Activity for Derek Elkinsâ€
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Edit | Post #285384 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Acceptable, usual to write $\ge 2$ pipes simultaneously? As mentioned in the answers you referenced in earlier versions of your question, $(-\mid-)$ is not standalone notation in usual probability theory notation.^[I have seen it used, e.g. in Jaynes' "Probability Theory: The Logic of Science", as standalone notation, but not in a way such that $P(A\mid B)... (more) |
— | over 2 years ago |
| Comment | Post #284788 |
@#53922 Calling a question a "soft question" doesn't suddenly make it being overly broad, primarily opinion based, and/or lacking context or research okay. (more) |
— | over 2 years ago |
| Comment | Post #284718 |
Finally, there is some context which isn't *technically* required but omitting it sets up confusion down the line. First, most discussions of tensors by physicists are actually discussions of tensor *fields*. A tensor field is a continuous (and usually smooth) assignment of tensors to points on a man... (more) |
— | over 2 years ago |
| Comment | Post #284718 |
Slightly less objectively, your wording and notation compounded by your inconsistent use and unfortunate choices of notation confuse the issue significantly. A key part of this discussion is that all this co-/contra-variant stuff has to do with how we represent vectors (and tensors generally) *with r... (more) |
— | over 2 years ago |
| Comment | Post #284718 |
There are several issues here. First, you call everything a "vector". What the notation refers to are *tensors* and vectors are just the rank-1 case. Anything with other than 1 index is NOT a vector. Your description of the Einstein summation convention is completely wrong. It is not a convention to ... (more) |
— | over 2 years ago |
| Edit | Post #284284 | Initial revision | — | over 2 years ago |
| Answer | — |
A: $\int dx dy dz d p_x dp_y dp_z$ Does it have any physical meaning? It's hard to answer your question specifically without the context, and obviously the physical significance of some expression depends on what the variables and operations in that expression stand for. Before considering this particular integral, I want to talk about integration generally and its not... (more) |
— | over 2 years ago |
| Edit | Post #284283 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Is Pythagorean theorem really valid in higher dimensional space? Consider a vector, $\mathbf v=(a,b,c)$, in $3$-space. We can project this onto the $xy$-plane, say, producing the vector $(a, b, 0)$ which we can identify with the $2$-vector, $(a, b)$. This two vector corresponds to the hypotenuse of a right triangle whose side lengths are $a$ and $b$. Therefore the... (more) |
— | over 2 years ago |
| Edit | Post #283885 |
Post edited: Talk about the actual total derivative |
— | over 2 years ago |
| Comment | Post #283900 |
I haven't downvoted (or upvoted) this meta answer, but I haven't yet completely decided how I feel. On the one hand, I think *in practice* there are indeed a lot of bad questions of the form discussed. On the other hand, I *am* making the case that there are often better answers than "experience, per... (more) |
— | over 2 years ago |
| Comment | Post #283900 |
It is also the case that the need for insight is often oversold. Many results about sums of binomial coefficients and closely related combinatorial identities have clever proofs involving insights and analogies. However, virtually all "textbook" identities of this form fall within the purview of [a d... (more) |
— | over 2 years ago |
| Comment | Post #283900 |
To give an example of the kind of thing I'm talking about, consider the following more positive rendition of the infinitude of primes: For any finite set of primes, there exists a prime not in that set. I can produce the following proof skeleton completely mechanically from the form of the propositio... (more) |
— | over 2 years ago |
| Comment | Post #283900 |
There is actually quite a bit that can be mechanized in proof finding. Up to and including completely deriving a proof mechanically. And I don't just mean that automatic theorem provers exist. A decent amount of a proof is highly constrained. In my experience, it is not uncommon for people to struggl... (more) |
— | over 2 years ago |
| Edit | Post #283947 | Initial revision | — | over 2 years ago |
| Answer | — |
A: What're the orders for equation expressing? This question contains a lot of confusion. First, an equation is something like $f(x) = g(x)$ (i.e. there's an equality sign). Solving an equation means finding (all) values for the free variables such that both sides become equal. In the above example, this would mean finding values for $x$ such tha... (more) |
— | over 2 years ago |
| Edit | Post #283885 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Getting backward of partial differentiation's chain rule Traditional mathematical notation for calculus (both integral and differential) is rather incoherent. I don't think there exists a write-up providing systematic rules that would allow you to correctly and unambiguously parse this kind of notation, i.e. the kind of notation used in a typical undergrad... (more) |
— | over 2 years ago |
| Comment | Post #282900 |
While it's fine to self-answer a question, why are you answering it as if you weren't the person to ask it, e.g. saying "your answer isn't correct" and "you got it wrong"? There is no need to pretend like you are a third party who just happened upon this question. In fact, it's a bit confusing and bi... (more) |
— | almost 3 years ago |
| Comment | Post #282780 |
I am talking about definite integrals because integration by parts is usually discussed in that context, and the bounds are often important (and sometimes annoying but critical) in applications. Either way, the definite integral formulation is only *more* informative than an indefinite integral. The ... (more) |
— | almost 3 years ago |
| Edit | Post #282780 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: methodology of integration by parts ($e^{ax}\cos (bx+c)\mathrm dx$) I haven't seen integration by parts written that way before, and the derivation you describe seems overly complicated, albeit not for the $I$ stuff. In particular, I don't understand the purpose of the trigonometric substitutions as the integral should be solvable already without them. Maybe there wa... (more) |
— | almost 3 years ago |
| Edit | Post #282713 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: How to derive some trigonometric formulas? Memorizing or using actual trigonometry to re-derive trigonometric formulas is a waste of time and mental resources. (This isn't to say it isn't useful to go through the trigonometric approach once and to understand how they relate.) Instead, there is just one relatively simple formula that one needs... (more) |
— | almost 3 years ago |
| Comment | Post #282657 |
I would not want to be a moderator at this point but likely would be more open to it in the future. My concern is that even rough outlines of the policies we'd want here are not clear. My hope is that next time moderators are needed there's more guidance from the community on what they want out of mo... (more) |
— | almost 3 years ago |
| Edit | Post #282375 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: Are challenge-like questions like these considered on-scope in Mathematics CD? If your question was closed for being off-topic, then you have your answer. The way your question is worded, it sounds like the "question" is more of a prompt and the "answers" to that "question" are really just demonstrations fitting the prompt. If that's accurate, then that indeed sounds a lot l... (more) |
— | almost 3 years ago |
| Comment | Post #282047 |
The bold statement is a sub-clause of a conditional statement that *explicitly assumes* that the players are rational. That real people aren't rational doesn't change what the theory predicts. It just means the theory isn't a particularly accurate model for humans. Either you are wondering, under the... (more) |
— | almost 3 years ago |
| Comment | Post #282046 |
Well, what probability do you assign to getting a red ball from urn B? If that differs from the probability of getting a white ball, why? If it doesn't, then the probabilities are the same in both cases. (more) |
— | almost 3 years ago |
| Edit | Post #282029 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: What was Justice Scalia's mathematical mistake in Penry v. Lynaugh (1989)? Consider the universal quantifier. I'll write it as: $\mathsf{forall}\ x.P(x)$ to be read as "for all $x$ in the domain $P(x)$ holds". We then have the logical identity $$(\mathsf{forall}\ x.P(x)) \land (\mathsf{forall}\ x.Q(x)) \to (\mathsf{forall}\ x. P(x) \land Q(x))$$ where $\land$ is logical con... (more) |
— | almost 3 years ago |
| Comment | Post #281586 |
@Istiak Right now, the only real written thing that gives an *idea* for the scope is the discussion at the [Site Proposal | https://meta.codidact.com/posts/277002] but even this should be taken as a starting place. The policy for homework questions hasn't been set but is likely to be vaguely similar ... (more) |
— | almost 3 years ago |
| Edit | Post #281866 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: How to show if a set is simply connected? Probably one of the simpler ways of establishing this is reducing it to a case where you already know the answer. I will assume that you have proven at some point that the circle, $\mathbb S^1$, is not simply connected. Simple connectedness is a topological property so it is preserved by homeomorphis... (more) |
— | almost 3 years ago |
| Edit | Post #281586 | Initial revision | — | about 3 years ago |
| Answer | — |
A: Can this site contains Physics's Math question? To start, what belongs on the Physics Codidact is up to the people active on the Physics Codidact. The question seems to have been well received there, and I suspect that it would also have been well-received here. Math questions of any sort are welcome here. However, when asking a question motiva... (more) |
— | about 3 years ago |
| Comment | Post #280910 |
Are you right about what? That your expression "approximates" the integral? What criteria are you using to decide that something is an "approximation"? On what domain are you considering? (more) |
— | about 3 years ago |
| Edit | Post #280866 |
Post edited: Minor tweaks and clarifications. |
— | about 3 years ago |
| Edit | Post #280866 | Initial revision | — | about 3 years ago |
| Answer | — |
A: Does every divergence-free vector field arise as the curl of some vector field? tl;dr We can formulate your question more nicely with geometric algebra. As r mentioned in a comment, there is a counter-example to your question on a simply-connected but not 2-connected domain. The counter-examples provided are Green's functions for the vector derivative. Formulating the problem in... (more) |
— | about 3 years ago |
| Comment | Post #280850 |
You've typoed the bolded sentence. It is $X \times (B/A)$, not $X \times (A/B)$. If you misread it this way, that might explain your confusion. Also, as with your other question, here "rounding up" seems to be being used in the sense of "rounding up cattle" as opposed to rounding up a number to an in... (more) |
— | about 3 years ago |
| Comment | Post #280849 |
"Group" is not being used in any technical sense here. Mathematicians can use words in their colloquial sense too. Also, there often are technical terms that are used for different things in different contexts, so just because a word is used one way in one place doesn't mean it is used that way every... (more) |
— | about 3 years ago |
| Edit | Post #280704 |
Post edited: This definitely isn't a number theory question. It's primarily about notation and generalized definitions. Abstract algebra seems the most appropriate and relevant field though the question arguably goes beyond it. |
— | about 3 years ago |
| Suggested Edit | Post #280704 |
Suggested edit: This definitely isn't a number theory question. It's primarily about notation and generalized definitions. Abstract algebra seems the most appropriate and relevant field though the question arguably goes beyond it. (more) |
helpful | about 3 years ago |
| Comment | Post #280653 |
I did not say that you needed to "render pictures as text/MathJax", I said to put as much of your question *as possible* in the form of text/MathJax. There is absolutely no reason for the second image. The relevant content of your second image is simply the equations 8 and 9 which you *can* easily re... (more) |
— | about 3 years ago |
| Comment | Post #280653 |
More specifically to your question, I have no idea what you are trying to communicate with the first image. As far as I can tell, you've simply added the text "$1/t, t \neq 0$ to it. Also, doesn't simply plotting $x = 1/t$ as a function of $t$ not already make it graphically and intuitively obvious t... (more) |
— | about 3 years ago |
| Comment | Post #280653 |
You should endeavor to put as much of your question as possible in the form of text/MathJax. This makes the question more accessible, e.g. to those using screen readers or who have custom fonts/text size such as for dyslexia or because they have difficulty reading small text. It also makes the questi... (more) |
— | about 3 years ago |
| Edit | Post #280496 | Initial revision | — | over 3 years ago |
| Answer | — |
A: Why does this definition of generalized forces work? This expression is not the clearest way of writing this, but the idea is that we are defining the components of the covector $Q(q)$ on a basis of differential 1-forms $dqj$, i.e. $Q = \sum{j=1}^k Qj dqj$. This is made more clear by Wikipedia's expression of this statement: $Qj = \sum{i=1}^n \langle \... (more) |
— | over 3 years ago |
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