A mathematician blogs.
Probably too late to use these in filling out your brackets, but these may be of interest:
Nate Silver’s advancement probabilities and bracket.
How to pick a winning bracket using analytics, from Laura McLay.
John Ezekowitz at the Harvard Sports Analysis Collective predicts the tournament and predicts the upsets.
And finally, Jordan Ellenberg’s math bracket, created by picking the school with the better math department to win.
Edited to add: a late breaking post from Laura McLay.
David Kung, Symphonic Equations: Waves and Tubes, a preview of Kung’s MAA Distinguished Lecture (via Ivars Peterson on twitter)
The econometrics of conclaves and For cardinals, advantages in choosing an older pope.
The math in Good Will Hunting is easy.
Sixty Symbols on negative temperature. They don’t come out and say it, but reciprocal temperature is the more fundamental quantity.
Here’s a roundup of pi-related links.
A poetic proof of the irrationality of pi.
Liz Landau on Daniel Tammet and pi.
A baker’s dozen of pie chart of pie recipes.
The Bayesian Biologist’s pi day special: estimating π using Monte Carlo.
Pi approximation day: “a holiday for people who are GOOD ENOUGH, just not transcendental”.
John Cook has five posts on computing π.
Jordan Ellenberg talks about pi day for Wisconsin Public Radio.
The Exploratorium in San Francisco will be unveiling its pi shrine today.
The Aperiodical has a podcast on memorizing pi.
Numberphile’s pi videos, including calculating pi using pies.
Vi Hart’s singing pi-gram.
From Dave Richeson. who first proved that C/D is a constant?
From the New York Times “Numberplay” blog:
An entrepreneur has devised a gambling machine that chooses two independent random variables x and y that are uniformly and independently distributed between 0 and 100. He plans to tell any customer the value of x and to ask him whether y > x or x > y.
If the customer guesses correctly, he is given y dollars. If x = y, he’s given y/2 dollars. And if he’s wrong about which is larger, he’s given nothing.
The entrepreneur plans to charge his customers $40 for the privilege of playing the game. Would you play?
Clearly the strategy is to guess that y > x if x is small, and to guess that y < x if x is large. Say you’re told x = 60. If you guess x is the larger variable, then conditional on your guess being correct (which has probability 0.6) you win an average of 30 dollars (halfway between 0 and 60). If your guess is incorrect you win nothing. Similarly, if you guess x is the smaller variable, then conditional on your guess being correct (which has probability 0.4) you win an average of 80 dollars (halfway between 60 and 100). So your expected winnings are 18 dollars if you guess x is the larger variable, and 32 if you guess x is the smaller variable. You should guess x is the smaller variable — that is, 60 is “small”.
This is surprising at first — 60 is closer to 100 than it is to 0, and if you’re just trying to guess correctly you’d guess that 60 was the larger of x and y. But the payoff is the unseen number y, and if x is the smaller variable then that biases the value of y upwards.
To simplify the analysis, I’m going to say that you’re given u and v, which are x/100 and y/100; so they’re uniformly distributed between 0 and 1. You’re told u, you get to guess if v is larger or smaller than u, and if you get it right you get 100v dollars.
You’re told u. If you guess u is the larger of the two variables, then conditional on your guess being correct — which has probability u — you win on average u/2 hundred dollars. And if you guess u is the smaller, then conditional on your guess being correct — which has probability 1-u — you win on average (1+u)/2 hundred dollars. So your expected winnings are 
So you should guess u is the larger variable exactly when 
What is the expected payoff? It’s an easy integral, namely
and that’s about 0.4024 — the expected value of this game is $40.24. So you should play! But on the other hand the casino operator might still make money, because are people really going to sit down and work out the optimal strategy?
Lots of solutions were offered at the post giving the puzzle; Bayesian biologist had a simulation-based approach.
(Finally, you might notice that I ignored the possibility where x = y. That’s not because I’m forgetful, but because it happens with probability 0.)
Brian Hayes on the baby Gauss story.
Deep Impact: Unintended Consequences of Journal Rank, by Bjorn Brembs and Marcus Munafo. h/t Jordan Ellenberg; Cathy O’Neil’s comments.
Frank Farris on forbidden symmetries in the Notices of the AMS. via Scientific American.
Natalie Wolchover profiles Doron Zeilberger, evangelist of mathematics using computers.
Neil DeGrasse Tyson, On Being Round.
Phase Plots of Complex Functions:
A Journey in Illustration by Elias Wegert and Gunter Semmler.
Evelyn Lamb has two posts on the four-color theorem: one, two.
An interview with Tim Harford (Financial Times’ “Undercover Economist”, More or Less presenter).
Dow 36,000 is attainable again, within three to five years, because the Dow has gone up from 6547 to 14397 in four years; that means a growth rate of 21.54% per year (the fourth root of 14397/6597), and growth at that rate for five years puts the Dow at 38188.
This is an astounding feat of extrapolation. I wonder – the Dow last peaked at 14164 on October 9, 2007. By March 9, 2009 it was at 6547. Would Hassett and Glassman seriously have suggested, four years ago today, that it should drop by more than half in every seventeen-month period — putting it at 741 today?
I think not.
A post at the New York Times Numberplay blog (of all places) includes the gambling machine puzzle, which is a nice one. (More on this puzzle later.) The same post indicates that the Roxie Theater in San Francisco (3117 16th St, between Valencia and Guerrero) will be showing four films by George Csiscery the week of March 18, in honor of Paul Erdos’ 100th birthday (he was born March 26, 1913):
Monday, March 18 at 7:45 pm: Taking the Long View: The Life of Shiing-Shen Chern
Monday, March 18 at 6:30 pm and 9:00 pm: Julia Robinson and Hilbert’s Tenth Problem
Wednesday, March 20 at 6:00 pm and 9:30 pm: N is a Number: A Portrait of Paul Erdos
Wednesday, March 20 at 8:00 pm: Hard Problems: The Road to the World’s Toughest Math Contest
The Chern film is new (this is the Bay Area premiere); I’ve seen the other three, and highly recommend them. Here’s the Roxie’s page for the marathon.
Sadly, I won’t be there, due to other obligations.
has Bayesian probability been banned in England?
At the New York Times, Shivani Vora has a conversation with author and mathematician Manil Suri.
Animated GIFs generated by Mathematica code, via metafilter.
Carl Bialik for the Wall Street Journal explores the upbeat stats on statistics.
Tim Gowers suggests a polymath project based on parallel sorting; Alexander Holroyd has a gallery of pictures of sorting networks.
Vincent Granville of analyticbridge gives a statistical analysis of forecasting meteorite hits and Stefan Geens reconstructs the meteor’s path
Ronald Minton asks do dogs know bifurcations? (between different strategies for optimizing running vs. swimming when moving around just offshore).
From flight stats, describing a flight that is the first leg of a two-leg itinerary I’m flying in the near future – obviously this is the sort of flight where one is interested in knowing whether it tends to be on time, because one does not like being stuck in Charlotte:
This flight has an on-time performance of 84%. Statistically, when controlling for sample size, standard deviation, and mean, this flight is on-time more often than 95% of other flights.
I didn’t realize one could control for standard deviation and mean.
(Presumably controlling for “sample size” could mean some Bayesian approach, where if there is a small amount of data for a flight they tend to give moderate predictions. This is probably not too influential as
Matthew Barsalou does a Bayesian analysis of the deaths of redshirts in Star Trek.
Charles Radin asks why can you stand on ice but not on water? in the Notices of the AMS.
Igor Pak has a blog; his most recent post is on the history of Catalan numbers.
Brian MacDonald has a paper on realignment in the four major sports leagues, with a view towards minimizing the total amount of travel required for teams. At Hockey Prospectus he’s written a three-part series on this paper (emphasizing hockey, of course): part one, part two, part three.
George Hart explains how he makes paper models of his sculptures.
From It’s Okay to be Smart, Drake’s equation applied to finding love.
Rick Durrett writes Cancer modeling: a personal perspective for the Notices of the AMS.
Disease spreads like ripples on a pond, but only if you have the right metric.
God plays dice 