A method for the numerical evaluation of the error term in Gaussian quadrature rules is derived by means of Chebyshev polynomials of the first kind.

The matrix diagonalization method is used to solve a limit problem.

Accurate and accessible expressions for the probability of having a matching birthday are obtained by using Stirling's formula and Taylor series. For interest, the results are applied to the planets of our solar system.

This article provides the rationale for using Fermi questions with eighth graders studying algebra. It describes the students' reaction to such questions as well as their thinking processes and solutions to questions posed to them by their teacher. (Contains 1 figure.)

Advances in the biological sciences necessitate the training of chemical engineers to translate these fundamental discoveries into applications that will benefit society. Accordingly, Tulane University revised its core chemical engineering curriculum in 2005 to include a new introductory course in bioengineering and biotechnology for sophomores.…

Research has established that children's development of addition and subtraction skills progresses through a hierarchy of strategies that begin with counting-by-one methods through to flexible mental strategies using a combination of knowledge of basic facts and understanding of place value. An important transition point is the shift from the…

This longitudinal study investigated the academic and cognitive characteristics of persistent mathematics difficulty (MD-p) from first to fourth grade. Ninety-nine children were retrospectively categorized into one of three groups: MD-p, transient mathematics difficulty (MD-t), or typically developing. MD-p was defined as persistently low…

Explains "Mathematical Mind Journeys," a lesson format that promotes computational fluency through variable practice that relies on mathematical memory rather than rote memorization. (Author/NB)

The greatest benefit of including leap year in the calculation is not to increase precision, but to show students that a problem can be solved without such presumption. A birthday problem is analyzed showing that calculating a leap-year birthday probability is not a frivolous computation.

The aim of the study was to analyze the development of children's adaptive expertise in computing sums and differences up to 100. We defined the adaptive nature of children's strategy choices on the basis of problem (addition, subtraction), achievement, and strategy performance (accuracy, speed). Sixty-nine 2nd graders of high, above-average, or…

The calculations of uncertainties in the formula or molar masses of compounds are streamlined. Three rules of increasing complexity are proposed, which overestimate the uncertainty so there is little if any risk that the true values are missed.

We investigate the pendulum equation [theta] + [lambda][squared] sin [theta] = 0 and two approximations for it. On the one hand, we suggest that the third and fifth-order Taylor series approximations for sin [theta] do not yield very good differential equations to approximate the solution of the pendulum equation unless the initial conditions are…

We study four non-Newtonian fluid mechanics problems using Mathematica[R]. Constitutive equations describing the behavior of power-law, Bingham and Carreau models are recalled. The velocity profile is obtained for the horizontal flow of power-law fluids in pipes and annuli. For the vertical laminar film flow of a Bingham fluid we determine the…

A majority of studies on learning disabilities have focused on elementary grades. Although problems with learning disabilities are life-affecting only a few studies focus on deficits in adults. In this study adults with isolated mathematical disabilities (n = 101) and adults with combined mathematical and reading disabilities (n = 130) solved…