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Oct
9
comment Best applications-oriented introductory calculus textbooks?
"justifying its inclusion in a liberal education for purposes other than contemptible ones like using it as a weeder for medical school or business school applicants." This kind of normative statement seems unnecessary in the question. I, for one, am glad these things help weed out such applicants, even though there are many better reasons to study the calculus.
Oct
9
comment What is the estimator of $P(X=0)$ for $X\sim\operatorname{Poisson}$
That's why I said, "as an aside." And by 'dimensionality' in my comment, I did not mean cardinality of the sample set. I meant the dimension of the space to which each observation belongs.
Oct
9
comment What is the estimator of $P(X=0)$ for $X\sim\operatorname{Poisson}$
As an aside, you may also consider the properties of the James-Stein Estimator if you ever encounter an example of this with dimensionality of three or more.
Oct
7
answered Where to take Real Analysis and Linear Algebra?
Aug
7
accepted Set of nodes to remove to leave zero edges with maximal summed node values.
Aug
7
comment Set of nodes to remove to leave zero edges with maximal summed node values.
Thank you! I suspected it had to be hard. The ad hoc algorithm was exponential time, and usually even for bad first attempts it's hard to make something exponentially slow unless it's just a hard problem.
Aug
7
asked Set of nodes to remove to leave zero edges with maximal summed node values.
Jun
23
awarded  Good Answer
Mar
14
awarded  Yearling
Mar
6
awarded  Popular Question
Mar
1
comment How can Radon-Nikodym and Borel-Cantelli be used to calculate Probability distribution?
@Did I apologize for trying to be helpful. Since you would rather win the argument than understand the paragraph, I will not bother you about it further.
Mar
1
comment How can Radon-Nikodym and Borel-Cantelli be used to calculate Probability distribution?
@Did The random variable induces a probability measure via is cumulative distribution function. This is standard in any probability theory textbook. If that measure is absolutely continuous w.r.t. the Lebesgue measure, then the random variable admits a probability density function (unfortunately often just called a 'distribution' function).
Feb
28
comment How can Radon-Nikodym and Borel-Cantelli be used to calculate Probability distribution?
@Did For instance, have you considered the Wikipedia article on the Radon-Nikodym Theorem? There it says: "... Specifically, the probability density function of a random variable is the Radon–Nikodym derivative of the induced measure with respect to some base measure (usually the Lebesgue measure for continuous random variables)."
Feb
28
comment How can Radon-Nikodym and Borel-Cantelli be used to calculate Probability distribution?
@Did I'm sorry that you don't understand the paragraph. It is a very nice way of explaining absolute continuity in the context of probability distributions here. Perhaps if you explain why you don't understand it, we can work together to provide a better explanation for you.
Jan
25
comment How to study math to really understand it and have a healthy lifestyle with free time?
Some of it is. But the linked articles on the lack of a wage premium for PhD holders in computer science and math over Master's degree holders, and also the rise of post-docs as principal investigators (hence more concentration of academic employment at the lower levels and less at associate or tenured professor positions) are from outside sources that derive from peer-reviewed research. Other observations such as having a limited time budget and needing to do something economically productive are more or less default attributes of nature. So if a person cares about these, it's less anecdotal.
Nov
11
awarded  Nice Answer
Jul
22
awarded  Nice Answer
Jul
21
comment Fastest numeric method for ODE
Also, FYI this question is probably better suited for either SciComp or Stack Overflow. It's not clear that this is due to your chosen algorithm. It could easily be due to an inefficient C implementation. If you post some code along with the question at either of those other sites, you'll almost surely get better help... and folks on those sites will also be able to suggest other mathematical algorithms to try if indeed that is the right way to solve the problem.
Jul
21
comment Fastest numeric method for ODE
Are you sure it is Euler's method that is slowing you down, and not the implementation? What language are you using? Is it a built-in or library function? What is your data set like? What sort of machine are you performing the calculation on, and with how much RAM? When you say it is 4-8 times too slow, what is this relative to and what timing benchmarks have led you to this conclusion?
Jul
21
accepted Necessary and sufficient conditions for a matrix to be a valid correlation matrix.