In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for 2×2 matrices. Suggested for…

The "word problem" is stated for a given collection. Facts regarding Dehn's Algorithm, definition of Thue systems, a rewriting system, lemmas and corollaries are provided. The situation is examined where the monoid presented by a finite Thue system is a group. (DC)

Provides four examples for testing the validity of logical arguments by using the method of truth trees. (YP)

Describes examples of rational representation as a guide for translating terminology and information encountered in manuals for computers. Discusses four limitations of the representation. (YP)

This article develops an algorithm to find all solutions to the problem, making all sums of a hexagram's nine lines the same. It shows how to exploit the geometric structure of the hexagram and its group of automorphisms. (YP)

Discusses how to express an n factorial as a product of powers of primes. Provides two examples and answers. Presents four related suggestions. (YP)

Describes Newton's method to locate roots of an equation using the Newton-Raphson iteration formula. Develops an adaptive method overcoming limitations of the iteration method. Provides the algorithm and computer program of the adaptive Newton-Raphson method. (YP)

Presents an easy method for constructing magic squares from three-by-three to general squares. Provides a computer program generating odd-order magic squares. Six references are listed. (YP)

A practical machine translation system called CULT (Chinese University Language Translator), capable of translating Chinese mathematical texts into readable English, has been developed during the period 1969-1977 at the Chinese University of Hong Kong. Programs for the system are written in Standard FORTRAN and run on the ICL1904A computer system.…

Examines the hypothesis that there are preliminary stages in problem solving that are often neglected in teaching chemistry. Discusses correlations calculated between the student's ability to handle disembedding and cognitive restructuring tasks in the spatial domain and ability to solve chemistry problems. (TW)

Describes the nature and use of computer algebra and its applications to various physical sciences. Includes diagrams illustrating, among others, a computer algebra system and flow chart of operation of the Euclidean algorithm. (SK)

Defines M-demand as the maximum number of schemes that the subject must activate simultaneously in the course of executing a task. Discusses the effect of M-demand on problem solving. Uses algorithms to reduce M-demand. Describes the role of algorithms in problem solving. (MVL)