Activity for Derek Elkins
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| 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) |
— | over 3 years ago |
| Edit | Post #282713 | Initial revision | — | over 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) |
— | over 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) |
— | over 3 years ago |
| Edit | Post #282375 | Initial revision | — | over 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) |
— | over 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) |
— | over 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) |
— | over 3 years ago |
| Edit | Post #282029 | Initial revision | — | over 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) |
— | over 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) |
— | over 3 years ago |
| Edit | Post #281866 | Initial revision | — | over 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) |
— | over 3 years ago |
| Edit | Post #281586 | Initial revision | — | over 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) |
— | over 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) |
— | over 3 years ago |
| Edit | Post #280866 |
Post edited: Minor tweaks and clarifications. |
— | over 3 years ago |
| Edit | Post #280866 | Initial revision | — | almost 4 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) |
— | almost 4 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) |
— | almost 4 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) |
— | almost 4 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. |
— | almost 4 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 | almost 4 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) |
— | almost 4 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) |
— | almost 4 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) |
— | almost 4 years ago |
| Edit | Post #280496 | Initial revision | — | almost 4 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) |
— | almost 4 years ago |
| Comment | Post #280068 |
Perhaps ironically, for CPUs, computing $1/\sqrt x$ is often faster than computing $\sqrt x$. One way to see why this might be so is to compare the Newton-Raphson iterations. For $y=\sqrt x$, we get: $y_{n+1}=y_n/2+x/(2y_n)$. For $y=1/\sqrt x$, we get: $y_{n+1}=y_n(3-xy_n^2)/2$. The key difference he... (more) |
— | almost 4 years ago |
| Edit | Post #280133 | Initial revision | — | almost 4 years ago |
| Question | — |
Marketing Math Codidact I don't think it's controversial to say that this site is currently suffering from a lack of new questions. I believe the main problem is lack of awareness. People aren't coming to this site because they have no idea it exists. A distant second concern, in my opinion, is the value proposition rela... (more) |
— | almost 4 years ago |
| Comment | Post #280120 |
I agree that this is a fairly clumsily presented definition. A precise and reasonably easy to understand definition is to define it inductively with the base case, $\prod_{\nu=1}^0 x_\nu = e$, and the inductive case: $\prod_{\nu=1}^{n+1} x_\nu = \left(\prod_{\nu=1}^n x_\nu\right)\cdot x_{n+1}$. (more) |
— | almost 4 years ago |
| Comment | Post #280118 |
Assuming $x_{(-)} : J \to G$, i.e. $x$ is a $J$-indexed collection of elements of $G$, then it can't be the case that $J \neq \varnothing$ while $\\{x_\nu \in G \mid \nu \in J\\} = \varnothing$. You could define a notion of product that took a finite multiset and compare that to a set-indexed notion ... (more) |
— | almost 4 years ago |
| Edit | Post #280069 | Initial revision | — | almost 4 years ago |
| Answer | — |
A: Why always rationalize a denominator? This answer combines the thoughts in both of the other (current) answers (tommi's and r's) but presents it in a more formal context. A significant portion of high school (and earlier... and a decent amount of later...) math is highly algorithmic, and, in particular, corresponds to the important id... (more) |
— | almost 4 years ago |
| Edit | Post #279055 | Initial revision | — | about 4 years ago |
| Answer | — |
A: Why does “unless” mean “if not”? The quotes from the books are exactly the kind of ridiculously naive and over-simplified linguistics in introductions to logic that I criticize in this blog article. Particularly for everyday natural language expressions, you will find no shortage of ways where this "translation" provides only a clum... (more) |
— | about 4 years ago |
| Edit | Post #278447 |
Post edited: |
— | about 4 years ago |
| Edit | Post #278447 |
Post edited: |
— | about 4 years ago |
| Edit | Post #278447 | Initial revision | — | about 4 years ago |
| Answer | — |
A: Existence of a set of all sets Sure. You can simply add $\exists V.\forall x.x \in V$ as an axiom to ZF(C), and you will have such an axiomatic system. Such an addition to ZF(C) would make it inconsistent, but it would still prove the existence of a "set of all sets" (along with everything else). As Peter Taylor points out in a... (more) |
— | about 4 years ago |
| Comment | Post #278382 |
Your first sentence is also potentially misleading. Math Codidact is also for people who aren't studying math and aren't professionals in related fields. We don't care (or have anyway of knowing) who the asker is or what their motivations are as long as the question is good and on-topic. (more) |
— | about 4 years ago |
| Comment | Post #278382 |
This is useless. People don't need detailed guidance about topics that are obviously on-topic anymore than they need guidance about topics that are obviously off-topic. This fails to accomplish even that as it's incomplete, as you say, and, more importantly, topicality isn't just a matter of subject ... (more) |
— | about 4 years ago |
| Edit | Post #278269 | Post edited | — | about 4 years ago |
| Comment | Post #278270 |
A problem that is almost certainly related is that sometimes the Markdown processor will convert substrings delimited by underscores to italics when those underscores are part of the MathJax, thereby breaking the MathJax. Peter Taylor's issue and this one are almost certainly due to the Markdown proc... (more) |
— | about 4 years ago |
| Edit | Post #278280 | Initial revision | — | about 4 years ago |
| Question | — |
Can we constructively find a third element of a set $X$ satisfying $X \cong X \times X$ given two distinct elements? Consider a set $X$ such that $X \cong X\times X$. It's quite easy to prove in a classical set theory, e.g. ZF, that $X$ must be the empty set or a singleton set or an infinite set. In other words, if we additionally assume that there exists $a, b \in X$ and $a \neq b$, then we know that $X$ is an inf... (more) |
— | about 4 years ago |
| Comment | Post #278270 |
I've suggested an edit that "fixes" the post (so if the edit is accepted people should look in the history to see the original form). That said, the intuition of the change I made is that the backslashes needed to be escaped. However, they probably shouldn't need to be escaped and so some MathJax or ... (more) |
— | about 4 years ago |
| Suggested Edit | Post #278269 |
Suggested edit: There seems to be some issue escaping backslashes(?). This edit fixes the issue now but may cause problems (extra vertical space) if the underlying issue is resolved. (more) |
helpful | about 4 years ago |
| Edit | Post #278145 | Initial revision | — | about 4 years ago |