Once upon a time, the only way to take a course taught by a professor employed by a great university was to attend a great university. With Coursera, you don’t have to leave your seat. Instructors from Princeton, Duke, Caltech and 13 other schools conduct online classes on everything from math to music, complete with video lectures, quizzes and homework. You might end up in a course with tens of thousands of classmates all over the world. And the site is free — no scholarship required.