Presents an approach to hybridization which exploits the similarities between the algebra of wave functions and vectors. This method will account satisfactorily for the number of orbitals formed when applied to hybrids involving the s and p orbitals. (GS)

Major interest is the derivation of a mathematical formulation and a demonstration of the effects of pooling two subgroups on the total group correlation coefficient, and additionally, a procedure to guide the decision concerning the pooling of data for the purpose of calculating a single correlation coefficient. (Author/RC)

Presents a technique, using the method of variation of parameters for solving differential equations, for introducing Green's function early in an undergraduate curriculum. Presents various examples. (Author/MLH)

This is part two of a three-part SMSG calculus text for high school students. One of the goals of the text is to present calculus as a mathematical discipline as well as presenting its practical uses. The authors emphasize the importance of being able to interpret the concepts and theory in terms of models to which they apply. The text…

THE NEEDLE TRADES INDUSTRY CONSISTS OF THREE TYPES OF ESTABLISHMENTS -- THE REGULAR MANUFACTURERS, THE APPAREL JOBBERS, AND THE CONTRACTORS. THE FUNCTIONS INCLUDED COVER A WIDE SCOPE FROM BUYING OF RAW MATERIAL TO SELLING OF THE FINISHED APPAREL. THE PURPOSE OF THIS STUDY GUIDE IS TO FURNISH BASIC KNOWLEDGE IN MATHEMATICS AND DEVELOP SKILL IN…

An overview of the Mathematical Problem Solving Project, MPSP, is given. The goals, organization, and history of the project are described and the progress toward those goals is discussed. The outcomes of the project are stated, a brief diary of activities given, and a listing of technical reports made. (MP)

POLYFACT is a learning program that attempts to factor multivariable polynomials. The program has been successful in factoring polynomials (in simplified form) with a maximum of 84 terms, each term consisting of as many as five variables and a maximum degree of 67. The complexity of this learning task placed unusual requirements on the…

This sourcebook contains mathematical exercises, problems, and projects concerning pollution which are accessible for students in grades 6-9. The exercises, which are designed to improve computational skills, are classified according to topics usually taught in the mathematical curriculum of the middle school. (CT)

The statistician has n independent estimates of a parameter he knows is positive, but, as is the case in components-of-variance problems, some of the estimates may be negative. If the n estimates are to be combined into a single number, we compare the obvious rule, that of averaging the n values and taking the positive part of the result, with…

The essays in this booklet have been written by persons who had ranked in the top one percent of the 1958-60 Upstate New York Mathematical Association of America Contests. Personal accounts are given of the role of mathematics in the authors' education and career. The careers described include applied mathematics, computer research and programing,…

The inadequacies in present measurement models are indicated and a description is given of how tree theory, a theory-generative model, overcomes these inadequacies. Among the weaknesses cited in many measurement models are their untested assumptions of linear order and unidimensionality and their inability to generate non-associational…

This report consists of three main sections: (1) Introductory comments on the field of statistics and its study at the graduate level; (2) A recommended undergraduate program for prospective graduate students in statistics; and (3) Implications of the recommendations for departments of mathematics and their students. The recommendations are…

Fixed-width confidence intervals for a population regression line over a finite interval of x have recently been derived by Gafarian. The method is extended to provide fixed-width confidence intervals for the difference between two population regression lines, resulting in a simple procedure analogous to the Johnson-Neyman technique. (Author)