Cool, thanks. It looks like that the same series, so is probably the kind of thing that I'm looking for.
Anyone know any good ones to gain an intuitive understanding of other algebraic structures, e.g., rings, fields?
Thanks.
Hello,
A couple of years ago I studied abstract algebra from Dummit and Foote. However, I was never able to gain the intuition on the subject that I would like from that book. I want to study the subject again, and I want to use a different book this time around - one that covers a lot of...
Sorry for bumping this, but I do want to know whether people who have a bit more experience than me with this topic think that my conceptual understanding in the previous post holds water. Any thoughts?
Thanks.
Thanks kith, that's great.
So to make sure I understand you correctly, a simple interpretation that follows from the definition of coherence in the original post would be something like, "coherence between two basis states is a measure of the degree to which those two basis states must be...
Hello,
In the density matrix formalism I have read in numerous places that coherence is identified with the off-diagonal components of the density matrix. The motivation for this that is usually given is that if a state interacts with the environment in such a way that the basis state...
Hello,
I asked this question on math stack exchange as well, it is answered there (or, as of this post, in the process of being answered at least). For anyone who wants to see it, here is the link...
Hello,
I know that the law of the excluded middle is implied in ZFC set theory, since it is implied by the axiom of choice. Taking away the axiom of choice, does ZF set theory (with axioms as stated in the Wikipedia article http://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory)...
Hello,
I'm thinking about the wavelength of a freely propagating photon vs. a freely propagating electron.
For the photon, we have the classical picture of oscillating E and B fields perpendicular to the direction of propagation, and we call the wavelength of the photon, which can be...
Hello,
On p.573 of Jackson 2nd Ed. (section 12.1), he says, "From the first postulate of special relativity the action integral must be a Lorentz scalar because the equations of motion are determined by the extremum condition, \delta A=0."
I agree that if the action is a Lorentz scalar, then...
Hello,
Is there a common word in the standard math vocab list (postulate, axiom, lemma, corollary, proposition, theorem, definition, claim, remark, etc.) for something that will be treated as a postulate for convenience, even though it is known to be provable from previous postulates and...
Thanks for the reply, micromass!
I understand - like functions will be in the same quadrant of the complex plane (or even better, "point" in the same direction in the complex plane) at the same time, or restricting ourselves to real functions, like functions will be positive or negative at the...
Hello,
I recently started going through some lecture notes on linear systems and Fourier optics. (By the way, I just started with these, but so far the lecture notes are excellent. If anyone is looking to learn the subject but doesn't want to spend money on a textbook, the lecture notes, and...
Greetings,
I have two semi-related questions.
1. When making the Lagrangian formalism of electrodynamics, why is it that we use the Lagrangian density \mathcal{L}, rather than the plain old regular Lagrangian L? Is this something that is necessary, or is it more that it is just very...
Greetings,
I used to sit in on an astrophysics course, where during derivations the professor would often absorb all of the constants in a given expression into a single ever-changing constant at the front of the expression. E.g., for a trivial example, let X be 3 times the circumference of a...
Hi WannabeNewton, thanks for replying so quickly - this is the second time you've helped me out in two days!
Regarding your analysis - that does look quite simple, and seems to do the trick.
Regarding what you mentioned in the paragraph before that - you read my post correctly, I have indeed...
Greetings,
I'm having some issues with a problem that I is related, though not identical, to Bell's spaceship paradox (this is not for a homework or anything, it just sort of occurred to me when I was thinking about something else).
Consider two particles that are initially at rest in some...
Greetings,
I have been studying stat mech lately, and while I have gotten good at using partition functions to solve problems, I wanted to check my interpretation of what a partition function is, and especially to contrast it with the number of states. So, I'm just looking for a yes or no to...
Greetings,
I'm not sure if this site, or this area of the site, is the most likely place for me to get an answer to the question I am about to ask - so if anyone reads the question and doesn't know the answer, but knows of a more likely place for me to get an answer, please let me know, it...
Hi, thanks for the response AlephZero.
So I just tried the secnumdepth thing you suggested, but it didn't work. The subsubsections are already numbered in the document, with or without secnumdepth. However, what I need is for the theorem counter to reset each time a new subsubsection is...
Greetings,
I am using LyX. When I type
\@addtoreset{thm}{section},
in the preamble, the theorem numbering is reset at each section, as desired. Similarly, when I type
\@addtoreset{thm}{subsection},
in the preamble, the theorem numbering is reset at each subsection, as desired...
Thanks for all of the responses everyone. A couple of weeks ago I bought Fowles, and have started studying it in my spare time. It's a pretty good textbook so far, I am quite happy with it.
That being said, your very high review of Jenkins and White, SredniVashtar, has made me excited to check...
Greetings,
I have never worked with any good data visualization tools, but it is a skill I would very much like to learn.
Does anyone know of some good free data visualization software?
If so, could you please describe it a little bit as well? Eg., is it code-based or drag-and-drop...
Greetings,
I have never formally studied optics, and am looking to do so. I have looked around a little bit, and I have the impression that there are not really any "go-to" textbooks on the subject that everyone uses.
Does anyone have any recommendations for a good (classical) optics...
Greetings,
Does anyone know of some good sources that explain classical perturbation theory, preferably using the Lagrangian formalism?
The sources that I have seen more-or-less say, "write L=L_{0}+λδL, where L_{0} is an unperturbed, soluble Lagrangian, δL is the perturbation, and λ is a small...
Thanks for replying, R136a1.
That's a cool argument, and definitely does the trick. So basically, when using the residue theorem, I will still usually need to do some outside-the-box thinking to focus in on the part of the integrals I want to evaluate, like your derivation above. That's a...
Greetings,
I am a bit confused on an aspect of contour integrals. Wikipedia gives the following example of an integral where the residue theorem can be used (it also finds the integral in a couple of other ways, but I am mainly interested in doing it using residues):
We want to calculate...
Hi, thank you very much for the replies.
As far as 2nd versus 3rd, then, it sounds like 3rd edition is a little better for content, and 2nd is better for format. I'll probably go for the 3rd edition then. If the units annoy me too much while I'm using it, or I feel like I'm developing some bad...
I am about to start using Jackson E&M, and I have consistently heard that it is a notoriously difficult textbook to use. Does anyone know of some good resources, textbooks or otherwise, to supplement it (other than Griffiths, which I already have)?
More specifically, I have been told that the...
Greetings,
For a homomorphism \varphi, I'm trying to show that elements of a fiber, say the fiber above a, X_a, are writable as a given element of X_a times an element of the kernel K. So, if a\in X_a and b\in X_a, then \exists k\in K such that b=ak.
I want to do this without using the...
Hi Jorriss, thanks for replying.
You are correct. However, I saw that article when I decided I wanted to learn about functional derivatives, so I sort of know those examples and need some new and different ones to practice.
Thanks again!
-HJ Farnsworth
Greetings,
I want to become more fluent using functional derivatives. Does anyone have a link to sets of problems involving functional derivatives or anything like that (e.g., a worksheet from a class where they were used or something)?
The lengthier the better, and ideally the solutions...
I figured it out.
Formula (1) is wrong, it should be S=∫2πf(x)dl, not dx, so there's actually no issue.
Also, the title of this thread should have had "surface of revolution", not "shell method" I always get all of those things mixed up.
Thanks.
-HJ Farnsworth
Greetings,
On page 7 of Landau and Lifschitz Vol. 1 3rd. Ed, it says
L(v'^2)=L(v^2+2\bf{v}\cdot\bf{ε}+\bf{ε}^2).
They then Taylor expand in powers of ε, getting (ignoring second order terms and higher)
L(v'^2)=L(v^2)+\frac{\partial L}{\partial v^2}2\bf{v}\cdot\bf{ε}.
The...
I don't know the answer, but I will at least try to brainstorm a little bit.
I would guess that the differential is defined differently in the stochastic calculus than in regular calculus. In regular calculus, a differential df is a synonym for an infinitesimal. Is the same true in the...
Greetings,
If we have a function y=f(x), we can calculate the surface area traced by that function when rotating about the x-axis as
1: S=∫dx\,2πf(x),
which makes perfect sense to me. I am told that, if we have x=x(t) and y=y(t), the equivalent expression is
2...
Greetings,
I learned E&M from Griffiths, and for the most part I understood everything - I am very comfortable using Maxwell's equations, at least in the E and B form.
However, the same is not true of D and H, which I really don't understand at all. The reason that I am having trouble...
Greetings,
Does anyone know of a way to define new math symbols in LyX, or define a command for putting symbols together in new ways?
For instance, let's say I wanted to define a command \fivefour that I could enter while in math mode that would stack the number 5 directly on top of the...
Greetings,
I think this will be a very quick thread. I am new to using Feynman diagrams, and have run into something that I find puzzling. The lowest-order Coulomb interaction Feynman diagram is (image from Wikipedia Moller Scattering article)...
Thanks for replying, WannabeNewton, as well as for your post that I was referred to earlier in this thread!
That may be just the thing I'm looking for, I'll look it up and learn about it.
This is a minor point, and could just come down to a notational difference, but wouldn't...
Hi tiny-tim, thanks for the response!
That is definitely a simple way to look at why they are different entities - a nice way to think about it using 0-2-tensors (or 2-0-tensors), since its a lot easier to see how those tensor components become different if the tensor is not symmetrical, and so...
Greetings,
There is an aspect of tensor-index notation that I want to know more about. For a simple example, let M be a 1-1-tensor (ie., a matrix), whose elements can be indexed by Latin letters.
What is the difference between the component M^a_{\hspace{2mm}b} and the component...
Thanks for the quick reply, UltrafastPED.
I think I understand - basically, it can be thought of in terms of free and bound variables. Even though ρ is a function of x, y, z, and t, the definite integral of ρ over a given volume is not dependent on any of the position coordinates - at that...
Greetings,
In Griffiths E&M, 3rd. Ed., on page 214, the following is part of the derivation of the continuity equation (the same derivation is shown on the Wikipedia article for the current density, under the continuity equation section: http://en.wikipedia.org/wiki/Current_density)...