Brian Vandenberg
Reputation
403
Next privilege 500 Rep.
Access review queues
 Aug 6 comment Can you complete the expression $2 \underline{ }\, \underline{ }\, \underline{ } \,\underline{ } 5 = 2015$? I suppose you could be absurd about it and define the meaning of the symbols since those definitions are only implied, but that's probably not what they're looking for. Aug 6 comment Can you complete the expression $2 \underline{ }\, \underline{ }\, \underline{ } \,\underline{ } 5 = 2015$? It implies decimal, but it's not overtly stated. You could choose a base higher than 10 with the obvious consequence that you'd be restricted to using only the 1st 10 digits of that base. Aug 6 comment Can you complete the expression $2 \underline{ }\, \underline{ }\, \underline{ } \,\underline{ } 5 = 2015$? @achillehui Since it's labeled with number theory & recreational math I'm inclined to think it's a strictly math question. The wiggle room I was asking about is things like: is the number system base 10 (eg, your base 8 answer below)? Are we limited to elementary algebra rules for the given symbols (eg, different types of algebras)? Is selecting nothing a valid selection from the set of symbols? ... etc Aug 5 comment Can you complete the expression $2 \underline{ }\, \underline{ }\, \underline{ } \,\underline{ } 5 = 2015$? Should the question be taken at face value, or is it possible it's playing a word game? For example the words with a selection of, with a loose enough interpretation, could include the option to select nothing, eg: 20__15 Jul 15 comment What's the name of this theorem? @Ant This is true. Jul 15 comment What's the name of this theorem? The question is "what's the name of the theorem". As correct as this answer is, it doesn't give the name. Oct 17 comment Self Study in Dynamical Systems Unfortunately, the link you've provided appears to be broken. Aug 11 comment Recommendation for a book and other material on dynamical systems I just ran across this course, for others who are interested: youtube.com/watch?v=mkfU9zVNGkQ&feature=relmfu Jun 28 comment Online tools for doing symbolic mathematics +1, this looks like an interesting tool. Jun 27 comment Online tools for doing symbolic mathematics It's as though everything lately has been telling me to learn Python. +1 for answering with precisely what I asked for: a web-based app that provides symbolic manipulation that isn't limited to one-liners. Jun 22 comment Using differentials @Noteventhetutorknows - The fractional notation helps give the notion of rates, but it also gives the impression you can just do normal algebraic manipulations on them -- which is definitely not true. It can be done, as Americo Tavares points out, but it must be done very carefully and rigorously. Jun 22 comment Using differentials +1 because it has the potential to generate answers to help explain proper use of differentials. Jun 22 comment Using differentials @Theo - That's fine. What affect does \$\$ have? Jun 22 comment Using differentials @Noteventhetutorknows - re: dubiousness, I was specifically referring to the homogeneous equation I wrote, but what you wrote is fraught with what I would consider to be inappropriate manipulations. The chain rule gives: $\frac{dy}{dx} = \frac{dy}{dt}\frac{dt}{dx}$. Nothing about the chain rule says it's safe or valid to swap denominators as though $\frac{dy}{dt}$ is a simple fraction. Jun 22 comment Using differentials Agreed. When I took my ODE class I just went with it, but as I went back and worked through some of that material years later it occurred to me that the homogeneous equation above is actually a partial differential equation in disguise, of sorts -- hence my addendum with $\frac{dy}{dt}$ (etc). Adding $t$ explicitly seemed to make it easier to 'guess' the solution for those problems. May 16 comment Convolution & DFTs: How much zero padding is necessary to avoid circular convolution? @joriki - Very good point, thank you. If you want to provide the correct answer and that note as part of your answer, I'll accept it. May 16 comment Convolution & DFTs: How much zero padding is necessary to avoid circular convolution? Scratch that. The answer is $2N - 1$ along each dimension. See the following: cnx.org/content/m10963/latest Apr 21 comment Is this a positive semi- definite matrix The OP didn't ask about 2x2 matrices. Apr 21 comment The 9 Billion Names of God Although this is an interesting experience, the format of your question is very open-ended. There's no way anyone can give a 'right' answer, and often no answer is selected to be accepted for open-ended questions. Apr 20 comment Maximization of Two Areas — Calculus 1 I'm a little unsure how to pull this off without another constraint. It seems like a circle is the most efficient shape in terms of containing the most area, so any expression you come up with would force the square's perimeter to zero and give you a circle with circumference = 10 meters.