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Tangoed

 The h Bar

General chat for Physics SE (physics.stackexchange.com). For M...
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Tangoed
Jun 4, 2021 15:02
@ACuriousMind Haha it's part of a pset
Tangoed
Jun 4, 2021 15:02
Thanks
Tangoed
Jun 4, 2021 15:02
Oh, so just working with units is enough
Tangoed
Jun 4, 2021 15:01
Hello everyone. Any hints in showing that $\int_V \rho \vec{u}\cdot \nabla \vec{u}\,\text{d}V$ is a force if $\vec{u}$ is acceleration and $\rho$ is density?
Tangoed
Jun 4, 2021 10:17
Hello everyone. If $\vec{b}$ is electric force and $S$ the cross-sectional area of a platinum wire, what is $\int_S \text{curl}\vec{b}\cdot dS$?
Tangoed
May 28, 2021 19:01
Ohhh, ok!! Thanks @ACuriousMind
Tangoed
May 28, 2021 18:58
@ACuriousMind I thought I could, giving me a tensor
Tangoed
May 28, 2021 18:57
Sorry if the question is too basic, I didn't know where to ask
Tangoed
May 28, 2021 18:57
Oh ok $\nabla$ is just the operator
Tangoed
May 28, 2021 18:56
$\vec{U} = \frac{\vec{u}}{|\vec{u}|}$ btw
Tangoed
May 28, 2021 18:55
But shouldn't it be $\vec{U}\cdot (\nabla \vec{u}(\vec{x_A}))$?
Tangoed
May 28, 2021 18:55
Hello everyone! I'm trying to interpret $(\vec{U}\cdot \nabla)\vec{u}(\vec{x_A})$
 

 Mathematics

Associated with Math.SE; for both general discussion & math qu...
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Tangoed
May 29, 2021 22:50
Hello everyone. Anyone here is a grad student considering leaving academia?
Tangoed
May 25, 2021 17:13
A good Tuesday to all of you. Bye.
Tangoed
May 25, 2021 17:12
@Quin Yes! Will do things calmly now.
Tangoed
May 25, 2021 17:04
@Quin What makes me feel like shit is that I honestly think it's not a hard concept at all hahaha
Tangoed
May 25, 2021 17:00
@Quin Thanks for your answer about homomophisms between free and symmetric groups again! Although I gave up on it because I can't give a 20 min talk about something I don't really feel like I know it truly.
Tangoed
May 25, 2021 14:57
@leslietownes hahah
Tangoed
May 25, 2021 14:57
@Quin Good hint! It'll definitely help. I guess this is too basic for groups, thanks again. I have to learn all of this today.
Tangoed
May 25, 2021 14:50
@Quin I'll look into presentation of a group! thx
Tangoed
May 25, 2021 14:47
@Quin Oh, yes, your terminology is correct, sorry. I'm talking about generating a free group with $n-1$ elements, that is, $\{a_1, a_2, \ldots, a_{n-1}\}$ so $a_1 a_2 a_3^{-1} a_{n-4}$ is a word in this free group
Tangoed
May 25, 2021 14:43
Hello everyone!! I'm trying to show that there is a homomorphism between the free group of $n-1$ elements and $S_n$, the permutation group for $\{1,2,\ldots,n\}$. Any hints on how to start this??
Tangoed
May 11, 2021 02:33
Sorry!
Tangoed
May 11, 2021 02:33
Yes!!! Ok!!
Tangoed
May 11, 2021 02:33
Oh, because to find an element of that finite field I would have to get a polynomial, divide it by $X^3+1$ and get the remainder
Tangoed
May 11, 2021 02:31
I'm sorry to bother this chat with simple and trivial questions but why is it that the polynomials of degree $\leq 2$ form a set of representatives for $\mathbb{Z}_3[X]/(X^3+1)$?
Tangoed
May 10, 2021 23:26
Hmmm ok!! Thanks!
Tangoed
May 10, 2021 22:52
Why is it that $f(x^q) = f(x)^q$ for each $f\in \mathbb{F}_q[x]$?
Tangoed
May 10, 2021 17:11
What got me confused was the $\langle \cdot \rangle$, I thought this meant something else, like some operation on $f$
Tangoed
May 10, 2021 17:10
@Thorgott Oh boy, $\mathbb{F}_2/\langle f \rangle$ is the same as saying $\mathbb{F}_2/( x^4+x+1 )$
Tangoed
May 10, 2021 17:08
@Thorgott I'm trying to understand how this field is built
Tangoed
May 10, 2021 17:07
Oh, ok, so in $\mathbb{F}_2[x]/\langle f \rangle$ the ideal is simply $\{af :a\in\mathbb{F}_2\}$
I'm sorry, I haven't studied algebra yet
Tangoed
May 10, 2021 15:12
I have an $f\in \mathbb{F}_2[x]$, with $f = x^4 + x + 1$ an irreducible polynomial. What is $\mathbb{F}_2[x]/ \langle f \rangle$? Specifically $\langle f \rangle$?
Tangoed
May 10, 2021 13:39
Hello everyone. Sorry if the question is too basic.

I have a finite field $\mathbb{F}_q$ and with $k,n\in\mathbb{N}$ we define $C\subseteq \mathbb{F}_q^n$ as a $k$-dimensional linear subspace, calling $C$ a linear code.

Now we can also say that the basis for $C$ provides an isomorphism $\mathbb{F}_q^k \to C$. Does this mean that $\text{Span}(\text{Basis}(C))=\mathbb{F}_q^k$?

Can we say that for $C\subseteq\mathbb{Z}_2^8$ with $\{(1,0,0,0,0,0,0,0),(0,1,0,0,0,0,0,0),(0,0,1,0,0,0,0,0),(0,0,0,1,0,0,0,0)\}$ providing an isomorphism to $\mathbb{Z}_2^4$? That is, we are saying in this case $k=4…
Tangoed
Apr 12, 2021 00:39
Anyway, thanks @TedShifrin @leslietownes and @Quin, I have this year to prepare myself as best as I can, so I may be panicking a little
Tangoed
Apr 12, 2021 00:38
@TedShifrin When I asked him if I could audit the course he only sent me to his notes and asked if I felt ok with it. It's a first year master's course, and obvsly they expect undergrad knowledge
Tangoed
Apr 12, 2021 00:37
@TedShifrin LOL sorry
Tangoed
Apr 12, 2021 00:36
The interior of the closure of S?
Tangoed
Apr 12, 2021 00:36
@TedShifrin You mean the closure of any set S?
Tangoed
Apr 12, 2021 00:33
@TedShifrin Ok... So maybe it isn't a good idea to take dif geo right now?
Tangoed
Apr 12, 2021 00:31
@leslietownes So to a first exposure to the theme it would be alright?
Tangoed
Apr 12, 2021 00:31
@TedShifrin Do you know Portuguese? His website
Tangoed
Apr 12, 2021 00:29
@TedShifrin Ok... but feasible?
Tangoed
Apr 12, 2021 00:29
Sorry, only the first one*
Tangoed
Apr 12, 2021 00:28
@TedShifrin From his website it seems that the two first books are the main ones, the others are only references or to be read only some annexes
Tangoed
Apr 12, 2021 00:27
Not sure if this is too much too
Tangoed
Apr 12, 2021 00:27
Analysis was the only proof-based course I did
Tangoed
Apr 12, 2021 00:26
do Carmo M., Differential Geometry of Curves and Surfaces
Duistermaat J. J., Kolk J. A. C., Lie Groups
Lee J., Introduction to Smooth Manifolds
Spivak M., Calculus on Manifolds
Wolf, Spaces of constant curvature
Tangoed
Apr 12, 2021 00:25
upper undergrad*
Tangoed
Apr 12, 2021 00:25
@TedShifrin first year master's/grad, or advanced undergrad not sure