1,591 reputation
615
bio website suitdummy.blogspot.com
location Cambridge, MA
age
visits member for 2 years, 4 months
seen Jul 8 at 19:04

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.

Jan
14
comment Splitting a sandwich and not feeling deceived
Thus, anyone cutting pieces has an incentive to make sure the worst off piece is at least good enough that whoever randomly draws it will decide to keep it, so that everyone gets to keep theirs too. My guess is this leads to some Nash equilibrium kind of thing where making equal cuts leads to the highest expected value.
Jan
14
comment Splitting a sandwich and not feeling deceived
I wonder if anyone has ever looked into a Dictator Game-based stochastic variation. In experiments with things like Dictator Game, people tend to reject unfair offers, even if it makes them uniformly worse off. That is, they are usually willing to pay some "fairness premium" and simply deny any form of splitting the resources unless they are equal to or better than all of the other players. If we assume humans will use this heuristic, then we could take any N pieces of a divided sandwich and randomly assign them to people in a Dictator Game, where the "worst-off" person is the dictator.
Jan
9
comment Pedagogy: How to cure students of the “law of universal linearity”?
Another point is that Greek symbols still "feel" "mathy" and are seen as "expected math symbols" even by young students. So using Greek symbols might actually be counter-productive: to the extent that a student has anxiety about what a symbol is allowed to mean and whether it has some special meaning, using Greek letters over more "regular" things like x and y might only make the anxiety worse. But using a symbol like a tree, fire hydrant, tulip, pineapple, or anything that's totally not at all possibly confusable with "official mathy type stuff" could have a better chance of working.
Nov
21
comment How to study math to really understand it and have a healthy lifestyle with free time?
Can you elaborate?
Nov
5
comment Is it worth pursuing a statistics minor? I want to go to pure math grad school.
Also, all else equal, extra time to absolutely destroy the Math GRE subject test is worth much more than the minor. So if classes for the minor would prevent you from utterly crushing the Math GRE, don't downweight that -- it could be and important consideration. (This is conditional on the desire to go to math grad school. The stats minor is probably more valuable unconditionally). Check this link for some other considerations.
Nov
5
comment Is it worth pursuing a statistics minor? I want to go to pure math grad school.
Another question: do you attend an undergraduate school where you feel the school's reputation for math majors is good enough to propel you into the pure math grad schools of your choice? If your undergrad school is extremely strong, then it's probably fine to spend extra classes on more well-roundedness (such as in stats). If the best PhD programs will cast any amount of skepticism on your undergrad math program's rigor, you'll be better served just cramming in as many advanced math classes as you can to prove you're good enough at it to be admitted.
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.
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.
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.
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.