I responded to a similar question here, if you're interested.

Basically, there was no such thing as a college major in the early nineteenth century, especially not in the United States. Most of the earliest American universities, most notably Harvard and Yale, were explicitly intended as seminaries. The student populations attending these schools were almost entirely drawn from the elite of society, and the bulk of them would either enter the ministry or go on to postgraduate study in the law. The curriculum was heavily influenced by the curricula of European universities, and would have included extensive study of both modern (French, possibly Italian and German) and classical (Latin, Greek) languages. Students would also have studied subjects like rhetoric, history, and the religious doctrines of whatever denomination controlled their school (at Harvard it was Unitarianism in the 19th century). The term "major" does not enter usage until the 1870s, when Johns Hopkins starts using it. Hopkins was one of the first universities that arose in United States as a result of the trend of large numbers of Americans traveling to Germany to earn PhDs, often in a discipline called philology, but also often in history. Philology is the study of written historical languages, kind of a mix of linguistics and literary criticism.

The idea of a major course of study arose out of this culture of increasing formalization, secularization, and professionalization of higher education in the United States, as the purpose of a college education began to shift away from preparation for the ministry or a general upper-class learned life and towards a more specialized view of education as granting mastery in a specific field. Before the late 19th century, however, all degrees would have been general B.A. (or A.B.) degrees.

Sources:

Diehl, Carl. Americans and German Scholarship, 1770-1870

Winterer, Caroline. The Culture of Classicism

Geiger, Roger. The History of Higher Education.