That the principal axis theorem does not extend to any finite field is demonstrated. Presented are four examples that illustrate the difficulty in extending the principal axis theorem to fields other than the field of real numbers. Included are a theorem and proof that uses only a simple counting argument. (KR)

Presented is an example of a question that can be used to investigate probability and random triangles. Included is the question, analysis, and procedure for solving the question. (KR)

Described is a geometric view of Singular Value Theorem. Included are two theorems, one which is a pure matrix version of the above and the other that leads to the orthogonal diagonalization of certain matrices, i.e., the Spectral Theorem. Also included are proofs and remarks. (KR)

Described is a decomposition theory from which the Cayley-Hamilton theorem, the diagonalizability of complex square matrices, and functional calculus can be developed. The theory and its applications are based on elementary polynomial algebra. (KR)

The implementation of the first phase of a project involving the use of computer software in a course on the mathematics of finance is discussed. Results of a controlled experiment indicated that the techniques employed seemed to have positively impacted the performance of the students. (CW)

A nonconventional graphical way to represent functions (the Parallel Axes Representation) is discussed. A computerized environment designed to support the exploration of the representation of linear functions is described. The didactical potential of this representation is illustrated. (CW)

Described are several programs that enable the user to evaluate derivatives to order n of any elementary function by using the combination of automatic differentiation method and A Programming Language (APL). Programs calculating first- and higher-order derivatives are presented. Selected APL symbols are appended. (YP)

Examined is the performance of men and women undergraduate students in mathematics using multiple-choice, relationship analysis, and true/false questions. Sex differences were reported. Implications of this research are suggested. (Author/YP)

Presents an example of a proof to the mathematical problem of the sum of the cubes of the digits. Provides a Pascal program to search for these results. (MVL)

Analyzed were 19 preservice teachers' understanding of division in 3 contexts. The teachers' knowledge was generally fragmented, and each case of division was held as a separate bit of knowledge. (Author/YP)

Discusses the use of the mathematics classroom for discovering the relationship among computers, mathematics, and real-world problems. Provides three probability problems and compares the results of three methods, actual trial, computer simulation, and mathematical solution. (YP)

Describes a five-dice game, horse. Discusses the offensive player's strategy using the ideas of probability, such as counting outcomes, mutually exclusive events, conditional probabilities, zero sum games, and the use of computer. (YP)

Reports on mathematics myths held by a group of preservice elementary school teachers. Describes some math myths surveyed. Discusses ways to change beliefs about mathematics and issues related to beliefs. (YP)

Hypermedia provides an easy-to-use option for adding visualization, via the computer, to the classroom. Some examples of this medium are presented, including applications in basic linear algebra and calculus, and a tutorial in electromagnetism. (Author)

Presents one model for a liberal arts mathematics course that combines probability and calculus. Describes activities utilized in the course to heighten students' interest and encourage student involvement. Activities include use of visualization, take-home tests, group problem solving, research papers, and computer usage with DERIVE computer…