Recorded are some biographical data about the late professor Freudenthal along with some indications about his mathematical work. In an appendix, a tiny part of his mathematical work which can be explained in a fairly direct manner is discussed. (Author)

Takes a brief tour through the history of analogic thinking in science. Discusses analogic thinking as reported by six students, three from calculus classes and three from a writing-intensive genetics class that also foregrounds language and imaginative thinking. (Contains 15 references.) (ASK)

Presents an early and informal report on some research on learning and assessment of university mathematics. Investigates the attitudes of students who were intending to teach mathematics in secondary schools towards their undergraduate mathematical studies. (ASK)

Tackles a tricky problem of probability based on the well-known carnival game Chuck-a-Luck which, at first glance, appears to favor the bettor. Presents an activity in which students correct a common fallacy in probabilistic reasoning and extend play to a gambler's ruin analysis. (Author/ASK)

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…

A special project which can be given to students of ordinary differential equations is described in detail. Students create new differential equations by changing the dependent variable in the familiar linear first-order equation (dv/dx)+p(x)v=q(x) by means of a substitution v=f(y). The student then creates a table of the new equations and…

Relations between pairwise correlations and the coefficient of multiple determination in regression analysis are considered. The conditions for the occurrence of enhance-synergism and suppression effects when multiple determination becomes bigger than the total of squared correlations of the dependent variable with the regressors are discussed. It…

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.

When discussing the topic of elementary complex variables, students are often mystified by the fact that ii is real. After seeing a proof of this statement, a standard question is "well, what about iii or iiii etc., are these real or complex?" In this paper the meaning of the infinite power-tower iii...is considered both from the "bottom-up" and…

The Bologna Declaration brought reforms into higher education that imply changes in teaching methods, didactic materials and textbooks, infrastructures and laboratories, etc. Statistics and mathematics are disciplines that traditionally have the worst success rates, particularly in non-mathematics core curricula courses. This research project,…

The first year college experience is anxiety producing, and for college students who represent traditionally underserved populations, particularly ethnic and linguistic minorities, the anxiety can be even more pronounced. Add to the mix a requirement for students to complete at least one course in mathematics during the first semester and the…