It is very well known that the Cauchy-Schwarz inequality is an important property shared by all inner product spaces and the inner product induces a norm on the space. A proof of the Cauchy-Schwarz inequality for real inner product spaces exists, which does not employ the homogeneous property of the inner product. However, it is shown that a real…

We describe a principled way of imposing a metric representing dissimilarities on any discrete set of stimuli (symbols, handwritings, consumer products, X-ray films, etc.), given the probabilities with which they are discriminated from each other by a perceiving system, such as an organism, person, group of experts, neuronal structure, technical…

Twelve resource units are presented for the teaching of science and mathematics to gifted students in secondary school. The units present an introduction, tips for teachers, objectives, activities, and materials lists. The units include: "Functions, Relations, and Graphs" (Priscilla Watts); "More Wham to the Gram (A Study of the…

This book is a revised edition of one of the products of a project, "Teaching Mathematics and Science Concepts, K-6, funded by the New York State Education Department. The project was a collaborative effort by mathematics and science education faculty at the State University of New York at Albany and representatives of eight school districts in…

This guide is designed to help classroom teachers implement the Alabama Course of Study: Mathematics K-12. It is inclusive also of the objectives tested by the Stanford Achievement Tests and the Alabama Basic Competency Tests. One characteristic of the curriculum guide is that it clearly states what students should learn in each grade level. These…