drbaskin's comments

drbaskin | 12 years ago | on: A Crash Course in the Mathematics Of Infinite Sets

A minor nitpick: It was Andrew Wiles who proved Fermat's last theorem. Andre Weil was another incredible mathematician (responsible for, among many other things, the celebrated Weil conjectures), but did not prove Fermat's last theorem.

Andre Weil was very opinionated and lived a very interesting life. I encourage you to read about it: http://en.wikipedia.org/wiki/Andr%C3%A9_Weil

drbaskin | 12 years ago | on: The Best Part of Grand Theft Auto V is the Stock-Trading Platform

I'm sorry to be so pedantic, but your math doesn't seem quite right. Should it instead be (1/100,000 chance of burning down each year) * ($200,000 cost if it does) = $2 per near expected damages?

drbaskin | 13 years ago | on: Interns: Everything you need to know about a summer in the Bay Area in one place

This property of Piedmont is not even unique within the Bay Area! Fremont (the fourth-largest city in the Bay Area) has an enclave of its own, Newark, which is its own city yet completely surrounded by Fremont.

drbaskin | 13 years ago | on: Evernote 5 for Mac

I use it for my weekly to-do list (since it then syncs across all computers and my phone), and it is a convenient way for me to keep track of my different projects. I type up a short summary for myself after meetings and I can also easily take a photo of a blackboard and include it with the notes. It's also a decent way to quickly record addresses or library call numbers, and to draft e-mails to send to my classes. (A proper e-mail client would work for this last purpose, but the only reliable way to e-mail all students in a course is through Blackboard, which is uniformly terrible.)

drbaskin | 13 years ago | on: Variable Pricing for Restaurant Reservations

To belabor the point: Keeping one of the prices fixed, you should prefer that it be 20 percent more expensive on the weekend. Assume for example that the price on Saturday is $10 and the price on Tuesday is $8. It is then "20 percent cheaper to come during the week" but it is 25 percent more expensive to come on the weekend!

drbaskin | 14 years ago | on: Being recruited in the USA

If you're handy with simple algebra (and can remember that the derivative of x^2 is 2x) then you can remember the picture. If f(x) = x^2 - N, then you're looking for the (positive) zero of f. You take a succession of tangent lines and look at the zeros of those. So, you start with a guess (call it x_0), take the tangent line at your guess (so it has slope 2x_0 and goes through (x_0, x_0^2 -N)), then find the x-intercept of this line and make it your new guess. This is all Newton's method is. With square roots, it takes the form of averaging your previous guess and N over it.

drbaskin | 14 years ago | on: Why you can't hire

Just to nitpick a bit -- your final three numbers add to 110, not 100. Perhaps you meant 49/31/20? I point it out only because 49/31/30 seemed too good to be true.

drbaskin | 14 years ago | on: Choosing the right sleep schedule to maximize time and keep you healthy

Or simple contraposition :-P

Please correct me if I am wrong, but if the relevant part of the article is "I do not have insurance, so it is important that I maintain my health", then the contraposition would be "It is not important that I maintain my health, so it follows that I have insurance." What you are suggesting as the contraposition is "I have insurance, so it is not important that I maintain my health", which is the inverse of the statement (and equivalent to the converse "If it is important that I maintain my health, then I do not have insurance."

drbaskin | 14 years ago | on: The College For-Profits Should Fear

The 30% profit margin sometimes also signals that there are high barriers to entry. (You already mention what I think is the big one: accreditation.)

drbaskin | 14 years ago | on: Beyond space-time: Welcome to phase space

I haven't read Smolin's paper, so I'm not sure exactly what this article is getting at. Is he suggesting that there should be a different connection (i.e., not the Levi-Civita one) on the cotangent bundle of spacetime or is it something more pedestrian? Is he just doing microlocal analysis on spacetime? If the latter is the case, this article doesn't describe what is (mathematically) new about it.

On a second read of this article, it seems clear that my interpretation above is incorrect. It might still be that they are coming up with physical interpretations of microlocal analysis on curved spacetimes. (Though how you fix a quantization, I'm not sure.)

I'm not a physicist and have not read the original source, so please take anything I say with a large dose of salt.

drbaskin | 14 years ago | on: Happy Tau Day

I'm sorry I wasn't more clear, but your interpretation is what I meant. Per your rule of thumb, seeing \tau should suggest that it has to do with circles or polar coordinates, and the square root points to how to get the polar coordinates.

drbaskin | 14 years ago | on: Happy Tau Day

I'm not a big fan of introducing a new constant (though I believe \pi should have been 2\pi), but I love thinking of the integral you wrote down as \sqrt{\tau / 2} because then the answer practically tells you how to derive it!

How to derive the value of the integral: Square the integral to make it an integral in two variables, introduce polar coordinates, then change variables.

drbaskin | 15 years ago | on: The Rise of "Logical Punctuation".

You should never end a sentence with a preposition.

The mathematician Paul Halmos loved issues like these and once constructed a sentence that ends in five prepositions: "What did you want to bring that book that I didn't want to be read to out of up for?"

drbaskin | 15 years ago | on: How I Turned Down $300,000 from Microsoft to go Full-Time on GitHub

I'm having trouble determining whether you are serious, but I suspect the original poster was referring to reddit's programming community.

drbaskin | 15 years ago | on: Classes of functions (partial, total, bijective, injective, etc)

I was aware of the group structure of the Rubik's cube (it is, after all, a subgroup of the permutation group on 54 elements), but apparently I had never given it much thought beyond that. Thanks!

drbaskin | 15 years ago | on: Classes of functions (partial, total, bijective, injective, etc)

Oh, fair enough! That's a fun example.

drbaskin | 15 years ago | on: Classes of functions (partial, total, bijective, injective, etc)

I don't follow -- what is the structure being preserved in this example?

drbaskin | 15 years ago | on: Classes of functions (partial, total, bijective, injective, etc)

I'm assuming you want non-trivial examples of non-bijective homomorphisms, but you can create a trivial one using the <= relation: Consider the two element set {0, 1} and the function f from {0,1} to {0,1} so that f(0) = f(1) = 0. f preserves the <= relationship but is not a bijection.

drbaskin | 15 years ago | on: The most ridiculous job interview questions

The a-ha answer still works, but the orignal answer given has you sum 2^(d-k) from k =0 to d, so in this example would be 2^1 + 2^0, suggesting that you would need 3 games to determine the winner.

drbaskin | 15 years ago | on: The most ridiculous job interview questions

Nobody, but it was implicit in the solution proffered by the post I replied to. If the game they are playing has 5623 participants with one winner and 5622 losers, you only need a single game!