I think I spotted an error... you were too quick with the cancellation. The main point is that P! / P = (P-1)!

> 27 million. Just go to amazon.com, choose the books department to the left of the search bar, don't enter anything in the search field, and press go. So that reduces the significance by a factor of 10. That said, it's still 0.2%, which is quite high considering they're not a traditional publisher.

http://mit.edu/urop/ The Undergraduate Research Opportunities Program. MIT will pay you or give you credit to do research, for professors. If you have good ideas for research that nobody is currently doing, the office or a professor can sponsor you, and you can get money to travel to facilities, run experiments, etc. The program not only makes doing research fantastically accessible to undergrads, but also maintains programs like MIT's FormulaSAE and SolarCar teams.

Buzzing speakers happen. I'm sure they happen at CalTech too. The claim that a buzzing speaker implies professors do not care about their students is outrageous.