Discussion of the preparation of knowledge for problems appropriate for expert systems focuses on relationships among problem attributes and their solutions through the creation of a solution matrix. Two examples are given, one for wine selection and one for decisions that an automobile manufacturer's sales force might have to make. (LRW)

The use of matrix multiplication in the theory of Markov chains is demonstrated without directly discussing any probability theory. The technique that is developed is applied to ratio and mixture problems that are in changing states. (JP)

A game is presented in which computation by a stepping-stone method is used to solve minimax problems. An additional application of this game is used for finding the Pearson correlation coefficient by non-parametric techniques. The game provides considerable computational practice as well as a motivational problem solving situation. (JP)

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)

This fourth in a series of edited transcripts based on a conference at Utah State University compares Gagne's Conditions of Learning with Merrill's Component Display/Design Theory, and suggests a merging of the two. Topics discussed include content structures, learning hierarchies, learning theories, learner control, problem solving, cognitive…

In this article an augmented matrix that represents a system of linear equations is called nice if a sequence of elementary row operations that reduces the matrix to row-echelon form, through matrix Gaussian elimination, does so by restricting all entries to integers in every step. Many instructors wish to use the example of matrix Gaussian…

In this note we consider a type of integral that is usually presented as an example in any textbook discussion of integration by parts. Invariably this integral is determined by integrating by parts twice and solving. We will present an alternate approach to this integral which makes use of the linearity of the integral, i.e., the fact that…

In an effort to increase the quality and quantity of service-learning assessment, this article provides a brief rationale for engaging in service-learning assessment and reviews a selection of available tools for doing so. The paper includes a matrix that lists cognitive outcomes, including critical thinking and problem solving, and the…

Students were presented with the problem of finding all magic squares of order three. (SD)

Methods for solving logic puzzles which focus on thought-free procedures that facilitate solution are discussed. Two of the procedures noted pertain to the interior of any submatrix, whereas others span several submatrices. A puzzle is presented at the conclusion as an exercise for practicing the methods promoted. (MP)

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)

Matrix organization can be used to construct math word problems for children with mild disabilities. Matrix organization specifies the characteristics of problems, such as problem theme or setting, operations, level of computation complexity, reading vocabulary level, and need for classification. A sample scope and sequence and 16 sample word…

In this paper, two classes of graphs of arbitrary order are described which contain unique Hamiltonian cycles. All the graphs have mean vertex degree greater than one quarter the order of the graph. The Hamiltonian cycles are detailed, their uniqueness proved and simple rules for the construction of the adjacency matrix of the graphs are given.…

This note describes a method for evaluating the sums of the m -th powers of n consecutive terms of a general arithmetic sequence: { S[subscript m] = 0, 1, 2,...}. The method is based on the use of a differential operator that is repeatedly applied to a generating function. A known linear recurrence is then obtained and the m-th sum, S[subscript…

The introduction of computer use in college mathematics classes for non-mathematics oriented students majoring in marketing, management, and other business-related fields is discussed. Results of a questionnaire of student opinions matched with pupil course grades is presented. It is noted students as a whole seemed satisfied with computer use.…