American University has decided to close its School of Nursing and discontinue doctorate programs in philosophy, English literature and mathematics, as part of an effort to concentrate on its academic "centers of excellence" and cut back in some of its weaker fields.

"No university can do all things for all people," university President Richard Berendzen declared yesterday at a breakfast meeting with reporters. "If we can't do something excellently, then we shouldn't do it . . . . We have to try to focus."

The decision to close AU's Lucy Webb Hayes School of Nursing, which dates to 1891, came after several years of declining enrollment and declining quality of applicants. The development is part of a nationwide slide in both the number and academic quality of nursing students despite a widespread shortage of nurses.

"As opportunities have opened for women in medicine, law and journalism, it's difficult to attract good students into nursing," Berendzen said. The field remains a traditional "women's profession," with women accounting for almost 95 percent of nursing students nationwide.

Berendzen said the university's rising admission standards "seemed to exacerbate our problems in nursing." The nursing school, he added, "has always been an anomaly {at AU} and when enrollment fell it became indefensible."

The school accepted no first- or second-year students last fall. The decision to phase out the school was made last winter by the university trustees after a study by a faculty committee, Berendzen said.

Patricia O'Connor Finn, the acting dean of nursing, said all students who would have been juniors in nursing this year have transferred to other schools and the final group of about 20 seniors will graduate in May 1988.

"It's sad this is happening at a time when educated nurses are very much in demand," said Finn, who had opposed closing the school. "But the university decided to close the school rather than sticking with it and seeing the cycle {of nursing enrollments} turn up again."

From 1983 to 1985, the number of nursing students at AU fell by more than 40 percent to just 74 enrollees, with a faculty of eight full-time and 15 part-time instructors.

Provost Milton Greenberg said the decisions to drop PhDs in math, English literature and philosophy were made as part of an extensive "program review" during the past three years. The three programs had small numbers of students, granting only a handful of degrees each year, and had relatively low rankings in nationwide ratings of graduate programs.

Berendzen said, "I think the way for us to go is to focus our resources on applied master's degrees and selected PhDs. For example, we're putting more into our PhD in U.S. history." Other programs that will receive extra funds and faculty as "centers of excellence" include studio art, finance, marketing and economics.

AU's nursing school was founded by a Methodist women's group and for many years was affiliated with Sibley Hospital. It became part of American University in 1965 when it switched from offering two-year diplomas to four-year bachelor's degrees.

Other nursing programs in the area have had enrollment declines but none has announced plans to close. Last winter, Georgetown University said it was studying the future of its nursing school. Its nursing dean, Alma Woolley, said yesterday that the school would remain open but was planning to adjust its faculty and program because of decreased enrollment and income.