/mg/ - maths general

[Anonymous No.14866559]

Formerly >>14856127

Talk maths.

[Anonymous No.14866577]

Give a topic faggot

[Anonymous No.14866582]

>>14866577
Uhhhhh G2 manifolds.

[Anonymous No.14866666]

[math]1 + 1 = 3[/math]
I won.

[Anonymous No.14866706]

>>14866666
based satan Cirno

[Anonymous No.14866717]

Do you have more math infographics? They are very useful.

[Anonymous No.14866720]

>>14866577
abelian varieties

[Anonymous No.14866725]

>>14866666
Nope.

[Anonymous No.14866758]

>going through the complicated process of multivariable calculus to generate a 3D integral to determine the density of a turd.
>Can simply just create a table of values x,y,z, with D as (x,y,z)/3, D being the density at a specified coordinate in space.
>Obtain same ability of density gradient discrimination without the use of calculus, and its computable.
Calculus is a fucking joke.

[Anonymous No.14866816]

>>14866577
Application of modular arithmetic in videogame puzzles.
I have noticed videogame puzzles are never frustrating anymore, they are always have something to do with modular arithmetic.

[Anonymous No.14866817]

Why can't i put infinity into the integral limits? Unironic question from someone in first year engineering in uni.
They just said you can't.

[Anonymous No.14866824]

>>14866817
You can if you are using extended reals. In standard real analysis, there is no number called infinity, but the whole infinity notation is just a shorthand for the actual limit definition. Of course, engineering, and applied "math" teachers in general, don't know shit about this; they just memorise a rule, and follow it without question.

[Anonymous No.14866834]

how to into algebraic geometry? i've already studied commutative algebra, what's the natural route from here

[Anonymous No.14866849]

>>14866834
why don't you show us the commutative algebra you studied
the thinking here is that progress depends on discharging your studies in some symbolic way, such as university credits for having taken a course
there are no courses here
there are no credits
nobody knows what it means to study commutative algebra
there is no standard
there is no curriculum
there are no lectures
you aren't telling us what you studied because...?

[Anonymous No.14866872]

how not to fail in math?
i was in uni and had no problem with anything outside of math
dropped after i couldn't pass final exam in 1st semester
i enjoyed geometry but polynoms, gauss, taylor etc were complete bullshit

is there any retard proof way to learn it?

[Anonymous No.14866922]

>>14866849
right
I'm familiar with the usual stuff. Results on the spectrum of a ring, noetherian and artinian properties. Integrality. Dimensional theory, some valuations. The topics covered in Atiyah-Macdonald. And then some results in homological algebra. I thought that a reading of Hartshorne's ch. 1 and 2 (varieties and sheafs) would be okay for the time being. Agree?

[Anonymous No.14866955]

>>14866824
There is no such thing as an applied math teacher, the lower level courses are taught by the same faculty. For calculus II, its hand waved away by convergence/divergence without reference to extended reals. I'm sure this is the exact way that you were taught, and it wasn't by lack of understanding for your professor, but to stay on track for the course.

As for engineers, they have no reason to know why the math works, the math for them is abstracted as a toolbox while they focus on their actual coursework. If they need additional assistance they can refer to people like you, who would be working as part of the team in the assigned task. Its no different than you not going in depth for the etymology of words you are using when completing your work, as the written language of choice is just an abstracted tool.
What a nasty, resentful, and uneducated post you've made. Grow up.

[Anonymous No.14866966]

>>14866872
>how not to fail in math?
study more

>dropped after i couldn't pass final exam in 1st semester
of what course?

> enjoyed geometry but polynoms, gauss, taylor etc were complete bullshit
If they were bullshit and you didn't enjoy them, then why do you want to learn it?

[Anonymous No.14866971]

Sometimes people on this board post how excluded middle or the axiom of choice is fake and gay and how construcive mathematics is based and redpilled. But I think they are missing the point HARD. What I mean is that geometrical existence is different from arithmetical existence (the two are in many ways related of course). Let's that the intermediate value theorem for example. At first glance, it's almost trivial, and you can literally draw a gorrilion examples to see it has to be true in some sense. But from constructive point of view, it's not so obvious. Indeed, without excluded middle, can't affirm IVT in it's entirety, or you have to add extra conditions for it to be true. So we are in quite a dilemma: If we use LEM, we neglect constructibility, while if we decide not to use LEM, things become more complicated, and it really feels like we are losing a geometrical feel to maths. So, Ideally, construcive mathematics shouldn't contradict classical mathematics, and classical math theorems should always have constructive analogs for them to be valid. I just feel that constructivists are just arithmetic autists who want to supress different traditions, and this causes harm in the mathematical activity. the axiom of choice is obviously bullshit tho

[Anonymous No.14866980]

>>14866966
>of what course?
mechanical engineering
>If they were bullshit and you didn't enjoy them, then why do you want to learn it?
i need to learn them to pass

[Anonymous No.14866984]

>>14866559
ok.
Who wants to be my private teacher for free?
Real analasys.

[Anonymous No.14866990]

>>14866971
>wall of schizoid text and philosophical nonsense

Solve this actual math problem. If you have an actual undergraduate degree in mathematics, this should be easy.

[Anonymous No.14866991]

>>14866980
If you don't enjoy the math you got filtered by Calculus II content (taylor series) you probably should not be an engineer. If you're barely passing now, you will absolutely not pass later.

[Anonymous No.14867015]

>>14866990
what is the set D supposed to be here?

[Anonymous No.14867043]

>>14867015
Its basic university geometry, the Poincare disk model. Do you want me to explain what [eqn] \in [/eqn] is as well?

I assumed that someone going on about "geometric feel" would know some basic geometry.

Sometimes, people on this board post about pseudointellectual philosophical topics in mathematics, but I think they are missing the point HARD if they don't actually know any math.

[Anonymous No.14867100]

>>14867043
Don't be an asshole. I've seen [math] \mathbb{D} [/math] used as the unit disk.

[Anonymous No.14867150]

basic group theory question (i think i got it, just want to double-check): if [math]G=\mathbb{Z}_8\times\mathbb{Z}_4[/math] and [math]H[/math] is generated by [math](2,2)[/math] (i.e. [math]H=\{(0,0),(2,2),(4,0),(6,2)\}[/math]), determine [math]G/H[/math]
my solution: [math]G/H[/math] has order 8, so the options are [math]\mathbb{Z}_2\times\mathbb{Z}_2\times\mathbb{Z}_2,\mathbb{Z}_2\times\mathbb{Z}_4,\mathbb{Z}_8[/math]. if [math](a,b)\in G[/math] is arbitrary, then [math]4(a,b)\in H[/math], because [math]4b=0[/math] and [math]4a=0,4[/math]. this means that all elements of [math]G/H[/math] have order dividing [math]4[/math] (therefore [math]\mathbb{Z}_8[/math] doesn't pass). however for the element [math]g=(0,1)[/math], [math]4[/math] is the least exponent such that [math]g^4\in H[/math], so there is an element of order [math]4[/math] in [math]G/H[/math], therefore [math]\mathbb{Z}_2\times\mathbb{Z}_2\times\mathbb{Z}_2[/math] doesn't pass either and [math]G/H\cong\mathbb{Z}_2\times\mathbb{Z}_4[/math]

[Anonymous No.14867254]

is game theory enough pure for a mathematician?

[Anonymous No.14867255]

>>14867150
You got it. Good job!

[Anonymous No.14867262]

>>14867255
thanks! i'm not new to the material by any means, but i'm generally not a very good problem-solver, so when i cleanly solve something it feels satisfying

[Anonymous No.14867271]

Here's a question with 2 parts.
ux, uy mean partial derivatives of ux or uy

yux + xuy = 0, u(0,y) = e^-y^2

a) Solve the pde.
b) In which regions of the xy plane is the solution uniquely determined.

Part a I managed to solve and get e^(x^2-y^2). I was wondering on how to solve part b.

[Anonymous No.14867283]

>>>/g/88760249

[Anonymous No.14867310]

Show

[math]\sqrt{3} - \sqrt{2} \notin \mathbb{Q} [/math]

[Anonymous No.14867330]

>>14867271
u is constant on the curves where y^2 - x^2 = c for a real c.
The boundary condition only tells you the value of u on those curves where c >= 0 but on the other curves u can have different values.

[Anonymous No.14867331]

>>14867254
My university doesn't have game theoretic lectures.

[Anonymous No.14867335]

>>14867310
If that were true, then also [math] \frac{1}{\sqrt{3}-\sqrt{2}} \in \mathbb{Q} [/math], and you could rationalize that to have [math] \sqrt{3} + \sqrt{2} \in \mathbb{Q} [/math] hence also [math] \sqrt{3}\in\mathbb{Q} [/math]. Contradiction.

[Anonymous No.14867340]

>>14867310
Suppose that
[math]\sqrt{3} - \sqrt{2} = \frac{p}{q} \in \mathbb{Q}[/math]
then
[math]\sqrt{6} = \frac{5 - (\sqrt{3} - \sqrt{2})^2}{2} = \frac{5q^2 - p^2}{2q^2} \in \mathbb{Q}[/math]
Contradiction so [math]\sqrt{3} - \sqrt{2} \not \in \mathbb{Q}[/math]

[Anonymous No.14867346]

Anyone got anything I can read about rotating strings in relation to discrete math or stuff like grammars.

[Anonymous No.14867352]

>>14867335
good job
>>14867340
explain why
>>14867310
>Suppose that [math]\frac{5q^2 - p^2}{2q^2} \in \mathbb{Q}[/math]
is a contradiction?

[Anonymous No.14867353]

>>14867335
good job
>>14867340
explain why
>>14867310
>[math]\frac{5q^2 - p^2}{2q^2} \in \mathbb{Q}[/math]
is a contradiction?

[Anonymous No.14867360]

>>14867353
Because the square root of 6 is irrational.

[Anonymous No.14867361]

What you think? True or false?

[math]\forall\;a,b,c,d \in \mathbb{N}\;\exists\;n \in \mathbb{N} : a^n + b^n + c^n = d^n[/math]

[Anonymous No.14867365]

>>14867361
False. Consider a=b=c=d=1. Then no matter what n is the LHS is 3 and the RHS is 1.

[Anonymous No.14867374]

what about a=1, b=c=d=0 ?

[Anonymous No.14867377]

>>14867365
my bad, it should have been

[math]\forall\;n \in \mathbb{N}\;\exists\;a,b,c,d \in \mathbb{N} : a^n + b^n + c^n = d^n[/math]

[Anonymous No.14867389]

>>14867331
maybe a shit university?

[Anonymous No.14867393]

>>14867389
nope

[Anonymous No.14867443]

>>14867377
So no one has any ideas?

[Anonymous No.14867447]

>>14867443
a=d
b=c=0

[Anonymous No.14867454]

>>14867447
nice try, [math]\mathbb{N}[/math] without 0

[Anonymous No.14867474]

>>14867377
For odd [math] n [/math] that's trivial, because you can push one of the terms to the RHS and factor the LHS and RHS using the standard method. For any [math] a,b,c [/math] it now suffices to find a suitable [math] d [/math]. The even case, well I think you could muster up a counterexample.

[Anonymous No.14867478]

>>14867454
2^2 + 4^2 + 4^2 = 6^2
3^3 + 4^3 + 5^3 = 6^3
95800^4 + 217519^4 + 414560^4 = 422481^4
No solution for bigger values of n.

[Anonymous No.14867483]

Is this true or false?

[math]\forall n \in \mathbb{N}: a_{1} = \pi \wedge a_{n+1} = \pi^{a_{n}} \implies \exists\;n \in \mathbb{N}: a_{n} \in \mathbb{Q}[/math]

[Anonymous No.14867487]

>>14867483
Oh that's a good one! If I recall correctly, it's not proven that [math] \pi^\pi [/math] is irrational. You can however, prove that [math] \pi^n [/math] is irrational for all [math] n [/math].

[Anonymous No.14867489]

>>14867474
>standard method
What do you mean? What is this?

[Anonymous No.14867492]

>>14867474
And just like this a random anon on /sci/ disproved the famous Lander, Parkin, and Selfridge conjecture.

[Anonymous No.14867494]

>>14867483
Probably false but good luck proving it

[Anonymous No.14867503]

>>14867483
>∀n∈N
>∃n∈N
I can't make sense of it. If I understand you correctly, it's a hypothesis which modern math probably can't tackle. As >>14867487 said, proving irrationality is hard.

[Anonymous No.14867504]

>>14867487
[math]\forall_{n \in \mathbb{N}}:x^n \notin \mathbb{Q} \implies x \notin \mathbb{A}[/math]

Isn't this obvious, because we know that [math]\pi[/math] is transcendental?

[Anonymous No.14867506]

>>14867503
That's why it's so interesting. You probably understood me correctly. It's about taking [math]\pi[/math] to the power of [math]\pi[/math] over and over again. The question then is, if you'd get a rational number at some point.

[Anonymous No.14867507]

>>14867504
This is wrong you know. All positive integer powers of [math]\sqrt{1 + \sqrt{2}}[/math] are irrational but [math]\sqrt{1 + \sqrt{2}}[/math] is algebraic.

[Anonymous No.14867513]

>>14867507
I didn't. Now I do.

[Anonymous No.14867525]

>>14867504
https://en.wikipedia.org/wiki/Transcendental_number#Possible_transcendental_numbers
>>14867506
Yeah, it's a pickle. Seems unlikely (since algebraic numbers are countable and transcendentals are the ones that make the irrationals uncountable), but so is Euler's Identity, I guess,

[Anonymous No.14867536]

>>14867483
[math]\exists{x \notin \mathbb{Q}}:[\, \forall{n \in \mathbb{N}}: a_{1} = x
\wedge a_{n+1} = x^{a_{n}} \implies \exists n \in \mathbb{N}: a_{n} \in \mathbb{Q}\,][/math]

This is true and solvable. What you think?

[Anonymous No.14867540]

>>14867536
[eqn] \sqrt{2}^{\sqrt{2}^\sqrt{2}} = 2 \in \mathbb{Q}[/eqn]

[Anonymous No.14867542]

>>14867525
>https://en.wikipedia.org/wiki/Transcendental_number#Possible_transcendental_numbers
Thanks, but I'll have to read this from a textbook. Wikipedia's seldom enough for me to truly comprehend a concept as complex as this.

[Anonymous No.14867546]

>>14867540
Pretty much.

[Anonymous No.14867562]

>>14867310
Notice that [math] \mathbb{Q}(\sqrt{2}) / \mathbb{Q} [/math] is a field extension, produced by the minimal polinomial [math] x^2 - 2 \in \mathbb{Q}[x] [/math] which is irreductible by Eisenstein's criterion. Idem for [math] \mathbb{Q}(\sqrt{3}) / \mathbb{Q} [/math] with [math] x^2 - 3 \in \mathbb{Q}[
x] [/math], and thus, both extensions are different, and by the law of towers is easy to conclude that [math] \mathbb{Q}(\sqrt{2}) \cap \mathbb{Q}(\sqrt{3}) = \mathbb{Q} [/math], therefore [math] \sqrt{3} - \sqrt{2} \notin \mathbb{Q} [/math] (otherwise it would be in the intersection).

[Anonymous No.14867625]

What does it mean?

[Anonymous No.14867655]

>>14866559
>brit OP doesn't like new thread in old
I fucking hate brits

[Anonymous No.14867662]

>>14867353
>"explain why" for guy using irrationality of sqrt(6)
>"good job" for guy using irrationality of sqrt(3)
That's some bullshit

[Anonymous No.14867664]

What's the easiest way to publish a small paper?

[Anonymous No.14867676]

>>14867664
You can publish it on /sci/.

[Anonymous No.14867677]

>>14867360
ah, stupid me, I see it now, thanks anon.
>>14867662
no thanks to you, you pedantic donkeywanker piece of moron.

[Anonymous No.14867678]

>>14867664
Write in very small font.

[Anonymous No.14867736]

>>14867676
I don't want to be associated with you.

[Anonymous No.14867777]

What determines whether a fraction is rational or irrational, and what determines whether the rational is terminating or nonterminating and repeating?

I made a table evaluating the denominators from 1 through 9 and found that there is a pattern formed with the denominators 3, 6, and 9 (assuming the pattern applies to all factors of 3) in regards to repeating, nonterminal decimals, and with 7, in regards to irrational values-all values with a denominator of 7 (excluding 7) are irrational (again, assuming this applies to all factors of 7).

The patterns are as follow:
[math]\frac{n}{3}[/math]: if n is a multiple of 3, the resulting value is whole, otherwise, it is repeating and nonterminating.
[math]\frac{n}{6}[/math]: if n is a multiple of 3, it is a terminating decimal (whole if it is a multiple of 6).
[math]\frac{n}{9}[/math]: if n is a multiple of 9, it is whole; all values (excluding multiples of 9) are nonterminating repeating decimals.

Is that it, or is there a more nuanced pattern/reason? Is there anything interesting that follows from this pattern?

[Anonymous No.14867783]

>>14866955
>t. applied "math" teacher

[Flammonde No.14867820]

>>14867777
I like those digits. I used them to generate some primes:
>[14839751], [123601391], [138202937], [2090464130560457], [1067612921856238151], [9035168616448028591] ...snip...

In any given base b, 'base'imal representations of a fraction that is a factor of the base itself can be represented in a cleanly terminating 'base'imal. (Decimal, hexadecimal, centoventimal, etc). Repeating 'base'imal representations appear in numbers that factor the number equal to b - 1. In the case of base 10, that's 9, so 3 and 6 repeat also. In the case of hexadecimal, that's 15, so 3 and 5 repeat. A base like 60 has a prime as its b - 1. I haven't explored what its ratios look like yet.
Primes that aren't a factor of b or b - 1 have a repeating decimal.

[Anonymous No.14867825]

How do I prove that a loop L in the group S^1 that intersects with a neighborhood of the circle S^1 (= Z) exactly three times can only be either -3 or 3? (The loop wraps around S^1 three times).
It seems obvious but I don't know what to do.

[Anonymous No.14867831]

>>14867777
Dude, this is borderline schizo-babble.

Every ratio of two integers is rational. That's literally the definition.
n/7 is rational for every integer n. The repeating pattern in the decimal representation is "142857" when n is not a multiple of 7.

[Anonymous No.14867839]

>>14867777
A fraction by definition is rational. The decimal representation is just a representation, and not the actual definition of the numbers.

[Anonymous No.14867847]

>>14867831
>>14867839
I'm an idiot. I didn't see that the values for n/7 do infact repeat, and failed to catch the fact that fractions are rational. Forgive my stupidity.

[Anonymous No.14867875]

>>14866922
Just pick up the book and read. If you don't know something check the references. For results in algebra he states results that are needed and says where to see the proof.

[Anonymous No.14868039]

How do I prove the set of infinite binary sequences has an equivalence relation for the relation aEb where b is a member of the natural numbers such that an = bn for all n >= n0

[joyofsatan dot org No.14868059]

>>14866559
>>14866577
>>14866582
¯\_(ツ)_/¯

[Anonymous No.14868072]

What is the "Germ theory" equivalent of Math? Doctors never practiced sterilization when they treated patients after performing autopsies, which lead to the death of a lot of pregnant women. When the idea of washing hands was first bought up, they laughed at it. Has something like that happened in Math, something major that was treated as a joke at first, but changed Math itself?

[Anonymous No.14868080]

>>14866955
>t. seething MechEng tranny

[Anonymous No.14868083]

>>14868072
Complex numbers come to mind

[Anonymous No.14868095]

>>14867335
nice

[Anonymous No.14868098]

>>14868072
Irrationals, negatives, complex numbers, countable/uncountable infinities...

[Anonymous No.14868106]

>>14868072
Rigor

[Anonymous No.14868130]

Do you need to understand CS and programming to understand Math? I'm technologically inept. Recently I've seen a lot of people talking about Math from CS perspective, Latex and what not. Is that necessary? Is the old method of pen and paper no longer applicable? I also don't have a computer.

[Anonymous No.14868135]

>>14868130
Latex is easy as fuck to learn

[Anonymous No.14868147]

>>14868130
Latex has nothing to do with programming.
It's just the standard tool to neatly type up your paper.

[Anonymous No.14868157]

>>14868135
>>14868147
I don't know what that is, a better way to frame my question would be is programming required for Math? Can I do Math(every field of math) without ever touching a computer? I've heard that some mathematical proofs were only verifiable with computer assistance.

[Anonymous No.14868212]

>>14868157
>is programming required for Math?
No.
>Can I do Math(every field of math) without ever touching a computer?
>EVERY field of math
No.

[Anonymous No.14868243]

>>14868212
>EVERY field of math
>No.
Where would I face the problem?

[Anonymous No.14868302]

>>14866666
Checked, keked, and my soul is fecked.

[Anonymous No.14868330]

>>14866955
No one's talking about what's required and what's not. Op simply asked why can't we put infinity, and the teacher said they just can't without directing to further reference, showing not only indifference to ignorance of the subject, but also enforcement of rules bred from said ignorance. Also, if they don't care about rigour, they could just write infinity, what's the problem?

[Anonymous No.14868332]

>>14868243
Computational fields.

[Anonymous No.14868337]

>>14868147
It's Turing complete though. I personally know autists who wrote Runge-Kutta solvers in LaTeX

[Anonymous No.14868352]

>>14867662
>good job" for guy using irrationality of sqrt(3)
I'm a girl

[Anonymous No.14868357]

>>14868352
Oh. Then explain why. Cunt.

[Anonymous No.14868369]

>>14868357
Let [math] p [/math] be prime. Suppose [math] \sqrt{p} = \frac{a}{b} [/math] where the numerator and denominator have no common factor. Then [math] pb^2=a^2 [/math] and hence [math] p | a [/math] and in particular [math] p^2 | a^2 [/math]. Then also [math] p | b^2 [/math] and in particular [math] p | b [/math]. Thus the numerator and denominator are not reduced. Contradiction.

[Anonymous No.14868372]

>>14868369
Prove that [math]pb^2=a^2[/math] implies [math]p|a[/math] without using Euclid's lemma or the Fundamental Theorem of Arithmetic.

[Anonymous No.14868410]

>>14867825
I don't follow.
If you mean that the loop crosses through a section of the circle three times (going from one side to the other) that doesn't imply it's either 3 or -3, it can also be 1 or -1.

[Anonymous No.14868417]

the path to salvation.

[Anonymous No.14868541]

>>14868332
So, just applications of Mathematics and not the theory itself?

[Anonymous No.14868582]

>>14868410
I meant something like pic related.
Sorry I made a mistake in the original post (it should be the group [math]\pi_1(S^1)[/math] instead of just group [math]S^1[/math].

[Anonymous No.14868586]

>>14866577
Maid Books.

[Anonymous No.14868602]

I'm pretty sure in the year 2022, math is a solved field. Everything there is to know has been discovered. We will see diminishing returns from here on out.

[Anonymous No.14868607]

>>14868602
Why do you think that?

[Anonymous No.14868608]

>>14868607
Because it's just adding numbers, math has always been the study of adding numbers and subtracting them in various ways. With calculators in the 20th century we didn't have to even know how to do that, now in the 21st century with AI we will not need people to input things into calculators anymore and the study of mathematics will stop entirely.

[Anonymous No.14868609]

>>14868608
How is it just adding numbers though?

[Anonymous No.14868612]

>>14868609
Well everything in the universe boils down to numbers, there is nothing beyond that.

[Anonymous No.14868679]

How do you find good problem sets when self-studying? I self-studied Linear Algebra but struggled with the problems my professor gave us. This has been a problem with previous modules as well. Knowing the theory is all well, but finding problem sets is hard.

[Anonymous No.14868693]

>>14868679
Exercises from "mature" books.
For example:
>Friedberg, S.H., Insel, A. J., & Spence, L.E. (1979). Linear algebra.
>Rao, R.A., & Bhimasankaram, P. (2000). Linear algebra.
>Halmos, P.R. (1995). Linear algebra problem book.

Give an example of you professor's problem set so we can see what we are dealing with. Preferably from vector spaces, I have never studied Matrix algebra so I can't judge.

[Anonymous No.14868721]

>>14868608
AI is less powerful than you believe. With today's computers you can't efficiently automate the majority of mathematical proofs. Not to mention that some problems can be mathematically proven to be unsolvable for today's computers.

[Anonymous No.14868723]

>>14868612
I believe there are more fundamental concepts than numbers.

[Anonymous No.14868729]

>>14868612
I think numbers are the best description for the world that humans have come up with. Math doesn't have to be the best description that is possible, however. Neither does it have to be equivalent to the object it describes.

[Anonymous No.14868745]

>>14868723
I’m of the belief that somehow consciousness is the fundamental force of reality. I don’t Know what the observer effect implies, but maybe there could be experiments in consciousnesses relationship with matter. If there is any.

[Anonymous No.14868749]

>>14868745
Where's the difference between your view and solipsism?

[Anonymous No.14868755]

>>14868749
My view is not a position on what can be known to exist, it is a view on composition of what is known to exist. It’s called panpsychism and I’m not the only person who thinks this way.

[Anonymous No.14868774]

>>14866559
Monoid sounds like a 4chan slur desu.

[Anonymous No.14868815]

Here’s a thought experiment on the nature of matter. What if we had a computer that could simulate physical reality with 100% precision with unlimited resources. Could the “thoughts” of the computer operator alter the physical reality of the simulation?

[Anonymous No.14868830]

>>14866559
I dont know if this happens to much people but im self-studying math and I have moments where I think Im the smartest person to ever live because I understood something and moments where I feel like the most worthless garbage because I didnt understand something. I cant take this cycle of motivation and demotivation

[Anonymous No.14868843]

>>14868372
Because if a^2/p we’re not an integer then b^2 is not an integer implies b is not an integer, but it must be because we assumed sqrt(p) was rational

[Anonymous No.14868846]

>>14868830
I’m giving up math to get a hussle in industry to support myself. But I would like to go back to it later for the pure passion of it, that is never ending.

[Anonymous No.14868855]

>>14868846
I did the same. I'm currently funding my own masters. I actually think the time away from academia was good for me.

[Anonymous No.14868856]

>>14868582
You're trying to prove that your intuition implies the definition which is the absolute peak of dumbassery,

[Anonymous No.14868861]

>>14868855
If only we didn’t have to work lol

Cheers

[Anonymous No.14868870]

>>14868855
I dont know if get into academia. I would love to make a living our of doing maths all day and night but it seems risky to try and stressful to mantain

[Anonymous No.14868895]

>>14868870
Takes a phd though, but if you have a PhD just for the sake of having one you’ll have nothing to research. I think the most important thing is finding and sharing the truth. If you do that your career prospects will be better than before.

[Anonymous No.14868931]

>>14868856
So you mean it's just a direct result of the definition and I don't have to do anything to prove that it's true?

[Anonymous No.14868933]

>>14868830
This is an extremely common feeling for 99% of math students. Don't worry.

[Anonymous No.14868946]

>>14868830
This is normal and it will only go away pretty damn late. But it will go away. Build up your resistance to failure and things not working out. Stop feeling demotivated, take errors as a lesson and never get demotivated. If you absolutely can't do that and sperg out every time it happens, math is simply not for you, independent of how clever you might be.

[Anonymous No.14868952]

>>14868856
>>14868931
Sorry I'm learning and I don't know if I'm making any sense. Staying up all night also didn't help.

[Anonymous No.14869071]

>>14868830
You will always know more than someone, and less than someone else. You just have to kind of... not think about that.

[Anonymous No.14869074]

>>14868693
How do you know what a vector space is if you've never studied matrix algebra? Matrices are usually introduced first.

[Anonymous No.14869120]

>>14869074
I mean I don't know formal matrix algebra. I know all the high school shit.

[Anonymous No.14869171]

How do I learn Math properly? I graduated high school but I feel like I wasn't taught math properly, for example, for integration we were given the formulae and asked to substitute values in them to get the results. Never been taught what it is, or how and why we do it that way.

[Anonymous No.14869175]

>>14869171
There is something called books that you can read.

[Anonymous No.14869177]

>>14869171
Go to your favorite university website.
Find math program curriculum, and recommended order to take courses.
Download the syllabus for the course and pirate the textbook.
Whalla, you know can learn math in the structured way.

[Anonymous No.14869180]

>>14869175
>>14869177
I'm really sceptical of the Universities in my country, which University do you guys recommend?

[Anonymous No.14869194]

>>14869180
I would recommend to start with learning Linear Algebra. Just pirate any Linear Algebra book and start reading. If you don't like the writing style of the author try a book by another author instead.

[Anonymous No.14869196]

>>14869194
What book would you recommend?

[Anonymous No.14869219]

>>14869196
The book by Hoffman & Kunze is a classic.

[Anonymous No.14869233]

>>14869219
Thanks? Titled Linear Algebra? Does the edition matter?

[Anonymous No.14869304]

>getting filtered by setting up integrals for surface areas of shapes, bisected by planes and other shapes.

[Anonymous No.14869316]

>>14869304
If you can’t rotate them in your mind, just draw them

[Anonymous No.14869329]

>>14869316
I do, they just take forever to work through and figure out the trickery to turn them into double integrals.

[Anonymous No.14869363]

how good is rudin first edition?

[Anonymous No.14869381]

>>14869363
You mean Principles of Mathematical Analysis?
It's good. In the later edition he changes the construction of the reals for 'pedagogical' reasons, not for logical reasons. The only other differences are in the end chapter(s). Which don't matter since you'll be moving on to another book.

[Anonymous No.14869411]

>>14869329
I just finished that paraboloid in a sphere problem I started when I took this picture. Took me 22 minutes... I can't take this, its so boring.... I want to go back to series and sequences or discrete math.

[Anonymous No.14869423]

>>14869381
nice

[Anonymous No.14869436]

AMA

[Anonymous No.14869459]

>>14869436
whats up

[Anonymous No.14869476]

>>14869459
I ate far too much on a work event. Am full. Want to read up on some physics. Editing Wikipedia. Might listen to a podcast on Kant.

[Anonymous No.14869483]

>>14869329
>>14869411
nevermind, I just solved four more problems in a few minutes each once everything clicked.

Just another time that this >>14868830
happens just like for this anon.

[Anonymous No.14869548]

>>14866666
nice

[Anonymous No.14869577]

>>14868830
Even if you don't solve a problem, you probably learned something by trying to solve it. Remind yourself of this, when you're feeling demotivated again.

[Anonymous No.14869846]

>>14869180
look up ocw.mit.edu
on youtube there's a bunch of full MIT courses. MIT 18.01 is singe variable calculus, and 18.06 is linear algebra. obviously, the material is excellent, and you can find lecture notes, problem sets and solutions, the course book, etc, at ocw.mit.edu. at least that's what i use to review a couple of math courses i didnt learn properly.

[Anonymous No.14869856]

i have a really basic question. y_hat/y is percentage change. but why can i write (Y/L)_hat as the subtraction of y_hat and l_hat ? is it because the variables are in logarithms?

[Anonymous No.14870021]

>>14869196
Literally Springer and if you disagree you have no future you are literally talentless, you must therefore feel sad.

[Anonymous No.14870064]

>>14870013

[Anonymous No.14870086]

>>14870064
Correct

[Anonymous No.14870101]

>>14869180
The university in your country is far better than whatever goyslop then have in US.

[Anonymous No.14870105]

>>14869856
Economics is pseudoscience.

[Anonymous No.14870117]

>>14868243
The four colour theorem.

[Anonymous No.14870128]

>>14869177
>Whalla
Kek. It's voila, unless you're a Muslim.

[Anonymous No.14870132]

>>14870128
You're thinking of "wallah", a contraction of "wa" (I swear to) and "Allah" (god).

[Anonymous No.14870137]

>>14869856
I think so. There's no telling what your economics prof means with these letters, but when e.g. estimating a log-linear model you usually interpret the dependent variable at percentage change. I imagine something similar is going on here.

[Anonymous No.14870142]

>>14870132
Actually, here in the Netherlands street language has morphed that into whalla

[Anonymous No.14870156]

>>14869856
Muh hat this hat that. What the fuck are you talking about? Economists are retarded.

[Anonymous No.14870191]

>>14869856
>calling delta a hat
A hat is what you put ON TOP of your head.

[Anonymous No.14870209]

>>14870021
Author?

[Anonymous No.14870535]

>>14870209
It's a meme, he's trolling. How good are you with college algebra?

[Anonymous No.14870544]

>>14870535
What's college algebra? Stuff about groups, rings and fields? Can't you study Linear Algebra before that?

[Anonymous No.14870620]

>>14870544
The stuff thirdies do in middle school, and burgers do in semester 1. Basically precalculus. Basically olympiad level questions.

>Can't you study Linear Algebra before that?
Linear Algebra is build on definition of groups, fields, and isomorphisms, though it's not as important to read Abstract Algebra before.

[Anonymous No.14870734]

Are there fields of math that require an intuitive grasp of 4-space? Seems really daunting and confusing, but maybe it would make sense if I studied it and didn't just look at some wikipedia articles

[Anonymous No.14870737]

>>14870734
Complex Analysis
Riemann surfaces live in [math]\mathbb{C}^2 = \mathbb{R}^4[/math].

[Anonymous No.14870746]

>>14870734
>>14870737
Not even Riemann surfaces, just functions from C to C.

[Anonymous No.14870748]

>>14870737
C no C2

[Anonymous No.14870796]

here's a personal question. would you guys want to live inside my computer??!?!

[Anonymous No.14870807]

>>14870796
Here you go >>/vg/401014686

[Deko<3 !A4jsQTgi.Q No.14870817]

>>14870807
I honestly have lots of questions, more than answers.

Alan turring, what is a computable and non computable problem, given that the universe is computable, what is the realistic limit of computing power

If we could understand this we could maybe answer more questions.

[Anonymous No.14870821]

>>14870817
crazy how you're still asking stupid questions 10 years later. One would think you'd opened a book in the meantime but the answer is of course no.

[Anonymous No.14870826]

https://www.youtube.com/watch?v=zn7-fVtT16k

>what the thread is about to devolve into

[Anonymous No.14870908]

>>14866559
Im almost finishing to self-study abstyract algebra with fraleigh's book (excellent book btw) but I have the feeling that im going way too fast, I understand everything and do 7-14 theoretical excercises per section. Ive done the first 400 pages in 2 months when this book is intended to be worked out through an entire semester. I put 3.5-4.5 hours per day. Am I going too fast? Am I doing anything wrong that im not realizing?

[Anonymous No.14870947]

>>14870908
I doubt it. Don't know Fraleigh's book, but it's possible that it is too easy. Try some exercises from Lang's Algebra (or just any more advanced book) on subjects you think you know well. May help really solidify it. There's also Skopenkov's problem.

[Anonymous No.14870962]

>>14870947
i dont think is too easy because i usually struggle to understand proofs (have to read them a shit ton of times)

[Anonymous No.14870970]

>>14869120
Niggas b givin recs on textbooks they've never actually gone through

[Anonymous No.14871009]

>>14870970
OP asked for Linear Algebra, but I don't find it interesting, so what else am I supposed to do, since none of you retards would answer. Whatever chapters I read, I found the exercises engaging enough. So unless, the book suddenly becomes easier, I think I have every right to recommend it unlike (you).

[Anonymous No.14871023]

I want to self-learn higher-level math. I applied for a job that requires only basic math, but in-depth knowledge of other subjects(social sciences). It'll take around 2-3 months for the "tests" to be done and everything to be finalinized. Should I wait till I secure the job and then start my math course, or do I do them together starting right now?

[Anonymous No.14871030]

>>14871023
star tnow

[Anonymous No.14871182]

How do I proof that

[math](a_{n})n \in \mathbb{N}[/math] with [math]a_{1} := 1 \wedge a_{n + 1}:= \frac{1}{2}a_{n} + \frac{3}{2a_{n}}[/math]

converges to [math]sqrt{3}[/math]. Is it possible to it with induction?

[Anonymous No.14871212]

>>14870817
>Alan turring
Pretending Turing is the computer hero is much more politically acceptable than admitting that computing/computer science is another very useful advanced research area we rely on, which was invented and pioneered by people who wanted Hitler to win WWII.
Turing "invented computers" not because that is actually true, but because it's easier than telling people Konrad Zuse invented them, because Zuse was a nazi.

[Anonymous No.14871309]

>>14871182
Note:
[math] x = \tfrac{1}{2}x + \tfrac{3}{2}/x \iff 2x^2 = x^2 + 3 \iff x = \sqrt{3} [/math]
So if it converges at all, the fixed point of the series should be sqrt(3).

From another angle:
[math] a_{n+1} = \tfrac{1}{2}a_n + \tfrac{3}{2}/a_n [/math]
[math] a_{n+1} = a_n \left( 1 +( \sqrt{3}/a_n)^2 \right) / 2 [/math]

So also here the fixed point is clear.

Leaves to find some argument for why the starting point 1 converges. I'm sure there's both standard sequence arguments as well as a more tailor made fixed pont convexity case to be made for it

[Anonymous No.14871342]

>>14871309
Actually I ignored -sqrt(3).
Just checked and for negative a1 it quickly converges against that one, so it will be a tad more annoying (since dependent on a1)

[Anonymous No.14871353]

>>14871212
>which was invented and pioneered by people who wanted Hitler to win WWII
That's a bit of an oversimplification, since analogue computers were invented by Charles Babbage. Digital computers rely on Boolean logic (which was invented by George Boole after being inspired by Indian formulations of logic that British people became aware of during the colonial period). Late 19th century work on logic and the foundations of mathematics is what paved the way for lambda calculus, which became the basis for modern programming languages and formal proof systems.

[Anonymous No.14871383]

>>14871309
(Note, for negative starting points one has a symmetric situation with -sqrt(3), but I suppose that's not of interest here)

[Anonymous No.14871515]

AHHH IM PLOOTING

[Anonymous No.14871521]

>>14871515
>doesnt even care about numbers
>just ploots

[Anonymous No.14871535]

>>14871521
what the fuck is a taylor series?
IM GONNA PLOOT

[Anonymous No.14871546]

>>14866971
>constructivists are just
people who want an instantiation of a variable that classical nerds claim to exist but can't give a value to
if a variable exist it has a value, if you cant come up with a value then doesnt exist simple as

[Anonymous No.14871550]

>>14868072
negative distance
negative temperature
negative probability

all due to physics btw, physics chads of the world UNITE

[Anonymous No.14871553]

>>14871182
See if it's eventually monotonic and bounded. All monotonic and bounded sequence must converge.
Then compare the limits of [math] (a_n) [/math] and [math] (a_{n+1})[/math].
Finally take limits on both side.

[Anonymous No.14871589]

>>14870796
>would you guys want to live inside my computer??!?!
I already do, i also live inside your walls and head too

>>14871212
Salty chud, the first computer was invented by Charles Babbage.

[Anonymous No.14871594]

>>14871353
>>14871589
If you're going by analog computers, then the Greeks had the first one.
https://en.wikipedia.org/wiki/Antikythera_mechanism

Average ancient Greek had the IQ of Witten.

[Anonymous No.14871659]

>>14866971
>So we are in quite a dilemma: If we use LEM, we neglect constructibility, while if we decide not to use LEM, things become more complicated, and it really feels like we are losing a geometrical feel to maths.
The issue here is that the IVT you speak of is in terms of a geometry which uses the real number line (requiring set theory or second-order arithmetic to be formalized)
You can also do synthetic geometry, alla
https://en.wikipedia.org/wiki/Tarski%27s_axioms
https://en.wikipedia.org/wiki/Hilbert%27s_axioms
or more modern theories - but since model theory models all the math, people stopped teaching that.
Those geometries are decidable. (In fact that's why Hilbert had blindly assumed arithmetic would turn out decidable as well).

As far as I can tell, there's nothing fundamental that to suggest that we should model a line as an uncountable set of points. Fuck you Descartes.

In the last years I've come to join the constructivist crowd, but also because you can always just pick your foundational theory as constructive and then say "LEM=>IVT". It's not a big deal.

[Anonymous No.14871667]

>>14871659
model theory in terms of sets, that is.

Btw. I have no idea what a synthetic theory of continuous functions looks like - in the worst case maybe something like HoTT.

[Anonymous No.14871679]

>>14871515
>>14871521
>>14871535
comedy king

[Anonymous No.14871756]

>>14871667
well synthetic theory with toposes is this
https://en.wikipedia.org/wiki/Synthetic_differential_geometry

and just the usual topological spaces, it is the locales with geometric logic
https://mathoverflow.net/questions/27181/stone-spaces-locales-and-topoi-for-the-relative-beginner
this is the article teaching the basics
https://www.cs.bham.ac.uk/~sjv/LocTopSpaces.pdf

a locale is the proper way to do topology with constructivism.

[Anonymous No.14871784]

>>14871353
>which was invented by George Boole after being inspired by Indian formulations of logic that British people became aware of during the colonial period
That’s a funny way to say Leibniz

[Anonymous No.14871818]

>>14871756
I happen to be aware, but something like synthetic differential geometry are not constructive theories, but instead anti-classical theories which become consistent when adopting axioms on top of a constructive context. One would hope to find some more lightweight synthetic theory that validates the IVT.

[Anonymous No.14871821]

Is it true that some anon solved a previously unsolvable math problem based on the best viewing order of Haruhi episodes? What's the truth behind that story?

[Anonymous No.14871824]

>>14871821
It's true. Matt Parker has a video on it. 4trans including /pol/ has done quite a lot of things like that.

[Anonymous No.14871945]

>>14871821
He found a better limiting bound, not the actual number. It was still a significant advancement of the problem, though, which itself is a fairly significant combinatorics problem.

[Anonymous No.14871955]

>>14871945
>which itself is a fairly significant combinatorics problem.
No one has really cared for Superpermutations except for /a/

[Anonymous No.14872077]

>>14871030
Thanks.

[Anonymous No.14872093]

>>14871784
Leibniz is said to have been amazed by a copy of the Yijing brought to him by Chinese missionaries who'd been to China, which he in turn related to pairs of 0s and 1s, not unlike the modern binary counting system.

[Anonymous No.14872123]

>>14872093
Every great thinker in history has been a sinophile

[Anonymous No.14872170]

>>14872093
>Yijing brought to him by Chinese missionaries who'd been to China
I've seen this propping up recently. Slowly hinting every western mathematical or scientific idea was inspired by some China shit. Five years from now, it will be full "we wuz", and Chinese claiming they were the original Greeks, etc.

[Deko<3 !A4jsQTgi.Q No.14872257]

you guys are really smart :L. I barely graduated highschool I'm a total mathlet. I am years behind the average /sci/ poster and it will probably take me more than the average amount of years to catch up. But I won't give up. I'm not sure if this is what I'm meant to do, but it's a fun hobby!

[Deko<3 !A4jsQTgi.Q No.14872266]

>>14872257
https://www.youtube.com/c/TheMathSorcerer

also, I'd like to plug the math sorcerer because he's probably the best math person for beginners on youtube and is more rigorous than khan academy. Although I think with books for logic/proofs/advanced topics and with khan academy for arithmetic and algebra. In case anyone else is self studying math. Which I'm sure some are.

[Deko<3 !A4jsQTgi.Q No.14872272]

>>14872170
Chinese are based and I love them....

[Anonymous No.14872290]

>>14872257
just start working through math books. You'll thank me later (in a few years)

[Deko<3 !A4jsQTgi.Q No.14872297]

>>14872290
I actually enjoy working through all the elementary school problems on khan academy...

[Anonymous No.14872300]

>>14872297
Don't be afraid of studying less elementary stuff.

[Deko<3 !A4jsQTgi.Q No.14872303]

>>14872300
I'm not, but it sucks trying to learn math when you don't have a solid foundation. I struggle a lot. But I'm convinced I can learn anything.

[Anonymous No.14872319]

>homework worth 20% of grade
>homework problems are absolutely massive algebra distribution pain in the ass bullshit time wasting problems

Yeah fuck this. Just gonna set up the triple integral properly, plugging it into symbolab, and sloppily copying the distributions down.
Who honestly wants to waste time distributing (x-4)^5 - (x-4)^6 - (x-4)^3

[Anonymous No.14872332]

>>14872319
>\mathrm{Steps\:are\:currently\:not\:supported\:for\:this\:problem}

I copy pasted that too

[Anonymous No.14872341]

>>14872319
And why exactly would you expand it? It sounds more like you need to get good

[Anonymous No.14872344]

>>14872341
even expanding it is less work than substituting and redefining the bounds of integration for the remaining integrals. Just outsourcing my expansion/distribution to a computer.

[Anonymous No.14872346]

Consider Baker's function [math]B:[0,1] \to [0,1][/math] with
[eqn]B(x) = \begin{cases} 2x & \text{for } 0 \leq x \leq \frac{1}{2} \\
2x - 1 & \text{for } \frac{1}{2} < x \leq 1 \end{cases}[/eqn]
Let [math]f(n)[/math] be the number of n-periodic points of [math]B[/math].
What is a closed formula for [math]f(n)[/math]?


For example [math]f(1) = 2[/math] since 0 and 1 are the fixed points of [math]B[/math].
It's easy to see that the n-periodic points are exactly the solutions of [math]B^n(x) = x[/math] that aren't also solutions of [math]B^k(x) = x[/math] for a [math]k[/math] with [math]k|n[/math]. This gives the recursion
[eqn]f(n) = 2^n - \sum_{\underset{k \neq n}{k|n}} f(k)[/eqn]
So anyone knows how to turn it into a closed formula when n has many different prime factors?

[Anonymous No.14872349]

>>14872319
I mean...I would.

Two things: Pascal triangle and exponent pattern
The triangle can be made quickly or memorized
and the term pair of exponents add to the current
power of the binomial. In about five minutes by
hand, it's solved without simplifying anything.

[Anonymous No.14872365]

>>14872346
Nvm, I just found the right formula to solve it
https://en.wikipedia.org/wiki/Möbius_inversion_formula
so
[eqn]f(n) = \sum_{k|n} \mu(k) 2^{\frac{n}{k}}[/eqn]

[Anonymous No.14872397]

Is there an intuitive way to understand why lim (x->0) x ln(x) = 0 ?


My intuition always told me that the answer to this limit should be -infinity, since x goes to zero pretty slowly whereas the value of ln(x) decreases incredibly fast between 1 and 0. So it looks like the x term should be negligible, and that the limit should be the same as the one of ln(x). Yet that is absolutely not the case...
For instance the limit (at + infinity) of (e^x) / x is +infinity because e^x increases incredibly fast and 1/x does not decreases to zero that fast. I don't really undertand why this reasoning could not be applied to xln(x).

[Anonymous No.14872404]

>>14872397
See that xlnx =lnx^x and check out what x^x does at 0

[Anonymous No.14872406]

>>14872397
The intuitive way is
[eqn] \lim_{x \to 0} x \log(x) = \lim_{x \to 0} \frac{\log(x)}{x^{-1}} = - \lim_{x \to 0} \frac{x^{-1}}{x^{-2}} = - \lim_{x \to 0} x = 0[/eqn]
by L'hospital's rule.

[Anonymous No.14872428]

Don't think the DM42 will be here before the end of the term... Spent the textbook stipend for my general courses and a few math courses on it. Rather get the Springer books on my courses over the actual course books, tbpqh

[Anonymous No.14872548]

>>14867150
Correct; another way to think about it is that for any element in G/H you can keep adding/subtracting (2,2) from it to reach an element (x,y) where x is 0 or 1 and y is 0,1,2, or 3. So trivially G/H = Z2 x Z4.

[Anonymous No.14872882]

>3 weeks to stokes theorem and final

[Anonymous No.14872949]

>>14872882
Skip it and go straight to generalized stokes theorem on manifolds

[Anonymous No.14872951]

>>14872949
Stokes theorem is the carrot on the stick. From there I want to learn whatever else I need to learn how Navier-Stokes works. I'm not sure what I have to read for that beyond Calculus 3 content.

[Anonymous No.14872962]

Maths is the language of Satan, the language of the New World Order, of transhumanists, of people who want toe replace mankind with artificial intelligence.
Maths make you lose touch with reality so you believe in infinity, in Hell, in being stuck without an escape.
Verification not required.

[Anonymous No.14872993]

>>14872962
Stop making us sound so cool

[Anonymous No.14873136]

>>14871182
>induction
Induction can be used for some of it, but I'm not sure how you would prove convergence by induction... maybe if you found a nice bound on epsilon in terms of n. Anyway this is how I would solve it from scratch i.e. assuming we don't have any nice "known lemmas" to fall back on
>1. the sequence is bounded (use induction here)
>2. since it's bounded it has a cluster point (bolzano weierstrass)
>3. since it has a cluster point, it converges (cause the function f(x)=x/2 + 3/2x is continuous)
>4. the limit is a fixed point (again cause continuous)
>5. solve for fixed point: x=+-sqrt3

[Anonymous No.14873150]

>>14873136
>since it has a cluster point, it converges (cause the function f(x)=x/2 + 3/2x is continuous)
What theorem is this?

[Anonymous No.14873160]

>>14871212
>Zuse
Yeah, he's a hero no doubt. A better comparison for Turing, though, is Emil Post, who invented exactly the same thing at exactly the same time
https://en.wikipedia.org/wiki/Post%E2%80%93Turing_machine#1936:_Post_model
>>14871821
>>14871945
>fairly significant combinatorics problem
oh fuck of Robin you got your 15 minutes of e-fame, it's over
>>14873150
oh yeah that step is false, I guess you do have to be a little more hands on than this then

[Anonymous No.14873252]

I am reading Abbott's Analysis, but it seems he never defines the trigonometric and other standard functions rigorously, hence never derives their derivatives or continuity completely.

[Anonymous No.14873268]

>>14873252
>never defines the trigonometric and other standard functions rigorously
What does he do? Just use trig identities with the limit definition of derivative? That’s fine with most people. The other thing you could do is define them as power series, but then you would probably be asking for a whole rigorous theory for manipulating those

[Anonymous No.14873277]

>>14873268
Just assumes the derivative is that, even though he promises to define them later but never does (at least from what I saw skimming through). He does derive or leave as exercise the continuity and derivative of functions like [math] x^a sin (1/x) + bx [/math] at 0.

[Anonymous No.14873544]

How can I 'intuitively' think of functions that prove equipollence between say, [math](-1,1) \, and \,
R[/math]. I've seen examples on stack exchange like this (https://math.stackexchange.com/questions/28568/bijection-between-an-open-and-a-closed-interval)) but I want to know how you come up with them.

[Anonymous No.14873564]

>>14873544
Notice how the two intervals in the example are almost the same. You could ALMOST get away with making the bijection the identity, if it weren't for the endpoints.
So what can you do? Just map two points to them. Now you filled the gaps there, but created two new gaps. So do it again. And again. And again.
What you are basically doing here is the same thing as Hilbert's infinite hotel, moving residents around.

The case you're talking about with (-1,1) to R is actually easier, since you want the preimage of an open set to be an open set (so you can use a continuous function). One function to map a finite interval to all of R is tan(x), going from (-pi/2, pi/2) to all of R. Just modify it a little bit so that its domain is (-1,1).

[Anonymous No.14873567]

>>14873544
https://www.desmos.com/calculator/mcvfzcuwky

[Anonymous No.14873640]

>>14866559
exact solution please

∫ 0 to pi/2 ((ln(sin(x)) * ln(cos(x))) / (tan(x))) dx

[Anonymous No.14873679]

>>14873640
Write it in [math] \mathrm \LaTeX [/math] first, then I will answer.

[Anonymous No.14873705]

>>14873679
\int_{0}^{\pi /2}((ln(sin(x)) * ln(cos(x))) / (tan(x))) dx

[Anonymous No.14873709]

>>14873705
Nope.

[Anonymous No.14873889]

>>14873640
>>14873705
Okay, I'll bite.
Start with partial integration:
[math]\displaystyle I=\int_0^{\pi/2} \frac{\ln\sin x\ln\cos x}{\tan x}dx = \Bigl[\frac12\ln^2\sin x\ln\cos x\Bigr]_0^{\pi/2} + \frac12\int_0^{\pi/2}\ln^2\sin x\frac{\sin x}{\cos x} dx[/math]
The first term is zero at both limits. The integral can be put to recognizable form with a few substitutions:
[math]\displaystyle I=\frac12\int_0^{\pi/2}\ln^2\sin x\frac{\sin x\cos x}{1-\sin^2x} dx = \frac12\int_0^1\frac{t\ln^2t}{1-t^2}dt=\frac12\int_{-\infty}^0\frac{e^{2u}u^2}{1-e^{2u}}du=\frac1{16}\int_0^\infty\frac{e^{-v}v^2}{1-e^{-v}}[/math].
If you haven't seen the last integral, the trick is to use the geometric series:
[math]\displaystyle I=\frac{1}{16}\int_0^\infty\sum_{n\ge 1} v^2e^{-nv} dv = \frac{1}{16}\sum_{n\ge 1}\int_0^\infty v^2e^{-nv} dv =\frac1{48}\sum_{n\ge 1} \frac1{n^3} = \frac1{48}\zeta(3)[/math],
where ζ is the Riemann zeta function. ζ(3) has no known closed form, so this is as good as it gets.

[Anonymous No.14873898]

>>14871182
Addition and division are contained in the positive reals, therefore:
[eqn] a_1 > 0 \iff \forall n \in \mathbb N \quad a_n > 0 [/eqn]
Hence, [math] \{ a_n \}_{n \in \mathbb N}[/math] is bounded below. In fact:
[eqn] a_{n+1} {}^2 = \frac{9}{4} a_n {}^2 + \frac{1}{4} a_n {}^2 + 3 \implies a_{n+1} {}^2 > 3 [/eqn]

Moreover:
[eqn] a_{n+1} - a_n = \frac{3}{2a_n} - \frac{a_n}{2} \\
\phantom{a_{n+1} - a_n} = \frac{3 - a_n {}^2 }{2a_n} \leq 0 \impliedby a_n {}^2 \leq 3 \land a_n > 0
[/eqn]
The sequence satisfies both these conditions as shown above. Hence, the sequence is decreasing and bounded from below, which is a sufficient condition for convergence.

Now, the sequence defined by: [math] \{ a_{n+1}\}_{n \in \mathbb N}[/math] converges to the same limit as the original sequence, say [math] a[/math], since the former is merely a subsequence of the original.

Taking limit on both sides, and using algebraic limit theorem:
[eqn] \lim a_{n+1} = \frac{1}{2} \lim a_n + \frac{3}{2} \frac{1}{ \lim a_n} \\
\iff a = \frac{1}{2} \lim a + \frac{3}{2} \frac{1}{a} \iff a = \sqrt 3 \qquad \qquad \blacksquare [/eqn]

>>14873889
You shouldn't have answered until he wrote it in [math] \mathrm \LaTeX[/math] fag

[Anonymous No.14873907]

>>14871182
>>14873898
Actually last step, you should use the order limit theorem to declare that the limit must be nonnegative, hence: [math] a \geq 0 \implies a = \sqrt 3 [/math].

[Anonymous No.14873962]

Have zero time to study after spending 20 hours a week doing homework for a single math class.
How am I supposed to get ahead. Is it always like this for brainlets, just eternal homework struggles to trip over myself on exams?

[Anonymous No.14874061]

>>14873962
The trick is to PAY ATTENTION IN CLASS AND ASK QUESTIONS AND STOP LOOKING AT YOUR PHONE YOU DUMB FUCK TEENAGER

[Anonymous No.14874066]

>>14874061
I am a 30 year old boomer taking a a PDE course in 8 weeks. There are no classes or lectures, I just read the book, do the homework, take exams.

[Anonymous No.14874203]

Idea for a Cauchy-sequence that doesn't converge in [math](\mathbb{Q} + \mathbb{Q}\sqrt{2}, +, *)[/math]?

[Anonymous No.14874221]

>>14874203
You could take this one >>14871182

[Anonymous No.14874242]

When you have to figure out a complicated proof. Do you do it on paper first or do you work with LATEX and paper simultaneously. Or do you maybe use another method?

[Anonymous No.14874264]

>>14874221
that was actually me and that was the way I did. Thanks, anyways

[Anonymous No.14874295]

>>14866559
Proving monotonicity and boundness WILL NOT WORK!
Fixed points WILL NOT WORK!
Taking limit on both sides WILL NOT WORK!
Let's see who is smart enough to solve this.

[Anonymous No.14874335]

>>14874295
convergence against 1.0772172

[Anonymous No.14874344]

>>14874295
>homework-level question
Not doing your homework for you.

[Anonymous No.14874350]

>>14874295
Squeeze theorem

[Anonymous No.14874409]

>>14874335
Now find a closed form solution. Let's see how your epic calculator helps with that.

>>14874350
Squeeze between what?
>inb4 deez nuts
or some reddit "joke" like that.

>>14874344
This is from an entrance exam of a master in STATISTICS programme. So it even easier than a homework problem. The fact that (you) cannot do it, shows that your mathematics degree is worthless.

[Anonymous No.14874430]

>>14873252
If you care about stuff like that why read Abbot? Just go to Amann & Escher.

[Anonymous No.14874459]

>>14874335
>1.0772172
My calculator says 1.0270398670

[Anonymous No.14874460]

>>14874295
Got it
[eqn]x_n^3 - x_1^3 = \sum_{k=1}^{n-1} (x_{k+1}^3 - x_k^3) = \sum_{k=1}^{n-1} \frac{1}{k (k+1) (k+2)} = \frac{1}{4} + \frac{1}{2n + 2} - \frac{1}{2 n} [/eqn]

so
[eqn]x_n = \sqrt[3]{ \frac{5}{4} + \frac{1}{2n + 2} - \frac{1}{2 n}} \longrightarrow \sqrt[3]{ \frac{5}{4}} [/eqn]

[Anonymous No.14874480]

>>14874459
nevermind I had an index off by 1

[Anonymous No.14874481]

>>14874460
Winner of /mg/!

[Anonymous No.14874495]

>>14874481
Take your homework to sqt next time brainlet

[Anonymous No.14874518]

[math]\forall n \in \mathbb{N} : a_{1} := 1 \wedge a_{n+1} := \frac{1}{1 + a_{n}} \implies a_{n} \to a[/math]
[math]a[/math] is a famous number..

[Anonymous No.14874576]

>>14874518
Popsci

[Anonymous No.14874582]

>>14874518
if you don't see that this is phi then you're retarded

[Anonymous No.14874590]

>>14874518
[math](a_{n})_{n \in \mathbb{N}} \iff (\frac{F_{n}}{F_{n + 1}})_{n \in \mathbb{N}} [/math]

with [math]F_{1} = F_{2} := 1[/math] and [math]F[/math] being the set of Fibonacci-numbers.

[Anonymous No.14874619]

My dick is so big that bitches had to invent an entire field of mathematics to find it's length. How this make you feel wh*Te boy?

[Anonymous No.14874687]

Could you use the principle of induction on [math]R[/math], if you used Dedekind cuts for the induction hypothesis and step?

[Anonymous No.14874688]

Somehow I keep thinking that the formula for the smallest superpermutation on n symbols is [math]n! + (n-1)! + (n+2)! + 2^(n-3) - 1[/math] for [math]n ≥ 3[/math] and I don't know why. (Here, the solution to the Haruhi problem would be 93884315647.) I know I might be wrong but fuck it, I don't know why I keep thinking this.

[Anonymous No.14874689]

>>14874688
Oh for fuck's sake.

[math]n! + (n-1)! + (n+2)! + 2^{(n-3)} - 1[/math] for [math]n ≥ 3[/math]

[Anonymous No.14874702]

>>14874687
Firstly, I remember that that question has been asked on SE.
Secondly, I don't know exactly how you imagine the cuts to help with the inductions step. If you mean from left to right, then the issue is that there's no start to start from.
Thirdly, classically there is some ordinal that's in bijection with R and there's induction on that ordinal. E.g. if CH, then it's \omega_1.

[Anonymous No.14874715]

>>14874619
great book on par with rudin

[Anonymous No.14874761]

>G2 manifolds
>Kähler manifolds
Recommend me some more cool classes of manifolds

[Anonymous No.14874767]

>>14874702
That wasn't me. I was curious, if this is a technique that exists. Thank you.

[Anonymous No.14874770]

>>14866817
you can, ignore the retard before me. just look up 'improper integrals'

[Anonymous No.14874796]

>>14874689
The (n+2)! Term seems way off. Did you mean (n-2)! ? Then yours at least matches up with the answer 33 for n=4

[Victor Isai Mazariegos, Ph.D, J.D. No.14874805]

My profile pic

[Victor Isai Mazariegos, Ph.D, J.D. No.14874818]

The Continuum Hypothesis

[Anonymous No.14874820]

[math]\frac{d}{dx} x^x[/math]

[Anonymous No.14874825]

>>14874805

[Victor No.14874862]

>>14874818
you can't fail this paper, protip: you can't

[Anonymous No.14874864]

>>14874862
Meds

[Anonymous No.14874893]

Let [math](a_{n})_{n \in \mathbb{N}}[/math] be a sequence in [math]\mathbb{K}[/math] with

[math]\forall_{n \in \mathbb{N}} : |a_{n} - a_{n + 1} \leq q^n|[/math].

The sequence [math](a_{n})[/math] is a Cauchy-sequence, when [math]0 \leq q < 1.[/math]

>Turn sequence to series
>Geometric series converges
>sequence converges (comparison test)
>convergence means Cauchy-sequence

[Anonymous No.14874898]

>>14874796
Yeah, fuck me. Meant n-2. I keep making mistakes, I need sleep.

[Anonymous No.14874901]

[math]\pi \notin \mathbb{Q}[/math]

How to proof this?

[Anonymous No.14874913]

>>14874893
>>sequence converges (comparison test)
I don't think you need this.

[Anonymous No.14874927]

Still don't know enough to read through this....
>sobalev spaces
I've read about these briefly in a theoretical numerical analysis book from springer, but im only a sophomore undergrad. All the cool topics are years away, and its frustrating.

[Anonymous No.14874937]

>>14874901
[math](\forall n \in \mathbb{N} : \sum_{k = 1}^{n} \frac{6}{k^2} \in \mathbb{Q})\implies \pi^2 \in \mathbb{Q}[/math]

https://youtu.be/ryex7piXx78?t=139

[Anonymous No.14875030]

>>14874805

[Anonymous No.14875039]

>>14874901
Usually done with lindemann weierstrass

[Anonymous No.14875082]

Is becoming a quant worth it? How long does it take to learn stochastic calculus from Basic calculus?

[Anonymous No.14875099]

Hey guys I feel like grades are a scam keeping me from actually mapping out the content of the subjects intuitively to actually be able to do research, am I being too arrogant? The exercises make me feel like an ant, sure I learn a lot by going back to use the definitions, but sometimes the definitions used in a book are obscured by being too specific when in fact you could be comparing definitions with the general case and working through examples to make a better picture. I feel like I could be quite good in grad school if I didn't force my grades to be too high and I rather used part of my time to get ahead

[Anonymous No.14875105]

>>14875099
You can only have one course below a B(~83%) in the majority of graduate programs.

[Anonymous No.14875109]

>>14874619
I'm sure the bitches would find your dick length
of [math]\sum_k|I_k|<\epsilon[/math] from trial
measures to be noteworthy for their purposes.

[Anonymous No.14875116]

>>14875105
I know it's that way IN graduate school, my average grades are above 80% and that's because I was depressed and didn't even try. Now I feel very arrogant like a maniac because I discovered I had ADHD and now I can pull out hours of studying and get great insights with the help of little rests and meditation, and of course Ritalin.
It's not that I couldn't get a better grade, but that if I force myself to not do every single exercise I will have more time to check advanced things I want to study in grad school like Functional Analysis some Topology, Manifolds, Optimization, etc. There's a lot of things I think work great together but it's overlooked in undergrad education and not even many grad schools do put those things together. So I want to prepare specifically for one school that does works on the intersection without wasting too much time in a single topic.

[Anonymous No.14875139]

>>14866559
https://www.youtube.com/watch?v=60z_hpEAtD8
any book or resource to go deeper in video related?
Geometric algebra if you don't want to click the link.

[Anonymous No.14875180]

reposting here hoping one of you graph chads can help a brother out
>>>/g/88823641

[Anonymous No.14875184]

>>14874409
>maybe if I do an le epic 1337 trollsey on him he'll do my homework
What are you, five? Do your own homework and stop e-begging, it's why you're failing your class.

[Anonymous No.14875536]

Kline, or Stewart? Was told Kline's text is more of a "pop sci done right", but I've also heard the Stewart over explains in some parts and doesn't give much explanation in others. One point for Kline's is that it has fully worked solutions, so there's that.

[Anonymous No.14875553]

how do i learn/study/practice topics concerning matrices? i was in tears trying to solve by gauss jordan elimination method.

[Anonymous No.14875611]

>>14866559
missing from math:
math is simple
nothing complex exists
but the way it is taught is intentional obtuse at times
>>14866666
so? put base
and not to mention
a lot of this numberology in maths is pissing in the wind
chasing patterns
is there a high level discussion to address what is useful in math?
if 62/63 digits of pi are all that can be physically accommodated in a causal universe, what does that say to what we think is important in math?

[Anonymous No.14876059]

https://youtu.be/Eqfa6MhAqcw

Question for Americans: is this university level? I saw some people in the comments mentioning this book helped them with calc 1 and calc 3, and I was wondering if those courses are university level, or college, or like precollege if something like that exists. I'm from Europe so I don't know how the overseas system works

[Anonymous No.14876197]

Would you say Real and Complex Rudin is worth a read? I'm at the third chapter and so far it just seems like basics of a mix of real, complex and functional analysis.
Ie. will I get something new from the read if the subject material is known to me?

[Anonymous No.14876274]

>>14876059
Try this instead

[Anonymous No.14876326]

>>14876197
idk nigga check the index and see if there's something you don't already know

[Anonymous No.14876418]

>Calculus 3 course
>professor skipped coverage of the Jacobian and went straight to vector fields and line integrals
uhhhh..?

[Anonymous No.14876444]

>>14876418
A Jacobian is the Fréchet derivative of a vector field. How would you teach it before vector fields?

[Anonymous No.14876448]

>>14876444
I don't know I'm just a student in calculus 3. But the textbook section on changing variables in multiple integrals and using the jacobian comes before the section on vector fields. Is the textbook not in order?

[Anonymous No.14876512]

>>14876448
You can define it directly and teach the geometric interpretation afterwards. This is common.

[Anonymous No.14876614]

i want to learn about directed cyclic graphs what do i read?

[Anonymous No.14876751]

Someone make the new thread a pic of a dinosaur with glasses.
That would be super cool

[Anonymous No.14876758]

>>14876751
no