This is excellent advice. But for those foreign students who can afford to apply to elite state schools like the University of California, a first rate graduate education can be had for less than at the more competitive private schools like Harvard or Stanford. If you can Obtain acceptance at Harvard, the school has a large endowment and a good deal of financial aid for students so the overall cost could be lower than at a state school. The main problem is clearing the hurdle for admission. If you can give papers at a conference, or somehow make yourself known to key members of the faculty at the school where you would like to study, this can help you obtain both admission and financial support. If you read a scholarly paper by a faculty member you wish to study with, send them an e-mail, complimenting them on their work, asking questions and expressing your interest. It may only take a few minutes of your time, but it could really pay off in the long run.