A page for randomness

The Monty Hall Problem has struck again, and this time it’s not merely embarrassing mathematicians. If the calculations of a Yale economist are correct, there’s a sneaky logical fallacy in some of the most famous experiments in psychology.

Even some of the smartest mathematicians initially come up with the wrong answer to the Monty Hall Problem. Perhaps the best way to understand it is to play the game yourself.
TierneyLab

The economist, M. Keith Chen, has challenged research into cognitive dissonance, including the 1956 experiment that first identified a remarkable ability of people to rationalize their choices. Dr. Chen says that choice rationalization could still turn out to be a real phenomenon, but he maintains that there’s a fatal flaw in the classic 1956 experiment and hundreds of similar ones. He says researchers have fallen for a version of what mathematicians call the Monty Hall Problem, in honor of the host of the old television show, “Let’s Make a Deal.”

Here’s how Monty’s deal works, in the math problem, anyway. (On the real show it was a bit messier.) He shows you three closed doors, with a car behind one and a goat behind each of the others. If you open the one with the car, you win it. You start by picking a door, but before it’s opened Monty will always open another door to reveal a goat. Then he’ll let you open either remaining door.

Read more: Cognitive Dissonance in Monkeys - The Monty Hall Problem - New York Times

As you may or may not know, today is PI day. So go out and have some fun!

Mr. McCain has 703 delegates so far, Mr. Huckabee, 190, and Mr. Paul, 42.

Mr. McCain is far enough ahead in the delegate race that his advisers have said it would be all but impossible for anyone else to win the nomination. His other chief contender, Mitt Romney, bowed to those odds when he suspended his campaign on Thursday.

But Mr. Huckabee, a pastor before he became governor of Arkansas, said, “I didn’t major in math. I majored in miracles, and I still believe in them, too.”

Source

This [Cartesian Coordinate System] is not the only coordinate system in
the world.
There are millions of other coordinate systems in the world.
- My Calc III teacher

Cramer’s Rule
Given a system of linear equations, Cramer’s Rule is a handy way to solve for just one of the variables without having to solve the whole system of equations. They don’t usually teach Cramer’s Rule this way, but this is supposed to be the point of the Rule. Instead of solving the whole system, you can use Cramer’s to solve for just one variable.

Look at the following system of equations:

2x y z = 3
x – y – z = 0
x 2y z = 0

Looking at the system, you have the left-hand side with the variables and the right-hand side with the answer values. Let D be the determinant of the coefficient matrix of the above system, and let Dx be the determinant formed by replacing the x-column values with the answer-column values.

http://personal.stevens.edu/~nkahl/Top100Theorems.html

The millenium seemed to spur a lot of people to compile “Top 100″ or “Best 100″ lists of many things, including movies (by the American Film Institute) and books (by the Modern Library). Mathematicians were not immune, and at a mathematics conference in July, 1999, Paul and Jack Abad presented their list of “The Hundred Greatest Theorems.” Their ranking is based on the following criteria: “the place the theorem holds in the literature, the quality of the proof, and the unexpectedness of the result.”

The Wolfram Integrator is an online tool that will take a function and integrate it for you, provided by the mathematica folks.

Well you can get it to a million places!

16 is the only number of the form xy = yx with x and y different integers.
18 is the only number that is twice the sum of its digits.
24 is the largest number divisible by all numbers less than its square root.
26 is the only number to be directly between a square and a cube.
http://www.stetson.edu/~efriedma/numbers.html