Commonly used methods to simulate the oxidation-reduction (redox) titration curves include the three-step method and the rigorous method. The simple three-step method simulates the redox titration curve with the assumption that the reaction is complete, which is widely used in undergraduate quantitative analysis courses. For the rigorous…

Sixty (35 girls) ninth graders were assessed on measures of algebraic reasoning and usage of visual and symbolic representations (with a prompt for visual use) to solve equations and inequalities. The study grouped visual representations into two categories: arithmetic-visual, which entailed the use of real-world objects to represent specific…

This paper presents an application of the Kalman filter in signal processing in instrumentation systems when the conditions of the environment generate a large amount of interference for the acquisition of signals from measurement systems. The unwanted interferences make important use of the instrumentation system resources and do not represent…

Presents a method for solving linear equations involving the use of inverses instead of memorizing rules. (MKR)

Two mathematical topics are interpreted from the viewpoints of traditional (performing algorithms) and contemporary (creating algorithms and thinking in terms of them for solving problems and developing theory) algorithmic mathematics. The two topics are Horner's method for evaluating polynomials and Gauss's method for solving systems of linear…

The suggestion that the IDIOSCAL model be fitted by the TUCKALS2 algorithm for three-way components analysis is examined. The claim that resulting coordinate matrices will be identical is supported when the data matrices are semidefinite. Counterexamples for indefinite matrices are also constructed. (SLD)

Polynomial algorithms are presented that are used to solve selected problems in test theory, and computational results from sample problems with several hundred decision variables are provided that demonstrate the benefits of these algorithms. The algorithms are based on optimization theory in networks (graphs). (SLD)

A model for solving very large item selection problems is presented. The model builds on binary programming applied to test construction. A heuristic for selecting items that satisfy the constraints in the model is also presented, and various problems are solved using the model and heuristic. (SLD)

An attempt is made to show that algebra is rarely obvious, and merely expecting children to learn rules is an oversimplification. Sections cover: (1) The Non-visual Nature of Algebra; (2) The Apparently Arbitrary Nature of Algebra; (3) The Relationship Between Symbolism, System and Question; (4) The Complex Nature of Algebra; and (5) Some…

Provides a short list of integral triples for the design of problems employing unit fractions (so solutions will be positive integers). Also presents an algorithm whereby both primary and imprimitive sets of triples can be easily obtained and shows how to extend the algorithm to solve three-variate unit fraction equations. (JN)

Presented is a method where a quadratic equation is solved and from its roots the eigenvalues and corresponding eigenvectors are determined immediately. Included are the proposition, the procedure, and comments. (KR)

Applied mathematics is seen often to involve the solution of single equations or systems of equations. A particular technique for solving equations in the context of functions on the real line is examined. This technique includes an iterative process, which is viewed as an algorithm that can be implemented readily on inexpensive and widely…

This article, which is organized around a single, well-known algorithm for root extraction, presents a way of incorporating dynamical systems into the teaching of mathematics. Included are sample exercises using complex numbers and the computer where students have the opportunity to do some analysis on this algorithm. (KR)

This article gives a comprehensive description of a theory for efficient assessment of knowledge. The essential concept is that the knowledge state of a subject, with regard to a specified field of information, can be represented by a particular subset of problems that the subject is capable of solving. (SLD)