Brian Vandenberg
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 Apr 19 comment how do you solve $y''+2y'-3y=0$? @night - That notation is not at all uncommon. I've encountered it in 3 texts for undergrad study, and it's one of the most useful techniques discussed in the differential equations "Problem Solvers" book -- with plenty of examples given, albeit more awkwardly typed. Apr 12 comment Genetic Algorithms The next step will be to choose something you want to encode for the algorithm to work with. The two most obvious (only?) things you can model (or use to model) are actions to take within the game, and current/previous game state/actions. One way to handle it could be to use your genetic sequence to weight how important information is about current/previous game states and previous moves, then use some type of weighted sum to determine future moves. The paper you linked to probably describes the encoding they used. Apr 8 comment Rules of Division @Bill - Well put. Apr 8 comment Rules of Division @Bill - No. You made a good argument for a more general treatment of the topic. I'm arguing that there should be a "simplified" treatment as well. My point about the math jargon was to make the point that it doesn't need to be only readable by someone who has a desire to invest themselves in math enough to understand the more general/rigorous treatment. Apr 8 comment Rules of Division @Bill - That's an excellent point, but in this case the OP needed it for the GRE. One of the more frustrating things for me 'growing up' in math was trying to digest material in Mathworld and Wikipedia math entries -- mostly because they were loaded with math jargon I was unfamiliar with. If someone's studying for the GRE, they shouldn't have to know a lot of math jargon just to learn a couple of divisibility tests. Apr 8 comment Rules of Division @Bill - An answer is an answer. If original content was the requirement, most answers would be illegitimate because in most cases people would be quoting from, or regurgitating material from another source -- often without credit given. Apr 8 comment Rules of Division +1, I was tempted to down-vote because the motivation behind stackexchange-like sites -- at least, based on the FAQs I've read -- is to become something like Wikipedia, but designed in such a way to motivate people to more proactively contribute content. Wikipedia doesn't just contain external links, they actually provide content. If the link was to some message forum or some other site that didn't have a high likelihood of long-term survival, I probably would've down-voted. Apr 6 comment $\ln(x^2)$ vs $2\ln x$ @Americo - That's only true for real $x$. $(a + b i)^2 = a^2 + a b i - b^2$, whereas $|a + b i|^2 = \sqrt{(a + b i)(a - b i)}^2 = \sqrt{a^2 + b^2}^2 = a^2 + b^2$. The two are not the same. Apr 5 comment Relation between complex Jacobian and differential of a complex number I don't see the question. J is a gradient operator, and it appears the author is stating (not claiming or ignoring a proof for) that the jacobian matrix is $J\{e^{i \phi(u,v)}\} = f'(u + iv)$ -- which is a matrix of 1st derivatives w/respect to each variable. The ambiguity I see is in the definition of $f'(.)$; is it the derivative with respect to the single complex variable $z = u + i v$? Apr 1 comment Summing the power series $\sum\limits_{n=0}^\infty (-1)^n \frac{x^{2n+1}}{2n+1}\prod\limits_{k=1}^n\frac{2k-1}{2k}$ @Mitch - ${-n \choose k} = (-1)^{k}{{k - (n + 1)} \choose k}$, for positive $n$. The $(-1)^{k}$ coefficient keeps the value of the quantity positive (provided $n > k$?). Ignoring sign, this is the number of ways to arrange $|k - (n + 1)|$ items taken $k$ at a time. The $\frac{1}{2}$ I don't have a great intuitive description for, sorry. Apr 1 comment Summing the power series $\sum\limits_{n=0}^\infty (-1)^n \frac{x^{2n+1}}{2n+1}\prod\limits_{k=1}^n\frac{2k-1}{2k}$ @Mitch - The negative value is talked about in the wikipedia link I'm about to link to. The non-integer values could be covered by the interpretation $n! = \Gamma(n+1)$ -- though I'll confess, I don't know if there are any technicalities I'm missing with that blanket statement about non-integer $n$. Wikipedia link to binomial coefficients: en.wikipedia.org/wiki/… Apr 1 comment Summing the power series $\sum\limits_{n=0}^\infty (-1)^n \frac{x^{2n+1}}{2n+1}\prod\limits_{k=1}^n\frac{2k-1}{2k}$ @Mitch - I suppose that's one interpretation. I see the stackexchange-style sites as a far more global resource. While the answer may only serve the OP by doing his homework for him, this isn't an IRC chat-room or newsgroup post where a small audience will get something out of the response. Apr 1 comment Summing the power series $\sum\limits_{n=0}^\infty (-1)^n \frac{x^{2n+1}}{2n+1}\prod\limits_{k=1}^n\frac{2k-1}{2k}$ @Mitch - If you don't like the question, downvote it. If you think the answer given is badly written or contains errors, downvote it. But this is just not classy. Mar 28 comment General Introduction to Functional and other Mathematic Notations @Garet - Older math textbooks (particularly if they're aimed at juniors/seniors/grad students) are more in-line with what you'd see in an RFC. They're often very short books (eg, I have a book on complex analysis that's about 70 pages long, but it covers most of the material you'd see in a typical complex analysis class). I'm not overly fond of the style. As with programming books, I like to see a lot of examples. But, that might not be a bad place to look if that's what you want. Mar 26 comment General Introduction to Functional and other Mathematic Notations @Myself: That was a response to you, not him. Mar 26 comment General Introduction to Functional and other Mathematic Notations Yikes. No more late-night posting for me. I deleted the first two because they had nothing to do with responding to your comment. Mar 26 comment General Introduction to Functional and other Mathematic Notations or string the ideas together into a coherent and correct proof. Mar 26 comment General Introduction to Functional and other Mathematic Notations My point is it isn't just some set of axioms and rules. It IS a language with a logical flow or rhythm. If sentence words threw I order any did, I together a in then the sentence wouldn't be readable to you. The same thing is true in math. Just because you know the words and symbols doesn't mean you know how to string them together in a manner that is readable. Mar 22 comment The phrase “coordinate-wise” and its meaning So, another potential interpretation of that, it sounds like, is you can apply a function $f: \Re^1 \mapsto \Re^1$ coordinate-wise to a matrix or array by applying it element-wise. Mar 22 comment The phrase “coordinate-wise” and its meaning Ah. I see your point. So, if for example I have a scalar function $\sigma$ I want to apply to the elements of a vector/matrix (eg, $\mathbf{Y} = \mathbf{\sigma}(\mathbf{X})$ ), I could say $\mathbf{\sigma}$ is evaluated "coordinate-wise" on elements of $\mathbf{x}$. You should write up your response as an answer so I can accept it.