A continuous representation of a hybrid method with three "off-step" points is developed via interpolation and collocation procedures, and used to obtain initial value methods (IVMs) for solving initial value problems. The IVMs are assembled into a single block matrix equation which is convergent and A-stable. We note that accuracy is improved by…

This article is concerned with how computer science, and more exactly computational complexity theory, can inform cognitive science. In particular, we suggest factors to be taken into account when investigating how people deal with computational hardness. This discussion will address the two upper levels of Marr's Level Theory: the computational…

When solving systems of equations by using matrices, many teachers present a Gauss-Jordan elimination approach to row reducing matrices that can involve painfully tedious operations with fractions (which I will call the traditional method). In this essay, I present an alternative method to row reduce matrices that does not introduce additional…

In this article, we derive one-parameter family of Schroder's method based on Gupta et al.'s (K.C. Gupta, V. Kanwar, and S. Kumar, "A family of ellipse methods for solving non-linear equations", Int. J. Math. Educ. Sci. Technol. 40 (2009), pp. 571-575) family of ellipse methods for the solution of nonlinear equations. Further, we introduce new…

This paper discusses a talent management and career planning system designed based on the performance and qualifications of a group of interns working for an emerging social media company located in Istanbul. The proposed model is dynamic, comparative, and perceptional in constructing a talent pool for an organization. This system was developed…

This module was initially developed for a course in applications of mathematics in biology. The objective of this lesson is to investigate how the allele and genotypic frequencies associated with a particular gene might evolve over successive generations. The lesson will discuss how the Hardy-Weinberg model provides a basis for comparison when…

The Lithuanian Informatics Olympiad is a problem solving contest for high school students. The work of each contestant is evaluated in terms of several criteria, where each criterion is measured according to its own scale (but the same scale for each contestant). Several jury members are involved in the evaluation. This paper analyses the problem…

When we use technology to teach mathematics, we hope to focus on the mathematics, restricting the computer software systems to providing support for our pedagogy. It is a matter of common experience, however, that students can become distracted or frustrated by the quirks of the particular software system being used. Here, experience using the…

The solution of a system of linear, inhomogeneous differential equations is discussed. The particular class considered is where the coefficient matrix is skew-symmetric and orthogonal, and where the forcing terms are sinusoidal. More general matrices are also considered.

In this note, a method of converting a rhotrix to a special form of matrix termed a "coupled matrix" is proposed. The special matrix can be used to solve various problems involving n x n and (n - 1) x (n - 1) matrices simultaneously.

The article is aimed at a partial problem of science process skills development--the evaluation of educational outcomes. In comparison to evaluation of obtained knowledge, the skills development is not so easy to be objectively evaluated. The article provides a proposal of an evaluation tool and describes the first results of its research…

As is known, a semi-magic square is an "n x n" matrix having the sum of entries in each row and each column equal to a constant. This note generalizes this notion and introduce a special class of block matrices called "block magic rectangles." It is proved that the Moore-Penrose inverse of a block magic rectangle is also a block magic rectangle.

In this paper "Derive" functions are provided for the computation of the Moore-Penrose inverse of a matrix, as well as for solving systems of linear equations by means of the Moore-Penrose inverse. Making it possible to compute the Moore-Penrose inverse easily with one of the most commonly used Computer Algebra Systems--and to have the blueprint…

A simple mathematical model for the behaviour of how vehicles follow each other along a looped stretch of road is described. The resulting coupled first order differential equations are solved using appropriate matrix techniques and the physical significance of the model is discussed. A number possible classroom exercises are suggested to help…

Charles Dodgson (Lewis Carroll) discovered a "curious" method for computing determinants. It is an iterative process that uses determinants of 2 x 2 submatrices of a matrix to obtain a smaller matrix. When the process ends, the result is the determinant of the original matrix. This article discusses both the algorithm and what may have led Dodgson…