/mg/ - Math general

Threadly reminder to ignore physishits .

>>9113829
Axler's linear algebra, pros and cons?

>>9113837
>Axler's linear algebra, pros and cons?
Why don't you open it and find out?

>>9113853
Looking for other people's opinions, my guy.

>>9113861
I'm not 'your guy', or even a guy, at all.

>>9113866
Physishit/redditor spotted. Fuck off to your containment thread.

>>9113866
Checked. You need to take a chill pill, my duder. You're having a case of the 'tisms and i'm just trying to be reasonable

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>>9113829
Wtf is category theory good for?

>>9113866
Here is a special thread for you >>9113879

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>>9113884
Mathematics.
Other disciplines for the less gifted (such as physics) also find a use for it.

>>9113829
Shilov's linear algebra is complete garbage.
>>9113837
Good

>>9113837
>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.

>>9113884
Very general proofs. It's a way to make abstract statements about the relationships between objects.

>>9113945

axler does determinants....in the last chapter

>>9113829
Finally, a place to talk about applied math

>>9113884


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

>>9113983
>applied math
This would be the correct thread for discussing that >>9113879

>>9113981
>>9113985
see >>9113829
It clearly says "no redditors".

>>9113829
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

>>9113981
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).

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>>9113998

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.

>>9114017
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.

>>9114090

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.

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best linear algebra book coming through

>>9113837

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

>>9113829
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.

>>9114309
>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]
?

>>9114358
Why is that anime glorified by /mg/ when it doesn't even make sense mathematically speaking?

>>9113837
Axler assumes the reader is brainlet; read > linear algebra via exterior products - winitzki.pdf

>>9114387
forgot, he also assume the reader is brainlet, but it's better

>>9114382
She is the queen of //sci//, she gets free pass on any general.

>>9114371
Nevermind. Developing the sums show that it's trivial.

>>9114382
>anime
>steins gate
Spotted the redditor.

>>9114434
"Hurr durr tis a visual novel fag redditor" GO FUCK YOURSELF WITH YOUR CRAPPY ANIME GIRLS WEEABOO PIECE OF SHIT

>>9114503
Lol this mad

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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?

>>9114569
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.

>>9114503
>CRAPPY ANIME
Redditor spotted.
>>>/r/eddit/

>>9114503
>Hurr durr tis
>Makise Kurisu
>anime girls
>>>/r/eddit/

>>9114503
see >>9113868

>>9114569
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.

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

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>>9113884
You can use it to have fun.

>>9115786
Truly this. Also it can be used to gain a better understanding of anime.

>>9113829
>that book
literally who
Hoffman & Kunze or bust

>>9114940
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!

>>9116072
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.

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>>9116096
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]?

>>9116801
no

>>9116830
How to prove it?

>>9116839
counterexample

I want to put my benis in makoto

>>9116801
[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.

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>>9114358
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

>>9117190
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?

>>9117525
>he's never worked with clopen sets before

>>9117540
Yes I have, [math]\mathbb{R}[/math] :^)

>>9117423
>>9117525
>meme
>:^)
>>>/r/eddit/

>>9117544
>[math]\mathbb{R}[/math]
He said sets.

>>9117603
[math]\mathbb{R}[/math] is a clopen subset of [math]\mathbb{R}[/math]

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Any suggestions on how to solve this problem?

>>9117618
I don't know, just plug the definition of ring homomorphism into it?

>>9117613
>[math]\mathbb{R}[/math]
>set
[math]\mathbb{R}[/math] cannot be shown to be a set.

>>9117823
why not?

>>9117877
It can't be shown to be finite.

>>9114392
>infantile cartoon
>queen
Lmfao

>>9118108
>infantile cartoon
>lmfao
Subhuman redditors aren't welcome here.
>>>/r/eddit/

>>9117885
dude what

>>9117885
Are you rejecting infinite sets?

>>9118293
What do you even mean by "rejecting"? I'm simply saying that sets which are "not finite" can't be shown to exist.

>>9118308
>can't be shown to exist.
exist where ? in the real world ? in ZCF ? in some other formal system you are working with ?

>>9118321
>exist where ?
In any consistent sufficiently powerful formal system. And please don't use French here, this is an English speaking board.

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[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

>>9118474
SQT please

>>9118444
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 =
<A>[/math]. Therefore, there exists a surjective homomorphism [math]\phi: F(A)
\rightarrow G[/math] which means [math]G =
<\phi(a_1), ..., \phi(a_n)>[/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?

>>9114769
>>9114772
>>9117600
>>9118256
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?

>>9118659
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?

>>9118728
>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 ">>>/r/*ddit" because someone calls you out on it is just as pathetic. Stick to engineering, kiddo.

>>9118728
>insulting anime is feigning maturity
wew, talk about digging a deeper hole

>>9118775
>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 4chan, because I don't watch anime?

>animefag
Bad assumption.

>>9118604
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?

>>9118878
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.

>>9119377
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.

>>9121346
>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?

>>9121433
>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?
No because if it's not bijective then there's no inverse.

Consider f(x)=x^2 from R to R, which has no inverse

>>9118659
>getting this mad
It is not like this website originated as an anime board..

>>9121532
But if I set f(x)=y and solve for x, I get x=+/-sqrt(y) which has a domain of all positive R, which is the same as the range of f(x).

Maybe calling it the inverse was wrong, but I'm not seeing how this method is wrong.

>>9121433
>So you can find the range of a function by finding the domain of its inverse.
Uh, no. You are thinking of codomain, not range.

>>9121532
>...if it's not bijective then there's no inverse.
False. Consider e^x over R. Not bijective, but it has an inverse - namely, ln(x).

>>9121591
No, I am talking about specifically the range.

>>9121598
ln(0)=?

>>9118659
I think recognizing that people can have interests other than yours happens around sophomore year of college. Don't worry anon, you're almost there.
Also, it's wrong of you to think that because we know math that we're knowledgeable about other things, cultured, or even wise. Math is just another subject to study, and you should have your own personal reasons for pursuing it - there is nothing inherently elite about it.

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>>9121598
>Consider e^x over R. Not bijective, but it has an inverse - namely, ln(x).

>>9121612
-∞

>>9121598
[math]\exp :\mathbb{R} \to {\mathbb{R}^ + }[/math] is bijective. [math]\ln :{\mathbb{R}^ + } \to \mathbb{R}[/math] is its inverse.

>>9121627
not real.

>>9121624
>>9121628
>>9121612
oof, my math degree is worthless

>>9121637
>>9121598
Is this what people are referring to when they say math degrees are 'hard'? lmao

>>9121581
Can someone please answer this post?

>>9121681
to start, x=±√(y) is not one function but two. if you were to combine them, you would not have a function since, by definition, a function cannot be multi-valued for any one point.

>>9121698
Ok, then I can take any of those two functions and still get the exact same domain.

>>9118256
>newshit using the term redditor
Oh the ironing

>>9121433
Bijective functions are synonymous with invertible functions.

When you say [math]\ln x[/math]
is the inverse of [math]e^x[/math], you're thinking of [math]e^x[/math] as a function from [math]\mathbb{R}[/math] to [math]\mathbb{R}^+[/math], not to [math]\mathbb{R}[/math]. You force it to be a bijection by restricting its domain and codomain.

So in a sense, any functions admits an "inverse" provided you whittle down the sets you're working over enough. But your "inverses" won't be unique anymore, since you can just keep restricting your domain further. So to answer your original question, no.

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>>9118444
>too dumb to take a derivative
get out of my board subhuman

>>9121820
I'm still unconvinced.
And I'm not sure you understood my question properly.

I already know that non bijective functions can't have inverses, I'm not arguing that.

Basically what I'm saying is,
Given a function f(x), an easy way to find the range of it, is to solve for x in terms of y, and find the smallest domain of whatever x equates to. That domain is the range of f(x).
As far as I can tell, this method works.

Eg:
f(x) = x^2 = y
y = +/-sqrt(x) (we will take the positive sqrt, but any works)
Smallest domain of +sqrt(x) is all positive R, which is the same as the range of f(x).

Do you understand what I'm getting at?

>>9121882
And if the domain of f(x) is only a subset of R, say [0,1] union [2, infinty)? How does this work?

I study CS, I did a very complex program relating math javascript

>>9114309
>this general has turned to shit
This happens to every general without fail.
This is a fucking MATH and science board, it's like having a cooking general on /ck/. It's asinine.

>>9121891
Ok, I see what your saying, it doesn't work there.
But it at least works to find the largest possible range right?

Are there any other ways to easily find the range of any function?

In my experience, the field axioms do not of-themselves include the property of cancellation (if ab = 0 , then this implies that a = 0 or b = 0), which is specific to domains, and particularly integral domains (as developed in wiki's current treatment).

Here is my question. Is there a convenient phrase which encompasses ALL of the field axioms and the integral-domain "cancellation" property all-at-once? Since the reals and complexes are important fields, it would seem that this would be a word-short-phrase worth coming up with.

>>9122061
>In my experience, the field axioms do not of-themselves include the property of cancellation (if ab = 0 , then this implies that a = 0 or b = 0), which is specific to domains, and particularly integral domains (as developed in wiki's current treatment).
It follows from invertibility of all non-zero elements

>>9114621
There are about a hundred thousand papers in mathematics each year, so there is clearly some judgement that needs to occur to gain the most insight. That said, the fact that a basis exists for a field should not be taken for granted, especially since it does not necessarily exist for rings over modules.

>>9113829

I swear this Makoto fan art is way cuter than the one in the game.

>>9114621
Ideally, you should have some idea of how to prove just about everything you use.
It's easier said than done and, whereas it's (more or less) doable during your undergrad, when you get to grad school, you will likely not have time for that (you need to start working on your own stuff), but it's always important to have that goal in mind. Proofs of basic results give you inspiration when you have to do something original (you have an array of ideas you can try to tweak in order to see if it helps you)

>tfw theres a physishit in the back of your calc 3 class who wont shut the FUCK up

How do I make him disappear?

>>9122288
You need to stand up to him and put him in his place.
I'd say something like " I bet you, just like most physicstards, got your ""passion"" by watching The Big Bang Theory and figuring out that you could leech off the stereotype of the genius physicist, guess what, you don't fool me, I see through your bullshit facade, I know your program, you are a glorified fucktarded engineer. Be fucking mad that if I ever choose to go to physics graduate school I will have a bigger chance at becoming a major physicist than your dumbed down engineer brain. You do not fool me, faggot. I see through your pathetic attempt at convincing the world that you're smart, and convincing yourself that you're smart. That is the sole reason you picked this garbage major."

>>9113829
Hey Math my calc teacher doesn't allow calculators in class, quizzes or exams. This is exciting and I'm ready but up till now my classes have been calculator heavy.

How is this going to work with all the trig and stuff ? For example a hw question has asked me to use a table to find limit of a rational trig function f(x) = tan(9x)/tan(4x) as x approaches 0 and the answer can't contain pi

> maths ai creaded
> we input riemann hypothesis
> after some time we get a message that hypothesis is correct
> proof is 2000Gb file
What happends next?

[eqn]666 * 777 = 517 482[/eqn]
[eqn]517 + 482 = 999[/eqn]

MIND = BLOWN

I just discovered this, will I get some award for this?

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>>9122359
Memorize angles. Anyway I did your problem but can't latex because I am on my phone at school. Feel free to rotate my picture and copy it. I did it without l'hopital for style points.

While learning group theory I encountered an exercise asking me to draw a picture of a group [math]\frac{\mathbb{R} \times \mathbb{R}}{\mathbb{Z} \times \mathbb{Z}}[/math]. At first I assumed it is a surface of a sphere(don't know the English term for this) and later I realized Torus will do as well? Am I right? I don't know anything about topology(or whatever this is)

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Real analysis exam in 8 hours
im nervous

>>9122492
Real analysis is the study of one definition. You'll be fine.

>>9122425
Binary or the highway, pleb.

>>9122484
"draw" the group?
there's a bijection between [0,1]x[0,1] and this set, that's all i can tell.

>>9122452
Thanks man that makes slot of sense
Appreciate the effor

I guess I just need to get back in the swing of the trig properties and all

is it natural to feel burnt out even though i still like math? im just sick of most of the grad school stuff, but ill do research with friends and read math stuff on my own that has nothing to do with what im doing in school. im gonna just try to finish this phd.
>>9122501
lebesgue measure?
>>9122404
the AI put at least 1999gb of paul erdos memes in it

Are prime numbers useful anywhere outside crypto?

>>9122721
Yeah. Tell cool properties about primes at the club to get mad pussy.

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>Go into uni
>First math course has this "Calculus 6e, Early Transcendentals, Matrix Version, Edwards & Penney,"

What am I in for?

>>9122753
>What am I in for?
Calculus 6e, I imagine.

>>9122771
Whats calc 6 though? Highschool didnt have these fancy names, it was math class 1,2,3 etc

>>9122778
just download the book and read brainlet

>>9122484
Yes it is a torus.

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What are the best Combinatorics textbooks?

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>>9122889

>>9121274
>now, if anime is being used in such a way to take the thread off topic
Read the fucking thread you idiot. Most of the discussion concerns anime. God you're dumb. Get off /sci/

>>9121362
We do by telling you to leave/stop posting anime. If you weren't 12 you'd listen.

>>9121577
Take it to /a/ fag. Quit the fallacies

>>9122929
>We do by telling you to leave/stop posting anime. If you weren't 12 you'd listen.
I wasn't the one posting anime

Irregardless, the solution is to post mathematics, whining about it will more than likely just make people post more anime, if you weren't 12 you'd understand.

>Taking probability theory
>Learn probability is just combinatorics with some extra axioms

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>A dotted
>spiral bound
>notebook

>is nowhere

>to be found


Questions:
1.) Is this really too much to ask?
2.) Am I the only person who desires such a thing?

>>9122953
> combinatorics
You mean measure theory, r..right?

>>9122966
combinatorics is a subset of measure theory

>>9122942
>irregardless
Now I know you're dumb.

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>>9122987
>muh semantics

>>9122956
Spiral notebooks are the devil.

t. leftie

>>9122993
For portrait maybe, but I'm a landscape bro.

>>9122966
We are using measure theory but we are still formalizing finite probability (we just started class) so the more analytic aspects have not yet popped up. This is basically combinatorics because finding the probability of an event amounts to counting how many elements it contains.

>>9122991
welcome to math

>>9114211
seconding this

Is OxfordAnon here? I have a question for him.

(I'm an American applicant, so you may be unfamiliar with some of the things I talk about.)

I'm applying to Oxford this year, which is also my gap year (after having finished my 12th year of school). My high school was absolutely terrible; the majority of its graduates end up attending a community college after finishing school. (Enrolling in a community college is kind of like doing foundation courses in the UK). In short, its education standards (and many of its students' prospects) are mediocre. The most rigorous class I've taken is AP Calculus BC. Would you happen to know how this might affect my application? How do I inform Oxford about my circumstances?

It seems that Oxford likes it when A-Level pupils take Further Maths, which I imagine is more difficult/rigorous than AP Calculus BC, right? The most advanced concept we got to in BC Calc was Taylor series. Would that make me seem unqualified and/or hurt my chances?

Unrelated question I was curious about: do the students that apply at age 16 have an edge or a disadvantage in comparison to those who are 17/18 at time of application?

Thanks a lot senpai

>>9122991
>reddit frogs
>>>/r/eddit/

>>9123153
How is this related to math? Make a separate thread.
Also, fuck off with your retarded reddit spacing.

>>9113884
It's great for art majors who enjoy drawing

How do you handwrite [math]\mathbb R \mathbb Q \mathbb Z[/math] ?

>>9118659
>"why are people posting 2d on a corean praxinoscope BBS!?"
>>>/r/eddit/

>>9123256
Just add an extra line to the normal letter

>>9123251
It's also great for math majors who enjoy drawing.

>>9122484
[math]\frac{\mathbb{R} \times \mathbb{R}}{\mathbb{Z} \times \mathbb{Z}} \cong
\frac{\mathbb{R}}{\mathbb{Z}} \times \frac{\mathbb{R}}{\mathbb{Z}}
[/math]

[math]\mathbb{R} \, /\ \mathbb{Z}[/math] is just a circle, which was probably somewhere in your text. The torus is just the product of two circles.

>>9123291
I end up turning it into a think line every time

set A = {1,2,3,4}

what is UA?

the axiom of union says that for all sets A there exists a set B such that for all elements x x is an element of B if and only if there exists a set t such that t is an element of A and x is an element of t.

since set A doesn't have any sets t as elements would UA equal the empty set?

>>9123613
Try posting without reddit spacing.

>>9123613
In axiomatic set theory sets are all that there is, so numbers are defined in terms of sets. Specifically, [eqn]
0=\varnothing \\
1=S(0)=0\cup\{0\}=\{\varnothing\} \\
2=S(1)=1\cup\{1\}=\dots [\eqn]
And so forth. Specifically, in your example [eqn] \bigcup A=1\cup2\cup3\cup4=\{\varnothing,\{\varnothing\},\dots\}[\eqn]
You get the idea, I'm too lazy to write it all out

>>9123613
>>9123722
[math]\LaTeX [/math] failed, reposting

In axiomatic set theory sets are all that there is, so numbers are defined in terms of sets. Specifically, [eqn]
0=\varnothing \\
1=S(0)=0\cup\{0\}=\{\varnothing\} \\
2=S(1)=1\cup\{1\}=\dots [/eqn]
And so forth. Specifically, in your example [eqn] \bigcup A=1\cup2\cup3\cup4=\{\varnothing,\{\varnothing\},\dots\}[/eqn]
You get the idea, I'm too lazy to write it all out

>>9123234
>not even spacing is safe
You really need to chill out with this Reddit meme. And I posted it here so that the post doesn't die quickly.

>ctrl+f reddit
>1 of 13
Jesus Christ.

Daily remainder that pure mathematicians who denounce real world problems and applications are just too dumb for them and just mask their plebiness.

>>9123760
No, it is actually just politics. After the days of Gauss were over and mathematics started becoming much more abstract we were attacked by the mainstream and even other academics for focusing so much time and energy into solving problems that have no real world value. That was a crucial turning point for math because at that point history split on two. There were two choices:

1) Our timeline
2) Scientists and the mainstream media destroy mathematics and then only applied math remains, with pure mathematicians being exiled from academia for "wasting resources"

So obviously we ended in the good timing but how did we do it? Simple. We saw that there was another group of academics who spent their days masturbating and yet no one ever bothered them: the philosophers. How could the philosophers not produce jack shit from society and still not get as much criticism as pure mathematics? The answer was simple: by creating an air of mystique around philosophy, surrounding themselves with snobs and autists, and by proposing that their field (philosophy) was the only worth while field while everything else was garbage.

So we learned from the best and we created the following memes
>Numberphile (to attract snobs, autists and autistic snobs)
>Other popmath videos
>Claiming pure math is the only right way to do math
>Shitting on scientists and engineers for not being as pure as us
>Telling the mainstream media whenever we can that our work is highly intellectual and therefore should be respected

And it fucking worked. We ended up in the good timeline. Must suck to be in the applied math timeline.

Opinions on Algebra by Artin? Is it easy enough to follow for self studying?

>>9123989
Check out Algebra Chapter 0 by Aluffi as well. I liked it more myself.

Algebra question: If the kernel of a group homomorphism is trivial, does this imply the map is isomorphic? I understand that a trivial kernel means the map is injective but I'm not sure if the leap can be made into saying the map is an isomorphism.

>>9123779
I have nothing against pure/abstract math, that wasn't my point. My point is that any physicist with good math bases can skim through pages and pages of formalism and notation without having a breakdown while it's near to impossible for a mathematician to comprehend an upper level physics paper or text. That's just from experience.
>>9124025
No not in general.

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>>9124025
It is an injection iff the kernel is trivial. That injectivity implies trivial kernel is easy to see, because identity elements are mapped to identity elements. Conversely, [math]f(x)=f(y) \Leftrightarrow e'= f(x)f(y)^{-1} = f(x)f(y^{-1}) = f(xy^{-1})[/math], so [math]xy^{-1}\in\text{ker }f[/math], which, with a trivial kernel, means [math]xy^{-1}=e \Leftrightarrow x=y[/math]. Similarly, a homomorphism is surjective iff its cokernel is trivial. An isomorphism can then be characterized by saying it is a homomorphism with trvial kernel and cokernel.

>>9124030
>any physicist with good math bases
So basically no physicists?

>>9124040
that clears things up, thanks

>>9124041
>Who is le phenotype man

>>9124044
Who are you quoting, redditor?

>>9124044
So basically no physicists? One person (which most physicists aren't (including you)) isn't "all physicists".

>>9124025
of course not, the map need not be surjective. nevertheless, the image f(G) is a subgroup of the target group and the map becomes an isomoprhism when considered as G -> f(G).

>>9124044
>le
see >>9123208

>>9123727
No, they are not "defined" like you wrote it, they are defined in terms of axioms, and then it is usially shown that it is possible to construct something which obeys said axioms.

>>9118604
Not quite right. There's no way the kernel can be finite (if w is a nontrivial element in the kernel, then w^n is as well, and because we are working in a free group, the w^n are pairwise distinct). What you must prove is that the kernel is *finitely generated*.
I think the simplest way to see this is to take A=G and prove that case, the kernel is generated by "the multiplication table of G" (ie. generated by the products [math]xyz^{-1}[/math] whenever [math]xy = z[/math] for [math]x,y,z \in G[/math])

>>9124142
Thanks, I got it

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>>9122484
I see you're reading through Aluffi as well.

>>9122484
>Torus will do as well?
it is a torus but not "as well", sphere is a different topological space (and it is not a group in any way). don't let this bother you too much, it will become clear once you learn some topology.

>>9124216
You're right.

>>9124216
>>9124218
me too. do you bother with every exercise ?

>>9124030
You're a moron.

>>9124219
Yes, so far I've completed every exercise I encountered(I haven't advanced too much yet though, only starting group actions today). Sometimes it takes me much time but I enjoy algebra and I like the feeling of understanding topic better and better after some challenging and insightful exercises

>>9122484
The only group associated with the surface of a sphere I know about is trivial, so that's probably not it.

>>9124253
>>9122484
well the sphere is in a bijection with, say, the real numbers so you can use the group structure on R to induce a group structure on the sphere via the bijection. this is of course completely useless and ugly, you need to somehow connect the group structure with the topological one. so there's the notion of a topological group, where the underlying set is a topological space and the group operations (multiplication and taking an inverse) are required to be continuous maps (or even differentiable - in this case it's called a lie group). it is a hard theorem of topology that the only spheres admitting a topological group structure are 0-sphere (discrete group with two elements), 1-sphere (unit complex numbers) and 3-sphere (unit quaternions).

>Go to tutorial
>Not a single female present

Have I reached the point of no return?

>>9124424
>unironically wanting to see females
Kys

>>9124270
>well the sphere is in a bijection with, say, the real numbers
Are you implying spheres don't exist?

Did anyone ever answer that one anon's question about whether there are two infinite fields F and G such that the multiplicative group of one is isomorphic to the additive group of the other?

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>>9123779
10/10 post, my man.
You truly understand the essence of pure math.

Just started Calc 1, how do I get gud?

>>9113829
y u hate us so much?

>>9125789
careful algebra

>>9125813
They envy us. Like everyone here, their smugness is a sign of weakness and sadness.

>>9113829
I'm a neet and I'm going to take my time to study linear algebra seriously for the first time soon. Is pic related a good book to use?

>>9125789
Memorize the 13-or-so differentiation rules. Calc1 is nothing more than glorified algebra.

>>9125840
>They envy us.
Why would humans envy lesser beings? Seems pretty weird to me.

>>9125813
>>9125840
>>9125863
Make your own thread. Physishits aren't welcome.

>>9125813
>math thread
>no physishit avatarfags
i really wonder as well

Is there a name for the matrix where element
A_{i,j} = |i-j|
So basically the diagonal is zeroes and the more elements away from the diagonal you are the larger the integer.
Is there an efficient way to create a matrix like this in Matlab?

Also, if I have an equation for an element in the matrix, e.g. the one above, what's the easiest way to find a formula for the ij element of the inverse?

>>9125866
This. I think dog-eating subhuman Taiwanese avatarfags should be allowed in these threads.

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>>9122753
it literally means its the 6th edition of the book
come on man....

>>9125813
Physishits are mostly manchildren, very few are good at math, most got into physics for watching sci-fi bullshit and they're autistic.

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>Show that [math]3^n>100n~for~n>5[/math]

I understand that
assume [math]3^k>100k[/math]

[math]3^{k+1}>100(k+1)[/math]
[math]3\cdot3^k>3\cdot100k[/math]
But how can we do [math]300k>100(k+1)[/math] or why this proves it.

>>9126226
Suppose [math]300k \le 100(k+1)[/math]. Then [math]200k \le 100 \Leftrightarrow k \le \frac{1}{2}[/math].

>>9126237
That didn't help. But It just clicked.

if [math]3^k>100k[/math] is true then [math]3\cdot3^k>300k[/math] must also be true.
For some reason I glanced over that.

>>9126241
If [math]3^k > 100k[/math], then [math]3^{k+1}>300k>100(k+1)[/math] because [math]k \ge 6 >\frac{1}{2}[/math].

Why is f(x) used instead of xf or (x)f to denote the value of a function at x? You could xf read it as "x to f" and function composition would be much more simpler: [math] A \xrightarrow{f} B \xrightarrow{g} C [/math] would be composed as [math] f \circ g [/math] instead of the non-intuitive and retarded [math] g \circ f [/math] where the order is unnecessarily reversed.

>>9126248
>[math]g \circ f[/math]
This is just [math]g(f(x))[/math].
[math]x(f)[/math] is a lot more retarded.

>>9126253
>This is just g(f(x))
I know that but in the sequence [math] A \xrightarrow{f} B \xrightarrow{g} C [/math] f comes first and then g so being able to write [math] f \circ g [/math] would obviously be more appropriate.

>lot more retarded
It just seems like that because you're not used to it.

>>9126255
>[math]f \circ g[/math] would obviously be more appropriate.
You could just translate in your head. I have some non-standard conventions too.
>It just seems like that because you're not used to it.
Doesn't make it any less retarded.

>>9126263
>You could just translate in your head
I could but that would require unnecessary effort. Mathematical notation is supposed to simplify ideas not complicate them.

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What's the formal way of saying "This part of the proof is trivial and I can't fucking be bothered to prove it"?

>>9126268
It is clear that...
It can be easily shown that...

Hello, x - x * 15,5 / 100 = 2,27

What is x please ?

>>9126268
The reader should be able to easily verify that..

>>9126268
"Mathematica said so"

>>9126286
>15,5
>2,27

Seems you have a syntax error senpai

>>9126334
Why?

>>9113884
Fair Silke-chan, you are a witch and should already be acquainted with categorical mysticism. But, imagine that you could step outside of a universe of things and examine them globally? What if you could compare entirely different theories by constructing universal bridges (AKA adjunctions) between them? You would be a happy witch indeed. That's what category theory is good for.

Brainlet taking pre-college level math in college here

Why is it that the math makes sense in class when the professor explains it but it all flies out the window when I go home and try my work

Could it be my dyscalculia

>>9126334
ah yes lol

Here, the correct equation:
x - x * 15.5 / 100 = 2.27

But i don't know if it's calculable.

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Rate my math assignment, /mg/.
This is 1/3 of it.

>>9126364
Do you actually have dyscalculia? If it makes sense in class you probably don't. It's much more likely that you think it makes sense in class because someone is doing the work for you and holding your hand. You need to fully understand the concept.

>>9126383
I've been diagnosed with it, but I'm making attempts at living with it and improving my math skills regardless

>>9126369
[math]x - x * 15.5 / 100 = 2.27[/math]
[math]\frac{100}{100}x-\frac{15.5}{100}x=2.27[/math]

>>9126382
it would appear that this is either from highschool or you are a brainlet.

>>9126962
That first one.

>>9118604
there's a canonical way to do it in this case.

For any group G, you can take the underlying set |G| and free group F(|G|). There is a canonical homomorphism F(|G|)-->G taking an element of F(|G|) - thought of as an expression of symbols of G, mod group laws, to their actual product in G.

Now do this to any finite group. Since |G| is already finite, you have your finite presentation.

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reading on collision math bros??
i only know how to check if 2 2d circles intersect, but what about all the other shapes?

>>9126248
i picked up a Dover abstract algebra book with postfix notation, would not recommend it if only for that reason

>>9122064

>I look again and all three of my books on the subject contain a clear statement that all fields are integral domains shortly after their respective definitions of a field

I'm a dumbo

>>9126334
Retard

>>9113829
i'm about to meme myself an chose math as a major, what should I expect?

>>9127833
flipping burgers after graduation.

>>9127833
/sci/ got me to choose math five years ago, best decision i ever made

>>9128070
>best decision i ever made
Elaborate?

>>9127833
Seconding the other guy. /sci/ pushed me to major in math two years ago. Best decision I've ever made.

>be me
>have ADHD
>choose to study maths
Realize how fucked I am

>>9127833
If you are good at it and specialize at something like statistics or computer science, then you're gonna get a really good job with lots of money.
If you are not good at it and you are not willing to self learn a lot of stuff, then don't expect much.

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-0.08+.12(5000-y)=0.05
W-A says the answer is 3528.94 but I've done it three times and gotten 2400 each time
Where am I going wrong?

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>>9128400
Let's try again

>>9128400
>>9128406
>>9128412
You have to be at least 18 to post here.

>>9128423
I am, I'm taking retard math in college. That's why I'm asking for help

>>9128425
Your reasoning is correct, should be 2400. Wolfram gives me the exact same answer, recheck the question you actually gave WA to calculate, probably forgot a y like in your first question.

>>9128400
>-0.08+.12(5000-y)=0.05
but the first line in your work shows
[math] -0.08y + .12(5000 - y) = 0.05y[/math]

which one is it?

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>>9128486
>>9128433
Sorry for the late reply, for the sale of clarity here's the original question direct from the study guide

>>9128582
Brainlet detected

What the fuck is COQ?

>>9128582
you're doing it right. [math] y = 2400[/math] is the solution.

Hey guys.

How do I pass subjects that are weighted 70% exams and 30% Assignments/Tests?

I failed Real Analysis and Abstract Algebra; yes I've fallen for the pure maths meme, but god damn its sooo addictive, and fun. I'm already working like a horse trying to get by Complex Analysis; which I find easier than Real Analysis and Abstract Algebra. The only subjects I did well were Linear Algebra, Vector Calculus, and Differential Equations.

Please help a brother out. I want to be like you guys and I'm 23 years old with aspergers/dyslexia; my get my undergrad when im 25. I want to get a PhD in Pure Maths in my early thirties!!!! And become smart ofc course.

abstract algebra sucks until i think about it then it's easy pz what is with that? i'm gonna stick with analysis as long as i can. also mathematical physics suck it redditchan.

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Does anyone here know any decent math books that cover ALL the topics present in the art of problem solving books: volume 1 and 2?

I already have the first book but can't find the second one anywhere so I think I will have to give up on this series.

Here's the list of contents in the 2 two books:
>Vol .1
https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/aops-vol1/toc.pdf

Vol. 2
https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/aops-vol2/toc.pdf

Thank you.

>>9128086
no

CSfag here please no bully.
How good is the linear algebra course from MIT OCW?

>>9129001
it's ok
if you're a real og you'll just read hoffman & kunze

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>>9126226
Reframe the question if you're unsure of it.

Assume 3^k>100k for k:[6,inf). Then n>(10/log3) +log (n)/log3>logn/log3.

Begin your induction from this point and the answer should become obvious.

>>9119030
94 you fucking idiot.

>>9129153
you're the fucking idiot, it's 9999

>>9128913
I just watched a ted video regarding top students. Their secret? They focus on mock exams.

Think about it. Your job is to pass the exam, so why would you practice anything else?

>>9128913

Not sure if this is bullshit, but how did you "Fail" Real Analysis and Abstract Algebra? Did you even study? What was your exposure with proofs before those classes?

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Is it humanly possible to condense year one and year two undergraduate math into six weeks of intensive study?

>>9129297
lol no

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>>9113829
>>9113834
What's the best book on probability theory( for beginners)?

>>9126268
The proof is trivial and has been left as an exercise to the peer reviewer.

>>9129311
Luis Rincón Introducción a la Probabilidad.

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>>9129347
>not even in english

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Who here has a math learning disability but loves math? It's like being a wheelchair athlete. I'm slower than everybody else but I love studying.

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>>9129386
>this
hopefully i know how to fix it.
Just stay at home, learn by yourself. Books are the way to go

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>>9129386
>>9129397
Yes.

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>>9118659
You can either accept it or leave.

>>9125813
Because we make more income then them and get more of the media spotlight. Math is just a tool, there's very little in terms of societal progression It's applicable. They do this shit for free, It's a labor of love and hobby at best.

>>9125813
Because your kind routinely shits up these threads with avatarfagging and posting about how "infinity" "doesn't make sense".

6^2÷2(3) +4
10 or 58

>>9129690
It's 58 /but/ no sane person would set the equation out in that way.

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Surely there's one of you in this thread who knows how to solve >>9129741
It's a far better use of time than arguing about infinity and whether or not animeposters should be lined up against the wall and shot (they should)

Just how lazy are you allowed to be with proofs?

An exercise asks me to proof
[math]\sum_{j=0}^{n}\binom{n}{j}=2^n[/math]

Can't I just write it as [math]\sum_{j=0}^{n}\binom{n}{j}1^{n-j}1^j=(1+1)^n[/math] And claim it's true because the binomial theorem is true?

>>9129836
Have you proven the binomial theorem in class?

>>9129844
Yes.

>>9118659
are you the guy that posts about jezabels on /lit/?

>>9128970
Bump.

>>9129846
I assume you are allowed to use anything proved or otherwise stated in class, so that ist probably the intended solution.

>>9129836
>Just how lazy are you allowed to be with proofs?
Depends on the proposition. In your case you could just write "Trivial."

>>9113829
Ha, you said nothing about Chemists.
Haha.

>>9129949
Chemists are definitely closer to humans than physicists.

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Sooo....

This is the mathematics circle jerk

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>>9130002

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>>9113829
>>9113884
>>9113903
>>9114920
>>9115786
>>9118444
>>9122492
>>9122753
>>9122889
>>9122956
>>9122991
>>9124040
>>9124216
>>9125569
>>9127021
>>9129297
>>9129386
>>9129419
>>9130002
>>9130005

>>9113853
Because when your two dads were evaluating the pros and cons of having a child, they adopted the same guess method and just bought you on the black market - and look where we are now eh? Sometimes it's better to have better judgment with the help of others in order to avoid life ruining trajectories

>>9113866
Well, tits or GTFO then

>>9117823
>>9117885
>>9118308
>>9118325
Behold, a Grand Master of Autism is amongst us

Share your forbidden knowledge with us master, we beg you

>>9129290
I did study, but I wasn't exposed to much proofs. Only a bit in Linear Algebra...

>>9129386
>but loves math
Prove it.

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>>9130310
>I did study
>I wasn't exposed to much proofs

>>9128210
I'm ADHD and doing good, have you tried not being a brainlet?

>>9128086
>>9127833
>he asks for career advice on ego board
Just kill yourself, you dumbfuck brainlet.

Hi, I'm relearning math from scratch. I've started with Kiselev's Geometry I.

Is it a good choice? If no, what are alternative geometry materials?