interval definitions more restrictive than Cauchy's equivalence classes, or otherwise definitions that are presented jointly with the intended real number arithmetic (unlike defining a set of cardinality 2^N and then defining arithmetic over it)

[Anonymous No.12062471]

>>12062081
It's a real nice book. The category theory presentation is a bit odd since it takes so long to define functors, but generally the first half of the book is just very easy going and clear.

>>12060854
Depends on what you mean by "the reals". The class of Dedekind reals have a relatively hard time being a set, if you like weak axiom systems, and then Dedekind and Cauchy don't really agree, even. There's also various interval definitions more restrictive than Cauchy's equivalence classes, or otherwise definitions that are presented jointly with the intended real number arithmetic (unlike defining a set of cardinality 2^N and then defining arithmetic over it).
There's also stream approaches to the reals that I find interesting.
But tbqh I can't say much if you don't break too far from the standard setting.

[Anonymous No.12062534]

God damn I love doing a bunch of bullshit with special functions.
I don't even know why and I don't care how obscure of abstract or a waste of time it is. Give me gamma functions, give me theta functions, give me polylogarithms, Clausen functions, I don't give a fuck, it's a whole lot of fun.

[Anonymous No.12062545]

>>12062534

[Anonymous No.12062610]

>enroll in a masters program
>have to take online classes
>all the teachers do is read from the book or their slides

[Anonymous No.12062630]

>>12062610
anything other than self-study is a waste of time if you're learning math, lectures exist so you can ask questions and engage with your professors, that's what you pay for in university

[Anonymous No.12062647]

>>12062305
you'd have to construct [math]\mathbb R[/math] through Dedekind cuts or some other wizardry which is often too boring for an undergraduate course. it's best to just mention it and if your department has a fundamentals course they can take that later
pic related constructs [math]\mathbb N[/math] from the Peano axioms in the first chapter, but then doesn't bother with building [math]\mathbb R[/math] the same way and just presents it in an axiomatic manner (i.e. "there exists a complete Archimedean ordered field" basically)

[Anonymous No.12062689]

>>12062630
heh, I literally get paid for it

[Anonymous No.12062730]

Cool way to prove things in Linear Algebra (as long as you use the elementary operations on rows and columns).
If you apply the elementary operations on the identity matrix, it then becomes an "operation matrix" for left multiplication.

The operations that you probably already know:
E1. Multiply a row by a non-zero number;
E2. Exchange two rows;
E3. Replace the row L by the row L+k*M, where M is another row and k is a non-zero real.

Make three matrices ME1, ME2 and ME3, those matrices are obtained by applying the elementary operations on the identity matrix.
If you left multiply those matrices by any matrix A, you get the result of applying the elementary operations.

Example of proof:
Theorem: Given two square matrices of order n: A and [math]I_{n}[/math] (identity of order n).;
Apply the same (finite) elementary operations on A and I, until A becomes I;
Then I becomes the multiplicative inverse of I, A^(-1).

Proof:
[eqn]A * A^{-1} = I[/eqn]

Left multiply both sides by the elementary operation matrices as necessary:
[eqn](ME1*ME3*ME2 * ... * ME1) * A * A^{-1} = (ME1*ME3*ME2*....ME1) * I_{n}
[/eqn]

By hypothesis, [math](ME1*ME3*ME2*...*ME1) * A = I_{n}[/math], therefore:
[eqn]I_{n} * A^{-1} = (ME1*ME3*ME2*...*ME1) * I_{n}[/eqn]
Therefore:
[eqn]A^{-1} = (ME1*ME3*ME2*...*ME1) * I_{n}[/eqn]

Pretty cool hm?

>>12062647
brazzers

[Anonymous No.12062736]

>>12062730
lmao

[Anonymous No.12062746]

>>12062730
alternatively, it's literally the definition

[Anonymous No.12062748]

>>12062730
I remember this from sixth form, except it was constructive by using row ops on [A|I] until it became [I|A^-1] - i.e. a nx2n matrix

[Anonymous No.12062749]

what number is missing in "12345, x, 101, 11, 2" and why?

[Anonymous No.12062766]

>>12062730
OF COURSE I HAD TO FUCK UP THE FORMATTING
EVERY FUCKING TIME

>>12062746
It is not, it shows that it always works.

>>12062748
I think that is how I first saw it too, but this one is much simpler.

[Anonymous No.12062795]

>>12062766
a demonstration of what elementary row operations are as part of constructing A^-1 would be more illuminating. There are very few people who know what row/column ops are, but dont know how to use them for this result.

[Anonymous No.12062816]

>>12062795
But that doesn't increase the level of abstraction, which is gay.

[Anonymous No.12062889]

How come Lyx is technically unknown when it's free and less contrived than TexMaker and other tex editors?

[Anonymous No.12062911]

>>12062816
neither does yours, it only introduces notation ME1,2,3 (hamhandedly too)

[Anonymous No.12062925]

>>12057137
I mean I doubt people were in doubt of this
Working memory plays a good part on intelligence, as usually measured

[Anonymous No.12062939]

>>12062911
>neither does yours
it does
>it only introduces notation ME1,2,3
This is abstraction. It also allows you to use the matrix multiplication properties.

[Anonymous No.12062973]

>>12061469
>>12055907
Why D, the numbers represent the number of 1/8turns

[Anonymous No.12063022]

>>12062647
Too bad I have done this already.

[Anonymous No.12063080]

>>12062939
doesnt seem anything more than an exercise in latex formatting
and no extensions into partitioning matrices [A|B]

[Anonymous No.12063125]

>>12062730
Based.

[Anonymous No.12063167]

>>12063080
You sound resentful for not being as smart as me.

[Anonymous No.12063193]

>>12063167
Your epic discovery is in every intro to linear algebra textbook.

[Anonymous No.12063233]

why is algebra so fucking difficult for me, how does anybody have intuition for this shit
at least in analysis and topology you can draw pictures

[Anonymous No.12063262]

>>12063233
i can't help you just from this post

[Anonymous No.12063277]

>>12063262
its just a general complaint really. here is an example.
compare these basic facts
algebra: an ideal is maximal iff you get a field when you quotient by it
analysis: a differentiable function is continuous
for the analysis fact, you can draw a picture, or think about how the derivative is a local linear approximation to the function. so the fact makes sense.
but the algebra fact is literally magic, there is no intuition for me.

[Anonymous No.12063287]

>>12063233
I mean, just think about the general formula for second order equations. How many people can come up with it just by playing around? I remember being pretty good at algebra as a kid and I wen they presented me with second order equations, I tried everything to solve it to no avail, but then our teacher showed us how to complete the square and holy fuck this really dumb trick opened a new range of possibilities my innocent mind was unaware off. Obviously you can develop some sort of algebraic intuition, but in general algebra deals with exploiting structure which means having general theorem is something difficult to grasp as you have to come up with a systematic way of solving things based on certain really strict rules.

[Anonymous No.12063299]

>>12063277
It literally isn't.
Also, think of the definitions of each component.

[Anonymous No.12063302]

[math] 0 \, := \, \{ x \mid \neg(x=x) \} [/math]

[Anonymous No.12063320]

>>12063167
Bro this is literally exactly how you're told to find an inverse matrix in every intro linear algebra class.

[Anonymous No.12063326]

>>12063287
he's talking about abstract algebra not moving the x around to the right side of the = sign

[Anonymous No.12063336]

>>12063277
Sounds like you don't have enough examples. Functional programming and quantum physics both have interesting examples.

[Anonymous No.12063352]

>>12063326
Yes, but you do understand they are related? Or you failed to understand the point of abstract algebra lmao.

[Anonymous No.12063401]

>>12063352
>it has the word algebra in it so that means it must be the same
did you get confused when SGA paused in the middle to give you workout instructions too?

[Anonymous No.12063452]

>>12063401
>They are related means they are the same
Are you personally offended or what you fucking faggot? Galois theory was founded on the problem of solving polynomials you retard
>SGA
Oh you just want to impress random people online about you knowing Algebraic Geometry? Kys

[Anonymous No.12063476]

Algebra is more of a meta-field than a field itself.

[Anonymous No.12063485]

>>12063476
yeah that's why the call them algebras over a field

[Anonymous No.12063495]

>>12056289
>>12056528
This

[Anonymous No.12063500]

>>12063495
Yeah it be that

[Anonymous No.12063501]

>>12063401
stupid joke but I keked

[Anonymous No.12063512]

>>12063485
Kek

[Anonymous No.12063558]

>>12063452
>it was founded on polynomials that means it's all just polynomials

[Anonymous No.12063565]

>>12063558
That's why a specifically mentioned galois theory you mongoloid. I never said all modern algebra is polynomials or even field/ring theory.

[Anonymous No.12063574]

Group theory is inarguably peak algebra.

[Anonymous No.12063587]

>>12063565
stop taking obvious b8

[Anonymous No.12063603]

>>12063587
make me

[Anonymous No.12063802]

How the fuck does uniform substitution work in logic? If |- a=>b is a theorem, and I'm allowed to use uniform substitution on theorems, can't I prove fucking anything? Suppose I substitute a v -a in place of a, and b&-b in place of b. That's going to result in a false formula. Am I fucking retarded?

[Anonymous No.12064132]

>>12063802
Yes, you're fucking retarded, because if you proved [math]\forall A\, B.\, A \Rightarrow B[/math] then you proved that your logical system is inconsistent to begin with.

[Anonymous No.12064145]

>>12064132
Based and Fregepilled.

[Anonymous No.12064228]

>>12064132
Here's my issue then. It appears I'm still somehow using it wrong, because applying uniform substitution in modal logic K isn't validity preserving.
https://philosophy.stackexchange.com/questions/76040/using-uniform-substitution-properly

[Anonymous No.12064255]

>>12051256
I wish I was told earlier that rules of inference was everything that I needed to write math proofs.
https://en.wikipedia.org/wiki/List_of_rules_of_inference

[Anonymous No.12064265]

>>12064255
Anon, are you now just finding this?

[Anonymous No.12064278]

>>12063476
It secretly is, but computer scientists are the ones who study it

[Anonymous No.12064306]

>>12064265
Yes, yes I am, my university professors taught me calculus without saying a word about rules of inference, yet demanding us to write math proofs. I don't feel enough to say I am mad but this sure is... Disappointing? Annoying?

[Anonymous No.12064691]

can one prove theorems, not via counter examples and the like, but by symbol manipulation, if you had unlimited computational powre