Beginnings
Early History of West Point
As this excerpt from the Centennial of the United States Military Academy shows, the beginnings of West Point were a time of significant flux. While the basic courses in mathematics, engineering and physical sciences had been taught since the beginning of its history as an academic institution in 1802, the organization of the departments was secondary. Indeed various subjects which are seen as elementary today such as English or history were at various times introduced, dismissed and reintroduced. This shows something fundamental about the education at the time, while the backbone of the institution in engineering and sciences was consistent, the accessory courses necessary to constitute a full course of study were still in debate. The idea of West Point being a true academic engineering institution was also in flux for some time, with little in the way of entrance requirements or a clear path in the educational program. There was significant reform around the 1820s as Sylvanus Thayer took over as the Superintendent. This coincides with the restructuring of West Point to follow the relatively newly established Polytechniques Napoleon had established in France. As a note drawing may seem a strange thing for West Point to include in its curriculum but technical drawing or drafting was a critical skill for all engineers and doubly so for officers who may be doing tactical drawings as well.
The basic instruction in mathematics was relatively simple compared to the breadth of mathematical knowledge taught in undergraduate education these days, but was for the time considered relatively comprehensive. It is noteworthy that all the textbooks are by French authors again possibly a nod towards the success of the Ecole Polytechniques in France. At the time many of the great mathematical minds who were active were French, with the exceptions of Bernoulli, Gauss and Euler. The math textbooks were examined as it was one of the original departments, and many of the textbooks still exist in the department library with notes pertaining to the courses taught, giving approximate dates on usage and other notes.
Brooklyn Polytechnic Early History
In much the same way that West Point was not cleary defined for its first few decades of existence Brooklyn Poly was in a similar state of change for much of its early history. While it was founded in 1854, this was primarily as a upper collegiate prep and finishing school rather than a full institution of higher learning. In 1890 the preparatory school was spun off and Brooklyn Poly became a full university. Notably, Brooklyn Poly and its preparatory school hold no affiliation beyond their shared history as opposed to the West Point preparatory school which serves as a direct pipeline into admission at the main campus.