In application-oriented mathematics, particularly in the context of nonlinear system analysis, phase plane analysis through SageMath offers a visual display of the qualitative behaviour of solutions to differential equations without inundating students with cumbersome calculations of the plane-phase. A variety of examples is usually given to…

Contrast analysis is a relatively simple but effective statistical method for testing theoretical predictions about differences between group means against the empirical data. Despite its advantages, contrast analysis is hardly used to date, perhaps because it is not implemented in a convenient manner in many statistical software packages. This…

Slater type orbitals were used to construct the overlap and the Hamiltonian core matrices; we also found the values of the bi-electron repulsion integrals. The Hartree Fock Roothaan approximation process starts with setting an initial guess value for the elements of the density matrix; with these matrices we constructed the initial Fock matrix.…

The design of research studies utilizing binary multilevel models must necessarily incorporate knowledge of multiple factors, including estimation method, variance component size, or number of predictors, in addition to sample sizes. This Monte Carlo study examined the performance of random effect binary outcome multilevel models under varying…

Matrix diagonalization, the key technique at the heart of modern computational chemistry for the numerical solution of the Schrödinger equation, can be easily introduced in the physical chemistry curriculum in a pedagogical context using simple Hückel molecular orbital theory for p bonding in molecules. We present details and results of…

A general program for item-response analysis is described that uses the stabilized Newton-Raphson algorithm. This program is written to be compliant with Fortran 2003 standards and is sufficiently general to handle independent variables, multidimensional ability parameters, and matrix sampling. The ability variables may be either polytomous or…

The reciprocal method of service department cost allocation requires linear equations to be solved simultaneously. These computations are often so complex as to cause the abandonment of the reciprocal method in favor of the less sophisticated direct or step-down methods. Here is a short example demonstrating how Excel's sometimes unknown matrix…

This article demonstrates how within an educational context, supported by the notion of hidden mathematics curriculum and enhanced by the use of technology, new mathematical knowledge can be discovered. More specifically, proceeding from the well-known representation of Fibonacci numbers through a second-order difference equation, this article…

Exploratory factor analysis (EFA) is a frequently used multivariate analysis technique in statistics. Jennrich and Sampson (1966) solved a significant EFA factor loading matrix rotation problem by deriving the direct Quartimin rotation. Jennrich was also the first to develop standard errors for rotated solutions, although these have still not made…

This note describes a method for evaluating the sums of the m -th powers of n consecutive terms of a general arithmetic sequence: { S[subscript m] = 0, 1, 2,...}. The method is based on the use of a differential operator that is repeatedly applied to a generating function. A known linear recurrence is then obtained and the m-th sum, S[subscript…