Arguably the first significant innovation in the undergraduate mathematics curriculum of the second half of the twentieth century was the finite mathematics course. The origins of this course lie in the excitement that arose, in the period around World War II, about applying mathematics to the social sciences. In this article we tell some of that…

Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense…

This article discusses the summability of some divergent series by Cesaro's method of successive arithmetic means. (MM)

It is in the field of numerical analysis that this "easy-looking" function, also known as the Runge function, exhibits a behavior so idiosyncratic that it is mentioned even in most undergraduate textbooks. In spite of the fact that the function is infinitely differentiable, the common procedure of (uniformly) interpolating it with polynomials that…

There is not just one mathematics taught at university level, nor is there one group of students. Mathematics is taught differently depending on the discipline and the perceived background of the student. There is engineering mathematics for the students heading towards engineering degrees, life science mathematics for those heading towards…

A novel approach for teaching interpolation in the introductory course in numerical analysis is presented. The interpolation problem is viewed as a problem in linear algebra, whence the various forms of interpolating polynomial are seen as different choices of a basis to the subspace of polynomials of the corresponding degree. This approach…

In this article, we take a rapid journey through the history of algebra, noting the important developments and reflecting on the importance of this history in the teaching of algebra in secondary school or university. Frequently, algebra is considered to have three stages in its historical development: the rhetorical stage, the syncopated stage,…

A formal approach to the differentiation of vectors from an axiomatic point of view is introduced, and applications to dynamics are presented. (DT)