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…

A survey was administered to calculus students who had previously been exposed to a course on integral calculus. The purpose of the survey was to explore students' understanding of the definition of a definite integral, their abilities to evaluate definite integrals, and their graphical interpretations of definite integrals. The analysis of…

This paper aims to show the close relation between physics and mathematics taking into account especially the theory of differential equations. By analysing the problems posed by scientists in the seventeenth century, we note that physics is very important for the emergence of this theory. Taking into account this analysis, we show the…

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.)

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…

Teaching the art of counting can be quite difficult. Many undergraduate students have difficulty separating the ideas of permutation, combination, repetition, etc. This article develops some examples to help explain some of the underlying theory while looking carefully at the selection of various subsets of objects from a larger collection. The…

In this short note, a mathematical proposition on a functional equation for f(xy)=xf(y) + yf(x)for x,y [does not equal] 0, which is encountered in calculus, is generalized step by step. These steps involve continuity, differentiability, a functional equation, an ordinary differential linear equation of the first order, and relationships between…

The starting point for this discussion of error estimates is the fact that integrals that arise in Fourier series have properties that can be used to get improved bounds. This idea is extended to more general situations.

Consider a sequence recursively formed as follows: Start with three real numbers, and then when k are known, let the (k +1)st be such that the mean of all k +1 equals the median of the first k. The authors conjecture that every such sequence eventually becomes stable. This article presents results related to their conjecture.

At the end of the first millennium, at a time when neither mathematics nor the papacy required much specialized knowledge, a mathematician became pope. This article describes the life and times of Gerbert of Aurillac, also known as Pope Sylvester II.

The primary use of the inverse secant in calculus is as an antiderivative. In this article, the author advocates taking advantage of properties of the hyperbolic functions instead.

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…