In the seventh century, around 650 A.D., the Indian mathematician Brahmagupta came up with a remarkable formula expressing the area E of a cyclic quadrilateral in terms of the lengths a, b, c, d of its sides. In his formula E = [square root](s-a)(s-b)(s-c)(s-d), s stands for the semiperimeter 1/2(a+b+c+d). The fact that Brahmagupta's formula is…

At the start of a freshman calculus course, many students conceive the classical definition of limit as the most problematic part of calculus. They not only find it difficult to understand, but also consider it of no use while solving most of the limit problems and therefore, skip it. This paper reformulates the rigorous definition of limit, which…

The results of a survey of the mathematics provision within UK university computer science departments are presented. In particular it is found that many academics are dissatisfied with the level of "mathematical preparedness" of their students. A number of recommendations and resources are suggested to address this. (Contains 6 figures.)

This report provides system-level summary highlights of pre-college course-taking behavior of high school graduates who attended a community or technical college in the year following graduation, and of those who delayed enrollment at the college for one or two years after high school graduation. The report contains information on these enrollment…

Placement tests are rapidly joining the ranks of high-stakes testing and college freshmen are required to take mathematics placement exams to determine their first mathematics course upon entering college. Unfortunately, these exams tend to place students in a lower-level or remedial course. As a result, additional expenses are incurred, degree…

In this paper, we report on an international study of undergraduate mathematics students; conceptions of mathematics. Almost 1,200 students in five countries completed a short survey including three open-ended questions asking about their views of mathematics and its role in their future studies and planned professions. Responses were analysed…

Confidence intervals are beginning to play an increasing role in the reporting of research findings within the social and behavioral sciences and, consequently, are becoming more prevalent in beginning classes in statistics and research methods. Confidence intervals are an attractive means of conveying experimental results, as they contain a…

This article, the second in a three-part series, outlines the qualitative research design and findings. The qualitative study was conducted three to five years after students completed their developmental mathematics course work at a large Midwest public university. The purpose was to collect students' points of view regarding what, if any,…

Nonstandard Analysis gives an alternative approach to teaching elementary calculus. This paper hopes to communicate to the reader the ideas of this recent development in mathematics and its implications in teaching undergraduate students. The development of the approach is first briefly traced. Then a method of constructing on ordered field…