BOSTON (AP) _ Before she even cracked a book for graduate school, Jennifer Jensen was handed one of the toughest assignments in Boston: competing with 67,000 other students in finding a place to live.

Ms. Jensen arrived in this college-rich city only to learn she was homeless. An apartment she found had been rented out from under her, a result of the tightest housing crunch in years.

The story is the same in cities across the country. Slim vacancy rates and anti-student attitudes are forcing young scholars to share apartments, to seek dormitory rooms and even camp out on campus.

Housing is so tight at the University of California, Berkeley that one student rolled out a sleeping bag in a Bay Area Rapid Transit district station. Another lived in a van. At Stanford University, some students pitched tents on campus to protest rental rates.

Boston's 3 percent vacancy rate, the lowest in almost 15 years, has students scrambling for housing before the semester begins.

``Loans for school are $22,000 a year and I'm gonna have debts for the rest of my life,'' Ms. Jensen said. ``I just didn't realize it would be so hard to find somewhere to live.''

Some students are clamoring to live in dorms. But Boston's 32 area colleges and universities cannot offer the same guarantee as small liberal arts schools, such as William College, which provide four years of campus housing.

And students who opt out of Boston University's housing system their sophomore year _ maybe for a cheaper apartment a few blocks away _ have no way back in.

Nationally, rents rose 3.2 percent between June 1997 and June 1998, according to a National Multi Housing Council report based on data from the Department of Labor.

In cities with large student populations, rents rose even faster.

In Berkeley, the average monthly rent now for a one-bedroom apartment is $763, according to college housing officials. Rents in the Boston area, where students pay from $800 to $1,400 for a one-bedroom home, increased an average of 4.3 percent during the year ending in June. In San Francisco _ the nation's second-most expensive real estate market, according to some surveys _ rents went up 8.3 percent in the same period.

Even in small cities, students face a crunch.

Landlords in Burlington, Vt. _ where the vacancy rate is only 1 percent and a one-bedroom place averages about $660 _ say it's not uncommon to receive 50 phone calls the first day an apartment is advertised. Prospective tenants often offer to pay more than the advertised rent, said Joan Tessier, owner of Apartment Finders.

And in Seattle, the vacancy rate has dropped to 2 percent, according to the Student Housing Office at the University of Washington.

At this time last year, the office was receiving 30 to 40 housing listings each day. Now, an average day brings only 14 listings. At the same time, rents for studios and one-bedroom apartments _ which range from $550-$700 _ are going up an average of $100.

``Our school doesn't start until the end of September, so a lot of problems haven't gotten that bad yet,'' student Alysia Madsen said. ``But in about three weeks students will start to freak out.''