The Math of March Madness
With the NCAA college basketball tournament now well under way, no doubt many of you are following the games closely, and vying for your teams to make it to that sacred promised land known as the Final Four. Even the President's caught some of the madness.
When filling out a bracket, of course you would like to predict as many games correctly as possible. No doubt a thorough understanding of the teams can help in this endeavor, as well as a careful analysis of their performance throughout the season. But none of us is perfect, and we are bound to make some incorrect predictions.
Even if you are quite skilled when it comes to picking winners, and can pick correctly 75% of the time, the odds of you selecting the correct winner for each game of the tournament are about 1 in 74,325,939. Roughly speaking, this means that even if the NCAA Tournament took place every day, rather than over the period of a few weeks once a year, it would take over 200,000 years, on average, for you to have...
Verizon Employees Suck at Math
If you've got the time, and/or the patience, listening to this audio clip of George Vaccaro try to deal with a series of Verizon representatives who claim that 0.002 = 0.00002 should be enough to strike fear into your heart regarding the future of mathematical literacy in this country. Then again, he's talking about problems he had while in Canada, so maybe the reps are Canadian. We'd never make such an obvious mistake here in the States, right? Right...
On a related note, I would encourage all of you to start writing the dollar amounts on your checks as more complicated mathematical expressions. Everyone could use a boost to their mathematical literacy, bankers included.
The audio clip is quite long, and the longer it goes on, the more depressing it gets.
Pi Day
Hot on the heels of Square Root Day comes Pi Day, a day held in honor of arguably the most famous mathematical constant, π. And like Square Root Day, I am forced to approach this holiday with a certain degree of hesitation.
There is no doubt that Pi Day is the most prestigious mathematical holiday, but this recognition usually only serves to illustrate the sad state of mathematical literacy in this country. For example, one year I remember reading a news article about Pi Day where the author described π as a number whose decimal expansion "was believed to go on forever." Of course, belief has nothing to do with it - this is a simple consequence of the irrationality of π, a fact which is apparently lost amidst the pie eating hubbub of this holiday.
Unfortunately, this is not an isolated incident - for as much as Pi Day aims to educate people about π, it seems to do just as good a job of showing how little people actually know. Searching Google News for articles on the upcoming...
Optimization at the Checkout
On more than one occasion, while waiting in line to buy my lunch on campus, the cashiers at the front have asked those of us in the line to split into smaller lines - one line for each cashier. This seems to be met with hesitation on the part of those of us who are in line, and rightly so. Perhaps I am simply projecting, but it seems like they all know the same thing I do: that having only one line feed into all the cashiers is the most efficient way to manage a queue.
One would think the cashiers should know this as well, but apparently not. So, if you have ever asked people to form separate lines when waiting to be helped, pay attention, because you need to learn why people in line rarely pay attention to you.
For a person waiting in a single line, there is little incentive to break into smaller lines. This is because using several lines leads to longer wait times on average. You don't need any sophisticated machinery to explain why this is true - if you ruminate on the two...
Square Root Day?
I just noticed this article on the front page of Yahoo, which discusses the pending celebrations for tomorrow, in honor of the square root function. Tomorrow is given the name "Square Root Day," naturally enough, because the date is 3/3/09. Seeing as how there are only 9 square root days per century, apparently the sparsity of this phenomenon is enough to make some people excited when such dates do occur.
Tonight we're gonna party like it's 3,996,0011/2.
I don't want to sound like a curmudgeon, but I'm not really sure who deemed this story worthy of inclusion on the front page of Yahoo. Similarly, I don't know what it means when the article says that tomorrow's "holiday" is met with great enthusiasm by "math buffs." The article seems to suggest that a celebration like this falls within the realms of mathematics, when it more appropriately falls into the realm of numerology.
One could just as easily put significance on equally unimportant sets of dates. For example, I could decide...
A Variant of the Traditional Football Pool
Update: Part two of this three-part series on football betting pools can be found here. Part three is here.
During this month's Super Bowl, like many of my fellow Americans, I participated in the great tradition of the football pool. This method of betting on a football game is quite simple. For those of you who have never partaken in this activity, here's how it works:
- You begin with a 10 x 10 grid of empty squares, which you auction off at a certain price ($1 per square, say). When someone buys a square, they put their initials in that square.
- Once all the squares have been purchased, each row and each column in the grid is randomly assigned a digit from 0 through 9. This means that each box will correspond to a unique pair of digits, from the 0-0 square through the 9-9 square. Since the assignment is random, there is no way of knowing which digits will correspond to your square when you purchase it.
- At the end of each quarter of the football game, the last digit of each team...
Math Gets Around: The Entomology of Civil Engineering
In the continuing saga of animals that are better than you at math, it now appears that ants are much better than most of us at optimization. Granted, they may not be able to think abstractly, but in concrete terms, they far surpass us with a particular type of optimization: the efficiency of traffic flow.
As anyone who has gone to a picnic will tell you, ants do a very good job of creating traffic streams - their foot traffic moves steadily, and without the major pileups to which my fellow residents of Los Angeles have become so accustomed. One could argue that the wide expanse of park area is proportionately much larger for the humble ant than what most motorists have to live with, but even so, the march of the ant colony often appears quite regimented, even with space enough to make a wider path. How is it that ants can control their traffic so well?
This article from the Wired Science blog discuss how ants succeed where we fail. At the heart of the matter is a study from the...
Commodify your Mathematics?
Here's an interesting article about Tom Farber, a high school Calculus teacher from San Diego who is fighting tough economic times and cutbacks in education spending in a rather novel way - he's selling ad space on math tests.
The goal here certainly doesn't seem to be the development of a second income. Many teachers report having to spend money out of their own pockets for school supplies - in this case, Mr. Farber is using the money to help cover the copying costs associated with making tests and practice exams to help students prepare for the APs. His intentions certainly seem benevolent, but are his actions as innocent?
It seems like the advertising is fairly non-intrusive. There are no graphics, and the ads run on the bottom of the page. The fact that a good chunk of the ad space was bought by parents who wanted to run supportive messages certainly makes this easier to swallow as well.
The article suggests that the main criticism with Mr. Farber's plan is that it is a...
Math in the News: Maybe the Sky Isn’t Falling, After All
Even though we'd like to accuse our math teachers of being more or less incompetent, there is at least one indication that math education in this country is making some progress. In particular, the results of the Trends in International Mathematics and Science Study shows American students have gained 11 points over their average performance in 1995. A comparison of US scores, along with an article describing the findings, can be read here.
With an international average of 500, American 4th and 8th grade students scored a respectable 529, on par with the Netherlands, Lithuania, Germany, and Denmark. As might be expected, however, we've still got a significant way to go when it comes to competing with other countries. Hong Kong made the top of the list, with a score of 607.
Of course, this data by itself doesn't do much to explain what factors may be driving our improvement. One suggestion is that we are simply aiming higher. The article linked above ends with the following:
...Math on TV: Look Around You
With the weekend close upon us, no doubt many of you are looking forward to a reprieve from the work week. The more popular among you may even have some engagements lined up. Even for those of you with "friends" or "hobbies," however, there always comes a point when the evening begins to come to a close.
Suppose it's late and you're looking for a good time. Temptation runs rampant in the midnight hour of a Saturday night, especially for those of us in the fast-paced world of graduate school. But before you open that bottle, or pick up the phone to talk to live singles in your area, let me take the opportunity to inform you of a new way to spend your time during the late night wind-down: starting this weekend, you will be able to relive your childhood through the nostalgia-inducing satire that is Look Around You.
That's right: starting this weekend, Adult Swim will begin airing the former BBC series on Sunday mornings (or late Saturday nights, depending on who you ask) at 1 a.m...
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