For the past three months, Benjamin H. Alexander, president-designate of the University of the District of Columbia, has been flying to town on weekends from his home in Chicago to win friends and influence people on the UDC campus. But what happens when Alexander begins talking is often something quite different.

When he met with the department chairmen of the university's liberal arts and education schools to seek out their views and foster a cooperative spirit, several of the professors walked away complaining that Alexander doesn't want to listen to the faculty and doesn't understand the mission of UDC.

He also created a stir, according to several university officials, when he told the predominantly black audience at a recent UDC lecture series that blacks are good runners because they have big nostrils.

Several faculty members say they are still upset over comments Alexander made, in the press and on a radio talk show here shortly after his appointment, to the effect that blacks should start calling themselves "Americans of African heritage" because the word black has too many negative connotations.

A former Washington resident who served as a D.C. school board member and a civic association president, Alexander, 60, staunchly advocates equal opportunity for blacks, but says they deserve no special breaks.

With those views, said one disgruntled faculty member, "he won't last six months" at UDC, where most of the 14,000 students need remedial help and few graduate in the traditional four years.

But the energetic Alexander says faculty opposition doesn't worry him. "The more they do that kind of nonsense, the more I'm determined to come," he says. "Would you be a quitter?"

A former research chemist with the National Institutes of Health, Alexander says his views on race may sometimes sound strange, but adds, "I am a scientist, I am trained to tell the truth. . . . I am only trying to teach my people not to be ashamed of their color. I love my people. This is why I say those things."

The statement about blacks being better runners, he said, merely refers to what he considers a biological truth: that blacks came from tropical regions and needed larger nostrils than people from cooler regions because there is less of a concentration of oxygen in hot air than in cool air.

"But both the large nostrils and the smaller nostrils are beautiful," he says.

At least partly due to the often-unorthodox views of the conservative educator, who is currently president of Chicago State University, a group--composed of 30 faculty members, 13 current or former students, one administrator and the citizens' lobby Common Cause--filed suit against the university's board of trustees in an effort to keep Alexander from taking over on Aug. 1.

The suit technically centered on the process that was used to select Alexander, although some UDC sources have said the suit's launching was also due to the fact that Alexander was the candidate chosen. A D.C. Superior Court judge dismissed the suit on Friday, saying only a member of the board of trustees would have standing to file such action. Now the faculty has asked the education committee of the D.C. City Council to hold hearings on the Alexander appointment.

Alexander rarely minces words. He marched for civil rights in the 1960s and publicly branded some of that movement's leaders as "hoods." He has been labeled an "Uncle Tom" and said that the term was a compliment, insisting Harriet Beecher Stowe's much-maligned character is really "a symbol of courage."

Marjorie Parker, chairman of the UDC board of trustees, said that despite the faculty complaints, the board continues to support Alexander, and "a majority of the university community supports him quite strongly."

Alexander insists the real issue behind the opposition "is academic excellence. I'm for excellence," he says, adding quickly, "and, I believe, so is the great majority of faculty members, deans and chairpersons at UDC."

Terry B. Thomas, a UDC trustee who served on the search committee that recommended Alexander, says he believes the faculty opposition is rooted in "fear . . . that they won't be able to get away with a lot of things. . . . Alexander is for accountability."

In the eight years that he has headed Chicago State, a school that has 7,000 students, Alexander has developed a reputation as a tough-minded administrator.

In his first few months there, he eliminated pass/fail grades, expelled 130 students whom he accused of just "hanging around" and placed another 1,200 on probation.

Several Chicagoans familiar with Alexander's years there, including the executive director and two members of the governing board that oversees Chicago State, two activists in the black community and a colleague of Alexander's in the Illinois college system, praised Alexander for raising standards and initiating several new academic programs.

Alexander maintains the UDC flap is the work of only "eight or nine" people. "There are approximately 570 faculty members at the university. There are about 30 on the suit--whom I hope to win over when I get there. Say that. That's more positive."

"Positive . . . absolutely beautiful" is the way he describes his meetings thus far with faculty members, students and administrators. But, said Kelsey A. Jones, chairman of the criminal law department, "If he doesn't realize there was sharp disagreement in his meetings with the faculty , he is being totally unrealistic."

Besides objecting to Alexander's views on race, Jones and other faculty members criticized his assertions that UDC must begin better to serve the needs of Hispanic students (most of UDC's students are black Americans or come from African nations) and that students who appear incapable of succeeding in a four-year program should be channeled to other programs.

They also said they believe Alexander's public statements that he intends to make UDC "the number-one university in the nation" put the school in an awkward position.

"We want to be a university of excellence," said Wilmer L. Johnson, the president of the Faculty Senate, " but we can't become the number-one university in the nation with an open admissions policy. . . . We don't have the resources, nor do we attract the right kind of student for that at the present time."

Johnson, as a member of the search committee, voted against Alexander.

Alexander's meeting with UDC deans apparently went more smoothly than the faculty meetings, according to two of the deans. "If there were any feelings of dismay, no one represented it at all," said John D. Butler, dean of the college of liberal arts.

At the heart of the Alexander controversy, say the professors, is also a dispute over how much power should be vested in the board of trustees and how much say the faculty should have.