How Linear Algebra Entered the Curriculum of the First Brazilian University

2018-12-01T03:05:19Z (GMT) by Gabriel Loureiro de Lima Eloiza Gomes
<p></p><p>Abstract A major factor resulting in the consolidation of linear algebra as a new branch of mathematics in the early 20th century was the efforts made by 18th and 19th-century scientists to develop a system of calculation that, intrinsic to geometric elements, allowed geometry problems to be solved by using the analytical method. Drawing on this premise, we describe in this article the process by which linear algebra was initially introduced as a teaching content, before gaining the academic course status, into the undergraduate programs in mathematics and engineering at the University of São Paulo (USP). Particularly relevant to this process was the role played by French mathematicians, especially members of the Bourbaki Group, who taught at USP during the 1945-1966 period. In the mathematics program of USP's School of Philosophy, Sciences, and Languages, linear algebra was a teaching content on the Geometry Complements course from the early 1950s up until 1964. Only in 1965 was a course entitled Linear Algebra introduced into the program's curriculum. In the São Paulo Polytechnic School's Engineering Programs, however, linear algebra had been taught since 1961 as a full-fledged course called Elements of Linear Algebra and Analytical Geometry, renaming the course previously called Elements of Analytical and Projective Geometry, in which linear algebra had constituted a teaching content since 1958.</p><p></p>