When Gerald Tesauro, first in his class at Anne Arundel County's Southern High School, began to look around at colleges a year ago, it seemed only natural to aim high.

With a score of 790 out of a possible 800 on the math section of the Scholastic Aptitude Test and a finalist's ranking in the National Merit Scholar competition, Tesauro had little difficulty winning admission to Massachusetts Institute of Technology.

But when he inquired about financial assistance to help pay the $7,000 to $8,000 it costs to attend MIT, he was told that his father, a successful lawyer, made too much money and he was ineligible.

Today, Tesauro is enrolled in an honors program at the University of Maryland and he has a $500 scholarship that covers about 60 per cent of his tuition. He is one of 10 "Chancellor's Scholars" to receive such fall to attract top students to Maryland.

Tesauro is illustrative of a trend that has gained significant momentum here and elsewhere in recent years. As costs at private colleges have soared, many of the large public universities have begun to compete more aggressively than ever before for the brightest students. Moreover, they are increasingly accepting the notion that academic scholarships, without regard to financial need, are legitimate recruiting devices to lure such students.

Once reserved exclusively for bright students whose families were too poor to pay their way, scholarships at many fo the large public institutions are now becoming available to middle and upper income students as competition to enroll the gifted becomes keener. Many state schools are organizing or revitalizing undergraduate honors programs for the academically talented once they arrive on campus.

Virginia Polytechnic Institute at Blacksburg, for example, has launched an ambitious campaign to attract top students and next year it will begin offering them scholarships of up to $2,500, regardless of financial need.

Maryland began its "Chancellor's Scholars" program with the 10 top entering freshmen this fall and it actively sought nominations of outstanding high school seniors around the state. The awards are renewable and the program will be expanded as subsequent freshmen qualify in future years.

Two yuears ago, Ohio State Universtity made a conscious decision to recruit National Merit finalists by offering them $500 scholarship. Since then the number of National Merit finalists to enroll at Ohio State has almost tripled, rising from 57 to 162.

"Most of the large public institutions are gearing up to the notion that you ought to pass out money in support of merit," says Andrew deRocco, a professor of molecular physics at the University of Maryland and the president of the National Collegiate Honors Council.

"The public institutions are beginning to recognize that they owe something to the superior student. It's a notion that goes hand in hand with the fact that the American middle class is a tough place. Those people, if they have several children, will have a hard time if they try to send them to a good private college."

"What we're seeing is a very subtle change in the sociology of the university," says a Maryland English professor." More and more of the children of the upper middle class and professional people are picking the state universities over the places like Harvard and Princeton."

On some campuses the new emphasis on seeking top students and gearing programs to them has raised questions of elitism and whether that is the proper direction to follow.

"AThere has been talk of a conflict of purpose," says Eugene W. Carson Jr., a professo of agronomy at Virginia Tech. "Here we are, a major land grant university here to serve the people. Some raise the question, 'Can we afford to spend this money and time to serve a small number?"

"But most of us think it would be unfair to the brighter students not to offer them the best we have," Carson continued.

Thus, beginning next year, Virginia Tech plans to set aside $250,000 in scholarships to be awarded on the basis of merit alone.

In March, the school will invite about 350 of the top high school students - as determined by SAT scores and National Merit standings - from Virginia and other middle Atlantic states to the Blacksburg campus fora weekend visit. The new honors program at Virginia Tech will be promoted and scholarship offers will be made to about half the visiting students, said assistant provost Ronald J. Nurse.

"You can attract the best with scholarship money, but you've also got to attract them with a good program," Nurse said. "We've really energized our honors program in the last year.

"We've created here an academy of teaching excellence and it includes 30 of our best faculty members. They teach honors seminars, no more than 15 students on a class. It's an attempt to combine our most distinguished faculty with our most talented students."

"The administration here," says agronomy professor Carson, "has let it be known that participation by faculty in honors programs will be considered when it comes time for decisions on tenure and promotions."

One of the main attractions of the undergraduate honors programs, say the students involved, is the chance for academically talented students to meet and learn from each other.

"One of the things I like is the opportunity to meet other students who are into the subject as much as I am," said Craig Haines, a senior from Norfolk, Va., who is one of eight-enrolled in an honors seminar exploring the origins of American involvement in Vietnam.

Part of the trend toward awarding scholarships on the basis of trains alone, says John Portz, who "directs the honors program at the University of Marysland, is a desire to project the image of the university as a major center of intellectualism and learning.

"I think the university can use its honors program to project the kind of image it deserves . . . the kind of image it ought to have," said Portz. "Now it projects the image of a jock university, because it has striven for that image.

"The chancellor's scholars program is a step in the right direction," he added," but it is a very small step."

Part of the image problem at Maryland, says Ben Sandler of Baltimore, a senior enrolled in the honors program, is that "within a state, people tend to think very poorly of their own state university. The school has to let everybody in, so the student with a 90 average says, 'Why should I go to college with all the people who never did any work?'"