/mg/ - Math general

Mathematics.
Other disciplines for the less gifted (such as physics) also find a use for it.

Shilov's linear algebra is complete garbage.
Good

>Pros
Easy, clear and well written.
>Cons
Doesn't do enough stuff, avoiding the determinant is nice but it's ultimately something you need to learn. Avoids being more general.

I think if you're new to proofs Axler is good, but otherwise a book like Hoffman and Kunze is a lot better.

Very general proofs. It's a way to make abstract statements about the relationships between objects.

axler does determinants....in the last chapter

Finally, a place to talk about applied math

nothing (shhh...it's a secret)

>applied math
This would be the correct thread for discussing that

see It clearly says "no redditors".

just a freindly reminder OP that the textbook that bitch is holding is a shitty LA book for a beginner, i bought that bitch and understood everything up until chapter 5 and that took me a whoe summer.

Matrices and Linear Algebra by Hans Schneider is a way better beginner book

I used the word "avoid" in the sense that he does things without using it, even in places where it normally would be used (because it's at the end of the book). In any case, Axler's approach to the determinant is bad (he doesn't talk about the determinant as a multilinear function, and I think he also doesn't write the permutation formula).

while it is true he doesn't talk about k-forms at all, I don't know what you mean by permutation formula. He defines the determinant with the usual Leibniz definition, pic related.

It's been a while since I've read it, so I wasn't quite right. To review what Axler does, he defines the determinant for a transform as the product of eigenvalues, then for matrices by Leibniz definition (this is what I meant by permutation formula, because you sum over permutations). Then he shows these are the same.
I don't like either as a definition, the first definition is bad because it only works correctly with transformations on complex spaces, he uses a hack to get it to work on real spaces. It certainly doesn't work on rings. The Leibniz definition is bad just because it comes out of nowhere, it makes more sense when you derive it from a definition which is understood.
The k-form definition is excellent because you can start with the vague idea of measuring the "signed volume" of a transformation. Just from this idea you can figure out some of the axioms a function would need to satisfy, and go from there.

starting with signed volume seems like an arbitrary or poorly motivated place to start, what's nice about starting with the algebraic approach is that it relates the determinant directly to the solvability of a system of equations, which is, atleast supposedly, the point of linear algebra.

best linear algebra book coming through

It's pretty much the best from a theoretical perspective.

I like smart cute anime girls

Geez, I'm fucking embarassed by this general and the fellow mathematicians that post here. Literally every other general theead in every board has an OP with explanations and material recommendations for noobies, but this one only have "le anime girl durr" and some internal joke about the last thread in it. And don't even get me started on the amount of shitposting and people posting their homeworks here. This general has turned to shit.

>le
>durr
>cancerous "explanations and recommendations for noobies"
I'm not your "fellow mathematician". I don't associate with redditors.

...

Why the fuck does
[math]\sum_{p=0}^{n-1}\sum_{q=p}^{n-1}\binom{q}{p}w^{p+q}=\sum_{q=0}^{n-1}\sum_{p=0}^{q}\binom{q}{p}w^{p+q}[/math]
?

Why is that anime glorified by /mg/ when it doesn't even make sense mathematically speaking?

Axler assumes the reader is brainlet; read > linear algebra via exterior products - winitzki.pdf

forgot, he also assume the reader is brainlet, but it's better

She is the queen of /Veeky Forums/, she gets free pass on any general.

Nevermind. Developing the sums show that it's trivial.

>anime
>steins gate
Spotted the redditor.

"Hurr durr tis a visual novel fag redditor" GO FUCK YOURSELF WITH YOUR CRAPPY ANIME GIRLS WEEABOO PIECE OF SHIT

Lol this mad

Can anyone help with pic related? The idea is to write the inside of the sum of the left in terms of an integral and then you change the order so that the integral is outside and the sum inside. But what i get is not what the exercise asks for. I don't know what I'm doing wrong.

Do you go through each theorem? Or you just skip some, which are too tedious? Like when I started linear algebra, I had a theorem saying "basis exists", but I haven't proved it. Is it ok?

What do you do when you go through a theorem, and it uses another one, proof of which you dont remember?

The sum on the right is constant when p_n < t < p_n+1 where p_n is the n-th prime and it changes discontinuously when t is prime, so you can split the improper integral into an infinite sum of proper integrals. Once you find the values of these integrals you can use some simple indexing tricks to get the LHS.

>CRAPPY ANIME
Redditor spotted.

>Hurr durr tis
>Makise Kurisu
>anime girls

see

Wait, I think I got it. But someone please correct me if what I say is retarded. I noticed that:
[math] p^{-\epsilon} = \epsilon \int_p ^{\infty} \frac{dt}{t^{1+\epsilon}} [/math]

Therefore
[eqn] \sum_{p>exp(1/\epsilon)} p^{-1 - \epsilon} = \sum_{p>exp(1/\epsilon)} p^{-1} p^{-\epsilon} = \epsilon\sum_{p>exp(1/\epsilon)} \left( p^{-1} \int_p ^{\infty} \frac{dt}{t^{1+\epsilon}} \right)[/eqn]

That gets me the sum and the integral. Where p and t run through:
[math] exp(1/\epsilon) < p < \infty \\ p < t < \infty[/math]

But the region of the p-t plane described by these inequalities is the same as:
[math] exp(1/\epsilon) < t < \infty \\ exp(1/\epsilon) < p < t [/math]

So I can change the order of integration and get:

[eqn] \epsilon \int_{exp(1/\epsilon)}^{\infty} \left( \frac{dt}{t^{1+\epsilon}} \sum_{exp(1/\epsilon) < p < t} \frac{1}{p} \right) [/eqn]

Which is the theorem. I think this is right, the only problem is
>tfw in calculus 3 you never had to change the order of integrals in infinite regions so now you can't even do number theory

Life is suffering. Hopefully someone who had a better calc 3 professor can tell me if this change is correct.

Can someone please help me understand the step by step math to get from 7.32 to 7.33?

You can use it to have fun.

Truly this. Also it can be used to gain a better understanding of anime.

>that book
literally who
Hoffman & Kunze or bust

if i had to guess, subtract y_t from y_(t-1) you brainlet

What textbook should I use to self study multivariable/vector calculus?

How much calculus should I know beforehand?

Currently reading a real classic, Fourier Series and Orthogonal Functions. Pic related, very much enjoying it. Just got to chapter 4, intro to PDEs. Its an original printing of the book. It has a smell like it has been sitting in a personal library for decades. Great condition!

Understand Differentiation, Integration, and what Convergence of a series means. I used Vector Calculus by Marsden and Tromba, but I thought it was only mediocre.

Forgot my fucking pic kms

If [math]H[/math] is a subgroup of two groups [math]G_1[/math] and [math]G_2[/math] and if [math]\frac{G_1}{H}\cong \frac{G_2}{H}[/math], does it follow that [math]G_1 \cong G_2[/math]?

no

How to prove it?

counterexample

I want to put my benis in makoto

[math]G_1 = \mathbb{Z}_4, G_2 = \mathbb{Z}_2 \times \mathbb{Z}_2[/math]
Hope you can at least figure out what H should be.

That girl sure looks like she knows her physics and particularly her biology and some chemistry there too but we can be sure Okabe is way better at physics but yet is the first to time travel oh gosh must be nice to actually apply your numbers sometimes

You don't even need physics for time travelling. Math is actually enough.

>every open set is closed
What did p-adic numbers meme by this?

>he's never worked with clopen sets before

Yes I have, [math]\mathbb{R}[/math] :^)

>meme
>:^)

>[math]\mathbb{R}[/math]
He said sets.

[math]\mathbb{R}[/math] is a clopen subset of [math]\mathbb{R}[\math]

[math]\mathbb{R}[/math] is a clopen subset of [math]\mathbb{R}[/math]

Any suggestions on how to solve this problem?

I don't know, just plug the definition of ring homomorphism into it?

>[math]\mathbb{R}[/math]
>set
[math]\mathbb{R}[/math] cannot be shown to be a set.

why not?

It can't be shown to be finite.

>infantile cartoon
>queen
Lmfao

>infantile cartoon
>lmfao
Subhuman redditors aren't welcome here.

dude what

Are you rejecting infinite sets?

What do you even mean by "rejecting"? I'm simply saying that sets which are "not finite" can't be shown to exist.

>can't be shown to exist.
exist where ? in the real world ? in ZCF ? in some other formal system you are working with ?

>exist where ?
In any consistent sufficiently powerful formal system. And please don't use French here, this is an English speaking board.

[eqn]
\ddot \varphi(t) - sin(\varphi(t)) + \alpha\varphi(t) = 0\\
V(x,y) = cos(x) - 1 + \frac{1}{2} *(\alpha x^2 + y^2)
[/eqn]
Show that [math] V(\varphi(t), \dot \varphi(t)) [/math] is constant

>tfw stuck on the first problem of the introductory chapter

Best easy guide to learn how to write proofs? I'm going to fail my computational theory class because my puny brain can't do maths. I just want to write code

SQT please

dumbass

Guys, I need to prove that every finite group is finitely presented.
My attempt:
Assume group [math]G[/math] is finite and let [math]A \subset G[/math] be a generating subset of [math]G[/math], that is, [math]G =
[/math]. Therefore, there exists a surjective homomorphism [math]\phi: F(A)
\rightarrow G[/math] which means [math]G =
[/math]. Now, since [math]G[/math] consists of all products of the form [math]\phi(a_1)\phi(a_2)...\phi(a_n)[/math] and the number of such products is finite( group is finite) the number of products equal to the identity element is also finite. Therefore, [math]ker \ \phi[/math] consisnts of all words [math]a_1...a_n[/math] such that [math]\phi(a_1...a_n) = e_G[/math] which makes it[kernel] finite. [math]F(A)/ker\ \phi \cong G[/math]. Hence, group [math]G[/math] is finitely presented by [math]ker\ \phi[/math].

Is it ok, did I miss something?

WHy is this board so plagued by cartoon-loving delinquents? One would think developing an appreciation for maths (assuming you're not all larping) would impose some kind of normal functigonality on these creatures, but I'm proven wrong every time I come here. Stop, it's annoying. Go back to /b/ so you can touch yourself to feet. And cartoons are for kids. Just because all the love you ever had in your life wasn't reciprocated doesn't meant you need to annoy others online. Quiet now children.

Does anyone know of anything like Dirichlet's Kernel that can be employed to simplify the Fourier series of functions?

A telltale sign of an adolescent's mentality is attempting to appear more mature than one actually is, to look up to and emulate adulthood, and become hostile towards things he views as childish. Therefore, I have to ask the question: Are you actually 14 years old, or are you just acting like a 14 year old?

>irony: the post
I'm 24. Not claiming to be more mature. That's your projection, animefag. I said anime is cartoons, defending them is pathetic, and "*ddit" because someone calls you out on it is just as pathetic. Stick to engineering, kiddo.

>insulting anime is feigning maturity
wew, talk about digging a deeper hole

>I'm 24.
So the answer to my question is that you were just acting like a 14 year old. That's really embarrassing for you.

>Not claiming to be more mature.
>cartoon-loving delinquents
>And cartoons are for kids.
>Quiet now children.
>kiddo.
Really looks to be the opposite. Trying to put people below you is the same thing as trying to put yourself above them.

>That's your projection
I don't think you know what that word means. I'm projecting onto you, a sense of maturity I have over people who post anime on Veeky Forums, because I don't watch anime?

>animefag
Bad assumption.

I don't know shit about presentation theory, I had to look up on wikipedia what exactly finitely presented means. But can't you just take G as the generating set and list all possible binary products (gh = something), as the relations ?

What's 9 x 4?

If you like anime to the point where you get mad at others and shit up an entire board because they don't like you shitting up the board with anime to begin with, yeah, you're pretty fucking annoying and pathetic

>hurr you called them kiddo so you have the mentality of a 14 yo
Kindly fuck off. Stop trying to claim the moral high ground because nitwits shitting up a board you actually enjoy doesn't piss you off. Spamming ">>\r\*ddit" is also fucking annoying, and it just so happens to be the same anime kids.
>I'm not part of the group you're targeting, but let me go out of my way to criticize you and call you a child because you're getting frustrated at the frustrating and childish behavior of other people.
Please grow the fuck up and contribute to the thread.

>admitting to literally browsing reddit
Your subhuman kind isn't welcome here.

>Fourier series of functions
>contribute to the thread

reddit doesn't belong here
anime does belong here
if you don't agree with those points, then you don't belong here because those were facts about this place long before you were here. it's as simple as that. now, if anime is being used in such a way to take the thread off topic, that's bad, but that isn't anime's fault.

I sure love it when /mg/ is more talk about Anime than actual mathematics.

>I sure love it when /mg/ is more talk about Anime than actual mathematics.
I sure love it when people point out problems instead of working to solve them

So you can find the range of a function by finding the domain of its inverse.
Does this work even if the function isn't bijective?

My thoughts are that as long as the y has at least one corresponding x, then the y is in the range. So finding the inverse of a non bijective function for the purpose of finding the range is valid.
Is there anything wrong with this reasoning?