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…

The concept of determinant plays a central role in many linear algebra concepts and is also applied to other branches of mathematics and science. In this study, we focus on the application of determinant and inverse matrix concepts, in solving systems of equations by a group of 116 in-service mathematics teachers who were studying the topic at a…

This article outlines a problem-centered approach to the topic of canonical matrix forms in a second linear algebra course. In this approach, abstract theory, including such topics as eigenvalues, generalized eigenspaces, invariant subspaces, independent subspaces, nilpotency, and cyclic spaces, is developed in response to the patterns discovered…

We represent the main stages of the process of mathematical modelling as fuzzy sets in the set of the linguistic labels of negligible, low intermediate, high and complete success by students in each of these stages and we use the total possibilistic uncertainty as a measure of students' modelling capacities. A classroom experiment is also…

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

The well-known Frobenius rank inequality established by Frobenius in 1911 states that the rank of the product ABC of three matrices satisfies the inequality rank(ABC) [greater than or equal]rank(AB) + rank(BC) - rank(B) A new necessary and sufficient condition for equality to hold is presented and then some interesting consequences and…

Examines the similarities and fundamental differences between procedural programing and logic programing by comparing LogoWriter and PROLOG. Suggests that PROLOG may be a good first programing language for students to learn. (MVL)

This article gives an overview of the new field of complexity theory which links computer science to mathematics, and ultimately to the solution of theoretical as well as practical problems in society and technology. (Author/MK)

A sample of novel verbal problems which can be solved by using systems of linear equations with free variables is presented. The procedure of Gaussian elimination is used to solve the system. (KR)

Examples are presented of the use of the direct product in chemical group theory. (BB)

Discusses the theoretical and practical importance of linear algebra. Presents a brief history of linear algebra and matrix theory and describes the place of linear algebra in the undergraduate curriculum. (MDH)

A nontechnical exposition of graph theory is presented, followed by survey of the literature on applications of graph theory in research in education and related disciplines. Applications include order-theoretic studies of the dimensionality of data sets, the investigation of hierarchical structures in various domains, and cluster analysis.…

The problem of controlling the grizzly bear population at Yellowstone is described. The results are presented in graphical form and discussed. A computer program is included. (MNS)

Explores applications of the Fibonacci series in the areas of probability, geometry, measurement, architecture, matrix algebra, and nature. (MDH)

Presents a short study of proper values of two-by-two matrices with real entries. Gives examples of symmetric matrices and applications to systems of linear equations of perpendicular lines intersecting at the origin and central conics rotated about the origin to eliminate the xy term from its equation. (MDH)