Mathematics Education at West Point: The First Hundred Years

Author(s):

V. Frederick Rickey and Amy Shell-Gellasch

When Albert Church arrived at West Point in June of 1824 at age sixteen, the entrance requirements were simply arithmetic, reading and writing. During the summer the cadets “received daily and very thorough instruction” in arithmetic by cadet Dallas Bache, and recited daily to him. Like Ross, Bache served as acting assistant professor of mathematics while a cadet. It was then the practice to have a few outstanding cadets serve as instructors — and Bache was outstanding, for he later became Superintendent of the United States Coast Survey and President of the National Academy of Sciences.[1] Cadet Bache knew who the “duly qualified” were before the oral entrance examination in August and so their examination in arithmetic was “hurried and slight” with not more than one or two questions asked. But the proficiency of the weaker cadets was “fully tested.” Every cadet was “required to read and write in the presence of the Academic Board.”[2]

During his first year, Church and his classmates studied algebra, but “the best text book that could be obtained, in the English language, was a poor translation of Lacroix” so they used it.[3] Also, they used Legendre’s geometry,[4] Lacroix’s trigonometry,[5] both in translation, and Crozet’s book on descriptive geometry.[6] These were all fine books and provided an excellent curriculum.

During the second year, Church and his classmates in the higher sections used Jean Baptiste Biot’s Essai de géométrie analytique, appliquée aux courbes et aux surrfaces du second ordre (second edition 1805) for analytic geometry and Silvestre François Lacroix’s Traité élémentaire de calcul différentiel et de calcul intégral (first edition 1802) for calculus.[7]The lower sections used Jean-Louis Boucharlat’s Elémens de calcul différentiel et de calcul intégral (first edition 1812) for calculus. (Again, the French the cadets studied every afternoon of their plebe or freshman year was so that they could learn their mathematics during their first and second years as well as their later engineering studies.) Albert Church graduated first in the class of 1828 and, like Davies, was commissioned in the Artillery, there being no vacancies in the Corps of Engineers. Thayer requested that Church stay at West Point to teach mathematics, and there he remained except for the two years, 1832-34, when he joined his artillery unit. In 1837, he became professor of mathematics, succeeding Charles Davies. Church served as professor until his death in 1878, a total of fifty years.

Professor Church wrote four textbooks, all of which were used by West Point cadets:

1842 Elements of the Differential and Integral Calculus.

1851 Elements of Analytical Geometry.

1864 Elements of Descriptive Geometry, with its Applications to Spherical Projections, Shades and Shadows, Perspective and Isometric Projections.

1869 Plane and Spherical Trigonometry.[8]

These textbooks were also used at many other schools, but were not as widely used as those of Davies. Note that these titles were meant to be improvements on what was already being taught. There was no broadening or deepening of the curriculum. Church himself admits that once the mathematics curriculum was set in place, it did not change substantially for the rest of the century. Notable additions to the mathematics curriculum included determinants and the method of least squares in the 1880s.[9]

The texts of Church, and even more so Davies, dominated the curriculum at the Academy for the majority of the nineteenth century. Within a decade of their introduction at West Point, the Davies and Church texts were being used across the country at schools such as Union College and The University of Michigan. In the closing years of the century, texts from yet another author connected to the Academy were introduced in the curriculum.

Edgar Bass (1843-1918) graduated from the Academy in 1868. He returned after a year to teach natural and experimental philosophy from 1869 to 1874, and again from 1876 to 1898, succeeding Church as head of the Department of Mathematics in 1878. The two intervening years in the 1870s he spent on the US expedition to New Zealand to observe the transit of Venus.

Bass marks the beginning of a transition away from the traditional modes of instruction started in Thayer’s time, and away from the traditional texts of Davies and Church. In order to clarify the older texts, and incorporate more of the calculus, he wrote a series of pamphlets for the use of the cadets. These later became his Elements of Differential Calculus, which replaced Church in 1896. He also wrote Elements of Trigonometry in 1888 for use at the Academy.

[1]The 1821 Annual Report of the Superintendent of the United States Military Academy, as quoted in the 1896 Report, p. 44, indicates “The superintendent was authorized to detail cadets to act as assistant professors, each to receive $10 per month for extra services.” However, Lester A. Webb, Captain Alden Partridge and the United States Military Academy, 1806-1833 indicates on p. 172 that cadets were already being used as instructors in 1816. There is no evidence that either Davies or Church was a cadet instructor.

[2]Albert E. Church, Personal Reminiscences of the Military Academy, from 1824 to 1878, West Point, 1879. See pp. 39-41. Available from the United States Military Academy Library: http://digital-library.usma.edu/cdm/compoundobject/collection/persrem/id/85.

[3]Silvestre François Lacroix, Elements of Algebra, Translated from the French for the Use of Students of the University of Cambridge, New England (first edition 1818). In 1821, neither mathematics professor David Douglas nor Superintendent Thayer were aware that John Farrar had published this English translation of Lacroix [The West Point Thayer Papers 1808-1872, edited by Cindy Adams, 1965, Norton to Thayer, August 13, 1821]. The 1823 Board of Visitors report indicates that an English translation was used, so this confirms Church’s recollection. The 1825 report lists Lacroix’s Algebra, but whether it was in French or English is unclear. The “Tentative List of Text-Books” in the first Centennial volume indicates that a French edition of the work was used, and an 1825 French copy in the library bears the stamp “Textbook West Point 1823 to ,” but we have come to distrust these stamps, which were probably inserted when Edward Holden was preparing the Centennial volumes. Professor Davies would have to have been very unhappy with the Farrar translation to have the cadets use the original French.

[4]Adrien-Marie Legendre, Elements of Geometry, Translated by John Farrar, For the Use of the Students of the University of Cambridge, New England (first edition 1818) is the edition that Church used. This is a translation of Éléments de géométrie avec des notes (first edition 1794). The West Point library has the tenth (1813) edition in French in a Thayer binding, indicating that it was purchased by Thayer while in France. For information on which editions are in the West Point library, see Albree et al., cited in note 2.

[5]Silvestre François Lacroix, An Elementary Treatise on Plane and Spherical Trigonometry, and on the Application of Algebra to Geometry; from the Mathematics of Lacroix and Bezout. Translated from the French for the Use of the Students of the University of Cambridge, New England (first edition 1820) by John Farrar.

[6]That Church used these books is indicated in Church, pp. 46-47.

[7]The use of textbooks in the original French, and especially which editions, is difficult to document due to the paucity of records. There is a copy of Silvestre Francois Lacroix’s Traite elementaire de trigonometrie rectiligne et spherique (1813 edition) in the West Point library that was owned by Lt Samuel Stanhope Smith. He graduated in 1818, but the fact that he included his rank may indicated that he procured this book later while teaching mathematics at West Point from 1818 to 1823. After that he taught Natural and Experimental Philosophy until his death in 1828.

[8]For information about editions of these books, see Albree et al.

[9]Annual Report of the Superintendent, 1896, pp. 61-63.

Editor's note: This article was published in May of 2008.

V. Frederick Rickey and Amy Shell-Gellasch, "Mathematics Education at West Point: The First Hundred Years - Albert E. Church, Mathematics Professor, 1837-1878," Convergence (July 2010)

Convergence