Plan for the Education of Women in Connection to Columbia College
The Plan for the Education of Women in Connection to Columbia College (also known as the Collegiate Course for Women) was a predecessor of Barnard College in the history of women's education at Columbia. Women who could pass all the exams that a Columbia College student needed to take to get a degree, could get a "certificate" from the school in return for five dollars.
Facing various calls to do something about higher education for women, the Columbia Trustees were dead-set against actually admitting women to the school. So, in a compromise they created the "Plan." By resolution of June 9, 1883, the trustees offered a plan by which any woman over the age of 17 who could pass an entrance test was welcome to sit for the same exams for each class that Columbia College students took, and upon successful passage would be entitled to a certificate bearing the seal of the trustees and the signature of the school President attesting to their passage of as many courses as they successfully completed. The students were on their own with respect to learning the material.
In short, the trustees managed to pay lip-service to education for women and even pocket a few bucks without ever admitting a single woman to the school. No doubt they were quite proud of themselves.
It is possible that this tradition, beginning with the granting of certificates bearing the seal of the trustees and signature of the president, to the granting of BA degrees, translated over to the founding of Barnard College. Fast forward 130 years and Barnard graduates still receive their diplomas from Columbia University, despite Barnard being an independent institution.