In 1965, Congress established Title I, Part A (herein referred to as Title I) as a part of the landmark Elementary and Secondary Education Act (ESEA). Congress noted two issues that it hoped to address through Title I funding: schools needed additional financial assistance to provide services to children in low-income families, and school…

Evaluators of education interventions are increasingly designing studies to detect impacts much smaller than the 0.20 standard deviations that Cohen (1988) characterized as "small." While the need to detect smaller impacts is based on compelling arguments that such impacts are substantively meaningful, the drive to detect smaller impacts…

This paper illustrates a biological application of the concepts of relative change and area under a curve, from mathematics. We study two biological measures "relative change in cardiac output" and "cardiac output", which are predictors of heart blockages and other related ailments. Cardiac output refers to the quantity of…

The paper shows how to find the min and max extreme interval values for the exponential and triangular distributions from the min and max uniform extreme interval values. Tables are provided to show the min and max extreme interval values for the uniform, exponential, and triangular distributions for different probabilities and observation sizes.

This note offers a derivation of the Euler-Maclaurin formula that is simple and elementary. In addition, the paper shows that the derivation provides Euler-Maclaurin formulas for a variety of functionals other than the trapezoid rule.

A simple and novel method for evaluating the partial fraction expansion of proper rational functions is presented. The technique involves simultaneous determination of the partial fraction coefficients associated with each of the multiple poles in the expansion in turn. Only synthetic division is required, which makes the process very suitable for…

When first-year calculus students are interested in studying double integrals, they can find, in standard textbooks, a detailed description of the different regions of integration. The aims of this paper are: to give a criterion to select the plane that will be projected, to classify the projections, and to give a simple rule to obtain them.…

This document shows a different way of adding lists of numbers to find a way of getting general formulae for figurate numbers and use Gauss?s method to check it.

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.

In this paper, using the Lambert series and other known results, the authors consider the computation of a class of series involving the powers of generalized Fibonacci and Lucas numbers, and obtain their approximate values.

If the point of suspension of a multiple pendulum is suitably oscillated then the pendulum can remain in motion in an upside-down position. Since such pendulums can model flexible materials, this inverted motion is sometimes referred to as an 'Indian rope trick'. Despite the complexity of the governing differential equations, this rope trick can…

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.

The mean and variance of the number of turning points in random permutations of two kinds of distinct elements are evaluated. These results are applied to a Wald-Wolfowitz run test.

In this note 4 x 4 most-perfect pandiagonal magic squares are considered in which rows, columns and the two main, along with the broken, diagonals add up to the same sum. It is shown that the Moore-Penrose inverse of these squares has the same magic property.

This note provides a self-contained introduction to conics as loci of points equidistant from circles, lines and points, including a study of the loci of points equidistant from two circles, separated, intersecting or touching. (Contains 1 table and 8 figures.)