Technological advances have significantly affected education, leading to the creation of online learning platforms such as virtual learning environments and massive open online courses. While these platforms offer a variety of features, none of them incorporates a module that accurately predicts students' academic performance and commitment.…

This article aims to illustrate a process of making connections, not between mathematics and other activities, but within mathematics itself--between diverse parts of the subject. Novel connections are still possible in previously explored mathematics when the material happens to be unfamiliar, as may be the case for a learner at any career stage.…

Purpose: The paper aims to discuss current Technical Education scenarios in India. It proposes modelling the factors affecting quality in a technical institute and then applying a suitable technique for assessment, comparison and ranking. Design/methodology/approach: The paper chose graph theoretic approach for quantification of quality-enabled…

This paper deals with the ancient origin of matrices, and the system of linear equations. Included are algebraic properties of matrices, determinants, linear transformations, and Cramer's Rule for solving the system of algebraic equations. Special attention is given to some special matrices, including matrices in graph theory and electrical…

The uses and methodology of factor analysis are widely debated and discussed, especially the issues of rotational use, methods of confirmatory factor analysis, and adequate sample size. The variety of perspectives and often conflicting opinions can lead to confusion among researchers about best practices for using factor analysis. The focus of the…

This thesis investigates and develops a few acceleration techniques for the search engine algorithms used in PageRank and HITS computations. PageRank and HITS methods are two highly successful applications of modern Linear Algebra in computer science and engineering. They constitute the essential technologies accounted for the immense growth and…

Combinatorial scientific computing plays an important enabling role in computational science, particularly in high performance scientific computing. In this thesis, we will describe our work on optimizing matrix-vector multiplication using combinatorial techniques. Our research has focused on two different problems in combinatorial scientific…

A graphical method is presented for assessing the state of identifiability of the parameters in a linear structural equation model based on the associated directed graph. We do not restrict attention to recursive models. In the recent literature, methods based on graphical models have been presented as a useful tool for assessing the state of…

The authors explore the importance of "range" and its relationship to continuously differentiable functions that have inverses when their graphs are reflected about lines other than y = x. Some open questions are posed for the reader. (Contains 5 figures.)

When conducting an exploratory factor analysis, the decision regarding the number of factors to retain following factor extraction is one that the researcher should consider very carefully, as the decision can have a dramatic effect on results. Although there are numerous strategies that can and should be utilized when making this decision,…

A theorem is proved stating that the set of all "minimax links," defined as links minimizing, over paths, the maximum length of links in any path connecting a pair of objects comprising nodes in an undirected weighted graph, comprises the union of all minimum spanning trees of that graph. (Author/SLD)

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…

General strategies used to help discover, prove, and generalize identities for Fibonacci numbers are described along with some properties about the determinants of square matrices. A matrix proof for identity (2) that has received immense attention from many branches of mathematics, like linear algebra, dynamical systems, graph theory and others…

Structural models that yield circumplex inequality patterns are reviewed, focusing on a model developed by T. W. Anderson (1960). A modification is proposed to this model to allow for negative correlations. This model may be reparameterized as a factor analysis model with nonlinear constraints on the factor loadings. (SLD)

A graphical method is proposed which allows one to visualize a real matrix and its inverse. In this scheme, various special properties of the matrix are easily recognized. Up to 5x5 matrices can be graphed on an average page if the range of values does not exceed two orders of magnitude. (Author/LS)