The harmonic series is one of the most celebrated infinite series of mathematics. A quick glance at a variety of modern calculus textbooks reveals that there are two very popular proofs of the divergence of the harmonic series. In this article, the authors survey these popular proofs along with many other proofs that are equally simple and…

Today's college ACCUPLACER System's Computerized Placement Test (CPT) plays a major role for determining whether post-secondary students are ready for placement into Arithmetic, Elementary Algebra, Intermediate Algebra, or College Mathematics courses. It is widely used in most college systems in the U.S. This paper discusses some of the issues to…

The cross-product is a mathematical operation that is performed between two 3-dimensional vectors. The result is a vector that is orthogonal or perpendicular to both of them. Learning about this for the first time while taking Calculus-III, the class was taught that if AxB = AxC, it does not necessarily follow that B = C. This seemed baffling. The…

In 1750, the Swiss mathematician Gabriel Cramer published a well-written algebra book entitled "Introduction a l'Analyse des Lignes Courbes Algebriques." In the appendix to this book, Cramer gave, without proof, the rule named after him for solving a linear system of equations using determinants (Kosinki, 2001). Since then several derivations of…

In 2004, the Lumina Foundation for Education approved a generous grant to support validation research to explore and document the validity of the Community College Student Report (CCSR), add to the higher education field's understanding of student engagement, and help to identify research or institutional practices that require further attention.…