The Mathematics, 3D Printing, and Computational Thinking Through Work-Based Learning (MPACT) program relies on teacher professional development, specialized curriculum and materials, and STEM industry mentors to provide grades 4-7 students with project-based experiences implemented across three learning modules. This technical report presents…

The Mathematics, 3D Printing, and Computational Thinking Through Work-Based Learning (MPACT) program combines teacher professional development, specialized curriculum and materials and STEM industry mentors to provide grade 4-7 students with project-based experiences implemented across three learning modules. This technical report presents…

In this note we give closed forms for a class of logarithmic integrals in terms of Bernoulli polynomials. This provides a method for unifying a large class of definite integrals.

The telescoping sum constitutes a powerful technique for summing series. In this note, this technique is illustrated by a series of problems starting off with some simple ones in arithmetic, then some in trigonometry, famous families of numbers, Apery-like formulas, and finally ending with a class of problems that are solved by computer.

In this note, we give a method for finding the inverse of a three by three magic square matrix without using the usual methods for finding the inverse of a matrix. Also we give a method for finding the inverse of a three by three magic square matrix whose entries are also matrices. By using these ideas, we can construct large matrices whose…

This paper investigates a general identity which expresses an apparently complicated and intriguing sum of fractions as an elegant and straightforward sum of simple terms.

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.

Euler gave a simple method for showing that [zeta](2)=1/1[superscript 2] + 1/2[superscript 2] + 1/3[superscript 2] + ... = [pi][superscript 2]/6. He generalized his method so as to find [zeta](4), [zeta](6), [zeta](8),.... His computations became increasingly more complex as the arguments increased. In this note we show a different generalization…

The Bernoulli numbers are among the most interesting and important number sequences in mathematics. They first appeared in the posthumous work "Ars Conjectandi" (1713) by Jacob Bernoulli (1654-1705) in connection with sums of powers of consecutive integers (Bernoulli, 1713; or Smith, 1959). Bernoulli numbers are particularly important in number…

This note takes up the issue of parallel curves while illustrating the utility of "Mathematica" in computations. This work complements results presented earlier. The presented treatment, considering the more general case of parametric curves, provides an analysis of the appearance of cusp singularities, and emphasizes the utility of symbolic…

The National Assessment of Educational Progress (NAEP) administered the selected supplemental mathematics exercises to 13-year-old students during October and November 1975 and to 17-year-old students during March and April 1976. This assessment represents a specially modified supplement to 1972-73 full-scale mathematics assessment and was…

This report describes the results of Connecticut's second statewide assessment of mathematical knowledge, skills and attitudes. The Connecticut Assessment of Educational Progress annually tests a sample of Connecticut students in grades 4, 8, and 11 in one or more subject areas. Students at each grade level were randomly selected to participate in…