/sci/ - Science & Math

Can one get a job in finance industry with just a bachelor's in maths? If not what should I do to get a job?

>>11956354
>Can one get a job in finance industry with just a bachelor's in maths
yes
>what should I do to get a job?
send out job applications

math is fucking gay

butt sex

>>11956790

help the retard reee

>>11956850
drop the class

>>11956318
>Elliptic curves

>>11956354
>Can one get a job in finance industry with just a bachelor's in maths?
Yes.

>>11956318
From/x/
Is vortex math capable of producing equations ?

>>11956960
>From /x/
go back
>>>/x/

>>11957189
I'm already there, though.

does anyone have the /sci/ sellout chart with books on like financial mathematics

>>11957349
>>11955513

mathematicians are hot

>>11957446
Correct.

>>11957455
I mean, who else would go out of their way and use proper letter capitalization and punctuation for a low effort post like that. it's a special kind of autism that makes my peepee really happy

>>11957446
Some are. My office mate is really cute and under different circumstances I would probably hang around his desk so that our h*nds could accidentally touch and mmhm. There was also a super cute guy in a conference earlier this year and I would have liked to make moves on him.

>>11957538
>There was also a super cute guy in a conference earlier this year and I would have liked to make moves on him.
Unfortunately, Peter Scholze is married with kids.

>>11957554
No no no, not him. This guy was surprisingly from England. I hope we meet again at some point after corona. I want to see his face and butt again. But hey, maths...

>>11957604
>I want to see his face and butt again.
But what does he research? How many publications and citations? Does he have a chance at tenure? Don't go after Mr. Struggle anon.

>>11957623
He had just started his PhD and I think it was something related to simplices. I had hard time concentrating on what he was saying because of his looks and voice. I'm not going after him, though. I will only have him as my occasional eye candy and forbidden fruit.

>>11957554
he looks like a 20 year younger nerd

>>11957636
Scholze is 32, are you saying he looks like a twelve year-old?

Sorry if this should go on sqt, but what are some pure math topics that a person with no experience in pure math can approach, that isn't set theory.

>>11957692
Algebra
I recommend Pinter's book.

>filtered by a problem on a Madagascar cleaning board

>>11957698
Is it easier than Artin? I had a tough time with Artin and gave up.

>>11957698
Doesn't Pinter require a first course in proofs?

>>11957708
Probably, but I'm comfortable with after attempting some of spivak and apostols chapters on sets

>>11957705
Yes. It starts assuming no knowledge whatsoever of algebra but ends up at Galois theory. It's a great introductory book to pure math.

>>11957446
tropical geometer here

>ywn have sex with a hot /mg/ tranny

>>11957798
Guess being one is the next best thing. If only you knew enough about abelian categories...

>>11957798
You never know!

>>11957798
>hot /mg/ tranny

>>11957672
yeah okay, 10 years younger then

I somehow meme'd my way in my mech e degree with knowing enough math to slam exams, but not really "learn" anything. Is pic related a good entry point to finally git gud?

I don't want to go all the way back to algebra but willing to read something theory-leaning in that regard

>>11957851
Spivak's Calculus is a widely regarded classic and it would be hard to go wrong with reading that book. You'd have a great understanding of one dimensional calculus after that book. It is necessary that you have a decent amount of mathematical maturity though.

>>11957805
thank you... for giving me the hope...

>>11957851
Start with this.

>>11957866
I think I have the maturity, I'm just awful at rudimentary math because of naturally built aversion. I can get As in proof-based courses (automata, complexity theory) but fucking freeze when I have an unruly integral and just opt for plugging it into Wolfram without caring about the why or how.


>>11957879
Thanks anon, I'll look into this

>>11957897
If you're already comfortable with proofs, then you probably don't need Vellman, but it's a good book nonetheless.

>>11957726
Cool man cheers! Excited to try it out.

>>11957805
Is that an invitation? Wanna have disgusting sex with an old man?

>>11958016

ich hasse Anime maedchen

>>11958180
Speaking non-English outside of /int/ is a bannable offense.

>>11958309
¿Then why don't edgy kids get banned for memespeak?

>>11958016
Redid it, should be better now.

Are the Gelfand books any good?

>>11958444
>be patchouli
>always complain about marisa stealing your books
>voluntarily give a book on riemannian geometry away nevertheless
I guess the message of the picture is that Riemannian geometry sucks.

>>11958462
Why don’t you read them and tell us anon?

>>11958542
fine, be back in two weeks

>>11958588
Ganbatte!!

>>11956960
wtf does any of this mean? I really can't parse any of this

>>11957766
>Double dubs
kek

>>11958736
With these there's often some actual patten they like involving modular arithmetic, but then they make up a bunch of mystical stuff surrounding it.

How come math is hard? How come math isn't easy?
>inb4 ur a brainlet
How come I'm a brainlet?

>>11958847
What, in particular, is tripping you up?

>>11956318
Been working on a 3 axial number system where each axis is split by 60 degrees and lies on a 2 dimensional plane. Shits pretty interesting and the algebra is nice if anyone wants to see. If i post it feel free to work on it / develop whatever you want, math is everybody's property.

>>11956960
See what i just posted, the plane that the 3 dimensions exists on looks nearly identical to this. Shit makes me thing some equation using the plane could generate whatever the fuck im looking at here

does someone have the learning maths pathway with best girl on it?

>>11959044

>>11957554
>kids
He has more than one?

>>11959050
na the one with Kurisu Makise on it

>>11958872
you mean the extension field of the third root of unity?

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

>>11956318
Noob here. I have a simple math question. Refer to the Two Queens Problem (google it). I couldn't derive a recurrence relation or a closed form formula for it. In fact I'm almost never able to derive recurrences or closed form formulae. Is there something I can do or read to get better at this?

>>11959150
There is a cool way of solving sudokus (and counting the number of solutions) with groebner bases. You can encode the sudoku constraints as polynomial constraints. I don't think it's very efficient though.

>>11959081
Oh, should have said so from the start.
/sqt/'s OP pasta, shitty charts folder, https://i.imgur.com/esqDGl8.png

>>11958462
Yes, his calculus of variations isa must for anyone who want to understand analytical mechanics.

what maths do i need for comp sci? books?

this book is god tier because it shows that the distinction between abstract nonsense and useful math is completely artificial

>>11960117
Linear algebra, linear algebra, linear algebra. Some graph theory, number theory, and calc would also be helpful.

That said, here's MIT OCW: https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-fall-2010/

bros...
Serge Lang comes in my dreams...

>>11960148
prime numbers are just numbers we haven't discovered any more factors for

a mystery of science...

Why are proofs "easier in complex vector spaces" than in real ones? You could say real spaces have less degrees of freedom maybe, but what's the literal mathematical reason that complex space proofs get to rely on eigenvalues rather than 2-dimensional spaces, and why real space proofs always require some sort of quadratic polynomial? Like, how does injecting imaginary numbers somehow was away the for some arduous polynomial, how does i equate to it in this use case?

>>11960140
post some pics from it

>>11960176
over complex numbers, every polynomial factors into linear terms
this makes life easier

>>11960180
Because of every complex polynomial has a root, which you can inductively factor out. But I just can't *see* how this connects to turning a two dimensional eigenspace into a 1D eigenvector. A root is an eigenvalue, sure, but how does the fact that real polynomials end up factorizable down the 2nd order connect with the fact that a 2D real space is 1D in C given complex rotation?

https://youtu.be/Fme_r-nE4CI?t=1400
Rare footage: some of world's top mathematicians arguing which problems are good and which problems are trash

>>11960195
eigenvalues = roots of characteristic polynomial
i don't think about this in any geometric way

>>11956318
>Ekeland
Once gave a talk in a seminar a few years back about one of his papers, but I simply cannot remember what it was about lol. Also his name sounds funny if you're German.

>>11960176
>>11960195
Geometrically speaking, and this is a top schizo obviously-incorrect-but-also-makes-some-distant-sense explanation, matrices can skip out on having eigenvalues because they have 2d rotations.
However, multiplication by a unitary complex number induces a 2-dimensional rotation, so rotations become eigenvalues.

>>11960140
seconding this
to be fair, every book by Arnold is great

>>11960257

imagine wildberger in this

>>11960297
ye but how is it rigorously showable

>>11960257
>geometric way
You should. If the matrix is symmetric and positive definite at least, the eigenvalues are the "length" of the principle axes of the corresponding ellipse for chosen linear coordinates.

>>11960305
It's rigorously showable by using the fact that complex polynomials have a bunch of roots.

>>11956955
poor elliptic curves uber chad, none gives a fuck anymore.

>>11957446
my fiance agrees, but for her math teachers.

>>11960329
i meant how do you rigorously show an intuition
the roots thing is like two separate branches that turn out to coordinate

>>11960179
what you want?

>>11960391
sections 17 and 40

>>11960442

>>11960442
nothing really interesting happens in section 40, but I'll give you this appendix instead

>>11960518
>nothing really interesting happens in section 40
He just defines the Poisson bracket?

>>11960442
>>11960518
https://imgur.com/a/63icCdQ

>>11960355
>how do you rigorously show an intuition

>>11960611
Kek

>>11958847
Math is easier than sociology. In math you just need to memorize definitions, play with equations and do proofs. In sociology on the other hand you need to understand complexity way beyond anything that can be described mathematically.

>>11960679
>memorize

>>11960679
I know this is bait, but this is what sociology professors have to tell their students to jusitfy their absolutely shit field.

What notebooks did you guys use during uni?

>>11960148
The judge ruined it for me. That only implies the non-existence of a finite list of all primes.

>>11960787
none

>>11960148
objection: the list is actually empty, so there's nothing to multiply with each other

>>11960801
Which is a clear contradiction to Edgeworth's claim. The real hole is that no one pressed Phoenix on proving that [math]n[/math] and [math]n+1[/math] are coprime.

>>11960168
this
eventually scientists will find their factors through experiments and the scientific method
they will even be peer reviewed

who has the highest bench press on mg? i did 100kg today

>>11960787
5 subject spiral bound notebooks with printer paper in the pockets.

>>11960801
t. Brouwer.

Proof that there are uncountably many prime numbers:
Assume that we have an enumeration of the set of all primes. Then, we multiply all of them together in order to obtain a number [math]n[/math]. Then, [math]n[/math] and [math]n+1[/math] are coprime, so none of [math]n+1[/math]'s factors are in the enumeration, q.e.d.
I would like to thank mister Ramanujan and mister Tooker for collaborating with me on this proof, none of it would be possible without them.

>>11960469
>>11960531
cool thanks

>>11960843
Yes, it is a claim that would imply that Edgeworth's claim is false, however no proof for the infinite list's existence is given.

>>11960148
where did you find this?

>>11957851
As another engy, it's a pretty fun book actually. The exposition is nice, it's pretty rigurous if you're a person who's curious about math stuff, and it even has more book recommendations in the back. It's a cool book. Funnily enough it's even recommended for Mech E at my uni

>>11960147
What does he tell you?
Also what are you actually reading by him

>>11960148
I really enjoyed this

>>11960915
>uncountably many prime numbers
Wrong

>>11960895
retard here, how do such n-subject books work
do they have tabs for a predetermined number of pages?

>>11956318
Trade chad here
Wassup nerdy losers how much money can you guys squeeze out of those cubic functions

>>11956955
Based

>>11960915
u have 2 sho pi product of countable primes is a finite number, gegocheb

>>11961593
all the money is in quintics boyo
big man galois made sure of that, he has a gun you know

>>11961337
>>11961559
I made it here.
http://objection.lol/

>>11962089
You fugged up on the first part with the Gumshoe tho
"we found all a list of all..."

>>11962102
I saw that after the fact. I'm too lazy to go through the process again just to fix one grammar error.

What calculator should I use for my undergrad?

>>11962171
Bold of you to assume you'll need a calculator, let alone be allowed to use one on exams.

>>11962171
If you're lucky, SHARP EL-W516X, it can do matrix multiplication, sigma summation, complex arithmetic and some differentiation and integration.

If you're normal, any dollar store calculator because that's all you're allowed to have

>>11962188
>Bold of you to assume you'll need a calculator
What's 6*8?

>>11962192
a product of 2 single digit numbers

>>11962192
[math]48[/math]

>>11962198
nope

>>11962195
B+

>>11962189
>Current year
>Still no calculators that can compute a Lie algebra from a given Lie group

>>11962203
>tfw your scientific calculator can't compute the homology groups of a topological space

could someone give me a hint as to why if T is normal then its minimal polynomial has no repeated roots? just a HINT dont solve it for me

>>11962309
Over R or C?

>>11962192
8*6, since multiplication is commutative

>>11962355
A+ WAY TO GO

>>11962329
either

>>11962355
>multiplication is commutative
Not in [math]\mathbb{H}[/math].

>>11962355
not in M(V)

>>11960801
Faggot

>>11962384
C is the center of H, so anon just needs to show 8 or 6 is complex

>Prove that a, a+1 are coprime without using the fundamental theorem of arithmetic
I've stared at this and the definitions for over an hour and can't tell if this is a trick question or if I'm getting filtered. Surely coprimality depends on having a unique set of prime factors?

>>11962529
i dont think you need FTA to say, assume that p is a factor of a and a+1, then blah blah contradiction

>>11962529
[math] p|a\Rightarrow a=0\ (\text{mod}\ p) \Rightarrow a+1=1\ (\text{mod}\ p) \Rightarrow p\nmid a+1 [/math]

>>11962502
Isn't R the center of H or am I retarded

How long did it take for you to learn LaTeX?

How does one determine the exact Qibla (Islamic Holy Direction) to face from any given point in a Hohmann transfer orbit from Earth to Mars?

Asking for Al-Amal.

>>11962763

>>11962773
fraction: 3 seconds

\frac{10}{3}
\dfrac{a}{b}

>>11962787

>>11960195
>real polynomials are factorizable down the second order
what about X^4 + 1

>>11960305
SO(2) is isomorphic to the unit circle in C

>>11962847
https://www.wolframalpha.com/input/?i=x%5E4%20%2B%201%20%3D%200

I may end up a math tutor for some highschooler, how do I prepare?

>>11962529
euclidean algorithm yields
a + 1 = 1*a +1
a = a*1 + 0
therefore gcd(a+1, a) = 1

>>11962847
imagine not knowing this trick from the high school competitions:
[math]x^4 + 1 = x^4 + 2x^2 + 1 - 2x^2 = (x^2 + 1)^2 - (x \sqrt{2})^2 = (x^2 - x\sqrt{2} + 1)(x^2 + x\sqrt{2} + 1) [/math]

>>11961951
The product of two numbers is a number, then use transfinite induction.

>>11962864
Study Bourbaki and print out every Touhou image you can find

>>11962837
Are prayers affected by gravity towards the center of the earth like planes?
I thought aiming towards the mecca the prayer went straight to the mecca like a person would do if it could go through walls and walk above water.

Miss the maths but i love money more. Wish i could continue studying math. I am interested in cryptography but I dont want to go back to school.

Help please or should i forget about it?

>>11963160
this, prayers travel along spherical geodesics

>>11963023
heblo where are the succ and lim case proofs

Can we make axioms for a group with infinite multiplications?
Something like: [math] G [/math] is a set, [math] C \subset G^{/mathbb{N}}[/math] are the convergent series and [math] \Sigma: C \longrightarrow G [/math] is the infinite group composition.
Then [math] C_0 \subset C[/math] is the subset of sequences which only have finitely many nonidentity elements. We would requite [math] \Sigma \big\vert_{C_0} [/math] to fulfill the normal group axioms for finite multiplication. What other axioms should we have for C and [math] \Sigma [/math]?

>>11963292
Basically we can define +: GxG -> G as [math] g+h = \Sigma (g,h,1,1,1,...) [/math] and we then know that + fulfills the group axioms. Then it would make sense to require C to be closed under the operation + induces on sequences, i.e. [math] (g_i), (h_i) \in C \Rightarrow (g_0+h_0 ,g_1+h_1,...) \in C [/math].
Hey, basically this just means [math] C \subset (G,+)^{\mathbb{N}}[/math] should be a subgroup.
Axiom of closedness (C),
C should be closed under

>>11956318
>>11956318

>>11963292
[math] (g,g,g,...) \in C \Rightarrow g = 1[/math].
I'll stop spamming now but sounds like it could be interesting.

>>11963292
What already works in Lie group s the Zassenhaus formula
[math] e^{t(X+Y)}= e^{tX} \cdot e^{tY} \cdot e^{-\frac{t^2}{2} [X,Y]} \cdot e^{\frac{t^3}{6}(2[Y,[X,Y]]+ [X,[X,Y]] )} \cdot e^{\frac{-t^4}{24}([[[X,Y],X],X] + 3[[[X,Y],X],Y] + 3[[[X,Y],Y],Y]) } \cdots [/math]
where X is the log of g=e^X and so on.

If you speak of convergence, you'll want some sort of norm (e.g. Haar metric above), or I interpret your product in some vague categorical product object kind of way.
I didn't put much effort in deciphering your formulas, tho

>>11963305
This somewhat reminds me of how the reals sit within the hyperreals,

>>11963318
>>11963292
I don't know lie groups. And I want am abstract axiomatized convergence, not conbergence through a metric or measure or something.
I found a better way to describe the problem. Let (G,+) be a group. We cpuld like to find a group homomorphism [math] \Sigma: G^{\mathbb{N}} \longrightarrow G [/math] with the property that [math] \Sigma(1,...,1,g,1,...) = g [/math] for any g in G at any position. This is probably not really possible, because what would [math] \Sigma (g,g,g,...) [/math] be?
The solution is to pick a subgroup [math] \subset G^{\mathbb{N}} [/math] which should be interpreted as the sequences which converge, and then define [math] \Sigma: C \longrightarrow G[/math] as only on this subgroup! If you find the right subgroup, sigma becomes a homomorphism in the above fashion.

>>11963361
The homomorphism you described is one reason why people work with direct sums of abelian groups (or modules more generally) instead of direct products, as then you only have a finite number of non-identity coordinates in each element of your sum group/module. However, there could be some way to take the direct product of a single fixed group and then consider the system of all the finite products of the group with itself and include those into the infinite product. I must be honest, I don't remember if the infinite product is a direct limit of such finite products, but if it is, then you would obtain the homomorphism you so much desire (after defining the homomorphisms from the finite products in some way compatible with the inclusions). Then you could try to investigate the convergence of this induced homomorphism by looking at how the finite cases work. You should check that out if you feel like it.

>>11956318
It seems that [math]\operatorname{dn}(x+iy,k)[/math] traces out an ellipse in the complex plane, and so does [math]\operatorname{dn}^2(x+iy,k)[/math] and so on. Does anyone know the equation of this ellipse with [math]u[/math] and [math]v[/math] the real and imaginary parts?

>>11963424
>[/math]tracesoutanellipseinthecomplexplane,andsodoes[math]dn2(x+iy,k)[/math]andsoon.Doesanyoneknowtheequationofthisellipsewith[math]udn(x+iy,k)[/math]tracesoutanellipseinthecomplexplane,andsodoes[math]dn2(x+iy,k)[/math]andsoon.Doesanyoneknowtheequationofthisellipsewith[math]u

>>11956318
Fucked up the latex from my last post. Tex preview was ok so I hope the issue is ok this time around.
It seems that
[math]\operatorname{dn}(x+iy,k)[/math] traces out an ellipse in the complex plane, and so does [math]\operatorname{dn}^2(x+iy,k)[/math]. Does anyone know the equation of this ellipse with [math] u[/math] and [math]v[/math] as the real and imaginary parts?

>>11963407
Thanks, I'll try to find sth about that.
By the way, an example of the kind of structure I want would be [math] (G,C,+,\Sigma) = (\mathbb{R}, \ell^1(\mathbb{R}), +,\Sigma) [/math].

>>11963428
>>11963427
no fucking idea what the issue with tex preview is. Just totally shits itself when I post

>>11963361
The multiplication map GxG - > G is homo only if the group is abelian. Just sayin

>>11963437
No problem. I am fairly sure that the thing I described could work. If it does, the nice thing is that your induced homomorphism will be unique and totally determined by the smaller parts. It could also be the case that the direct limit is not the same as the infinite product, but even then you would have a structure through which all your homomorphisms would factor. This would then allow you to define your C to be the set of all families [math](f_i \colon G^i \to G)_{i\in mathbb{N}}[/math] compatible with the inclusions [math]G^i \to G^j, i\le j[/math] (or equivalently the set of all the homomorphisms induced by such families). As long as you would work with abelian groups, this will be an additive thing and you can then define addition for your elements of C. I don't know, maybe this is a bad idea, maybe not. The best of luck with it anyway!

>>11963441
Remember to put a lot of spaces in your code. If the forced line break of your post happens in the middle of a command, it will blow up. To have control over this, you give it the potential line break positions yourself.

>>11963471
Oopsie shameful mathbb

>>11962937
how is the last equality true?

>>11962864
Answer this dude in /sqt/ as practice: >>11943986
>>11963584
[math]a^2 - b^2 = (a-b)(a+b)[/math]
He just arranged it funny and put the +1 at the end to fuck with you.

>>11963589
oooohhhh

I'm going to start my third year, what the fuck should I do for work? I wrote a few things at GitHub but I'm not sure if I should study more statistics or just algorithms and applied math.
Fuck pure Math
>>11956723
>>11956354
>>11956957
That's one recommendation, what else what would you like to do if you were an applied mathematician?

>>11963609
Math is a pretty open ended degree, in terms of job prospects: Finance, data science, teaching, cryptography, actuary, etc.

Abstract algebra is strange. It almost feels like I'm not studying math sometimes.

>>11963794
Lad, algebra is one of the purest forms of math.

>>11963805
I guess I'm just not used to it yet. I'm used to numbers and stuff. I just picked up a book on abstract algebra because it's summer and I'm bored.

>>11963811
Pinter?

>>11963825
Yeah. How'd you figure?

>>11963996
Because I recommended it to somewhere here not too long ago. It's also a pretty common first algebra text because of how easy it is to pick up while still being thorough.

Are there any other theorem's like the Jordan curve theorem that are intuitive incredibly obvious, but extremely hard to rigorously and mathematically prove?

>How real are real numbers? G. J. Chaitin
https://arxiv.org/pdf/math/0411418.pdf

>>11963825
suppose 1 =/= g in Gnoncyclic then order of g | p^2
not p^2 as G noncyclic, not 1 as g=/=1 so order g=p
then h =/= g^t has order p same argument
g^t * h^s s,t = 0,1,...,p-1 is p^2 elements so we get the Z/pZ ^2 whenever G non cyclic

>>11965001
how do you know g, h are commutative? there could, in principle, be some weird stuff going on, like [math]hg = gh^{p-1}[/math]

>>11965124
Not that anon, but I'm curious now. Do you have an example of a group where [math]hg=gh^{p-1}[/math]?

>>11965225
i was just trying to point out the gap
like in the dihedral group D_n, you have r, s such that r^n=e, s^2=e, the size is 2n, but the group is not Zn x Z2

Any suggestions on what a high school youngfag who wants to be a math major should do to prep? I’ll be taking calc senior year, but def need more rigor. Anything to study, should I do math olympiad/AoPS shit?

>>11965462
Do you have much experience with proofs? You could also start looking into learning basic algebra like group and ring theory. Neither one requires calculus to start learning.

Man, I really do hate that fucking OP facial expression. It does get under my skin, very much.

>>11965557
I am certain that this look is gang sign of the face. I think that gang is going to fare very poorly on the Day of the Lord.

what calculator do you use mathbois?

>>11965611
My brain

>>11964747
This is fun

>>11965611
The only calculator I need is understanding.

>>11965546
nah, except for some boring ass basic geometry ones with triangle congruence and shit. thanks anon. does programming help at all?

>>11965854
programming is for those that can't do math

>>11965854
Yes and no. Programming will certainly help you get into a certain mindset and you'll need to end up taking at least one CS class for undergrad anyways, so getting some programming experience is a good idea. I'd recommend going through pic related for proofs. You can probably find a PDF of it online, or if you prefer physical then it's relatively cheap to get on Amazon.

>>11965897
thank allah im not a codecel

>>11965950
i’ll take a look into them anon. how’d you consider the proof approach versus just stocking up on the high school path by learning trig and calculus on my own? also, what are your opinions on doing like AMC and art of problem solving shit?

>>11965955
pajeet? going from high level math to programming is easier than the reverse. everything theoretical and thus meaningful in programming (low level systems) builds off math and physics concepts.

webdev/JS and SQL apes are comparable to children drawing shapes

>>11966017
>webdev/JS and SQL apes are comparable to children drawing shapes
spot on fren

>>11965897
What if I told you that CS is math?

>>11965993
Are you interested in pure or applied math? Either way having a strong foundation in trig and calc is going to be super important regardless of which path you end up taking and while the AP Calc course (which is what I'm assuming you're taking) is fairly mediocre, it gets the job done and you can potentially use the AP credit to jump straight into Calc II your freshmen year.

>>11966198
>Are you interested in pure or applied math?
applied. eventually want to go into finance, hopefully graduate study as well

>Natural numbers don't exist
https://vixra.org/pdf/1212.0088v1.pdf

>>11966281
Nice, are you thinking of minoring in finance or anything related?

>>11966335
sure why not. still got 2 years left though, and gotta stay out of trouble lol

guys how do you induce order in the natural numbers

straight up a<b implies a c such that a+c=b kinda thing?

>>11966478
Well-ordering is a consequence of the AC

We consider the vector space [math](a, a) \in \mathbb{Q}[/math] with the usual inner product.
This vector space has no orthonormal base, because it has no unit vectors to begin with.
Are there any examples of the same in more than one dimension?

>>11966687
[math](a, a) \in \mathbb{Q}^2[/math]

>>11966687
>>11966692
Oh, right.
Forgot to mention that I want the inner product to be rational valued.

>>11966687
Take any vector [math]v_1 \in \mathbb{Q}^n[/math].
Consider the subspace [math]V := \{ v_1 \} ^ {\perp}[/math]. I claim that if [math]||v_1||[/math] is irrational, then [math]V[/math] doesn't have an orthonormal basis:

Assume there exists an orthonormal basis of [math]V[/math], let's call the vectors of this basis [math]v_2, \dots v_n[/math].
So the vectors [math]v_1, v_2, \dots v_n[/math] are all perpendicular. So you can compute the volume of n-dimensional parallelepiped spanned by those vectors in two ways:
[eqn]det [v_1, \dots v_n] = \textrm{volume} = ||v_1|| \cdot ||v_2|| \cdots ||v_n|| = ||v_1||[/eqn]
The determinant on the left is a rational number, hence also [math]||v_1||[/math] must be rational.

>>11966706
i don't know what do you mean by that

>>11963825
Let [math]x[/math] be a nontrivial element, if its order is [math]p^2[/math] we're done
so its order is [math]p[/math], and there is a nontrivial element [math]y[/math] in [math]G[/math] but not generated by [math]x[/math]
If the order of [math]y[/math] is [math]p^2[/math] then the group is cyclic, so its also [math]p[/math]
Since [math](x)[/math] has order [math]p[/math], it is normal in [math]G[/math], since its index is [math]p[/math], which is the smallest prime dividing [math]p^2[/math]
so the subgroup product [math](x)(y)[/math] is also a subgroup
and now [math]|(x)(y)| = |(x)|* |(y)| / |(x) \cap (y)|[/math]
since [math](x)[/math] intersect [math](y)[/math] is a subgroup its order divides [math]p^2[/math], and since [math]y[/math] is not in [math](x)[/math], its order is strictly less than [math](y)[/math]
so its just trivial
and [math]|(x)(y)| = p^2[/math]
so every element of [math]G[/math] can be written uniquely as [math]x^n y^m[/math]
likewise we could write everything as a power of [math]y[/math] then a power of [math]x[/math]

since [math](x)[/math] is normal, [math]xy = yx^n[/math], and since [math](y)[/math] is normal [math]yx=x y^m[/math]
then [math]xy = yx^n = yxx^{n-1} = xy^m x^{n-1}[/math] so [math]e = y^{m-1}x^{n-1}[/math]
by uniqueness and [math]e = y^0 x^0[/math], we have [math]m = n = 1[/math]
so [math]xy = yx[/math]
so now theres clearly an isomorphism to [math](\mathbb{Z}/p)^2[/math]

god, arent finite groups so elegant
what lovely counting arguments

>>11966821
Oooooooooh, very nice.

>>11966367
Another anon here, if you still got 2 years left then yes it's worth to do AOPS and olympiad shit simply because its much harder (and closer to the real deal) than regular high school shit. It's too late for you to chase olympiad medals and shit like that but it will prepare you for later for sure. And if you start to find it boring you can quit at any point and start studying higher math (which you should be doing your senior year anyway).
Start doing anything involving proofs ASAP, be it intro higher math or olympiads if you want to minimize your chances of being assraped your first year of uni.

>>11966853
this works, upvote sir

Does anyone have any good book recommendations for differential equations that approach it from a theory stand point? Something similar to Axler's LADR but for DEs.

Why do people even use this proof instead of [math]\phi (0) = \phi (0 \times 0) = 0 \phi (0) = 0[/math], which also works for characteristic two?

>>11967113
Arnold, its not like Axler, you will have to think a lot more deeply and its expected you’ve learned basic Real Analysis. The latter isn’t required but you will have some difficulty if you don’t understand metric spaces, convergence, basic pointset topology, continuity, the proofs behind differentiability.

>>11967530
why wouldnt this work for characteristic two?

>>11967541
It does work, I just do this stuff sometimes.

>>11967535
Thanks.

Is there a mega or torrent for a /sci/ library? I know /g/ has one

>>11961574
They have dividers with pockets

>>11967767
There have been a couple but I lost them. Also a huge one with every Springer book and more (from before they made them free) but that may have come from leddit. Maybe search for mega on the archives.

>>11967803
Huh, ok. They seem slightly smaller from what people use here.
I dunno how people deal with notebooks. Having your lecture notes, your book notes, and exercises together like that seems a bit challenging.

Are there any good problem sets for real analysis with answers? I want to unrust myself

>>11968120
https://ocw.mit.edu/courses/mathematics/18-100c-real-analysis-fall-2012/assignments/

>>11967530
1st, this does work in char 2
2nd, the proof also works for groups

>>11968134
I always forget how amazing OCW is

https://www.youtube.com/watch?v=Y2cBpBLJlfU

Using superscript to indicate power is harmful.

>>11956960
>not radians
kys

>>11968544
>Using superscript to indicate power is harmful.
It's right adjoint to the harm of using concatenation to indicate multiplication.

>>11968593
This too. We should either use square brackets to exclusively denote function's arguments or forbid void multiplication operator, or preferably both.

Ok I got into grad school with a good supervisor. How much more until people stop posting NGMI at me?

>>11968712
When you make it.

>>11968712
>going to grad school
ngmi

>>11968732
Please state sufficient conditions for 'making it'

>>11968736
Tenure track.

>>11968740
Oh so that's the endgame. I'm going to work my ass off and get a good postdoc position, then shoot for every fucking tenured position on the planet, JUST for the sake of getting you fags to shut up.
Wish me luck, btw fuck category theorists

>>11968743
Based.

If you don't like category theorists, it's a clear sign that you are simply a smoothbrain incapable of understanding category theory.

>>11968767
Incorrect. I use the theory daily but dislike many of the theorists as persons after meeting several and seeing how rude they are to each other.

>>11968712
Are you insinuating that getting INTO grad school is making it? Making it begins with getting OUT of grad school and getting a postdoc.

>>11968743
What field are you planning on?

>>11968712
>How much more until people stop posting NGMI at me
ngmi

>>11968965
Stochastic dynamical systems

>>11969216
ngmi, I'm sorry to say. That field is just too chaotic to find a stable job, no matter how strongly it attracts you.

>>11969224
lol

>>11969224
Kek

applied math chad here

>>11969348
post some of your applied math so we can r8

>>11969348
I’m going to apply this dick to your ass if you don’t shut up nerd.

Slow thread, lads.

>>11970105
Your threads have been reddit undergrad trash for over a month now you barely sentient faggot

>>11966478
use succ

Released in 1998 after two years of recording, Boards of Canada's debut "Music Has the Right to Children" explored the progression of sound beyond music. As music is the child of language tone and tempo, which in its turn comes from repetitive physical systems, brothers Canada posit a child to music. To great degree, their audio abstracts the meaning of form and discovers new solutions to the tone/tempo functions. Furthermore, their Child of Music progresses the trend from nature to information flow to meta-nature, information existing as another dimension of nature in its own right, a Phrygian scale as organic and real as the Cascadian Mountains.

Like early physics, like math, all explorations into new realms of reality start with basics. Audio nature is still simple, around the same complexity level as mathematics, though more likely to be akin to physics in its intent-generating structure and temporality. That being said, given our current low level systems, a Child of Music, and Math itself...

What is the child of math? Does math have the right to children?

>>11970105
Sorry I've been busy.

>>11970253
>What is the child of math?
Wouldn't you say computers and stuff? That's the first thing that comes to my mind.

>>11970447
I meant a form of thought that transcends math, somehow. I don't know if it could exist though. There is some interesting philosophy in compsci but most of it is just applied algorithms. It is an interesting topic/branch but I wouldn't say it transcends math

>>11970501
Not science or math. If I hear the word «transcend» it better be referring to a number which is not algebraic.

>>11970521
How do you know it's not science or math? Airplanes transcend the ground, and they count under science and math.

Do you enjoy doing math? I'm beginning to think math isn't for me. I like reading about it and attending lecture, but I don't (usually) particularly enjoy doing problems.

>>11970980
Usually yes, sometimes no. I enjoy trying to come up with solutions to different problems. That is what it is, and you should enjoy it if you want to get decent at it. Sometimes there is somebody handing you the exercise problems, sometimes it is just a book telling you to solve something, and sometimes you pose your own problems.

>>11970980
>Do you enjoy doing math?
Depends on the subject. I find algebra to be really fun and rewarding, for instance.

>>11956960
>>11958736
>>11958875
>>11968549
Vortex math is all about seeing patterns in digital roots of numbers, and they really like doubling and halving things
What they don't realise is that this is just arithmetic mod 9, which is a byproduct of our base 10 system
For example, you'll see references to an infinity symbol, which you get from the digital roots whenever you double numbers. If course this is just the cyclic group Z/9Z^x drawn in a circle, but these videos are usually targeted to less math literate people

>>11970949
All problems in CS are fundamentally related to computation and applied aims. They aren't capable of saying anything about mathematics itself and don't contribute to mathematical theory. CS isn't science because it doesn't study real physical systems and doesn't use the standards or methodologies demanded for proper rigorous scientific theory. Its just something that is very useful for modern civilization and for handling large amounts of information and because janny HATES US and wants us DEAD we have to tolerate them here even they break board rules every time they post about their gay autism. Sorry!

Is self-study just cope?

I somehow managed to complete an applied math degree without doing any of the standard, real deal courses (no real analysis, no abstract algebra, no point-set topology, and my linear algebra course was kind of a joke). This didn't raise any red flags at the time because I really didn't have a good understanding of what true mathematics is.

Now I'm working through Two's Analysis I. It's really fun and pretty relaxing, but I'm moving at a snail's pace. Probably moving slower than the equivalent 1 semester course. And then there's still more catching up to do.

Is the only answer pissing my money into a Master's?

>>11971441
>All problems in CS are fundamentally related to computation and applied aims. They aren't capable of saying anything about mathematics itself and don't contribute to mathematical theory.
>what is the connes embedding problem

>>11971515
You can learn on your own at a good pace if you actually have the study skills and motivation to do so. It sounds like you don't and unfortunately got absolutely gypped out of a math education. :/

>>11971535
You know where you belong, go there.

>>11956955
My nigga

>>11957726
Pinter sucks dick

>>11960335
I give a fuck

>>11971441
Imagine being so triggered by CS
Imagine not having respect for algorithmic complexity theory

>>11970105
It's great, isn't it?

>>11971515
Tao's real analysis books are intended to take around 10 weeks each to finish, so that's around one chapter per week for three months.

only thing standing between me and freedom from uni hell is abstract algebra. semester starts in about a month, how best should I prepare myself for this

>>11972363
I guess I'm not in that bad of a spot then. Thanks.

>>11972392
Pinter

Anyone got some book recommendations for Probability theory?

Is [math](\mathbb{Q}_{>0}, \times , 1)[/math] isomorphic to [math](\mathbb{Q}, + , 0)[/math]

>>11972520
No homework questions.

>>11972526
It's not a homework question.

>>11972520
no

>>11972520
No, consider a map [math]\theta: (\mathbb{Q},+) \rightarrow (\mathbb{Q}_{>0},\times)[/math] and assume that it IS an isomorphism. Now, because of that, [math]\exists a \in \mathbb{Q}[/math] such that [math]\theta(a)=2[/math]. Show that this isn't possible.

>>11972392
uni is a true test of endurance someone once told me. If you can thrive in such an environment, you're truly a stable person.

>>11972501
Mathematical Statistics and Data Analysis by John A. Rice

Operad conference if somebody is interested https://operads.com/

>>11972800
Operads are just abstract clones. Another shameless theft from universal algebra.

>>11972581
This looks perfect, thank you anon

I'm going into my first year of undergrad in Math and everything will be online. What are the essential supplies I will need? I have a PC, a calculator, some spiral-bound notebooks, and pens and pencils. What else?

>>11972922
A comfortable place to sit on, good shoes for taking walks, maybe some stuffed animal to hug.

Friendly reminder that the law of the excluded middle is not valid

>>11971441
Mathematics is literally a subcategory of computer science

>>11973008
It literally isn't.

>>11973013
False.
All mathematics is a form of manipulation of symbols according to rules i.e. computation.
The intuitionists and constructivists are correct and you are wrong if you disagree.

>>11972961
This

>>11972922
Dump that calculator

>>11972922
Also if u're messy person I'd really recommend some kind of tablet to take notes, improves your life extremly

>>11965462
I would recommend elementary number theory. my book has easy to follow proofs and programming exercises at the end of each section

I have the the system of differential equations matrix
{{3, 1,-1}, {-1, 1, 1}, {0, 0, 2}}.
I know the eigenvalue is 2 repeated thrice, but I'm a bit lost with finding the eigenvectors. I know from (A-landaI)u=0 you end up with the relation
x+y-z=0
But that's where I get stuck and don't understand how I proceed to get all the eigenvectors. I can't find any resource that explains this in depth.

So I've been reading about geometric algebra and how it's supposedly great because it simplifies lots of stuff.

Is it worth it to learn something if the majority of the literature isn't written with that algebra in mind? Idk how hard it would be to translate back and forth.

what do you guys think?

Bros, what is the differential of arch if the curve is a line going on top and against the x axis??
My physichit book says it is dl=dx but it makes no sense to me why it isn't dl=-dx. I actually never was actually thought what to do when the curves weren't "regular" i.e. they weren't differentiable.

>>11973255
here is the excersize. I dont understand what values should the limits take either....
the work i should calculate is of a force agaist the electrostatic force aka -1*the work of the electric force

https://www.youtube.com/watch?v=VvqeJkT3uyo

gl hf

>>11972999
this statement is either true or false

>>11971986
>>11972445
Explain

Can you guys recommend me a good geometry book? Most of my knowledge in geometry was stuff I picked up along the way from algebra my community college's math track. We don't have a proper geometry course, so my knowledge on it is pretty minimal. Just enough to get me through calc/ODEs/linear algebra.

>>11973743
Pedoe - Geometry: A Comprehensive Course
Hilbert - The Foundations of Geometry

>>11973763
Pedoe is like grad level isn't it?
>>11973743
If you choose Hilbert like the other anon said I think it's free on gutemberg. Geometry Illuminated is pretty also but I dunno how good it is.

>>11973837
>Pedoe is like grad level isn't it?
Yes. It's still a good geometry book.

If you haven't read this book, you're not a true mathematician.
>jk

>>11974215
i thought this was a novel
the subtitle gave it away though

Nouveau >>11975242