/mg/ - math general

>What homophobia?
The homophobic slur.

>I hate when the textbook don't show the proof or just "let it as exercise to the reader"
What makes it different from any other exercise?

to take or not to take the bergerpill, that is the question

Ok so I posted this in the stupid questions thread but I dont know if that will get answered there so I thought I would try here as well. Why doesn't this work, what am I doing wrong here?

Where did the [math]+2[/math] in [math] 4y^2 = e^{2x} + e^{-2x} (+ 2) [/math] come from? You have to add that to both sides. And it's actually [math]\frac{1}{2}\ln \left|2y^2-1\right|+C[/math] in your way but it's very wrong.

It should be [math]
2y=e^x+\left(e^x\right)^{-1} \\
2y=u+u^{-1}[/math]
And now it's trivial just solve for [math]e^x[/math] where [math]u=-\sqrt{y^2-1}+y[/math]

(e^x + e^-x)(e^x - e^-x) = e^2x - e^-2x

Can someone explain the significance of these to me? And what sort of crazy shit Watson was on to think these up in a dream?

>Can someone explain the significance of these to me?
Why do you think there is any?

Because the mathematics community spent 70 or so years solving them analytically.

I picked up George Shilov's Linear Algebra (Dover) last night and a lot of it's over my head. Other than that, meandering through Terrance Tao's Analysis I, reviewing proofs in "How to Prove it', and cruising through combinatorics in Lovasz's books.

I suck but I'm on the cusp of leaving this board in the dust.

How about you just read this you tard
inp.nsk.su/~silagadz/Watson_Integral.pdf

I have no clue what Watson's integrals are useful for, but that third one was a real bitch to solve. Even Wolfram says "fuck it" and gives up trying to explain it.

mathworld.wolfram.com/WatsonsTripleIntegrals.html

>However, to obtain an entirely closed form, it is necessary to do perform some analytic wizardry (see Watson 1939 for details). The fact that a closed form exists at all for this integral is therefore rather amazing.

Because most gays are annoying faggots, so deal with it.

LMFAO, best post on sci

take it, it' the path to mathematical enlightenment

Mathematics is mainly just autism.

Most of the shit pure mathematics majors learn is has absolutely no real world application, they basically do the equivalent of digging up piles of dogshit and record it and think what they do is valuable because they "increased knowledge" in the world by forcing the rest of us to learn about popular dogshitting locations. Its especially bad when they think they're smarter than the rest of society because they have complicated equations for finding out the precise locations of dogshit. Intelligence isn't impressive if it's sublimated into useless knowledge-wanking.

Pure math degrees is autistic applied maths, which in turn is autistic chemistry/physics, which in turn is autistic engineering.

Get a real job and apply yourselves.

did you fail calc 1 or something?

You're doing a lot at the same time, can't you slow down the pace? You can leave this board but stop the "I suck" attitude, you'll do fine!

Fuck off to

>Fuck off to y-you too

When you square both sides you get e^2x + 2e^xe^-x + e^-2x = e^2x + e^-2x + 2

Next week im going to start studying math.
Is it hard in the beginning?

I have literally learnt everything on khanacademy for the last month.
Algebra I , II , Precalculus, Calculus Ab and Physics 1.
But I still have a feeling that my foundation is not solid enough.
I have looked at the recordings of the lectures from last year and it has scared me to death. I dont even like math that much, I just think its the hardest topic to study and right now im in my best years and have very few distractions.

>Algebra I , II , Precalculus, Calculus Ab and Physics 1.
That's not math.

>That's not math.
What is it?

It's literally in the sentence you quoted.

>It's literally in the sentence you quoted.
Ok but then what are they?

He actually has some really insightful points about computability if you're into numerical computing.

They are not math. I believe I've said that already in the post you quoted.

>They are not math. I believe I've said that already in the post you quoted.
Ok but I asked what they are, not what they aren't.

Can you prove that this question is even answerable?

>Can you prove that this question is even answerable?
Didn't you already answer it?

According to you I didn't answer it. Since I didn't say what they are, I just said what they aren't.

>According to you I didn't answer it.
When did I say that? You simply gave a wrong answer

>Ok but I asked what they are, not what they aren't.
Didn't you say this just a few posts above? Or is there a third party involved in our conversation?
>You simply gave a wrong answer
It is correct though. They aren't math. Never were and never will be.

bump

>Didn't you say this just a few posts above?
What part of that quote implies that you didn't answer the question?

>It is correct though. They aren't math. Never were and never will be.
Proof?

Please don't impersonate It's very rude.

> (You)
>Please don't impersonate (You)
>It's very rude.
Is something confusing you? We're the same person

Unfortunately, that's not how language works. Don't test me.

>Unfortunately, that's not how language works.
What do you mean?

My time is too valuable. Who the hell are you?

>My time is too valuable. Who the hell are you?
What is making you so confused? I'm someone curious about what part of "Ok but I asked what they are, not what they aren't" implies that you didn't answer the question and what a proof for "It is correct though. They aren't math. Never were and never will be" looks like

666 you're doomed

This whole thread turned into a joke

You're too easy to bait, lurk more before posting next time

How do I find the determine the last two digits of 8^25 and 12^25?

If we counted in base prime then we could turn multiplication and division into mathematical operations that resemble addition and subtraction in our current numeric base.

BUMP

Explain further? I don't understand what you mean.

Can someone rec a book on PDEs? I just need something to learn how to solve them for my heat transfer course since I was apparently supposed to learn that.

>You're too easy to bait, lurk more before posting next time
I was just looking for the answer

Evans or don't bother

bump

Suppose I have eight socks, two of each color: (e.g. red, white, blue, black)., cyan, black, and white. I randomly draw four socks. What is the probability that I have exactly one pair of socks with the same color?

Can anyone help a brainlet? I'm trying to compute derivatives. Pic related.

I've gotten to this point, no idea how to substitute it into the formula and simplify. Any advice?

Hmm I don't know off hand a way other than l'Hopital and that involves taking the derivative, obviously not allowed. Let me think.

Wow

stupid question
i have a probability of 0.8 and if fails, i have another one with the same probabilty
is the second one 0.4 then?
what if i had a third one?

mlultiply by conjugate

Stupid question thread

which test should i use to test infinite geometric series for convergence?

does anyone know what kind of series this is and how to tell if it converges/diverges? not sure how to solve these with n as an exponent as well as a base

sum 2/n diverges so the whole thing diverges

split the sum
the first summand is a geometric series
the second summand is a harmonic series which diverges.

obviously diverges by the comparison test

thanks guys. is that how i solve this one as well? by splitting and testing both for convergence? also if they both converge can i find the sum by doing a/1-r for both and adding the result together?

any book for high school trigonometry?

The summation is just a shorthand for + so you can always "distribute" it over addition. In this case, you can just split the denominator over each term, then split the summation. the first term is a converging geometric series (2/e)^n, since e~=3 and 2/3 < 1. The second term is a diverging geometric series since e~=3 and 4/3 > 1

>so you can always "distribute" it over addition.
no

>reverse image search
>suggestions: mathematics

If [math]0 \le n < 99[/math] is such that [math]8^{25} = 100k + n[/math], then [math]8^{25} \equiv n \mod 100[/math]. Noticing [math]8^8 \equiv 16 \mod 100[/math], we get [math]8^{25} = 8\cdot 8^{24} = 8 \cdot (8^8)^3 \equiv 8 \cdot 16^3 = 32768 \equiv 68 \mod 100[/math]. Similarly, [math]12^5 \equiv 32 \mod 100[/math], so [math]12^{25}=(12^5)^5 \cong 32^5=(2^5)^5=2^{25} \mod 100[/math], but [math]2^{12} \equiv 96 \mod 100[/math], giving [math]2^{25}=2\cdot (2^{12})^2 \equiv 2\cdot 96^2 = 18432 \equiv 32 \mod 100[/math]. Transitivity now gives [math]12^{25} \equiv 32 \mod 100[/math].

>[math](12^5)^5 \cong 32^5[/math]
That was supposed to be [math](12^5)^5 \equiv 32^5[/math].

How does (the canonical embedding of) the group G act on the irreducible factors of the group determinant? That is, when the group determinant is seen itself as an element of C[G].

im having a real problem with my discrete math class can an user help another user?

Define f:R→R as a floor function: f(x)=⌊x⌋.
Answer the following questions using the definition of f given above. Your answers for (b) and (c) should each be a set. You may specify each set by listing the values, using set builder notation, or describing the set in words.
a) Draw the graph of the function f(x) for -3≤x≤3.
b) What is f({x│-1

what have you tried so far?

>real problem with my discrete math
heh

i get the how to do the floor function but in a very basic level. but at the moment of indicating the image and the preimage im troubled

It would be a numeric base where you represent all integers as a tally of their prime factors. To multiply by 3, you would simply increment the tally of the number of threes, and to divide by six you would would decrement the tally of how many twos and threes there are.

It would make multiplication and division computationally easier at the expense of addition and subtraction.

>Define f:R→R
That's already an impossible task.

What do you think about the limited amount of functions that maths has?

What I mean is that perhaps some nonlinear equations might have analytical solutions but the functions themselves are unknown and cannot get expressed in terms of sine, log, polynomials and others.
So that you must limit yourself to solutions that consist of just a bunch of components.

You mean shit like quintic polynomials and the fact they don't always have an analytic solution?

>Have you discovered something interesting in math recently?

Yeah actually. I had to tutor this girl in ODEs and I thought I'd be fucking horrible at it but with some refreshing I found the separable 1st order ODEs aren't too bad and I was pretty good at it. We were sitting there going through her homework online and all my answers were right. Love that feeling.

I mean things like the simple pendulum equation:
[math]\frac{\mathrm{d} \phi}{\mathrm{d} \phi}+\sin(\phi)=0[/math]
It has no known analytical solution due to the nonlinear nature of the equation. But perhaps there exists a solution but it just cannot be constructed with the limited amount of options that we have due to the limited amount of "ingredients". If we had more of these, we might be able to solve more problems.

Meant
[math]\frac{\mathrm{d}^2 \phi}{\mathrm{d} t^2} +\sin(\phi)=0[/math]

Can some mathematician expain to me why [math]\sqrt{-1}[/math] deserve a whole realm of mathematics while [math]\log{-1}[/math] does not.
What makes a non-allowed operation more valuable than another?

The root of -1 doesn't get a whole realm of mathematics. Rather, it's easier/more efficient to use i to denote the root of -1, and makes notation more efficient to write complex numbers as Re+iIm than in some other way

Complex analysis isn't about the root of negative one, it's about the complex plane and we found the fastest and most robust way to write it was with i.

once you go from reals to complex by working with sqrt(-1) you can define log(-1) by working with the complex logarithm
en.wikipedia.org/wiki/Complex_logarithm

Log(-1) :=
ln(|-1|)+ pi * i =
ln(1) + pi * i =
pi*i

The Industrial Revolution and its consequences have been a disaster for the human race

females have the same number of through-passing holes as males

>by splitting and testing both for convergence?
yes

Answer this FUCKING question