Mathematics

12:14 AM

related niceity: "almost-sure sense" or "almost sure sense"?

12:33 AM

@MatheinBoulomenos does 3x^3+4y^3+5z^3 (the famous counter-example of Hasse's local-global principle) have a solution in $\Bbb A_\Bbb Q$?

Victor

1:48 AM

Hi, anyone think without formal graduate education in math, it will be diffcult to generate a new proof for the general cases of Carley Hamiliton theorem?

Semiclassical

2:00 AM

Given how well-trod that ground is, I think the main work would be verifying that any particular proof is actually novel

Akiva Weinberger

4:32 AM

So

Israeli Elections 2: Elective Boogaloo

vimeo.com/137312014

11:00 AM

Hi Math SE I'm looking at a Cauchy-like matrix

The elements have the form $(y_j-y_i)/(x_i-x_j)$

So if I use mathematica to get an educated first guess about the closed form, I'm getting the heuristic

"Given that this matrix is $N\times N$, ...

Pick a set of $N/2$ elements $A$ and consider the set $N/2$ elements $B$ disjoint from $A$, one term in the summation that makes up our determinant will be the product of the differences of each element of $A$ with each element of $B$

Up to the sign that we can extract from multilinearity, so how would I write this expression in simple sigma pi notation :p

Sayan Chattopadhyay

1:26 PM

@TedShifrin Nah, my university has a habit of buying many copies of a book and missing out crucial ones because they spend their funding on many copies. For some reason they have 8 copies of Bourbaki's algebra but not a single copy of Arnold's ODE, Dusa Mcduff's Symplectic geometry, and not even classics like Dirac's book on QM.

s.harp

1:38 PM

@SayanChattopadhyay diracs book on qm is pretty bad

Semiclassical

2:20 PM

There’s an acronym for HW questions I’m forgetting

To describe ones where the OP only states the question and just says “I don’t know where to start”

I’ve gotten very tired of that

Ultradark

can one make a commutative diagram for an integer lattice, s.t. the objects are integers lol

and if you start anywhere on the lattice the path will lead eventually to (1,1)

maybe this doesn't make sense because the morphisms would be sending integers to integers?

s.harp

@Semiclassical psq , problem statement question

Ultradark

2:36 PM

"Sure you can. You just have to decide what the mappings between the integers are, and what composition is." -User: jgon

4

Q: Can we have the category of integers?

In beginning to learn category theory, I've tried to come up with my own examples of categories. Could we have a category Int, where the objects are integers, and arrows, all mappings between integers? If you can't (which I suspect might be the case), what can't be an object/arrow?

category-theory

Semiclassical

2:51 PM

@s.harp there it is

Which could more vulgarly be put as “piece-of-s*** question”

Ultradark

maybe they really don't know where to start?

Sayan Chattopadhyay

3:44 PM

@s.harp I like it. It's terse and not for a first intro but I prefer it over other books like Sakurai which are physicsy in nature. For mathematics there's always Takhtajan

Though you need books like Sakurai to do problems

Ryan Unger

You haven’t done QM if you haven’t suffered through problems

Samurai has some really hard ones

s.harp

@SayanChattopadhyay who does the book benifit if its too hard for a first intro, too basic for the grad student, is too theoretical for the experimtenal physicists and too unrigorous for the theoretical physicists

schn

4:06 PM

Given two vectors $\mathbf{u}$ and $\mathbf{v}$, how would one prove that an equilateral triangle, where the norm of $\mathbf{u}$ equals that of $\mathbf{v}$ and $\mathbf{u-v}$, is also equiangular?

Obviously $\cos{(\theta)}=\frac{ \mathbf{u} \dot \mathbf{v} }{ \lvert \mathbf{u}\rvert \lvert \mathbf{v} \rvert}$, where $\lvert\mathbf{u}\rvert=\lvert\mathbf{v}\rvert$.

Sayan Chattopadhyay

@RyanUnger Sakurai? Yeah it does

@s.harp I don't believe its too unrigorous for theoretical physicists. Many places its still a mandatory reading as a first course. I liked the Dirac-Sakurai combo. Though I guess you could just do sakurai instead.

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$Mathematics$ Mathematics