1,621 reputation
615
bio website suitdummy.blogspot.com
location Cambridge, MA
age
visits member for 2 years, 5 months
seen Aug 21 at 0:35

I once launched swi-prolog and asked it a question:

ely:~/home$ prolog
Welcome to SWI-Prolog (Multi-threaded, 64 bits, Version 5.10.1)
Copyright (c) 1990-2010 University of Amsterdam, VU Amsterdam
SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software,
and you are welcome to redistribute it under certain conditions.
Please visit http://www.swi-prolog.org for details.

For help, use ?- help(Topic). or ?- apropos(Word).

?- love(math) is unrequited.
true.

Oct
24
awarded  Citizen Patrol
Oct
9
comment Best applications-oriented introductory calculus textbooks?
I am more saying that there is some base rate of curiosity which is a required pre-req for understanding how a physical problem motivates a mathematical model. And most students who find they want or need to take calculus do not have that base rate of curiosity.
Oct
9
comment Best applications-oriented introductory calculus textbooks?
I understand. I guess I said it poorly. What I more mean is: a student who passes through calculus once is not equipped to understand the motivations for using calculus. Sure, they can recite platitudes about how it's used in some field, but that's about all they are in any position to appreciate. Which is probably why most "applications" sections (as you point out) just contain platitudes like "This can be used in fluid dynamics..." I'm not saying my point here is right. Just that my prior is that you can't motivate calculus from scratch with applications; it doesn't work well.
Oct
9
comment Best applications-oriented introductory calculus textbooks?
Maybe the book you're looking for is hard to find because it's just not very useful. In my own lectures, which admittedly focus more on probability, I've never seen students take to problems because of physical motivations. But after mastering a technique, like e.g. moment generating functions, then they are eager to see how it applied. I might just have outlier experiences, but both in my undergrad and grad school, and as a lecturer, it just never worked this way even for bright students. Is there evidence that it worked this way for bright students in the past?
Oct
9
comment Best applications-oriented introductory calculus textbooks?
The scope of the question is also hard to understand. For instance, in my own education I had to plod through two courses in advanced calculus, just doing lots of problems, mastering limits, beating all algebra mistakes out of my hand over and over. After that I read "Div Grad Curl and All That" and it was wonderful. If I had read such a book before doing all that gross rote algebra, it wouldn't have meant anything. Similarly, I had to slog through differential equations before coming across some useful boundary values problems books that motivated things with physics.
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.