/sci/ - Science & Math

>>9162159
you got the picture wrong, faggot

>>9162159
also you made a new thread too early, try again in 12 to 24 hours

>>9162245
>you got the picture wrong, faggot
Why the homophobia?

>>9162248
>also you made a new thread too early, try again in 12 to 24 hours
What do you mean? The other one is autosaging

>>9162245
what do you mean by this?

>>9162159
L O N D O N

What are the GOAT books for algebra and analytical geometry?

I hate when the textbook don't show the proof or just "let it as exercise to the reader"

I'm a brainlet, what's the point in buying a incomplete book?

>>9162255
What homophobia?

>>9162159
Topologically, is that female a male?

>>9162557
>What homophobia?
The homophobic slur.

>>9162543
>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?

>>9162159
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?

>>9162600

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]

>>9162600
(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?

>>9162916
>Can someone explain the significance of these to me?
Why do you think there is any?

>>9162921
Because the mathematics community spent 70 or so years solving them analytically.

>>9162159
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.

>>9162923
How about you just read this you tard
http://www.inp.nsk.su/~silagadz/Watson_Integral.pdf

>>9162916
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.

http://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.

>>9162255
Because most gays are annoying faggots, so deal with it.

>>9162562
LMFAO, best post on sci

>>9162598
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.

>>9162988
did you fail calc 1 or something?

>>9162929
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!

>>9162255
>>9162580
Fuck off to >>>/r/ibbit/

>>9163345
>Fuck off to >>>/r/ibbit/
y-you too

>>9162891
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.

>>9163595
>Algebra I , II , Precalculus, Calculus Ab and Physics 1.
That's not math.

>>9163623
>That's not math.
What is it?

>>9163629
It's literally in the sentence you quoted.

>>9163631
>It's literally in the sentence you quoted.
Ok but then what are they?

>>9162598
He actually has some really insightful points about computability if you're into numerical computing.

>>9163634
They are not math. I believe I've said that already in the post you quoted.

>>9163639
>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.

>>9163641
Can you prove that this question is even answerable?

>>9163644
>Can you prove that this question is even answerable?
Didn't you already answer it?

>>9163646
According to you I didn't answer it. Since I didn't say what they are, I just said what they aren't.

>>9163652
>According to you I didn't answer it.
When did I say that? You simply gave a wrong answer

>>9163657
>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.

>>9162532
bump

>>9163661
>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?

>>9163666
Please don't impersonate >>9163657
It's very rude.

>>9163667
>>>9163666 (You)
>Please don't impersonate >>9163657 (You)
>It's very rude.
Is something confusing you? We're the same person

>>9163669
Unfortunately, that's not how language works. Don't test me.

>>9163671
>Unfortunately, that's not how language works.
What do you mean?

>>9163673
My time is too valuable. Who the hell are you?

>>9163675
>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

>>9163666
666 you're doomed

This whole thread turned into a joke

>>9163641
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.

>>9162532
BUMP

>>9164197
Explain further? I don't understand what you mean.

>>9162159
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.

>>9164114
>You're too easy to bait, lurk more before posting next time
I was just looking for the answer

>>9164248
Evans or don't bother

>>9162532
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?

>>9165644
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.

>>9165120
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?

>>9165644
mlultiply by conjugate

>>9165866
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

>>9166225
sum 2/n diverges so the whole thing diverges

>>9166225
split the sum
the first summand is a geometric series
the second summand is a harmonic series which diverges.

>>9166225
obviously diverges by the comparison test

>>9166236
>>9166239
>>9166241
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?

>>9166343
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

>>9166361
>so you can always "distribute" it over addition.
no

>reverse image search
>suggestions: mathematics

>>9164191
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].

>>9166504
>[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 anon help another anon?

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<x<4})? That is, what set is the image of the set of values between -1 and 4? Explain.
c) What is f^(-1) ({x│ 2<x<5})? That is, what set is the preimage of the set of values between 2 and 5? Explain.

>>9166580
what have you tried so far?

>>9166580
>real problem with my discrete math
heh

>>9166585
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

>>9164221
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.

>>9166580
>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.

>>9167870
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.

>>9167876
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.

>>9167894
fuck, meant
[math] \frac{\mathrm{d}^2 \phi}{\mathrm{d} t^2} +\sin(\phi) =0 [\math]

>>9167894
Meant
[math]\frac{\mathrm{d}^2 \phi}{\mathrm{d} t^2} +\sin(\phi)=0[/math]

>>9167907
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?

>>9168173
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.

>>9168173
once you go from reals to complex by working with sqrt(-1) you can define log(-1) by working with the complex logarithm
https://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

>>9162562
females have the same number of through-passing holes as males

>>9166343
>by splitting and testing both for convergence?
yes

>>9162532
Answer this FUCKING question

>>9167879
What was your reward?

Hey /mg/, I can only negate the nag to commit suicide when I'm researching or reading. Any other math grad students experience this?

>>9162159
[math](a+bi)^n[/math]

=

[math][r(cos\theta+isin\theta)]^n[/math]

=

[math]r^n[cos(n\theta)+isin(n\theta)][/math]

Question: How and why does "n" get into the angle in the third step? I took a Trig/pre-Calc class and this was never really explained. I tried posting this yesterday and I just kept fucking it up. It's probably fucked up now too but oh well.

>>9169704

the identity can be easily proven inductively, basically it comes down to repeat application of identities, which is what you'd expect.

>>9169715
>it comes down to repeat application of identities, which is what you'd expect.
I see. That actually is what I figured. When I tried simply expanding it and multiplying the terms via distribution, I get a big mess to work with and wasn't really sure where to start with applying the identities, since there are many options.

>>9169704
[math] \cos \theta + i \sin \theta [/math] is [math] e^{i \theta} [/math], so it's nothing other than [math] \left( x^a \right) ^{b} = x^{ab} [/math].

>>9166591
You need to read the definitions of image and preimage again, because I don't think you fully understand them.

I'm a grad student enjoying his morning dump. Ask me anything.

>>9162532
Algebra Chapter 0 by Aluffi

>>9165644
do it for general [math]r\in\mathbb R[/math] and set [math]r=\frac14[/math]

>>9166580
(a) is a step function every integer from -3 to 3
(b) are the integers -1 to 3
(c) the reals from 2<=x<6

I don't understand calculus and I legit feel like I have a learning disability.

I'm working through Real and Complex Analysis by Rudin. I'm beginning to think Rudin is a meme, why do people like this guy's books?

>>9171094
>I'm beginning to think Rudin is a meme
good job, you figured it out

Has anyone worked through Ross's Understanding Analysis? Thoughts??

>>9171088
you just lack an imagination sorry

>>9162159
>Taking intro to proofs this semester.
>Need to read an academic article in math/applied math and submit a short summary by next week.
>Haven't read a math article in my life.
>Tried looking up some topics in linear algebra on google scholar, all of them are out of my league.
>Wildberger's rational trig paper is pretty accessible, but also a meme.
Any recommendations? Or even a starting point? I took Cal 1 through 3 as well as linear algebra already, if that helps.

>>9171094

you fell for the meme

>>9171115
I just looked through it, it looks cool.

I think it looks like a worthwhile read for someone unacquainted with analysis.

>>9171094
better than krantz's complex analysis book. that book is a mess

>>9171251
thanks! Yeah I have an understanding of proofs and am very good at calc but never done analysis

[math]x=cos(\frac{\pi}{3}) + i\cdot sin(\frac{\pi}{3})[/math]
[math]x^3 =[cos(\frac{\pi}{3}) + i\cdot sin(\frac{\pi}{3})]^3[/math]
[math]x^3 =cos(\pi) + i\cdot sin(\pi)[/math] by De Moivre thoerem
[math]x^3 =-1[/math]
[math]x =-1[/math]
[math]cos(\frac{\pi}{3}) + i\cdot sin(\frac{\pi}{3})=-1[/math]

What's going on here?

>>9171854
>What's going on here?
What is happening here is that instead of properly studying De Moivre's theorem you just read the first case for natural exponents, then went to smoke a blunt and get fucked in the ass by Tyrone and then went back to do complex algebra, which then led you to post this retarded piece of shit.

Dude. Just read what De Moivre's theorem actually says and stop being retarded.

>>9171854
x^3=-1 implies that x is one of the numbers in the picture
You just picked the "wrong" one at the end.

>>9171088
3blue1brown x F

>>9171854
[eqn]x = -1 \\
x^2 = 1 \\
x = 1
-1 = 1[/eqn]
exactly the same reasoning. you should figure yourself what went wrong.

>>9172112
there's a newline after x=1, apologies

>>9171216
easiest that comes to mind and is easily accessible is the series of papers on IUTT by Mochizuki

>>9172123
Seconding this. I used to struggle with proofs, but Mochizuki's graphic approach was really helpful.

Studying pic related. I wanna get into studying higher mathematics and work my way through apostol pt.1, but my mental arithmetic is really slow. I hope 25 isn't too late to get good at juggling numbers in my head.

>>9172141
I started studying that very same great courses series at age 27, so you're not the worst off in that regard. I'm an ignorant NEET loser though, so maybe that's not saying much.

>>9162159
systems interfacing and channel normalization

[eqn]
1.(\exists x)(Ax\RightarrowBx)
2.(Ax)
3.?
[/eqn]

>>9172155
can you do arithmetic in your head quickly?

>>9172230
I could when I was practicing. I'm rusty now but I did find the series useful for mental arithmetic. If you practice applying its techniques A LOT, to the point where they just become second nature, you will be glad you did. They are useful for impressing brainlets if nothing else.

Studying diff manifolds

>>9165120
https://en.wikipedia.org/wiki/Hypergeometric_distribution#Multivariate_hypergeometric_distribution

remember to find the number of rearrangements and multiply, (think multinomial coefficient)

i finished writing my first article and my advisor suggested sending the paper to some journal
how do i get to know if this journal is good/average/shitty?

>>9172298
ask your advisor and let me know the answer pls

>>9172298
check the impact factor

>>9171216
Look up the paper Gershgorin’s Theorem for Estimating Eigenvalues by Sean Brakken-Thal. It's an easy read.

studying linear regression. can anyone explain why we have to have the assumption that the residuals have to be normally distributed? Is it something like we want the errors to not have any sort of patterns in them? We want them to be sort of, 'perfectly random' like a normal distribution? Why do we need that to do linear regression?

>>9162159

Ok how the fuck do you memorize math equations. I understand the concepts and can do the examples but when asked in a question without a formula provided I cant remember them.

>>9173465
>I understand the concepts
You don't.

>>9172298
>>9173465
>>>/sci/sqt/

>>9173465
you don't

>>9173465
You are talking about physics/engineering right?

I have this (irrational?) hate of groups, maybe not as an object in general, but examples of groups make me dry heave figuratively. Examples like the integers (mod n) are OK. Above all though, the group I hate the most is the dihedral group. Just seeing it used as an example makes me want to punch somebody.

Is this normal? It doesn't happen with rings

>>9174644
>Is this normal?
no

>>9174645
Last year in my algebraic number theory class exam there was a question regarding finding the class group of some quadratic ring extension and it happened to be the Klein group and made me be angry for the rest of the exam

>>9172141
Paul Lockhart just released a nice book on Arithmetic. It's a super pleasant read and he makes it interesting and it interesting to learn about and understand instead of just memorising techniques. I'd definitely recommend it.
However, the truth is that arithmetic isn't important for higher math, and you shouldn't worry too much about mastering it before moving on to bigger and better things. If you can, you should consider starting with Apostol now, while you relearn arithmetic.

>>9174644
>Above all though, the group I hate the most is the dihedral group.
I fucking hate it how the results of composing two elements of it are supposed to be obvious.
NO MOTHERFUCKER THEY ARE NOT FUCK YOU.

Can anyone please help a dumb brainlet trying to learn basic statistics?

"Consider the joint P.D.F of two random variables, X and Y, as given in pic related, where X and Y are in the interval [0,1]. Given that f(theta) is a random P.D.F within the interval [0,1], prove that Cov(X,Y) > 0."

Any idead where I can start with this?

Does 𝜃(𝜃(f(n))) = 𝜃(f(n))? Would I be wrong to make that assumption for a math problem?

>>9174644
>I hate the most is the dihedral group
>not hating An the most

>>9174745
no it wouldn't, as long as you prove it ;)

brainlet here can anyone help me with proving this

Show that ¬ p → (q → r) and q → (p ∨ r) are logically equivalent.

im staring at a wall of differences and i have no idea how to do this

>>9174862
wall of equivalences **

>>9174862
Truth table??

>>9174914
it says i'm not allowed to use a truth table

>>9171094
Good you are a fucking retard. Take a couple weeks off of 4chan, bud.

>>9174955
>Good you are a fucking retard. Take a couple weeks off of 4chan, bud.
huh?

>>9171094
Rudin's books are horrible. Dry and disgusting.
They are not didactic.

>>9162159
Is the guy who does edits of anime images with math books still around?

>>9162532
bump. also need to know.

>>9174733
just draw a picture

Is >300k starting a meme?
What realistic opportunities (except post-grad research) would I expect with a BSc in maths?

>>9173455

do you mean error terms not residuals?

>>9175532

yes, 300k starting is a meme. Realistically, if you do some programming classes you can get a software dev job

>>9175153
Hi. How can I help you?

>>9162988
this
only useful maths are calculus, stats, and linear algebra

anything else is autistic masturbation. like when the autists try to masturbate in class, and the teacher doesn't know how to handle this because they haven't had the special ed training, so the teacher just ends up locking the wanking tard in the supply closet at the back of class, but then the tard is still staring out at you through the security glass window, and you can hear him shouting "I CAN STILL SEE YOU"

>>9174738
calculate the covariance brainlet

>>9175926
Hey, how's your post-doc going? You were supposed to start this fall autumn right?
>How can I help you?
Can you please edit this image >>9175153 with Lang's Linear Algebra (or some other aesthetic springer yellow book like you did before)? I've been reading it over the summer and I really like the style of the book. I want some memento but I suck at photoshop.

>>9174862
I guess set up a system with one of them negated and do a tableux/tree. Otherwise you could just use the fact that implication can be rewritten as the conjugation of the negated precedent and the antecedent.

For a nice variety [math]X[/math] over [math]\mathbb{C}[/math], can [math]\mathop {{H^1}}\limits^ \vee \left( {X,G{L_n}\left( {{\mathcal{O}_X}} \right)} \right)[/math] be given the structure of a complex vector space?

>>9162600
Multiply both sides by e^x for your first step, then use that to factor out an e^x later on.

>>9166225
You can split it up into two separate summations (a summation of sums is a sum of summations), and factor out a 2 from the second summation and use the p series theorem to prove it diverges.

>>9162159
I discovered you're a bunch of niggers!

>>9176214
>a summation of sums is a sum of summations
"no"

>>9176156
>post-doc
I'm doing a PhD. It's going steady.
>Can you please edit this image >>9175153 with Lang's Linear Algebra
I'll see what I can do when I get back from work.

Can someone help me with pic related?
Im not sure if I did this right(im pretty sure im wrong). Can someone show me the proper steps to get the correct answer?

A friend of mine showed me the following equation and I'm stunned. I have no idea how to solve it analytically for x and can't figure out if that's possible at all. This is the trigonometric equation:

[math]n * tan ( x ) = tan ( n * x )[/math]

I'm intrigued because it seems so simple. I was wondering if anyone has ideas?

>>9177043
>"real" numbers
It doesn't matter anyway.

>>9177498
>>"real" numbers
Who are you quoting?

>>9168252
>have been
they continue to be and will do so within the next 100 years

>>9168173
because sqrt(-1) makes the real numbers algebraically closed (every polynomial factors into linear terms)

what the fuck has log(-1) ever done for anyone

>>9169704
jesus, fuck all those trig functions and PLEASE use complex exponentials only

trig functions = hard, lots of memorization

comlex exp funtion = completely trivial to work with, elegant and simple, no memorization necessary

>>9177043
>I'm intrigued because it seems so simple. I was wondering if anyone has ideas?

I explored a couple of special cases (setting n to 2, 3, 0.5 and 0.2) and the solutions are pretty chaotic but it is easy to figure out why:

First, notice that if you take the restricted tangent function (the one defined only in -pi/2 to pi/2) then there is one and only one intersection (assuming n not equal to 0) at the point x=0.

Now going back to the normal tan function, the one that is defined for almost the entire number line, you can easily see that there will be intersections not only at x=0 but also at all the points that are "equivalent" to x=0. And those constitute an infinite family of solutions. For example, in the case n=7 then this infinite family of solutions in characterized by [math] x = 2 \pi z, z \in \mathbb{Z} [/math] but you can quickly see there are other intersections. There are other families of solutions. Why?

Because when you multiply the tan function like that, the curves either expands or gets squished and then two tangent curves that aren't even aligned can intersect at weird places, and there seems to be no pattern behind these intersections.

I mean, I bet that if you can turn up your autism and start studying this in depth you can find some law that at least generates a second class of solutions but I wouldn't do it. Maybe you'd like to.

I am an MLT major. Did you know that red blood cells start out with a necleus, but lose it as they mature. Also, when during the stages of red blood cell development, they start large and keep shrinking until they mature small enough to exit the bone marrow sinuses.

>>9177804
Yeah man, I learned that in high school biology. I can even go a step further and tell you that the reason they lose their nucleus is to have more room to store the shit they store.

>>9177548
log(-1) is pi*i, which also completes the reals
any non real completes the reals

>>9177804
>>9177806
>>>/b/

>>9177812
Not him, but you gotta admit that [math] i [/math] is the best candidate for a rectangular representation of complex numbers.

>9176967
You're derivation might be off
https://math.stackexchange.com/questions/84331/does-this-derivation-on-differentiating-the-euclidean-norm-make-sense

>>9176967
This
>>9177825

Good recent applied math papers?

https://arxiv.org/pdf/1709.05662.pdf

>>9177819
>Not him, but you gotta admit that i is the best candidate for a rectangular representation of complex numbers.
Why?

>>9177948
What do you mean why? In [math] \mathbb{R}^2, i = (0,1) [/math] which together with [math] 1 = (1,0) [/math] forms the canonical basis. Using anything else would make the coordinates of a complex number more complicated

>>9177965
>Using anything else would make the coordinates of a complex number more complicated
What's more complicated about the basis (1,0), (0,-1)?

>>9177930
>"applied "math""
>>>/lit/fiction/

Brainlet here
What do they mean by:
To find y^n we differentiate this expression for y' using the quotient rule

>>9177965
>In R2,i=(0,1) which together with 1=(1,0) forms the canonical basis. Using anything else would make the coordinates of a complex number more complicated
Why does the structure of the complex numbers as a real vector space take precedence? Seems completely arbitrary considering there's the set structure, the group structure, the ring structure, the complex vector space structure, etc.

>>9177969
I don't know man I guess we have a canonical basis only to jerk ourselves off

>>9177976
Dude, no one here is talking about what complex numbers are. I am explicitly talking about their rectangular representation. How else are you going to study the rectangular coordinates of complex numbers if not by viewing it as a typical vector space?

>>9177975
I don't know man. Do you have anything against the quotient rule? You can also differentiate it with the product or chain rule I guess, but I didn't know there was a growing movement of discrimination against the quotient rule. The quotient rule hasn't done anything wrong man. Ruleism is bad.

>>9177980
>I am explicitly talking about their rectangular representation. How else are you going to study the rectangular coordinates of complex numbers if not by viewing it as a typical vector space?
What's 'not rectangular' about any other basis where you use a multiple of i instead of i?

>>9177985
>What's 'not rectangular' about any other basis where you use a multiple of i instead of i?

Do you have the wrong type of autism or what? Those other systems are also rectangular, but they imply the use of a basis distinct from the canonical one, which just complicates things most of the time.

>>9177983
No I mean how does differentiating y' get you y^n

>>9177987
>Those other systems are also rectangular, but they imply the use of a basis distinct from the canonical one, which just complicates things most of the time.
How do they imply the use of a basis distinct from the canonical one? The canonical basis is in R^2, not in C...

>>9177991
You might wanna read that again. It says it gets you y''

>>9177993
Okay, lets think for a second. What are rectangular coordinates? We want a set of elements [math] x_1,x_2,...,x_n [/math] from the field so that we can write every element of the field as a linear combination of those numbers. You know, like when we write a + bi, which is a linear combination on [math] 1,i [/math].

Man... you know, I mean. If only there existed a field of mathematics in which we studied how to write things as linear combination of other things. If only it existed. Too bad it doesn't huh? It just doesn't exist. It has never been studied. Too bad. I mean, if it existed we could say it had to do with algebra and it would have to do with linear combinations, so we could call it linear algebra. Too bad it doesn't exist though.

>>9177996
>You know, like when we write a + bi, which is a linear combination on 1,i.
It's also a linear combination of 1 and c*i for any real number c, what's your point? You realize there's more than one isomorphism between C and R^2 right?

>>9177996
Also you seemed to have misread my post, my question was "How do they imply the use of a basis distinct from the canonical one?" which your post didn't seem to answer

>>9177995
How can I be this dumb

>>9177999
>It's also a linear combination of 1 and c*i for any real number c, what's your point?

But choosing to write things as a linear combination of [math] 1, \frac{i}{2} [/math] would be incredibly retarded because the canonical basis has many useful properties. That's why it is called CANONICAL.

For example, suppose we have the complex number (a,b) where a and b are the real coefficients. If we want to calculate, for example, the norm of that number we can immediately plug a and b into the expression for the norm.

On the other hand, if we had (a,b) be a the coordinates of a complex number in the base [math] 1, \frac{i}{2} [/math] then before we can calculate our norm we would have to transform b back into normal coordinates (b/2) and then calculate the norm.

>>9177999
>You realize there's more than one isomorphism between C and R^2 right?

This has nothing to do with anything. Stop whipping out the big words before you even understand the simple words.

>>9178002
>which your post didn't seem to answer

If you write a numbe as a linear combination of [math] 1, ci [/math] then you are now using the basis [math] 1, ci [/math], so you are using a basis distinct from the canonical.

I mean, that's self evident right?

Here to chime in that this is the ultimate future of math research: creating nanotechnological proteins/carbs/lipids for things we need done.

https://en.wikipedia.org/wiki/Molecular_logic_gate

yes creating MECHANICS at the nucleotide level to do things here is one example of this in action: recombinant plasmids that may actually live inside a bacteria. this plasmid is made out of synthetic materials in a lab. first evidence of abiogenesis.

nobel prize 2016:

https://en.wikipedia.org/wiki/Fraser_Stoddart

>>9178005
>But choosing to write things as a linear combination of 1,i2 would be incredibly retarded because the canonical basis has many useful properties.
You seem confused, the canonical basis (1,0) and (0,1) is in R^2, not in C. The corresponding basis in C depends on your (not canonical!) choice of isomorphism.

>For example, suppose we have the complex number (a,b) where a and b are the real coefficients. If we want to calculate, for example, the norm of that number we can immediately plug a and b into the expression for the norm.
You get the identical norm using an i -> -i automorphism.

>This has nothing to do with anything. Stop whipping out the big words before you even understand the simple words.
It has everything to do with it if you understood where the canonical basis lives.

>If you write a numbe as a linear combination of 1,ci then you are now using the basis 1,ci, so you are using a basis distinct from the canonical.
Wrong again, see above.

>>9178013
>any basis is canonical, you just gotta choose the right isomorphism

This is why I genuinely think you are retarded. This also makes me think you are some kid who got too excited after reading some wikipedia articles about algebra.

Stay in school kid. Engaging in this level of pedantry is crucial for success, but you are supposed to only be pedant about things that actually matter. If you want to hold this idea that by picking the right isomorphism we can make any basis canonical then that's good for you man. I am sure that next time you are doing a computation you can just start defining isomorphisms and then get your shit done instead of just immediately solving the problem by not being retarded and using the actual canonical basis we all know and love.

>>9178021
>>any basis is canonical, you just gotta choose the right isomorphism
Who are you quoting? I said there's a unique canonical basis (1,0) and (0,1) for R^2. There simply is no canonical basis for C.

At least give a definition of "canonical basis" if you're going to keep misusing the term so we can at least refer to the same thing. The only 'canonical basis' I've ever seen is the basis (1,0,...,0), (0,1,...,0), ...., (0,0,...,1) for the [math] F[/math]-vector space [math] F^n [/math]. C is not equal to R^2 as a set, and so (1,0) and (0,1) are (obviously) not even vectors of C, and so there is no canonical basis for C as a real vector space.

>If you want to hold this idea that by picking the right isomorphism we can make any basis canonical then that's good for you man.
Please learn to read, I said nothing about any 'right' isomorphism, in fact my post even said "(not canonical!) choice of isomorphism"

>>9178030
>There simply is no canonical basis for C.
If only C was also a vector space :(

>At least give a definition of "canonical basis"
See, this is your problem. When you learn math in college your professor will give you one. Wikipedia articles won't.

>[Insert the rest of you jerking off about F or something]
Good for you.

>C is not equal to R^2 as a set
Actually a common construction says that C is equal to R^2 as a set. It is not necessary to construct C from an extension. You can just take R^2 and give it a field structure, then call it C. Then if you need some more jerking off you can proof that this is isomorphic to the C constructed from an extension of R.

>and so there is no canonical basis for C as a real vector space.

Yes it is, it is called 1,i and that is why we write things like a + bi.

>>9177930
>https://arxiv.org/pdf/1709.05662.pdf
based

i'll read this when i get some time

>>9178037
>If only C was also a vector space :(
define "canonical basis"

>See, this is your problem. When you learn math in college your professor will give you one. Wikipedia articles won't.
Actually they will: https://en.wikipedia.org/wiki/Canonical_basis

>Actually a common construction says that C is equal to R^2 as a set.
Then you wouldn't be using 1 and i as basis vectors, since those aren't elements of R^2. You need to make up your mind instead of going back and forth between two distinct sets.

>You can just take R^2 and give it a field structure, then call it C.
Exactly "a field structure", of which you have many choices.

>Yes it is, it is called 1,i and that is why we write things like a + bi.
See above, if your construction of C is as the set R^2 then 1 and i are not elements of C. If your construction of C is as an extension, then this basis is not canonical.

>>9178021
I have a question for you. Let's take the set [math]A = \{ a + b \sqrt2 \mid a,b \in \mathbb{Q}\}[/math], a two-dimensional vector space over [math]\mathbb{Q}[/math]. In your opinion, does [math]A[/math] posses some "cannonical basis"?

(I'm not the other guy btw)

>>9178044
>define "canonical basis"
You already googled it so I don't know why you are even asking. Also when jerking off about F you mentioned one so you clearly know what it is.

>Then you wouldn't be using 1 and i as basis vectors

Google the construction. 1 = (1,0) and i = (0,1).

>Exactly "a field structure", of which you have many choices.

Vector addition and (a,b)*(c,d) = (ac - bd, ad + bc)

You are trying too hard.

>>9178053
>You already googled it so I don't know why you are even asking. Also when jerking off about F you mentioned one so you clearly know what it is.
Yes, for vector spaces F^n. If you want C to equal R^2 as sets then 1 and i are not elements and so can not be basis vectors. If C doesn't equal R^2 then the definition of canonical basis does not apply.

>Google the construction. 1 = (1,0) and i = (0,1).
Likewise, the construction 1= (1,0) and -i = (0,1).

>Vector addition and (a,b)*(c,d) = (ac - bd, ad + bc)
Yes, that's one choice of field structure, good work!

>You are trying too hard.
You're not trying hard enough, you still haven't provided a satisfactory definition of "canonical basis" that allows 1,i to be a canonical basis for C.

>>9178050
Yeah. That would be [math] 1, \sqrt{2} [/math].

>>9178057
>If C doesn't equal R^2 then the definition of canonical basis does not apply.

This is something I've wanted to write but I always forget: you are retarded. C does not have to equal R^2 to be a vector space. C is a vector space regardless of how you construct it. C is a fucking algebra fucking hell man are you high? What is all this bullshit?

>Likewise, the construction 1= (1,0) and -i = (0,1).

Then we get into the issue that when you want to compute the norm of a number given its coordinates, you can't simply input the coordinates into the formula for the norm. You'd first have to transform the coordinates.

>Yes, that's one choice of field structure, good work!
Autism

>you still haven't provided a satisfactory definition of "canonical basis" that allows 1,i to be a canonical basis for C.

Autism.

C is an algebra. It is always a vector space, regardless of you construct it. You are absolutely retarded. Are you in university? Do you actually know math?

>>9178066
>C does not have to equal R^2 to be a vector space
Agreed, that's why I said "if". Did you miss that part? I even specified the case where C doesn't equal R^2, where the definition of canonical basis can not apply since C is not R^2.

>C is a fucking algebra fucking hell man are you high?
Please refrain from the unnecessary profanities, they don't further your argument at all.

>Then we get into the issue that when you want to compute the norm of a number given its coordinates, you can't simply input the coordinates into the formula for the norm. You'd first have to transform the coordinates.
Given which coordinates? If I use the basis 1, -i I get the same norm you do without any need to "transform the coordinates".

>C is an algebra. It is always a vector space, regardless of you construct it.
Triviality, an algebra is a vector space by definition.

>You are absolutely retarded.
Irrelevant.

>Are you in university?
Not anymore.

>Do you actually know math?
I studied it for several years in university.

>>9178066
>Yeah. That would be 1,sqrt(2).
Which definition of canonical basis gives this?

>>9178089
>>9178092
I've been thinking about your discussion and I have to side with the anon saying that [math]\mathbb{C}[/math] "essentially" doesn't have a cannonical basis. Of course you can define [math]\mathbb{C} = \mathbb{R^2}[/math] (this gives you a cannonical basis), but you have to define the multiplication by an explicit formula. Is this ad-hoc multiplication special in some sense? Is it "cannonical"?

Imo the neatest definition [math]\mathbb{C}[/math] is as
[eqn]
\mathbb{C} = \text{linear span of }\{ \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix},\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix} \}\text{ in Mat}_{2 \times 2}(\mathbb{R})
[/eqn]where the multiplication is inherited from the ring structure. This is a "natural" construction (it doesn't require any choice) and it shows how complex numbers represent rotations and uniform scalings of the plane with the multiplication being just composition. If we put [math]1 = (\begin{smallmatrix} 1 & 0 \\ 0 & 1 \end{smallmatrix})[/math] and [math]i = (\begin{smallmatrix} 0 & -1 \\ 1 & 0 \end{smallmatrix})[/math], we obtain the usual description of [math]\mathbb{C}[/math]. But those two matrices are just one particular way of describing this subspace. Different choices lead to different isomorphisms with [math]\mathbb{R}^2[/math] AND (!!!) different coordinate formulas for multiplication. For example if I take [math]i = (\begin{smallmatrix} 0 & -2 \\ 2 & 0 \end{smallmatrix})[/math] for the second matrix, the multiplication now looks like this:
[eqn]
(a+bi)(c+di) = (ac-4bd) + (ad+bc)i
[/eqn]This means that I can take [math]\mathbb{R}^2[/math] and define multiplication with the above formula, and I obtain a structure which is isomorphic with the usual [math]\mathbb{C}[/math] as vector spaces, algebras, whatever. Is the usual structure more cannonical than mine? It's not. It all boils down to the choice of a basis of a certain subspace, and this choice is not cannonical in any way, only by an agreement.

>>9178418
I meant to quote>>9178066 also

Is someone in this thread really throwing a fit over describing {1,i} as the canonical basis for C/R? Jesus Christ, how pointlessly pedantic. I think anyone reasonable person would consider this the most natural basis for C.

>>9178557
Math generals exist for the following reasons:
(a) showing off to other undergrads
(b) avatarfagging with your husbando/waifu/favourite anime studio
(c) complaining about (b)
(d) finitism funposting
(e) general complaining about stuff
(f) n-level metaposting for every [math]n \in \mathbb{N}[/math]
Your post is (e), what you were complaining about is (a), and my post is (f).

>>9178092
Canonical/Natural doesn't really have a definition.
It's refered this way because most people feel like it is more natural, more simple.

Probably belongs in /sqt/ but figured I'd try here.

Does the difference of power sets get rid of the empty set? I wouldn't think so, but I figured I'd ask.

How does one go about integrating sin(x)/x?

>>9178580
Integration by parts

>>9178576
You mean like [math]\{ \emptyset \} \not\in \mathscr{P}(X) \setminus \mathscr{P}(Y)[/math] for all sets [math]X, Y[/math]? If so, then yes. It follows from the uniqueness of the empty set. I'll have you figure out the details.

>>9178557
>I think anyone reasonable person would consider this the most natural basis for C.
The argument stemmed from ways of studying the complex numbers in rectangular coordinates, in which case 1, -i is equally useful.

Use a truth table. Start with p, q, r then do one for all the operators. [math]\neg p, p/Rightarrow q, p\lor q[/math] etc. The last statements in your truth table with be the ones you are trying to prove are equivalent (i.e. the ones you put). If you don't know what it means for two statements to be equivalent ask yourself if p is equivalent to p, p is equivalent to q, p is equivalent to ~q. Pay attention to the entries in your truth table

>>9176171
no answers?

>>9178598
>[math]\mathscr{P}(X)[/math] for all sets [math]X[/math]
>sets
No such thing.
>It follows from the uniqueness of the empty set.
Sure, assuming it exists.

>>9162929
Just started with Tao too, how do i know if my proofs are rigorous enough? Sometimes they seem suspiciously short and easy.
Apart from that, learning linear algebra from a niche book made as a guide to my undergrad course, but it contains excercise that apparently are grad-level so i'm fucked and have to constantly bother TAs.

>>9179339
>Use a truth table.
But I don't use classical garbage, anon.

>>9179380
>Sure, assuming it exists.
Oh, that's a good idea! Let's use that as an axiom. Thanks, buddy.

>>9162159
That's a dude, isn't it?

FUCK I have the option to do my master's project with a top quality mathematician (40+ publications, has appeared on Numberphile) on a project I'm not interested in at all (Geometry of 3-manifolds, Thurston's conjecture) or with a younger mathematician with not many publications on a subject I'm really much more interested in - topological vector fields and vector bundles - and I want to continue doing for a PhD.

wat do

Just got introduced to partial derivatives today and I felt like a wizard writing down [math]\frac{\partial z}{\partial x}[/math]

>>9179517
>has appeared on Numberphile

>>9174668
>>9174644
I like you a lot

>>9179517
Geez, that's rough. I mean, it's amazing, congratulations. But I think you will find working something that will continue into your PhD better - I don't have a PhD so I don't think my advice is the best.

>>9179517
Pick the first option for the memes.

Lecture on Infinity Categories (with exercises)

https://arxiv.org/pdf/1709.06271.pdf

>>9174644
stupid moron

>>9174644
The dihedral "group" isn't even a fucking group.

>>9179114
And (1, -1) is just as reasonable for R^2, yet it's more annoying than the usual basis.

>>9179727
>And (1, -1) is just as reasonable for R^2
That's not a basis for R^2.

>>9179517
Let me ask you this, do you want a job in academia after getting your PhD? If so, go for the first option, a guy with a lot of weight to his name can get you into a good Post Doc position and very likely he's a great researcher so the papers you publish with him will go a long way to landing you a professorship, remember, if you wanna get into academia you can't just be good at what you do, you also need connections (Levi Civita ones, preferably). If you plan on going into industry, than why are you getting a PhD? It'll actually hurt your chances in some cases. You can also just talk to your adviser and say you want to do something else for your master's instead, just ask him and get his advice. There are also some cases in which if two profs know each other they will jointly advise a student, with one being primary and the other being secondary, see if that can work for you. Worst case, just work with the first guy.

Why does division by x or x^2 give different answers? Did I screw up along the way?

>>9179873
>"""=""" undefined
>Did I screw up along the way?
Yes, you did.

>>9179873
>"""=""" 1/0
>Did I screw up along the way?
Yes, you did.

>>9179882
The book I'm using uses the same notation tho

>>9179894
Your book is retarded engineer garbage if it misuses "=" in such a way.

>>9179894
I don't see any
>"""=""" 1/0
on that page

>>9179906
It's calculus by steward
>>9179915
Well yeah it's a different question

>>9162581
The problem is if I made the exercise correctly. There are some books without the answer.

How can anyone believe in the "law" of the excluded middle? Even real numbers sound more plausible.

>>9179873
They aren't different. When dividing out x^2, the top goes to 1, while the bottom goes to zero from the negative side, which means the limit is -\infty.

>>9175153
>>9175926
What's it like having literal autism?

>>9180288
What are you referring to?

tips?

>>9180326
fugg wrong image

>>9180327
pls respond

>>9180327
Take an element g of G different from the identity.
Consider the cyclic subgroup generated by it.
This cannot be isomorphic to Z because Z has subgroups different from itself.
Therefore, this Cyclic subgroup is isomorphic to Zn for some n.
n has to be prime because otherwise you'd get subgroups again.
Because G has no subgroups other than the trivial one anf G itself, it must be isomorphic to Zn.

>>9180333
I was writing a well-thought-out response, but then I saw the image you decided to attach to your post.

>>9180340
this is incorrect.

>>9180343
why?

>>9180341
I'm not a very smart man

>>9180333
>>9180346
>reddit frogs
>>>/r/eddit/

>>9180340
this is correct

>>9180345
i was just kidding. it seems to be correct.

>>9180327
Let [math]g\in G[/math]. Then the cyclic subgroup generated by [math]g[/math] has an order that must divide [math]|G|[/math]. Suppose a nonidentity element [math]h[/math] has a nonprime order, say [math]n=pq[/math] with [math]p[/math] prime. Then consider the subgroup generated by [math]h^p[/math], which has order [math]q[/math]. If [math]q\neq 1[/math], then we have successfully created two different subgroups that are not the trivial one. So [math]q=1[/math], contradicting the fact that [math]h[/math] has nonprime order. So the only subgroups that can be generated must have prime order. Now any two subgroups of different prime orders will be different, therefore there is only one subgroup of prime order, and it is [math]G[/math] itself.

QED

>>9169775
check your c)
f(2)=2, which is not in {x|2<x<5}.
Likewise f(5)=5, which again is not in {x|2<x<5}

>>9180293
>photoshopping math books into anime images
>needs to ask what's autistic about it

yeah..

>>9180376
What exactly seems to be autistic about it? Are you new on this website?

>>9180378
>What exactly seems to be autistic about it?
Everything.

>>9171094
Not the best if it is your only introduction to formal measure and integration as Rudin defines the Lebesgue integral, and uses this to derive the Lebesgue measure as opposed to measure first and then integral. Doing it both ways helps you gain a more complete understanding. The exercises are good (can be pretty challenging, but on successfully completing them your understanding will be excellent).
I like Functional Analysis, but the notation is outdated (Rudin talks of B* algebras), and also he loses some of the generality for the sake of ease of exposition (everything is Hausdorff, so you need to look elsewhere if you want to work with TVS's)

>>9162532
>learning from books
>not inducing and deriving its contents from wikipedia pages

kid... your not ganna make it

>>9162532
>>9180413
>not developing the fields on your own
>not writing your own books

Does someone know the programme ZoomMath 500? I really want to get it but it's not worth the $100. Anyone know how to crack it or how to otherwise obtain it illegally?

>>9180492
For the Texas Instruments calculators.

>>9162988
>>9175954

Weak bait, but waiting for my 300k salary slip so I'll bite.

have you losers ever heard of operations management, actuarial science, data analytics?but:
>Math is useless.
Lmao, don't get mad at the rest of us because you kids couldn't pass an introductory analysis course. Come on buddy really?lol

>>9163667
Please don't impersonate >>9163667
It's very rude

>>9180374
oops yeah did the preimage of the set {x|2<=x<=5}

Let's say there's a man whose internal temperature varies with time. The temperature of the air and the intensity of sunlight may also affect his temperature, both of which vary with time and his position on Earth. If the man's internal temperature falls above or below two defined value, he dies.
If I wanted to find all of the positions on Earth where the model man would die after 24 hours, what would be the best approach? Could you pick a shit load of random points and run them though the system if equations, or could you use inequalities to find the precise areas of Earth that satisfies the conditions for death after 24 hours?
Have any of these ideas been defined in the literature before? I would like to learn more about techniques for solving this problem.

>>9180797
This is called surface climate processes
Try reading Boundary Layer Climates by TR Oke
It's actually not a very new area of study

>>9180797
>>9180802
>>>/sci/sqt/

>>9179493
Yes it is, he's known as katzuka or something, he browses /g/ and is moderator arisuchan

>>9180802
This is exactly what I was looking for. Thanks.
>>9180876
>Stop discussing math in math general
>No questions in math general
OK kid.

Wrote up my first LaTeX proof for an assignment. I've been re-reading it for half an hour just admiring it. I think it's time to write up my CV in LaTeX

Suppose [math]j_1, j_2[/math] are (Lawvere-Tierney) topologies in a topos, and let [math]\land \colon \Omega \times \Omega \to \Omega[/math] be the classifying morphism of [math](t, t) \colon 1 \to \Omega \times \Omega[/math], where [math]t \colon 1 \to \Omega[/math] is a truth morphism. How do I prove [math]\land (j_1, j_2)\colon \Omega \to \Omega[/math] is a topology? It's probably some very simple thing I can't see, but I just can't.

>>9181545
Most TeX CVs look like garbage.

>>9181545
>write beautiful 2 page proof in LaTeX.
>flawless visually.
>turn in assigment.
>it's incorrect.
>graded zero.
>tfw brainlet but good looking.

Let V be a vector space over a field F.
Let W be a subspace of V.
Let A(W) be the annihilator of W.
Prove that dimA(W) = dimV - dimW

Proof(?)
Let v1,...,vk be a basis of W.
Extend this basis to a basis v1,...,vk,vk+1,...vn of V.
Denote by V* the space of all linear functionals from V to F.
Consider the map T:V*--->V* such that Tφ (v1) = φ(v1) , ... , Tφ (vk) = φ(vk) and Tφ (vk+1) = 0 , ... , Tφ (vn) = 0
This map is linear.
It's kernel is Ann(W).
We can naturally identify its image with W* via isomorphism.
From dimKerT + dimImT = dimV* and dimV*=dimV we get
dimAnn(W) + dim(W) = dimV which is what we needed to prove.


Is this proof correct?

>>9182192
Yes

>>9182192
the question should obviously have an assumption of finite-dimensionality but otherwise it seems fine

>>9182196
>>9182197
alright, thanks!

Which math textbook requires the highest IQ to complete?

Does your uni seperate mathematical statistics and statistics? I just learned that this is mostly a swedish thing. Here you can study statistics or begin a bachelor in math and after the second year you can choose to switch to the math stats specialization instead of math. Also we have a masters degree in actuary science that also is given by the math stats department (that is in the mathematical institution) and you must complete the masters programme to work as an actuary, I've heard that most countries doesnt do that as well

>>9182192
>vector space
>>>/b/

>>9162159
how do you get a math gf?

>>9181790
Depends on what you've seen

>>9181872
Don't scare me anon

>>9182483
>mathematical statistics
Sounds like chemical chemistry.

>>9182624
by attending classes at a math department

>>9162159

Anyone here got recommendations for pdfs/textbooks on number theory that show you how to actually make calculations based on the theory? Not anything totally basic like taking modular inverses, but rather say estimating the zeroes of a polynomial over a field, etc.

Especially anything related to group/field theory, power series, and p-adic analysis. I've read Koblitz and some other stuff, but it seems that they all proceed to very abstract stuff about varieties etc instead of delving on how to solve problems in practice.

>>9182897
Silverman's books tend to aim for a more hands on approach to arithmetic geometry if that's what your looking for. Of course, there will still be some general theory because you need theorems. I recently read a book by Cassels and Frolich about genus 2 curves that is very much based on calculating rational points, even resorting to computer calculations at times.

>>9183011

Thanks! I'll check them out.

Is Rotman's Introduction to Homological Algebra a good book?
I've had some experience with homological algebra already, but not too much.

>>9183131
Yes. I like it.

>>9182480
divine proportions

>>9162159
Hi there!
I'm attempting to cover all of trigonometry so I can do better at precalculus. From there, I will just move onto calculus. I REALLY want a good hold on calculus. Just for fun...
Also I'm covering some calculus III topics. I have no idea why though.

>>9182897
>>9182897
>Anyone here got recommendations for pdfs/textbooks on number theory that show you how to actually make calculations based on the theory?
Four of Cohen's books (Number Theory Vol 1, Vol 2, Course in Computational Algebraic Number Theory, Advanced Topics in Computational Number Theory)

I'm not great at maths, but am still fascinated with doing weird calculations with complex numbers and seeing what pops out. That being said:
[math] i + i = 2i [/math]
[math] i * i = -1 [/math]
[math] i^i = e^{-\frac{\pi}{2}}[/math]
[math] ^ii = ??? [/math]
How do you continue with tetration? Is it real or complex? What about pentation? Does a pattern form?
I couldn't find the answers to my questions, maybe you can.

>>9180341
>>9180353
grow up and take your roleplaying to >>>/qa/

>>9183332
>real
>complex
No such thing.

>>9183341
Ok! Can you answer my question now?

>>9183350
You are asking if [math]^ii[/math] belongs to a set which does not exist. It's neither real nor complex.

>>9171088
So after struggling for weeks calculus is suddenly brainlet easy mode. Not really certain why I get it now.

>>9183983
What is an integral?

Need some hints on proving that:
G is a group with |G|>1 and the only subgroups of G being {G, {e}}
I CANNOT use cyclic groups in the proof.

>>9184277
Missed the question part

>Prove that |G| is a prime and thus finite