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…

Two key concepts arising from Butler's work are the heterosexual matrix--the conflation of sex-gender-sexuality which leads to the normalisation of heterosexuality--and performative reinscription--the discursive process by which the marginalised Other brings new meanings to normative identity constructions. While we have found both concepts…

Preparing early childhood education (ECE) and early childhood special education (ECSE) professionals to work with young children with and without disabilities entails the acquisition of content, its application, and opportunities for reflection. This article describes a component of an ECSE assessment course focusing on the logistics and process…

Benford's law of the "first digits" states that in spite of intuitively expected equal frequency of 1/9 of the decimal digits r = 1, ... , 9 appearance on the first place of any number, various empirical studies show another pattern of these frequencies distribution, which is log[subscript 10](1 + 1/r). The article considers this law and other…

Presents an algorithm for the production of a graphical diagram from a matrix formula in such a way that its components are logically and hierarchically arranged. The algorithm, which relies on the matrix equations of J. McArdle and R. McDonald (1984), calculates the individual path components of expected covariance between variables and…

Effective strategic planning for community colleges contains four key elements: (1) It must be mission driven; (2) It must be integrated with capability and resources; (3) It must define measurable standards for determining outcomes; and (4) It must be transparent in its intent and strategic goals to all levels of the organization. Using a…

This article describes the sequence alignment problem in bioinformatics. Through examples, we formulate sequence alignment as an optimization problem and show how to compute the optimal alignment with dynamic programming. The examples and sample exercises have been used by the author in a specialized course in bioinformatics, but could be adapted…

Synthetic division is viewed as a change of basis for polynomials written under the Newton form. Then, the transition matrices obtained from a sequence of changes of basis are used to factorize the inverse of a bidiagonal matrix or a block bidiagonal matrix.

In this article we provide two detailed examples of how we incorporate biological examples into two mathematics courses: Linear Algebra and Ordinary Differential Equations. We use Leslie matrix models to demonstrate the biological properties of eigenvalues and eigenvectors. For Ordinary Differential Equations, we show how using a logistic growth…

A formula for the determinant of a partitioned matrix, possibly with singular submatrices, is derived and applied to some psychometric and numerical problems. (Author)

At United States Military Academy, a unit on biological modeling applications forms the culminating component of the first semester core mathematics course for freshmen. The course emphasizes the use of problem-solving strategies and modeling to solve complex and ill-defined problems. Topic areas include functions and their shapes, data fitting,…

To teach the rigorous skills and knowledge students need to succeed in future college-entry courses and workforce training programs, education stakeholders have increasingly called for more rigorous curricula, instruction, and assessments. Identifying the critical attributes of rigor and measuring its appearance in curricular materials is…

The hippocampal CA3 subregion is critical for rapidly encoding new memories, which suggests that neuronal computations are implemented in its circuitry that cannot be performed elsewhere in the hippocampus or in the neocortex. Recording studies show that CA3 cells are bound to a large degree to a spatial coordinate system, while CA1 cells can…

The residual variance is often used as an approximation to the uniqueness in factor analysis. An upper bound approximation to the residual variance is presented for the case when the correlation matrix is singular. (Author/JKS)

Proposes a comprehensive approach, generalized constrained multiple correspondence analysis, for imposing both row and column constraints on multivariate discrete data. Each set of discrete data is decomposed into several submatrices and then multiple correspondence analysis is applied to explore relationships among the decomposed submatrices.…