No college mentioned transgender people in its nondiscrimination policy until the 1990s, and most still do not. A small number have decided not to segregate housing or restrooms by sex, eliminating much of the need to determine who is female or male. Usually, it is not a matter of the colleges’ having policies that explicitly discriminate, but that “they haven’t really thought about it, they don’t have a stated policy and they would make decisions on a case-by-case basis,” said Genny Beemyn, director of the Stonewall Center at the University of Massachusetts at Amherst, who also tracks transgender policies at colleges around the country for Campus Pride, a national gay rights group.

Jaycen plans to have sex-reassignment surgery, but cannot afford it yet. The university says it will regard Jaycen as male if he undergoes surgery. “For 123 years, our housing policy has been to house students by their anatomy,” Mr. Felton said, adding that is “a question that a lot of institutions, religious and nonreligious, are struggling with.”

But many transgender people choose not to have those operations, or have only “top” or “bottom” surgery. But they often find that the world at large remains fixated on what anatomical features they have subtracted or added, not on how they identify themselves.

Colleges often go by whatever sex is indicated on an official document like a driver’s license or birth certificate, but policies on changing those documents vary widely from state to state.

Jaycen, who grew up in Portland and describes himself as deeply committed to his faith, began his transition to male more than a year ago; he quit the women’s basketball team when he started testosterone therapy. He seems outgoing and confident, but he says he suffers from depression, a common problem among transgender people, worsened by the strain of dealing with the university.

A study conducted by researchers at the American Foundation for Suicide Prevention and the Williams Institute at the University of California, Los Angeles, School of Law, released this year, concluded that people who identify as transgender or gender nonconforming attempt suicide at a rate that is nine times the national average.

Jaycen and his lawyer, Paul Southwick, negotiated for months with George Fox, trying to reach an informal agreement of some kind, though Mr. Southwick questioned whether the university was talking in good faith. He said that the university sought, among other conditions, to compel Jaycen to reveal his transgender status to his roommates, until he noted that that would violate federal law on student privacy. The roommates, in any case, already know, Jaycen said.