/sci/ - Science & Math

dynkin donuts
heh

https://www.youtube.com/watch?v=4QEntmb2xyE
https://www.youtube.com/watch?v=gcuqYsrCR5A

>>10322503
Given this diagram.
n.P(0)P(1) = 0
describe the points in the line P(0)P(1).
Doesnt this same equation represent points on line n^?

>>10322503
representation theory is a meme

What is the analytical continuation of the prime numbers?

At what point should I think I can do math? Ive taken mostly comp math so diff equations and calc and was wondering if i have what it takes to do abstract.

>>10320053
>>10319806
>>10319201
>>10319184
It was revealed to me in a dream how this double cover might work. Just project the curve onto the line and it will naturally give a double of the line except at the 4 intersection points.

Is this completely and hopelessly wrong?

>>10323139
Not genus one.

>>10323143
how do you make it then? Surely it needs to be somehow canonical, otherwise it wouldnt say it so non-chalantly, r-right?

>>10322503
So many of the math channels on yt are geared towards teach brainlets calculus and algebra, otherwise teach mathematical memes (((science communication))). What channel would you recommend.

>>10323211
Graduate mathematics

Has anyone calculated an analytic extension for the Collatz conjecture's function?

Does anyone know what he means by max or min here? Does he mean local max/min of the function f(x,y)?
For example, the curve [math]y^2=x^2(x-1)[/math] has an isolated point at (0,0) but it's not really a max/min of the curve, but it is a local min of the surface defined by f(x,y)=y^2-x^2(x-1).

>>10323335
My question is, how do you prove this? I could imagine there being some sort of bottleneck singularity, like a double cone situation.

>>10323335
>p(x, y)=y^2+x^2-x^3 has an isolated point at (0, 0)
It literally doesn't, and he obviously means local maximum or minimum.

>>10323348
I'm going to swiftly disregard your opinion

>>10323338
With analysis techniques. Suppose that there are two points in the isolation, and one is negative and another is positive, namely a and b. We trace the line between them, getting y as a linear function of x, and restrict the original polynomial to it, obtaining a new polynomial. Because polynomials are continuous, there's a zero in the path, and thus a zero in the original function.

>>10323418
I may be reading it wrong or you may have understood wrong. So you're taking two points in a neighbourhood of the isolated point when looking at the surface, one above and one below the isolated point, and considering the line through them.

What if the line is not contained in the surface, and in particular if it doesn't go through the isolated point?
Secondly, there's a zero in the path by assumption on there being an isolated point. I need to show that it's a local extremum

>>10323454
The line is in the x, y plane.
It isn't supposed to go through the isolated point, specially since it's a proof by contradiction. The point, being zero, is a local maxima or minima if and only if every point in a neighborhood is either positive or negative. We assume that there is a positive and a negative point in the neighborhood, and use that to show the zero isn't isolated.
The line is in the surface because the open ball is convex.
Now that I notice, there is the problem of the line going through the original zero, but there also has to be another negative point in a neighborhood of the previous point so we just take a new line.

>>10323467
Look at this graph >>10323353
An isolated point does not have to be a min/max in the plane, but in the 3D space, so your proof makes no sense, especially because you're taking points in the neighbourhood of the ISOLATED point. There are no points!

>>10323338
Pls answer my question here
>>10322982

>>10322988
no representation theory is cool because it leads to based character theory

Need some recommended literature for infinite dimensional projective spaces. Anyone know of any?

>>10323515
Explain your notation, brainlet

>>10323536
n.Vector(P-P0) = 0 is the equation that satisfies for all points in (P-P0) line.
I am asking is the same equation describes points on line parallel to Vector(n)?

>>10323588
Yes, you are right. A line in the plane is defined by either:
>2 distinct points
>a point and a vector
Hence given only a vector, you can only deduce that it pertains to a family of parallel lines.

>>10323598
but same equation cant descibe points on two perpendicular lines, here n vector and Vector(P-P0)
What am I missing to notice?

>>10323659
You need to learn some English because im barely understanding you...

But from what i gather, n is the normal to P-P0, and the equation n.(P-P0)=0 describes the set of points that are perpendicular to n. What you're confusing is that you think that this also describes the set of points on the line that the normal n defines. However, what you're missing is the fact that the "free variable" here is P. You know what n and P0 are, but P varies here, therefore n.(P-P0)=0 describes all points P such that when forming a line from P to P0, the vector n is perpendicular to that line. There is only one such line.

bit of a brainlet calc iii question here, but it came up in my physics class that when doing derivatives with Leibniz notation (ie dy/dx) shouldn't you technically always be using partial derivative notation? we were doing "particle in a box problems" schrodinger equation problems and he wrote down the equation using the non-italicized df/dg and someone asked if it should be the partial derivative operator, and he said that he wasn't sure, but as far as he was concerned pretty much all derivatives were partial derivatives. is this just physicist handwaving formality, or is there a serious difference between the dy/dx with straight back d's or the curly d's?

>>10323695
Understood.
From this equation.
n.(P-P0) = 0.
How do I go about finding some equation that describes points on Vector n?

/sqt/ sorta blows dick nowadays
I dont mean to pollute your intelligent general with my brainlet question but can anyone help me with this? >>10323673

>>10323729
In one variable they are the same for obvious reasons.

In two variables they are completely different, and your lecturer is a brainlet. One is the total derivative and the other is the partial derivative. The total derivative measures the total change.

For example, say we have a function [math]F(u(x,y),v(x,y))[/math].
The partial with respect to [math]x[/math] leaves [math]y[/math] constant.
The total derivative with respect to [math]x[/math] is defined as:

[eqn]\frac{\text d F}{\text d x}=\frac{\partial F}{\partial u}\frac{\partial u}{\partial x}+\frac{\partial F}{\partial v}\frac{\partial v}{\partial x} [/eqn]
And hopefully you can see they're not at all equal.

>>10323749
to add to that I've also used both 'x+4' and '4-x' as radii and still got the wrong answer

>>10323729
There is no serious difference. The straight d is for one dimension and the curly one is for partial derivatives. One might also use the straight one for time differentiation in order to single it out. Also, one needs to choose whether or not to use \mathrm{} in latex but maybe that's more relevant to integrals. It's just notation, use whatever you like.

>>10323745
If you want the equation of a line with vector n, and originating at point P0 (remember we need two things to define a line), then you can just write it as P0 + xn, where x is the "free variable" and defines points on your line.

>>10323749
>>10323759
fuck me nevermind
i forgot that -1 exists
sorry

>>10323729
Same same. But using the curly d is nice so you don't mix up the exterior differential.
>>10323758
Man. No.

>>10323793
lmaoing if you actually think that's wrong

>>10322988
>representation theory over fields other than C is a meme

Ftfy

>>10323773
>>10323773
Man. Analytical geometry and vector are closely related. Which is generalization and which is specialization?
For a line we have lots of equation in analytical geometry; point intercept equation, slope equation, two points equation.
Same line can be described in vector algebra as "set of points" given by n.(P-P0) = 0.
What benefit does vector or analytical geometry give over other? Doesn't the serve the same purpose? Describe points, lines and curves in space?

>>10323851
They describe the same objects, but the different descriptions lend themselves to different arguments and theories.
For example, vector geometry gives an easier description of higher dimensional calculus, and are integral to objects such as line or surface integrals, Stokes' theorem, etc, so differential geometry has a big influence from it, while analytic geometry tends to involve more algebraic arguments, and from them, algebraic geometry springs out.

>>10323880
This year I have decided to learn these things.
I have one abstract algebra book. Before that I will refresh my analytical geometry. Some trigonometry for simple angle line relation that would come up in proofs. Calculus with emphasis on lines and conic sections.
Then linear algebra along with vectors. Not sure how vector algebra, vector analysis and vector calculus are related or not. I will do them in sequence.

Then finally abstract algebra.

You do feel my sequence is good?

>>10323911
Yes. In my opinion, analytic geometry is one of the most important and interesting subjects. You should learn conics before you learn calculus in my opinion, since they belong to the subject of analytic geometry and their classification are one of the peaks of classical geometry. Any good book on analytic geometry should cover conic sections too. Trigonometry is more important than just angle-line relations too.

I think your sequence is good, but again, learn conic sections beforehand. You can always download free books from libgen anyways.

I'm not sure if abstract algebra is the best thing to learn if you don't really have motivation for it. In my opinion, you should read a small book on elementary number theory before you try abstract algebra. Otherwise, good luck.

>>10323849
>representation theory over fields other than C is a meme

And representation theory over [math]\mathbb{C}[/math] is a joke, what's you point?

>>10323758
You've literally written out the partial derivative [math]\partial_x F(x,y)[/math] and called it the total derivative. This can be most easily gleaned from the fact that y is treated as a constant as there is no [math]\partial y[/math] anywhere.

This is the total derivative I've just stolen from Wikipedia (which is effectively a normal derivative treating y as a function of x):
[eqn]\frac{\textrm{d}F}{\textrm{d}x}=\frac{\partial F}{\partial x}+\frac{\partial F}{\partial y}\frac{\partial y}{\partial x}[/eqn]
which can be expanded by chain rule if anyone's bothered.

>>10324689
Oh yeah, the [eqn]\frac{\partial u}{\partial x}[/eqn] should have been totals not partials

>>10323144
Any two double covers are birational and therefore isomorphic because they are smooth curves.

div curl and grad. Is this book good?
Can anyone brief the physical/geometrical significance of div, curl and grad?
I believe any abstract structure which has geometrical significance automatically implies it has physical significance.

>>10324981
well, but how do you get one then?

>>10325088
Fresh off the lecture, grad is a normal vector of the function graph's tangent plane;
moving orthogonal to it means (locally) keeping the function's value constant, while moving parallel to the gradient means maximally increasing/decreasing the value.
Remember, differentiable functions have
[math]f(\mathbf{x+h})=f(\mathbf{x})+\mathbf{h}\cdot\nabla f(\mathbf{x}) + o(||\mathbf{h}||)[/math]

>>10325095
For example if the points are distinct, then you can always arrange for one of them to be the point at infinity via a projective transformation. Further you may assume the line is given by (y=0) i.e. the x-axis.Then say x1, x2, x3 are the points on the line (not at infinity). Then y^2 = (x-x1)(x-x2)(x-x3) defines an elliptic curve going through all the points giving the required double cover.

>>10325110
I am at normal vector and transformation chapters of my linear algebra.
Getting really confused with orthogonal vectors(normal vectors) and projection of vector.
I have one doubt.
Can u explain me how did they find d as the shortest distance between plane and origin?
-(n.P0) is a negation of inner product. Inner products are just scalars but what do these scalars signify? And why did he say it is the shortest distance?

>>10325110
Previous page

>>10325159
wow thanks a lot, this makes a lot of sense considering how the next step is considering those curves whose j-invariant is 0.

But can you explain how this gives a double cover? I know I'm a brainlet. Is it because of the y^2?

>>10323758
>Total derivative
It's called differential you fucking subhuman, and it's written [math]D F[/math].

>>10325209
>arguing over notation
literally the lowest iq thing anyone can do

>>10325219
>Getting mad at people for calling out your shitty first year notation
Never gonna make it

I am not understanding what the fuck this means. Am I a brainlet?
It is asking for a Volume between two surfaces. I immediately assume a triple integral with no internal arguments and just a straight up boundary problem in the integrands.

I might not be explaining myself the best. My question is, would using a cylindical triple integral be the best way to solve both of these problems? I just want to visualize math. Self teaching multivariable calculus so I can then invent meme science with relativity. What does the Z integral in a triple integral mean specifically, height right? It's just another boundary for us to define 3d objects?

>>10325293
Wrong image. It should be this. I don't know why the fuck I made a screenshot of that one.

>>10325293
Like m8 you're dumb as a brick absolutely unbelievable fuck off to sqt.

>>10325306
My question was. How do I visualize triple integrals? Aren't they just another way to write a 3d volume between your "3D coordinates (X,Y,Z)" boundaries.

I made a cylindrical triple integral of the first one, but the 2nd one I have no fucking clue what it means since theres a god damn xy in the internal arguments being integrated by our 3d boundary integrands.

>>10325318
>How do I visualize triple integrals?
Just a linear functional on the space of measurable functions with values on a banach space over a field bro

>>10325323
I wrote 3D alot to sound smart.
What the fuck are you saying?

>>10325328
What I'm saying is that there comes a point where visualization does nothing. Integrals are just operators that act on functions, you won't get much understanding out of figuring out what volume they correspond to and sometimes you're better off seeing them as abstract objects.

>>10325339
My question is, how do I know what to put as my boundary of integration? Everyone online says to just "visualize it" so I would like to ask you professional anons, How do I visualize this triple integral so I can stop being a math chugging monkey that can solve problems but not figure out how to set them up.

>>10325352
Here's how I'm doing it with your example
>[math]x \in [0,3][/math]
>[math]y = \sqrt{9 - x^2} \iff y^2 + x^2 = 9[/math], which is a circumference. Therefore we have a quarter of a circle of radius 9 in the plane
>Finally the z axis satisfies the equation of a sphere of radius 9, so we have an eighth of a solid sphere
I haven't done this shit in years though so I might be wrong

>>10325318
The thing with triple integrals over functions of three variables is that, the idea of it representing the area or volume or whatever below the graph gets tricky, because the graph lives in 4-D space. So it's better to think about it like some sort of "density" function which assigns certain weights to every point of space and the integral gives you the total mass. But you could still say it's the hyper volume below the graph of the function [math]w=f(x,y,z) [/math] in [math]\mathbb{R}^4[/math] However, that's why the question is asking you about the domain of integration, which is a volume on 3D space and so you should be able to visualize it.
>>10325352
Again don't try to visualize a general triple integral, the important thing is the domain. Independent of the function you are integrating, your domain is given. The outermost integral has a nice domain, which means that your object has only an x coordinete between 0 and 3. Now, if you fix an x it tells you up to which point y can move which is when it reaches a circle of radius 3 and the same logic tells you that by fixing some x,y in the plane z can move from 0 to a sphere of radius 3. Don't listen to >>10325339
It's absolutely crucial to visualize, the point is to understand what you are working with.

>>10325389
>It's absolutely crucial to visualize, the point is to understand what you are working with.
That's all fine and dandy for easy problems that are meant to be visualized, but it's terrible advice once he hits something that's not tailor-made for a freshman calculus course.

>>10325375
why the fuck does x have to be an element of (0,3)? What does that mean?
Which one are you explaining? Problem 2 I suppose? I'll draw a diagram of what I think about when I visualize the boundaries of integration.

>>10325402
If you ever want to gain the intuition of why a particular set of axioms works for a more general theory, you need to see what they mean in euclidean space, or with a more basic example. Abstraction is powerful, but except you want to become a useless drone that manipulates symbols it's important to understand the motivation behind the objects you are working with.

>>10325403
>why the fuck does x have to be an element of (0,3)? What does that mean?
I'm explaining problem 2, yes. Look at the final integral, it's [math]\int_0^3 (\ldots) dx [/math], so the values for x are in that range. Also I fucked up and the radius of the sphere is 3.

>>10325410
Yes, but you don't bother visualizing the more general theory. That's my point, if trying to visualize things is stopping you from even starting to solve the problem then you should focus on more important things.

>>10325403
When you do a triple integral you essentially create a boundary region.
Z is the height of the function, it is defined as however.
When you iterate on Dy integral you technically iterate delta Z over the area of delta Y, which creates the "side" of a future 3d surface.
That technically is an area already so when you iterate on the boundary of X, you create the depth that the area needed to create a 3d object.

>>10325412
It's a sphere? Fuck. I thought it was something entirely different. I thought it was a paraboloid over the xy plane. How did you know it was a sphere? I could just plug this into geogebra, but that's not where intuition is built

>>10325429
Two different anons already explained it to you. Maybe you are retarded bro

>>10322994
that is literally meaningless

>>10323215
yes, its trivially easy and not useful at all

>>10325429
Not really a sphere, it's the intersection of a sphere of radius 3 with the first octant. I explained it here >>10325375. Just figure out the easy axis, then the next one by moving the first one, then the final axis by moving the first two.

fools, think of incognition. 3301

>>10325441
>>10325434
Hey genius can you help me here?
>>10325183
>>10325177

>>10325492
That's literally just two pages of definitions. There are no problems to solve. Are you just not understanding what it is saying?

>>10325177
>Can u explain me how did they find d as the shortest distance between plane and origin?
they took any vector from the origin to the plane and projected it onto the normal vector of the plane, that gives you a vector whose length is the shortest distance between the plane and origin
the inner product is just a relation to length and orientation of two vctors.

>>10325504
yes how d is the shortest distance from plane to origin?
How do I go about deriving shortest distance given only vector equation like n.(P-P0) = 0 represent points on plane. Which point is candidate for giving shortest distance? First I need to get the point and then find lenght of it using that square root of addition of square of components of point.

>>10325550

>>10325516
>they took any vector from the origin to the plane and projected it onto a normal vector of the plane, that gives you a vector whose length is the shortest distance between the plane and origin

>>10325557
why there is a negative sign on the distance? Does it have significance?

>>10325612
the picture literally says "signed distance" its negative if your point is on the other side of the plane

For a typical math catalog at a state school, what are the important math courses and not so important ones?

>>10325620
>>10325620
which point are u taking abt. A point in plane doesnt have side to choose. Only point towards normal are said to be in positive half space of plane and back side as negative half space of plane.

can someone help me with the four fundamental subspaces

>>10325711
>which point are u taking abt.
the fucking point youre finding the shortest distance to

If B = OA, where O is an invertible matrix, is the rank of A equal to the rank of B because O does not increase the amount of linearly independent rows?

>>10325728
why the distance is negative. Distance doesnt have have direction.
should it be interpreted as normal vector dot product (P0) position vector. Or opposite normal vector dot product (P0) .

>>10325757

>>10325620
>the picture literally says "signed distance"
signed distance has direction

>>10325767
So does that mean shortest distance is opposite to normal vector?
Also projection of P0 onto normal n vector will have same direction as normal vector unless the angle is obtuse.
Since projection is the shortance distance vector, as you said, why does it have opposite direction to normal vector

>>10325767
Lets say I have to compute points on the plane in computer. Using this single equation i.e n.(P-P0) = 0 how do I get all such points?

>>10325200
Yes it is because of the y^2. It's pretty obvious when you draw the real graph.

My ODE&PDE class this semester uses this book that is less pure math and from the get-go is heavily reliant on working with real life examples. It said something like "students work better when recognizing the utility of math than when only concerned with its beauty"
well I disagree and I was wondering what a good alternative book might be, we're only doing linear first order eqs so far

>>10325945

>>10326642
anyone?

>http://www.openproblemgarden.org
>list of math problems that literally no one can solve
>recommended for undergraduate
Huh?

>>10326792
It means they can start working in them and have a fighting chance to get something out of it. Not necessarily solve it completely. A bound to an open problem was given in a fucking Haruhi thread.

>>10326803
Have you ever managed to solve an unsolved problem before, Anon-kun?

>>10326816
don't ever call me anon-kun in your life you retarded faggot. kys

>>10326819
Ouch, you don’t need to be rude.

>>10326823
Die

>>10326005
Arnold is a closeted physicists so I don't know if that's a good recommendation. I think the point is to show that differential geometry and dynamical systems are beautiful and powerful tools.
>>10325945
ODEs and PDEs are that, equations. It's like a basic algebra course, you learn to solve equations through plenty of examples and its neat to find how to model real world problems with that. The thing is that, all the mathematical complexity of these fields comes from just how hard sometimes can it be to find a solution, or know if it even exists at all, but that usually goes into applications of certain results from mathematical analysis. So any introductory book will expose you to just what those equations are, why are they relevant and different techniques, because that's what the field is about. Also, just because it's applicable it doesn't mean it's not beautiful, that is pure math wankery.

>>10325945
If you haven't taken a proper analysis class, you shouldn't bother learning DE's / Dynamical Systems on a theoretical basis. It will just be frustrating.
You need the context of knowing how to solve linear DEs of various types in order to understand any of the interesting nonlinear theory.
You also need some understanding of how DEs model physical processes to be able to process certain theoretical existence and energy conditions effectively.
I'd just go with it.

>>10326645
do you know how to cross multiply vectors? show your work

>>10326642
what the fuck? No, it isn't. how or why did you multiply everything by cos?

It seems like the Indian student in my math class is constantly sizing himself up with the professor and other classmates (myself included). He proudly points out "errors" in our work or "faster" ways to prove theorems/solve problems. It's pretty damn annoying. Is he trying to establish dominance or is it some cultural thing?

>>10323211
Frederic Schuller and the WE Hereaus international winter school on gravity and light
I learned a LOT from those two

From around 1955 to 1970, algebraic geometry was dominated by Paris mathematicians, first Serre
then more especially Grothendieck and his school. It is important not to underestimate the influence
of Grothendieck’s approach, especially now that it has to some extent gone out of fashion. This
was a period in which tremendous conceptual and technical advances were made, and thanks to
the systematic use of the notion of scheme (more general than a variety, see (8.12–14) below),
algebraic geometry was able to absorb practically all the advances made in topology, homological
algebra, number theory, etc., and even to play a dominant role in their development. Grothendieck
himself retired from the scene around 1970 in his early forties, which must be counted a tragic
waste (he initially left the IHES in a protest over military funding of science). As a practising
algebraic geometer, one is keenly aware of the large blocks of powerful machinery developed during
this period, many of which still remain to be written up in an approachable way.

>>10328440

On the other hand, the Grothendieck personality cult had serious side effects: many people
who had devoted a large part of their lives to mastering Weil foundations suffered rejection and
humiliation, and to my knowledge only one or two have adapted to the new language; a whole
generation of students (mainly French) got themselves brainwashed into the foolish belief that a
problem that can’t be dressed up in high powered abstract formalism is unworthy of study, and were
thus excluded from the mathematician’s natural development of starting with a small problem he
or she can handle and exploring outwards from there. (I actually know of a thesis on the arithmetic
of cubic surfaces that was initially not considered because ‘the natural context for the construction
is over a general locally Noetherian ringed topos’. This is not a joke.) Many students of the time
could apparently not think of any higher ambition than Étudier les EGAs. The study of category
theory for its own sake (surely one of the most sterile of all intellectual pursuits) also dates from
this time; Grothendieck himself can’t necessarily be blamed for this, since his own use of categories
was very successful in solving problems.

The fashion has since swung the other way. At a recent conference in France I commented on the
change in attitude, and got back the sarcastic answer ‘but the twisted cubic is a very good example
of a prorepresentable functor’. I understand that some of the mathematicians now involved in
administering French research money are individuals who suffered during this period of intellectual
terrorism, and that applications for CNRS research projects are in consequence regularly dressed
up to minimise their connection with algebraic geometry.

Does anyone have a PDF of the 2nd edition of Aluffi Algebra Chapter 0?

Apparently the errata for the 1st edition is huge. Also, apparently, the 2nd edition isn't really properly labelled as such:

"There is no mention on the AMS webpage that this is a corrected reprint, but this version does incorporate the errata to the first printing (through 2015). If you run into this book and want to know whether it is the corrected version, look for a "Preface to the second printing" on p. xv. If it is not there, the version you are looking at is the first printing. If it is, you are looking at the corrected printing."

>happily work on something I think will turn into a fine paper for the past few month
>can probably even publish it in Phys Rev
>didn't check arXiv over that time
>suddenly see a late-2018 e-print that forbids one of my constructions few days ago
>that construction allowed me to apply the structures under study to classify the topological phases of a wide range of interacting non-Fermi liquid theories
>mfw the paper was by a guy I met at a conference I went to a few weeks ago
>mfw he didn't say a fucking word about it while I was blabbering on about my research

Anyone know of insightful lecture notes ( not more than 50 pages ) or moocs on introductory fourier analysis that don't mention physics for the most part? Thanks!

Calc 2 seems too easy as did Calc 1. Does math ever get hard? -Brainleto

>>10327538
He has autism. Just don't give him attention or act confused and clueless when he butts in. He probably will stop bothering you if you're not receptive.
The inclination is to be polite but that just doesn't work.

>>10328440
>>10328442
wa la.

>>10328796
>calculus
>math
lol

>>10327538
He is just taking his revenge for all the Indian tribes the US has oppressed.

>>10328442
Fucking kek.
>>10328676
Are you sure you can't restrict the construction to a subcase where it is allowed?

>>10328658
errata https://www.math.fsu.edu/~aluffi/algebraerrata.2009/Errata.html
also has link to errata of second printing

Fusion systems are quite cool.

>>10328796
No. Calc 3 is just calc 1 in more dimensions and ODEs (if you even bother) is just memorising like 8 methods. That's it, you're done with math then. I recommend buying Weil's Basic Number Theory for a different flavour however.

>>10329459
>ODEs (if you even bother) is just memorising like 8 methods
Which school for brainlets do you go to?

>>10329705
what, did yours teach 9 or 10?

>>10326792

Any mathematician who has only tried cherry picked problems with easily explainable solutions is nothing but a mere buffoon.

Also, you probably are overestimating how many people have actually cared enough to try and prove obscure conjectures about quasigroups, etc.

>>10329705
ODEs is a trivial class until you've taken real analysis, at which point an ODEs class can actually be interesting and nonlinear.

>>10330103
Post "Thank you for the existence theorem, Picard!" and analytic solutions to ODEs will come to you.

>>10330362
Thank you for the existence theorem, Picard!
(and f*ck lindelhof)

>>10327538

While I call it a good day if I have been called a nigger just once, other foreigners can do shit like this lmao

I have a really thin slice of math that interests me:
Math foundations
Cryptography
Complexity theory

Where can I go to study these things ? I already have the intro to Cryptography (did a senior project in Cryptography too) and I've taken an enderton set theory course. A lot of the crypto books I find are too introductory for me or are based in computer science application

I'm not an undergrad just want to rejuvenate myself by learning some math . I don't think I want to go to grad school either .

>>10330501
Arithmetic of elliptic curves, Silverman

Bump

>>10326645
>>10326642
>>10327057
See
>>10328102

what the fuck is the difference between internal and external direct products of groups

>>10330735
Just because they are equivalent up to isomorphism doesn't mean they are exactly the same mathematical objects. It just mean you can treat them as the same when considering their properties as groups.

>>10330746
No I understand that, what I don't get is how the internal and external definitions are different at all, you just write elements in one as ab and the other as (a,b).

>>10330781
The internal direct product is only defined between subgroups of a given group, and is another subgroup of that group. The external product doesn't have this restriction.
As said before, the two are isomorphic but not literally the same.

>>10330781
Well, they are completely different sets to begin with. One is defined as a product of normal subgroups of a given group and so ab has meaning as a group operation. and (a,b) lives in the cartesian product of two groups.

>>10330735
One is a construction from two groups (external), and the other is a structure found within a group (internal).

>>10330570
Elliptic curves was actually what my project involved
Thanks . Anyone have other stuff?

post you're bookshelf

>>10331207
>libgen

>>10331207
All those books and you still misuse “your.”
Shame.

>>10331207
amazing
i have so few math books, it's awful
one of these days i'm going to go around my math department and find old books people have left places that have been there a while, or books in recycling bins, and just collect a ton of used ones for free
any other tips for getting free physicals, just for the collection?

>>10331288
miro-R(3)

>>10331256
they'res no problem with the way he spelled it m8

>>10331207
But I don't identify as a bookshelf

>>10331311
>they'res no problem with the way he spelled it m8
I'm not a "he".

>this is real
what the fuck?? lmao

>>10331377
I need the source for keks.

>>10331384
Reid's Undergraduate Algebraic Geometry. So far it's an easy read. I also quoted >>10328442
>>10328440 from chapter 8 in the book

>>10331393
he wrote that? fuck, that book is probably great then

lmao where is the toymaker general?
fuck off you HEP FAG

>>10331402
you can get the latest edition on his page for free

to be fair it's a bit 'too much' at times, like he's very blunt at saying "this is fucking obvious" which gets annoying after a point

>>10331207
Please no bully

>>10322503
Is it possible to mathematically prove the existence of God?

>>10331546

A starter guide for any QFT!

>>10330501
Anyone?

>>10330501
Go study with Jeffrey Hoffstein

>>10331538
>264 files
Let me ask you something anon, are you one of those guys who sees a textbook recommended, goes to libgen, downloads it, then never actually reads the book pretending to yourself that as long as you keep those files around that you'll eventually get to it? Cause I am.

>>10331766
Know any books or things he's done that I can read? Aside from the intro book

Can someone verify the truth of my proof? It’s inelegant but I didn’t want to copy the bog standard solution like a shitter.

>>10331830
It's correct, but your proof writing is pretty awful. Also it might be better to avoid doing this in the case of a metric space. If the boundary point is in an open set that is disjoint from A, then its complement is a closed set containing A but not containing the boundary point. This contradicts the boundary point being in the closure of A.

>>10331830
Hard to read. Just do it like this:
A is disconnected iff there exists a continuous surjection A -> {0, 1} with the latter space being discrete. Suppose A is connected but cl(A) is not, and let f: A -> {0, 1} be a continuous surjection. We may assume f(A) = {0}, so we get [math]\{ 0, 1 \} = f(\text{cl} (A)) \subset \text{cl} (f(A)) = \text{cl} (\{ 0 \} ) = \{ 0 \}[/math].

>>10331820
I don't know but now I'm curious. I've only read the intro book

>>10331538
>>10331207
>>10331799
you are,, but a child

Why ax+by=0 is called homogeneous equation? What does homogeneous mean in this context? What I know is that line passes through origin. What is homogeneous about origin?

>>10332575
a polynomial is called homogeneous if all its terms have the same degree. your equation is in the form f(x,y) = 0, where f is a homogeneous polynomial.

>>10332596
A polynomial and equation of line are same thing?

>>10332617
no

>>10332575
Because if (x, y) is a solution, (tx, ty) is also a solution for any complex t.

>>10332617
an equation of a line is a polynomial, but not otherwise. A general polynomial in 1 variable is a curve, while in 2 variables or more they tend to be curves, surfaces, and higher-dimensional analogues.

For example, x^2+y^2-z^2=0 defines a double cone through the origin.

>>10332575
you can add two homogeneous equations together and get another one.

Where to start with theory of computation

Is [math]C[a,b][/math] complete under the metric [math]\displaystyle \int_{a}^{b}|f(x)-g(x)|dx[/math] ? I got a feeling it isn't but am not sure how to go about it

>>10332891
No

hey guys, what do it mean for a vector lets say 5i+2j+3k, to have a tangent vector <0,0,0>?

>>10334203
do you mean orthogonal?

[math]\textsf{New Thread: }[/math]>>10334233

>>10334335
any takers?

>>10334203
<0,0,0> is orthogonal to all vectors. Tangent is straight line touching a curve or a surface at one point.
Tangent to line... hmm not sure but your two vectors are surely orthogonal.

Make A as identity matrix and then you will have solution for Ax=B system of linear equation.
What did they mean by this? If for each line I made sequence of row operations to arive at solution, how do those lines move around in space?

need dating advice /mg/
>doing phd in algebraic curves/number theory
>on tinder
>say if i unlock their secrets, i could probably hack any online server
>she asks if im gonna do it (unlock secrets)
Would it be a bad idea to say "im almost there, just need your number for the final step"

>>10329448
Yes I'm aware the errata exists. I'm asking for a PDF of the corrected edition.

I suppose I could figure out how to edit a PDF and fix them all myself, but I'd rather not

>>10335916
bump, need to get laid pronto
then no girls till fields medal

>>10335950
there aren't that many to make it such an effort. I myself studied from that book and spent a lot of time looking for the second edition and didn't find it. Just have a tab open with the errata and keep in mind the errors in the next 5 pages or so (there's one every 3-5 pages on average).

Only thing to note is that after chapter5, the errata is not complete. I myself saw several errors on chapter 7 for example that were not in it, but should be spottable usually.

>>10335968
?

This text is well-known for having a huge errata

>>10335975
So? Atiyah-Macdonald also has a similar frequency of errors in the text and it's still not a problem for almost everyone?

>>10335982
?

He published a second edition for a reason. Clearly it's possible to just refer to the errata repeatedly. I'm just asking for my own convenience.

700/292 ~ 2.4.

So, no, there's an error on every 2-3 pages.

>>10335989
jesus dude, half the errors are simple spelling mistakes that have no bearing on the text

>>10335992

>>10335916
>>10335952
How about you say something akin to "I'd love to tell you more, but I can't say anything else. It's not safe to talk about these things online. If we were in a more private place, however, that's a different story."

https://www.youtube.com/watch?v=sUGXfC8LwwI
https://www.youtube.com/watch?v=pi4uChDbPcg

>open up Mochi's p-adic Teichmuller for jokes
>he gives literally no concrete definitions
>I've never heard of a group action of the fundamental group on the original topological space in my entire life and have no idea what he's talking about
>it's still somehow very legible

>>10323017
you need nothing really. most modern, elementary textbooks on algebra give you all the tools you need to know what's going on. of course having experience writing and understanding proofs helps, but you have to start somewhere.

https://arxiv.org/ftp/arxiv/papers/1901/1901.09668.pdf
>Proof of the Twin Primes Conjecture
>T.J. Hoskins
>(Submitted on 18 Jan 2019)

>Associate a unique numerical sequence called the modular signature with each positive integer, using modular residues of each integer under the prime numbers, and distinguishing between the core seed primes and non-core seed primes used to create the modular signatures. Group the modular signatures within primorials. Use elementary sieve properties and combinatorial principles to prove the twin primes conjecture.