coolstandingsYour team is six games back in August…What are their realistic chances of winning the division, winning the wildcard, or just making the playoffs? A couple of MIT alumni can help you there.

Theta Chi buddies Greg Agami ’93 and Sean Walsh’93  started coolstandings.com in 2005 when these Red Sox fans thought it would be fun to know exactly what chances the Sox had of making the postseason. Within a few months, coolstandings.com was online, simulating the remainder of the MLB season one million times each day to determine the playoff probabilities for every team.

“The model uses a modified version of the Bill James Pythagorean Theorem to determine the chance each team has of beating other teams on its schedule,” Agami says. “Home/away statistics and recent team performance are used as variables for the Monte Carlo simulation, and we even implemented the various tie-breaking rules as needed to determine divisional and wild card winners. We’ve used historical data going back to 1903 to evaluate and optimize the model.”

These days, you can follow football and basketball as well as baseball in the real season and a fantasy pre-season. And this is not even their day jobs—Agami is an engineer at Motorola, while Walsh is CTO at DestinationWeddings.com.

The formation of a phantom traffic jam.

The formation of a phantom traffic jam.

The most frustrating sort of traffic jam may be the one that has, apparently, no cause. Think road rage with no one to blame.

MIT mathematicians have been working on the problem. No, they didn’t find someone to blame. Instead, they have developed a model that describes the circumstances that prompt such jams to form. This model could help road designers minimize the odds of their formation. The model can also help determine safe speed limits and identify stretches of road where high densities of traffic—hot spots for accidents—are likely to form

The mathematics of such jams, which the researchers call “jamitons,” are strikingly similar to the equations that describe detonation waves produced by explosions, says Aslan Kasimov, lecturer in MIT’s Department of Mathematics. The equations, similar to those used to describe fluid mechanics, model traffic jams as a self-sustaining wave.

Sure, MIT’s acceptance rate is hovering around a record 10% right now, but back in the late 19th century, it was a different story. The first class of students who registered in 1865 weren’t required to take  formal entrance exams. They just needed to be “properly prepared.” Hm. Fast forward a few years when, in 1869, the MIT Corporation finally decided to add qualifying exams in required subject areas, including English, Geometry, Algebra, and Arithmetic.

Thanks to the folks at MIT Achives and Special Collections, you can give those exams your best shot. Algebra section below:

Algebra

Check your answers (or get a few hints), and try the English, Geometry, and Arithmetic tests.

Note about answers: Questions have been answered by 20th century persons and won’t always match those that might have been given by 19th century applicants (or 21st century applicants). You are invited to send comments and refutations to mithistory@mit.edu.

Spotted this at mitsecrets.blogspot.com, an infrequently updated site inspired by PostSecret.

math