Many dream in vain of attending Harvard, Stanford or MIT. But the deans of these three universities also dreamt in vain of Corrina Zygourakis, 19.

The young Texan, the daughter of Greek immigrants, corresponds exactly to the ideal picture of a dream student. She achieved the highest possible score on the SAT, the standardized test of performance taken by all applicants to US colleges and universities, and her grades were equally stellar. She won a number of science awards while still in high school, and during her summer vacations she worked as a research assistant for a Harvard professor, with whom she even co-published an article in a professional journal. On top of all that, she still found time to excel in other areas: as the editor of a student newspaper, as a violinist in a chamber orchestra, as a figure skater, and as a long-distance runner. She also speaks Greek and French fluently.

Everyone wanted Zygourakis, but she turned down offers from Harvard, Stanford and MIT. Caltech, in Pasadena, California, made her an offer she could not refuse: to convince the talented girl to attend, the world-renowned institution is not charging her any tuition or room and board - an offer worth 32,000 dollars a year.

"I was shocked when I read the letter," she says. "But it made the decision easy for me." For the past year and a half, she has been happily attending Caltech for free, majoring in neurobiology. She wants to become a doctor.

Caltech sees its waiver of Zygourakis' tuition as a good investment for the future. Without the offer, she probably would have selected another university. By accepting, however, she is helping to improve the quality of Caltech's student body, the true capital of an elite US university. After all, it is the caliber of students that triggers an astonishing performance spiral: outstanding students attract outstanding professors. Outstanding professors attract outside funding, which benefits research, which in turn attracts better students.

"The competition for students," says Gerhard Casper, the Hamburg-born former president of Stanford, "is the most important element for improving the quality of a university." And US colleges and universities are not just using academic means to compete for the best students. They also use scholarship money to attract talented students. The assets of students' parents are often irrelevant. Someone who is highly talented and wealthy can obtain a scholarship, even though he or she could easily have paid for it. Wealthy students often get even more financial aid than poor students, who frequently must take on tremendous debt to pay for their college dreams.

Because good students also like nice bathrooms and nice apartments, and like to play sports, even state universities are now spending millions of dollars to build gyms and luxury apartments on campus. This would have been considered wasteful in the paste. Nowadays, ambitious college deans treat such luxuries as necessary investments in the battle for the best students.

A university's ability to compete depends on how well its applicants did on the SAT. If a university is suddenly able to attract candidates with higher SAT scores, then everyone knows it must be doing something right. College students' SAT scores also play a role in the always controversial but nonetheless decisive college and university rankings published each summer by U.S. News & World Report.

The higher the ranking, the more a university can charge in tuition. One year at Harvard, for example, which is currently number one on the list, costs 38,000 dollars, according to information provided by the university. Nevertheless, this does not mean that only wealthy students can attend Harvard.

Whether or not someone can pay its tuition is not a criterion for admission to Harvard. The university values intelligence more than money. Harvard puts together a financial package composed of scholarships, subsidies and low-interest loans for anyone who is accepted but can't afford to attend. Only 19 percent of students at private US universities pay full tuition - and help subsidize the rest.