Exploration In Linear Algebra: A Viewpoint

Abstract

The emphasis in linear algebra was changed to a matrix-oriented course focusing on applications and cutting  down on the amount of time spent on idea abstraction as a result of the LACSG's recommendations. Although  this change in emphasis benefits maths majors as well as non-majors, abstraction is being treated unfairly by  being reduced to an 'also ran' when compared to applications. Since linear algebra's theory is so well-structured  and extensive while requiring few mathematical prerequisites, it was chosen to be the first serious mathematics  course in the undergraduate mathematics curriculum, according to Alan Tucker (1993) (p. 3). Even  undergraduate mathematics majors who excelled in calculus I and II face difficulties in linear algebra. Since  it is the first subject in which students are expected to prove theorems, it is crucial to their development as  conjecturers and writers of cogent proofs. According to Tucker, "a practitioner or researcher in most areas of  pure and applied mathematics needs to have a solid understanding of finite vector spaces, linear  transformations, and their extensions to function spaces". Determinants-more especially, the formulation and  validation of the determinant's fundamental properties-are one area that is being underemphasized.